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"Taking the _MATH_": 15, "Taking the time": 15, "The accuracy of": 97, "The basic idea": 216, "Table _REF_ is": 56, "The main focus": 20, "Then , it": 198, "This line is": 10, "The optimal solution": 26, "This is equivalent": 122, "The construction of": 101, "The computation time": 14, "The first question": 15, "The second question": 13, "Tables 2 and": 20, "The above inequality": 34, "The continuity of": 50, "The latter implies": 11, "The dynamics of": 200, "Theorem 1.2 in": 11, "Table 1 )": 72, "This point will": 11, "Thus , since": 46, "The reader is": 81, "Theorem _REF_ shows": 68, "Then _MATH_ since": 12, "This is how": 13, "This kind of": 156, "The amplitude of": 86, "The relation between": 107, "Then , taking": 42, "The first step": 226, "The pair _MATH_": 40, "The behavior of": 135, "The norm of": 23, "Then for _MATH_": 153, "Then , under": 42, "The solution _MATH_": 68, "The same situation": 11, "Then it is": 164, "The optimization problem": 41, "The difficulty of": 24, "The 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"Taylor expansion of": 89, "The novelty of": 29, "The constraints of": 12, "This result suggests": 22, "The advantage of": 258, "Then there is": 129, "Theorem _REF_- (": 13, "The parameters _MATH_": 145, "The last term": 79, "The case _MATH_": 156, "The set _MATH_": 232, "The property of": 22, "Therefore , as": 77, "To study the": 141, "The percentage of": 23, "The network is": 23, "Therefore , from": 114, "This part of": 24, "The task is": 18, "The output of": 116, "The first and": 95, "This corresponds to": 204, "Thus , this": 109, "The second and": 55, "The third term": 49, "The process starts": 11, "The time _MATH_": 11, "The time interval": 26, "The latter case": 21, "This approach has": 80, "The figure shows": 87, "The free energy": 24, "Theorem _REF_ also": 27, "The model was": 23, "The convergence rate": 16, "This yields a": 45, "The increase of": 53, "Thus , any": 41, "This process can": 30, "The region of": 22, "Then _MATHDISP_ for": 53, "The above -mentioned": 11, "Then : 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"Throughout this section": 73, "This allows a": 19, "The proofs are": 16, "To show (": 20, "The first inequality": 33, "The results reported": 18, "Thus , with": 51, "The group of": 21, "The value of": 459, "This confirms the": 30, "To obtain more": 10, "The mutual information": 13, "This expression can": 24, "Two of these": 11, "There are a": 139, "The processing time": 18, "They have the": 16, "The first is": 188, "Thus _MATH_ is": 205, "The transformation matrix": 12, "This section discusses": 29, "Then system (": 36, "Theorem _REF_ this": 11, "This is ,": 87, "There are mainly": 11, "The other way": 12, "The process of": 105, "Thus , more": 10, "The distributions of": 32, "The area of": 44, "The integration is": 11, "This contribution is": 17, "The two cases": 11, "The graph _MATH_": 26, "The main goal": 72, "Then _MATH_ if": 40, "Table _REF_ lists": 99, "The same is": 82, "To give a": 30, "To increase the": 43, "The virtual work": 15, "To handle the": 15, "The absence of": 54, "The first case": 53, "The second case": 34, "The mass of": 50, "The left-hand side": 45, "The main conclusions": 16, "The details of": 146, "To evaluate the": 127, "The first phase": 14, "The second phase": 16, "The data are": 79, "This approach was": 49, "Then , on": 18, "Taylor 's expansion": 19, "Theorem 3.3 ,": 10, "Theorem 3.3 .": 15, "To allow for": 24, "They assumed that": 14, "The time required": 11, "The running time": 27, "This proves the": 153, "The idea of": 225, "The columns of": 20, "Table 1 shows": 38, "There exist an": 13, "The reason that": 24, "The conditional probability": 23, "The cases _MATH_": 17, "Then all the": 13, "T. b. rhodesiense": 10, "Telescope ( SXT": 15, "This paper considers": 43, "This behavior was": 12, "The asymptotic distribution": 22, "This yields _MATHDISP_": 75, "Theorem 1 (": 11, "They are _MATHDISP_": 12, "The above results": 29, "The top row": 13, "The cosmological constant": 15, "Table 2 ,": 52, "Type III burst": 17, "This property ,": 11, "The most general": 40, "This model can": 37, "Theorem _REF_ will": 38, "The contribution of": 124, "This results in": 258, "The discovery of": 57, "Theorem _REF_ or": 28, "The conditions (": 16, "Then by (": 68, "The partition function": 13, "The total time": 17, "Then , they": 14, "Two types of": 52, "This is one": 69, "The propagation of": 31, "The evaluation of": 62, "The latter may": 11, "The sets _MATH_": 25, "The most likely": 14, "This gives an": 23, "The second one": 116, "The term _MATH_": 181, "The derivative of": 81, "Taking the limit": 56, "This coincides with": 14, "The first thing": 19, "Then , a": 124, "The knowledge of": 38, "To be precise": 82, "The same holds": 57, "Theorem 3.2 .": 28, "Telescope ( EIT": 49, "The square of": 17, "This is always": 14, "The potential energy": 16, "The proof will": 30, "The set _MATHDISP_": 18, "Theorem _REF_ yields": 48, "Theorem _REF_ holds": 63, "The results confirm": 12, "To achieve this": 125, "This shows the": 39, "Then by _REF_": 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13, "The hypothesis of": 12, "The utilization of": 12, "To get an": 29, "The first application": 10, "This paper has": 62, "They are not": 25, "The emergence of": 27, "The time step": 11, "The same reasoning": 13, "The consequence is": 22, "The population is": 10, "To ensure that": 53, "This paper shows": 17, "The results show": 167, "The most widely": 23, "The equation (": 20, "Theories of Gravity": 17, "Throughout , we": 17, "The model also": 25, "The simulation is": 14, "Type III radio": 60, "There are ,": 42, "The space of": 37, "This simple model": 15, "The choice of": 228, "The experiments are": 18, "The second order": 17, "The first derivative": 11, "To illustrate the": 162, "Then , following": 23, "The details are": 33, "Then one can": 46, "The semantics of": 13, "This will not": 15, "This will give": 17, "Theorem _REF_ gives": 60, "This formula can": 14, "Therefore we conclude": 16, "To remove the": 16, "The states of": 12, "Therefore _MATH_ ,": 41, "The substitution of": 18, "Then if the": 10, "The average values": 14, "The average _MATH_": 11, "The argument is": 18, "The Doppler velocity": 16, "These values are": 86, "The framework of": 15, "This difference can": 13, "TE and TM": 18, "The correlation of": 13, "To avoid confusion": 13, "They do not": 32, "The generating function": 22, "The peak of": 13, "The analysis has": 11, "This is probably": 53, "This is for": 16, "This suggests to": 10, "Then we must": 10, "Then the integral": 11, "These are shown": 13, "There have also": 11, "This feature of": 12, "The map _MATHDISP_": 19, "This system can": 24, "The nature of": 63, "To avoid these": 12, "The concepts of": 18, "This ratio is": 11, "This may also": 13, "This structure is": 32, "Table 1 in": 12, "To construct a": 27, "The black line": 14, "The above theorem": 22, "The graph of": 20, "These techniques are": 19, "The example of": 12, "Then , substituting": 16, "The system matrices": 14, "Tables _REF_ to": 18, "The general solution": 63, "Then _MATHDISP_ _MATHDISP_": 21, "Then _MATH_ by": 21, "The measure _MATH_": 41, "This result generalizes": 12, "The right hand": 16, "Taylor series expansion": 76, "The thickness of": 38, "Table 1 lists": 12, "The methodology is": 17, "The proposed algorithms": 10, "The maximum of": 30, "The outputs of": 19, "They suggest that": 13, "The topic of": 18, "The dependence of": 146, "The density of": 62, "This is easily": 32, "The first row": 34, "The former is": 57, "This paper also": 17, "These ideas are": 12, "The three main": 10, "This was done": 55, "The domain of": 26, "The proposed methodology": 15, "The governing equations": 31, "The focus of": 56, "The rationale is": 13, "These rules are": 11, "The next two": 37, "Then we obtain": 91, "The expression for": 85, "Tables _REF_ ,": 58, "This represents a": 26, "This subsection presents": 10, "The idea behind": 64, "Thus _MATH_ and": 87, "Thus , using": 80, "The symbol _MATH_": 73, "The calculations are": 21, "Two cases are": 16, "This point of": 14, "Then the equations": 11, "The amplitude _MATH_": 22, "Table 6 .": 13, "There are different": 51, "This assumes that": 11, "Theorem _REF_ implies": 90, "This article is": 44, "Theorem _REF_ that": 187, "These are used": 12, "This has the": 51, "This is well": 17, "The critical points": 13, "To do that": 20, "Therefore , each": 35, "Thus we obtain": 45, "The state of": 42, "To prove this": 93, "Turing machine is": 19, "This paper will": 16, "The real and": 22, "These terms are": 14, "The transformation _MATH_": 25, "The final step": 37, "The results presented": 71, "These estimates are": 16, "Take _MATHDISP_ .": 10, "This seems to": 36, "The power of": 40, "Therefore , under": 22, "To make a": 13, "The vertex _MATH_": 16, "This occurs when": 11, "The cost function": 34, "Then , every": 12, "The predictions of": 13, "The joint distribution": 13, "Therefore we have": 46, "They may be": 18, "The joint probability": 17, "This expression is": 48, "The intuition behind": 30, "The condition 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"These studies have": 14, "Then one has": 31, "The following statements": 27, "The solar wind": 53, "This was also": 18, "The second stage": 25, "Turing machine _MATH_": 32, "The remaining part": 26, "Therefore , Theorem": 18, "This statement is": 18, "This action is": 10, "The resulting _MATH_": 25, "Then the number": 19, "The solid lines": 32, "The convexity of": 11, "There are various": 57, "The simplest model": 12, "This is basically": 18, "The population of": 18, "This model assumes": 20, "The distribution _MATH_": 24, "To that end": 66, "The transformation of": 16, "The relationship between": 106, "The conservation of": 17, "Their results are": 14, "Typical examples are": 10, "This measure is": 17, "They conclude that": 10, "Two sets of": 12, "The total energy": 36, "This equation is": 80, "Theorem _REF_ there": 15, "The _MATH_ parameter": 28, "The outline of": 65, "Table I ,": 18, "Table I .": 30, "Thus the condition": 10, "Theorem 3.1 ,": 79, "The system of": 81, "Theorem 2.2 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"This further implies": 12, "The main question": 15, "This is where": 23, "To generate a": 15, "This scheme is": 22, "The distinction between": 25, "The weight function": 13, "Then for the": 47, "The initial and": 12, "These features are": 26, "The case where": 34, "Theorem _REF_ tells": 16, "They consist of": 14, "The architecture is": 10, "Theorem 2 in": 43, "The growth rate": 24, "Table _REF_ _CITE_": 12, "The transformation from": 11, "The model can": 36, "These parameters are": 46, "This brings us": 11, "The system under": 10, "This observation is": 50, "These results show": 57, "This points to": 13, "This is referred": 19, "TeV , the": 21, "Test _MATH_ and": 16, "This implies (": 18, "This implies _MATH_": 94, "The _MATH_ ,": 35, "The share of": 12, "The result then": 15, "The number density": 10, "This suggests a": 20, "The value function": 14, "The scalar field": 19, "These results have": 24, "This allows the": 56, "The method uses": 22, "The method is": 158, "The coupling 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obtained the": 12, "The parameter estimates": 19, "Theorem _REF_ states": 11, "The estimate of": 30, "The key difference": 16, "The coordinates of": 32, "This paper provides": 24, "They are given": 20, "Then , letting": 10, "Therefore , according": 31, "The simplest case": 15, "The relation _MATH_": 47, "These quantities are": 29, "Then , since": 99, "Table 4 .": 28, "T-S fuzzy system": 19, "The vector of": 27, "The unknown parameters": 11, "The straight line": 10, "The integral over": 21, "The only way": 33, "This approach to": 14, "Theorem _REF_ with": 71, "Then _MATHDISP_ with": 10, "Thus , their": 12, "The minus sign": 12, "These parameters can": 13, "The assumption that": 46, "The method of": 91, "The first problem": 21, "This , of": 17, "The integration in": 12, "These correspond to": 17, "The motion of": 69, "The above equation": 48, "To overcome these": 27, "TErrestrial RElations Observatory": 25, "The coefficient _MATH_": 58, "To obtain an": 36, "The classification of": 16, "There is not": 18, "The operators _MATH_": 33, "The symmetry of": 18, "This observation can": 14, "The superscript _MATH_": 25, "Then we may": 22, "This paper focuses": 37, "This is perhaps": 15, "To eliminate the": 23, "The only possible": 10, "Thus it is": 62, "The detailed analysis": 14, "To conclude this": 26, "The method in": 16, "The Hilbert space": 10, "The control algorithm": 13, "Thanks to this": 13, "The power spectrum": 22, "The transition probability": 18, "The symmetry group": 11, "There are only": 34, "The following three": 20, "Then by the": 67, "Thus , _REF_": 32, "Then , any": 17, "The class _MATH_": 20, "The family of": 59, "The lack of": 64, "The first statement": 20, "This is given": 20, "The Green function": 14, "The emission of": 15, "The easiest way": 17, "Then , starting": 16, "The importance of": 105, "The work is": 10, "To see why": 20, "They proved that": 23, "The decrease in": 20, "To demonstrate the": 57, "The energy of": 42, "The particular case": 18, "The good agreement": 12, "To control the": 21, "Theorem 4.3 in": 14, "Taking _MATH_ ,": 88, "Two of them": 21, "The power consumption": 13, "These types of": 29, "The projection of": 28, "Theorem _REF_ by": 49, "Table _REF_ (": 88, "The magnetic flux": 29, "The authors also": 27, "The mean values": 26, "The statistics of": 13, "The determinant of": 24, "This point is": 28, "Thus , all": 55, "The temperature dependence": 42, "The ratio _MATH_": 34, "The mathematical model": 31, "Table 2 in": 16, "The expressions of": 20, "The following definition": 34, "The first task": 11, "This is reflected": 16, "The layout of": 12, "This causes the": 29, "The most common": 85, "The data is": 29, "The temperature of": 33, "The average error": 10, "Thirdly , we": 28, "The expression of": 31, "This guarantees that": 16, "The possibility to": 22, "The final output": 11, "They found the": 11, "The Fourier transform": 30, "To verify that": 13, "Table _REF_ contains": 36, "The results were": 36, "Theorem _REF_ may": 17, "The whole process": 19, "Theorem 1.3 .": 14, "The following properties": 18, "The first class": 21, "The first category": 14, "The diameter of": 21, "The transition between": 17, "This is possible": 63, "This introduces a": 13, "Therefore , (": 111, "The standard deviation": 52, "This study shows": 10, "The images of": 16, "The first level": 12, "The processes _MATH_": 14, "This is quite": 30, "The important point": 25, "Theorem 1 can": 13, "That _MATH_ is": 18, "To generate the": 20, "TRACE 1550 \u00c5": 14, "Then _MATH_ defined": 10, "There is some": 39, "To better understand": 32, "The possibility of": 62, "Take _MATH_ such": 24, "The simulation result": 15, "This is less": 12, "The proof proceeds": 11, "The system uses": 12, "The approach is": 59, "This is obvious": 15, "The _MATH_ are": 65, "This chapter has": 22, "The function _MATHDISP_": 20, "This can also": 41, "Therefore ( _REF_": 10, "The difference of": 52, "Theorem _MATH_ ,": 18, "This follows by": 11, "This holds for": 21, "The algorithm for": 33, "This would imply": 15, "The weight _MATH_": 26, "To prove Theorem": 33, "This work is": 75, "The analysis and": 17, "The sets of": 17, "These differences are": 21, "The degree of": 81, "They will be": 13, "The characteristic equation": 40, "To simulate the": 26, "This problem was": 34, "This paper describes": 27, "The entries of": 20, "This plot shows": 11, "The normal form": 12, "The displacement of": 13, "This study is": 22, "This claim is": 16, "The methods presented": 12, "This gives _MATH_": 29, "The proof that": 23, "This is analogous": 25, "The unit cell": 11, "The notation is": 15, "The following statement": 15, "The last one": 14, "This model was": 26, "These systems are": 29, "The angular momentum": 12, "The study was": 11, "This idea is": 31, "This definition is": 26, "This is explained": 19, "The time series": 31, "The first few": 15, "The algorithm ,": 10, "The remaining _MATH_": 20, "The _MATH_ 's": 23, "The method has": 17, "The equations are": 13, "The forward and": 11, "The other two": 57, "This is certainly": 15, "The end of": 22, "This model is": 140, "To find an": 12, "This fact will": 10, "These results demonstrate": 19, "This reduces the": 56, "The path _MATH_": 12, "The next result": 51, "Tang ( 1987": 14, "Therefore , every": 20, "This translates to": 10, "The equations for": 26, "The proof relies": 23, "Theorem _REF_ page": 13, "The creation of": 21, "The higher the": 30, "The energy conservation": 11, "This implies a": 32, "Therefore , Eq": 19, "They found a": 10, "Then : _MATH_": 18, "The main advantages": 16, "Then the equation": 27, "To circumvent this": 18, "There is much": 15, "The main objective": 67, "The field is": 13, "Then , if": 98, "Type-II censored order": 11, "The problem _MATH_": 11, "The results we": 12, "The analysis shows": 23, "The first ,": 35, "The specification of": 20, "This gives _MATHDISP_": 59, "This is again": 22, "The model has": 39, "This technique was": 10, "The description of": 60, "Table _REF_ provides": 42, "The time complexity": 35, "The latest version": 10, "Therefore _MATH_ for": 14, "The variance of": 44, "This explains why": 49, "The other important": 12, "The work of": 53, "Theorem _REF_ using": 15, "The results from": 45, "To define the": 35, "The basic reproduction": 14, "This case has": 10, "Then , given": 32, "The skin friction": 15, "The Nusselt number": 12, "The following are": 46, "The relevance of": 25, "The asymptotic variance": 12, "Then , Eq": 19, "The component _MATH_": 13, "Theoretically , the": 25, "Then we find": 34, "The second set": 27, "Therefore , considering": 15, "The interest in": 26, "Then , assuming": 19, "To handle this": 10, "Therefore , after": 17, "The explicit form": 31, "The convergence of": 52, "This method was": 36, "This algorithm has": 15, "The probabilities _MATH_": 12, "This establishes the": 19, "The analysis is": 44, "Then the corresponding": 31, "The validity of": 62, "This is what": 57, "There , the": 47, "The metric of": 16, "The initial state": 31, "Then we compute": 17, "The first section": 14, "The above analysis": 19, "The phase of": 14, "These results can": 37, "They used the": 16, "The CME was": 18, "Then , due": 20, "They observed that": 15, "This demonstrates the": 18, "The correctness of": 16, "The frequency of": 45, "This result was": 53, "Taylor problem in": 12, "The results suggest": 20, "The field of": 41, "The order of": 73, "Theorem _REF_ the": 57, "The algorithm starts": 16, "Then the algorithm": 12, "The second is": 61, "Table 1 presents": 11, "To account for": 71, "They are the": 49, "The first _MATH_": 23, "The computation is": 17, "To find out": 12, "Then , based": 26, "Then , to": 38, "This chapter describes": 30, "Theorem B .": 12, "This approach can": 28, "The main feature": 28, "This highlights the": 16, "This criterion is": 16, "The character of": 18, "The proposed methods": 10, "To be specific": 40, "The author declares": 12, "The vector fields": 22, "To avoid such": 16, "The following equation": 12, "The criterion for": 16, "The major advantage": 13, "The location of": 68, "The equilibrium point": 12, "They are very": 12, "This result follows": 12, "To quantify the": 46, "This can easily": 16, "The general expression": 16, "The algorithm can": 20, "Then in the": 33, "The conditions on": 12, "The ability to": 60, "The method presented": 20, "This means _MATH_": 21, "Tevatron _CITE_ .": 14, "This yields that": 20, "The union of": 30, "This paper aims": 19, "The same procedure": 31, "The data for": 32, "The paper ends": 20, "This space is": 16, "This mode is": 11, "The square root": 10, "There are _MATH_": 96, "The monotonicity of": 14, "The main reason": 99, "The matrix elements": 21, "The following is": 88, "To facilitate this": 10, "The inclusion _MATH_": 13, "The filtration _MATH_": 12, "To begin ,": 29, "These values can": 11, "This also implies": 24, "To accomplish this": 40, "Then we discuss": 14, "The _MATH_ model": 16, "The discussion in": 12, "This information is": 45, "The temperature is": 13, "Theorem 3 of": 14, "These bounds are": 10, "Thus one can": 13, "The latter approach": 11, "This metric is": 12, "The continuity equation": 11, "The equation _MATHDISP_": 15, "The reason why": 45, "Therefore , _REF_": 29, "Thus _MATHDISP_ and": 14, "Thus , system": 12, "The authors in": 48, "Technology ( NIST": 11, "This makes it": 53, "The time scale": 10, "The work by": 21, "The theorem is": 78, "To match the": 11, "This yields an": 15, "Then we consider": 25, "This model ,": 13, "To clarify this": 10, "This is confirmed": 60, "Table _REF_ with": 35, "This chapter presents": 46, "The approach in": 12, "The index _MATH_": 40, "This means ,": 33, "To investigate this": 18, "The observations were": 16, "The dimensions of": 13, "This _MATH_ is": 29, "The model that": 12, "The lower limit": 11, "This induces a": 10, "TeV and _MATH_": 30, "This case corresponds": 11, "Thus far ,": 20, "Theorem _REF_ at": 11, "The change of": 69, "The wave functions": 13, "The representation of": 20, "The main challenge": 17, "This limits the": 14, "Theorem _REF_ follows": 40, "The part of": 17, "The first line": 20, "The transition matrix": 16, "To produce the": 10, "The effect on": 13, "The angular velocity": 15, "Then the solution": 47, "These data were": 15, "Thus , on": 30, "To verify the": 58, "The fourth column": 12, "Table _REF_ show": 51, "This strategy is": 16, "Theorem 2 .": 107, "Theorem _REF_ on": 21, "Then , clearly": 11, "Then by Lemma": 40, "The interpretation of": 60, "This ends the": 27, "The most commonly": 41, "Three types of": 19, "Therefore , both": 27, "This justifies the": 18, "To illustrate how": 19, "Throughout this book": 11, "To build a": 11, "The proposed framework": 13, "The effectiveness of": 39, "The dispersion relation": 20, "The comparison with": 23, "The uniqueness of": 41, "Thus , these": 49, "The density is": 14, "The changes in": 29, "The transition to": 12, "Then we apply": 27, "The distance of": 12, "There are basically": 13, "The corresponding time": 10, "The essence of": 21, "The second ,": 22, "These imply that": 12, "The Dirac equation": 11, "The right panel": 46, "The detection of": 42, "The source of": 26, "To check that": 12, "The _MATH_ distribution": 13, "The last column": 22, "This is generally": 12, "To extend the": 14, "To address the": 42, "The last row": 11, "This lower bound": 13, "They used a": 28, "The smaller the": 28, "This paper studies": 58, "The real part": 12, "Theorem 3.4 .": 14, "The _MATH_ terms": 11, "To finish the": 24, "The second method": 35, "This method ,": 18, "The controller is": 18, "The point of": 49, "The _MATH_ in": 15, "This and (": 13, "Table 3 ,": 51, "The characterization of": 23, "This formulation is": 10, "The vertices of": 29, "The second statement": 15, "Therefore _MATH_ .": 38, "The dependence on": 36, "To take into": 21, "Then we conclude": 10, "The measure of": 10, "The differential equations": 16, "This is only": 33, "This fact was": 13, "The power law": 10, "The control law": 17, "Thus , due": 15, "These results indicate": 35, "This value of": 15, "The activation functions": 11, "Then based on": 14, "This contradicts the": 78, "To clarify the": 15, "The product of": 34, "The approach taken": 10, "The approach of": 28, "This form of": 27, "Table 2 shows": 22, "The model takes": 11, "There was also": 11, "The best known": 28, "This example is": 33, "The work in": 30, "Turing machine .": 29, "The proposed circuit": 13, "To achieve the": 36, "These equations can": 29, "The procedure for": 23, "Their approach is": 15, "The model for": 26, "The stability and": 10, "The general form": 47, "The lower the": 11, "These expressions are": 13, "Thus , such": 11, "The overall system": 10, "Type III-like bursts": 42, "Type III bursts": 31, "Therefore in the": 17, "Taylor expansion ,": 24, "Transform ( FFT": 15, "The availability of": 33, "The improvement in": 10, "Then Theorem _REF_": 22, "Theorem _REF_ reduces": 11, "Theorem 4.1 ,": 25, "The model we": 23, "These kinds of": 28, "The collection of": 37, "They are based": 20, "The state transition": 16, "The state and": 14, "The second equality": 32, "The integral is": 13, "The most relevant": 14, "The method we": 22, "To test the": 70, "This ensures that": 58, "The corresponding values": 15, "The boundary _MATH_": 10, "The above condition": 13, "Taylor coefficients of": 16, "Taylor series .": 11, "This procedure can": 16, "The contributions from": 19, "This suggests the": 26, "The price of": 15, "The intuition is": 19, "The only thing": 19, "This may not": 11, "The observations of": 27, "The minimum of": 18, "This tells us": 14, "This turns out": 16, "The average number": 24, "The problem can": 34, "To distinguish between": 10, "Table 2 .": 108, "The computational cost": 14, "The approach we": 23, "The identification of": 37, "Thus we find": 21, "They did not": 14, "Then _MATH_ in": 29, "Theorem _REF_ provides": 33, "The metric (": 11, "This argument is": 18, "The obtained values": 12, "The latter are": 46, "The challenge is": 18, "There are at": 33, "This illustrates that": 10, "Therefore , although": 21, "The first approach": 34, "The following set": 10, "The last relation": 10, "The first condition": 32, "Taking this into": 19, "The consistency of": 18, "The characteristic polynomial": 19, "Table 2 and": 11, "Theorem 1.1 in": 13, "The top left": 17, "The first was": 14, "The two other": 14, "This requires the": 25, "The system parameters": 16, "Theorem 1 and": 42, "The present study": 34, "The obtained results": 57, "The basic tool": 11, "Theorem 4.1 .": 22, "The graphs in": 10, "The first test": 12, "To model this": 16, "The simplest example": 21, "To apply the": 38, "Then _MATH_ as": 33, "Therefore , with": 37, "The primary objective": 10, "The numbers of": 28, "The following lemmas": 16, "The comparison between": 45, "The two main": 27, "Thanks to (": 12, "The components of": 71, "The scalar product": 19, "The most striking": 12, "The parameters for": 21, "This immediately implies": 21, "The calculation is": 15, "The conclusion is": 42, "This theorem is": 25, "This fact can": 29, "This appears to": 13, "The plasma density": 13, "The points in": 11, "Theorem 2.1 and": 13, "There exists an": 84, "The electron density": 25, "Theorem _REF_ as": 37, "This procedure was": 11, "This parameter is": 19, "The issue of": 45, "The contents of": 17, "The larger _MATH_": 14, "The basis functions": 10, "The main theorem": 15, "The sum _MATH_": 17, "That means _MATH_": 11, "The values are": 25, "The family _MATH_": 14, "The work presented": 20, "They find that": 26, "The result shows": 24, "The model (": 23, "Taylor series in": 13, "The relation (": 18, "Traveling Salesman Problem": 18, "The lengths of": 11, "The spectral index": 10, "The question arises": 28, "Theorem 2 are": 10, "There may be": 31, "To explain this": 17, "Theorem _REF_ asserts": 11, "Thus , even": 33, "The paper deals": 11, "The images are": 22, "The configuration of": 19, "The two most": 16, "The growth of": 20, "This is indicated": 16, "The mean and": 25, "Then under the": 15, "The transition function": 10, "Thus , instead": 20, "To reach this": 12, "Ti : Sa": 11, "These values of": 13, "Theorem ( see": 23, "The subset of": 10, "This result shows": 23, "The key property": 10, "The expansion of": 27, "Taking the derivative": 43, "The uncertainties are": 13, "The fraction of": 37, "This extension is": 11, "The history of": 14, "The remaining parameters": 11, "The values for": 38, "The kernel of": 25, "The numerical value": 10, "The fractal dimension": 12, "The system has": 36, "To validate the": 17, "They showed that": 88, "The total magnetic": 14, "The field equations": 14, "Therefore _MATHDISP_ .": 74, "This means the": 23, "The latter two": 23, "Table _REF_ indicate": 10, "The underlying idea": 23, "This estimate is": 16, "The energy density": 30, "This paper discusses": 18, "The notions of": 15, "The other type": 11, "This is essential": 12, "The spectral density": 16, "The total decay": 11, "Therefore , combining": 12, "Then the trivial": 23, "The same arguments": 14, "These assumptions are": 20, "This possibility is": 10, "This not only": 11, "Thus _MATHDISP_ ,": 37, "The figure also": 21, "This gives a": 65, "The acceleration of": 13, "To formulate the": 21, "The mean of": 29, "The tensor _MATH_": 16, "The problem (": 13, "Theorem 3.2 ,": 36, "The assumption _MATH_": 21, "This is now": 11, "These methods can": 10, "The conditions _MATH_": 16, "The method used": 22, "The vertical axis": 10, "The simulated results": 11, "This causes a": 12, "Take _MATH_ .": 41, "The observations are": 13, "The differences in": 30, "The argument for": 12, "This would allow": 25, "These points are": 13, "The results ,": 22, "Take , for": 16, "The other parameters": 27, "To illustrate this": 81, "The active region": 23, "The wave function": 18, "Thus there are": 17, "Type I singularity": 11, "The main differences": 15, "This section contains": 15, "This will allow": 30, "The differences are": 10, "The subscripts _MATH_": 12, "The partial derivatives": 17, "Then the Cauchy": 10, "The obtained result": 11, "The above two": 35, "The subsystem (": 11, "Then , an": 25, "To compute _MATH_": 40, "The correlation coefficient": 23, "Table 1 summarizes": 14, "The adjacency matrix": 12, "This also means": 19, "To this purpose": 38, "The subscript _MATH_": 21, "The comparison shows": 13, "The profiles of": 19, "Thus we need": 14, "The velocity field": 12, "Then by Theorem": 31, "This method does": 16, "This finding is": 27, "The first equation": 34, "Thus , without": 13, "Table 2 )": 36, "This requirement is": 18, "The vertex set": 11, "The reduction in": 17, "The criteria for": 10, "The factors _MATH_": 10, "The Lyapunov exponents": 11, "The experimental data": 21, "The critical path": 14, "The actuarial present": 11, "To solve (": 11, "The Lagrangian of": 27, "Third , it": 14, "The order _MATH_": 11, "The paper also": 14, "The lemma follows": 23, "The matrix function": 12, "Telescope ( SOT": 27, "The most notable": 12, "This set of": 57, "The system consists": 12, "The initial value": 45, "These functions are": 34, "To compare our": 17, "There should be": 16, "The _MATH_ case": 16, "This picture is": 14, "The conditions of": 19, "Tsuneta et al.": 14, "The word ``": 11, "Take _MATH_ and": 33, "This in particular": 10, "Thus _MATH_ has": 23, "This is actually": 13, "The same result": 25, "The Hubble parameter": 11, "These results were": 37, "The basis of": 35, "This matrix is": 30, "The second algorithm": 10, "The idea was": 12, "The output is": 17, "This finishes the": 43, "Theorem 1 )": 28, "The second equation": 28, "The convergence in": 11, "The vanishing of": 14, "Thus , two": 13, "The cardinality of": 13, "The neural network": 14, "This is made": 14, "The bandwidth of": 16, "The samples were": 15, "The laser system": 10, "The key observation": 19, "Transfer Protocol (": 12, "Third , in": 11, "This reveals the": 10, "There also exists": 10, "The states _MATH_": 11, "The state _MATH_": 14, "The nodes of": 13, "The imaginary part": 33, "To design a": 10, "The core of": 43, "The polarization of": 22, "The standard model": 15, "The boundary condition": 31, "The point is": 35, "This will help": 10, "Thus there is": 30, "The case with": 14, "Typically , we": 21, "Then the initial": 10, "There exist several": 21, "To begin with": 66, "To simplify notation": 20, "To illustrate ,": 23, "Then _MATH_ where": 10, "The plots of": 13, "The relative error": 10, "That is _MATH_": 14, "Theorem _REF_ requires": 14, "The above mentioned": 18, "This result could": 10, "The dotted line": 16, "The second example": 34, "The third example": 10, "Then we set": 17, "Then _MATH_ (": 17, "The sensitivity of": 44, "The present analysis": 12, "To make it": 17, "The magnetic fields": 12, "This chapter deals": 21, "There are now": 11, "The bound on": 13, "The roots of": 22, "The success of": 35, "Theorem 3.1 .": 68, "The outcome of": 28, "The optimal policy": 14, "To prevent the": 16, "The masses of": 25, "The integer _MATH_": 11, "The usefulness of": 14, "The proof uses": 17, "Taylor 's series": 11, "The form factor": 17, "There was no": 12, "To perform this": 10, "Two examples are": 17, "T cells .": 13, "The formula for": 31, "Traditionally , the": 24, "The signs of": 12, "To extract the": 25, "The plot shows": 23, "The error dynamics": 10, "This transformation is": 16, "The proposition is": 14, "The system was": 15, "This distribution is": 18, "This aspect is": 15, "The crux of": 13, "This fact has": 22, "Together with _MATH_": 11, "Taking the supremum": 11, "The construction is": 14, "Theorem , the": 23, "The presented method": 15, "The sample mean": 10, "The desired result": 11, "The same applies": 24, "The morphology of": 13, "The terms _MATH_": 41, "Taylor series expansions": 14, "This case can": 12, "This relation is": 26, "To explain the": 42, "To consider the": 22, "The coupling of": 23, "This is easy": 17, "To sum up": 28, "This confirms that": 23, "The bound of": 11, "The uncertainty on": 10, "The current version": 12, "The main point": 30, "To design the": 14, "The relations (": 12, "The critical temperature": 11, "The problem that": 10, "This completes our": 11, "This is partly": 19, "Then _MATHDISP_ where": 33, "Therefore , instead": 15, "The most prominent": 22, "Table 4 ,": 19, "To alleviate the": 11, "This section will": 14, "These data are": 41, "The most simple": 13, "The large number": 20, "This is necessary": 20, "Taken together ,": 21, "The input is": 11, "The data ,": 11, "The correlation function": 10, "The decay width": 11, "This data set": 36, "The last step": 44, "These authors found": 15, "To prove _REF_": 19, "The two models": 13, "The corresponding _MATH_": 22, "The difficulty is": 10, "The cost functional": 12, "This provides an": 24, "They are usually": 14, "The parameter values": 30, "This method requires": 11, "The output _MATH_": 11, "That is because": 21, "Theorem 2 )": 23, "Theorem 3 )": 12, "The results have": 22, "Third , we": 56, "These methods ,": 12, "The task of": 35, "The differential equation": 26, "The eigenvalues _MATH_": 28, "The reconstruction of": 20, "This mapping is": 14, "The null hypothesis": 18, "The strategy of": 16, "The assertion follows": 13, "This result implies": 14, "This section also": 17, "The inequality _MATH_": 25, "The angle _MATH_": 31, "Therefore there exists": 14, "This solution can": 11, "The consideration of": 20, "The technique of": 20, "The pair of": 18, "Theorem , there": 15, "The two components": 11, "The operation _MATH_": 20, "The other cases": 11, "This is based": 32, "The branching ratios": 11, "The parameters in": 17, "To further improve": 13, "The decomposition of": 21, "The algorithm _MATH_": 12, "The second point": 12, "T cells ,": 21, "The following section": 12, "The necessity of": 14, "The value _MATH_": 79, "Thus _MATH_ for": 33, "The _MATH_ of": 14, "The fact is": 11, "Then the problem": 29, "This is likely": 17, "The production cross": 14, "The result will": 16, "The most straightforward": 21, "To obtain these": 11, "The third step": 10, "The reason lies": 11, "The third and": 19, "This is exactly": 48, "The same approach": 16, "To solve the": 89, "The literature on": 30, "This process was": 10, "The coincidence of": 10, "The maximum likelihood": 22, "To interpret the": 10, "This construction is": 15, "The result in": 34, "The data in": 18, "Then it can": 18, "To produce a": 13, "Then the unique": 13, "The meaning of": 36, "The signal-to-noise ratio": 10, "This effect was": 14, "This is no": 15, "This is followed": 36, "The relation of": 14, "This problem has": 49, "The link between": 11, "The proof in": 18, "The mean number": 10, "The same conclusion": 21, "The region _MATH_": 10, "The formal definition": 13, "The density _MATH_": 10, "The separation between": 10, "The exact solution": 25, "To construct the": 29, "The third row": 11, "To apply this": 19, "Terrestrial Relations Observatory": 36, "The boundaries of": 13, "The rationale behind": 15, "This value can": 13, "Ti : Sapphire": 17, "The beam is": 11, "This configuration is": 10, "The plan of": 38, "The origin is": 10, "To give an": 26, "Then the random": 13, "Toward this end": 15, "To remedy this": 17, "This is known": 47, "Thus , although": 25, "Telescope ( XRT": 18, "The transfer function": 30, "The sum over": 13, "To overcome the": 49, "This indicates the": 24, "This is most": 20, "The sign of": 50, "Then the time": 10, "The rates of": 11, "Then we prove": 13, "The slope of": 35, "The top quark": 23, "The basis for": 12, "This defines the": 21, "These oscillations are": 16, "Type 1 and": 10, "The black hole": 15, "The second result": 15, "The second -order": 18, "The paper concludes": 13, "This way we": 26, "This approach will": 10, "The second row": 20, "The scheme is": 21, "Type II radio": 13, "The main technical": 15, "Thus we see": 19, "This applies to": 12, "The concentration of": 21, "The analytic solution": 12, "This mechanism is": 28, "Take an arbitrary": 12, "Tan et al": 11, "The realization of": 14, "This is usually": 46, "The difficulty with": 10, "They have also": 19, "Theorem _REF_ above": 25, "The form factors": 26, "The numerical solution": 26, "To summarise ,": 14, "This equation can": 53, "To fix ideas": 12, "Theorem A .": 15, "Thus we may": 22, "Theorem 2.2 is": 10, "Then we see": 10, "The third equation": 13, "This part is": 13, "To illustrate our": 11, "The results indicate": 31, "The latter has": 17, "The benefits of": 22, "These include the": 28, "Theorem 3.1 of": 11, "The following examples": 18, "Taylor expansion .": 14, "Theorem 5 .": 12, "The trajectories of": 23, "This section shows": 19, "They also found": 21, "The leading term": 12, "To the authors": 14, "This is expressed": 11, "The precision of": 20, "This book is": 14, "Therefore , Lemma": 13, "The critical manifold": 11, "This hypothesis is": 12, "These effects are": 24, "The other terms": 11, "The case when": 21, "The following notation": 22, "This bound is": 20, "Therefore , given": 16, "This class is": 13, "This discrepancy is": 10, "The stability condition": 14, "This contrasts with": 19, "These plots show": 10, "The fixed point": 26, "The main issue": 17, "The principle is": 10, "Theorem ( _REF_": 15, "The Jacobian of": 16, "Thus , significant": 14, "The random vector": 10, "These regions are": 18, "The states are": 11, "The two types": 12, "The characteristic function": 20, "The study is": 10, "This aspect of": 11, "The frequency responses": 10, "The basic concept": 12, "The second column": 25, "The third column": 22, "The method for": 14, "The second technique": 10, "The minimization of": 20, "They are obtained": 19, "The closed-loop system": 21, "The coupling constants": 10, "The model in": 17, "The more general": 13, "This quantity is": 36, "The similarity between": 21, "The second integral": 16, "The architecture of": 21, "The coordinates _MATH_": 13, "Then we show": 23, "Thus , its": 18, "This assumption implies": 10, "They are shown": 16, "TeV , _MATH_": 23, "TeV , and": 10, "Then _MATH_ must": 14, "This algorithm can": 10, "This would also": 10, "The approach described": 12, "To understand this": 21, "Theorem ) .": 14, "The decrease of": 21, "The results also": 24, "This indicates a": 16, "To calculate _MATH_": 26, "The subspace _MATH_": 12, "The Hawking temperature": 23, "The function is": 10, "The vector space": 12, "There is then": 16, "They argued that": 13, "This property can": 21, "They pointed out": 12, "The calculations of": 13, "This family of": 11, "The idea that": 12, "The detailed description": 11, "Thus _MATH_ can": 16, "To create a": 16, "Taking account of": 15, "The latter condition": 20, "The distance _MATH_": 19, "The result was": 12, "The radiative corrections": 10, "To express the": 11, "Theorem 3.2 in": 12, "The generating 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"Theorem _REF_ has": 30, "Then the total": 15, "Thus , taking": 21, "Theorem 5 in": 11, "The contribution to": 16, "The expression in": 13, "The estimation error": 12, "Then the operator": 24, "The _MATH_ term": 28, "The total _MATH_": 11, "This creates a": 14, "To explore the": 15, "The case in": 17, "Thus the proof": 14, "This then means": 10, "The paper _CITE_": 27, "The model consists": 15, "Then by using": 12, "The field lines": 19, "This represents the": 20, "The arrival rate": 10, "This requires that": 15, "The function of": 16, "These are then": 14, "The understanding of": 12, "The first attempt": 13, "The distance from": 14, "The frequencies of": 16, "The probability density": 23, "The production of": 40, "These models have": 17, "This defines a": 20, "The Hamiltonian of": 18, "The following sections": 23, "The comparison results": 12, "The condition that": 23, "The motivation of": 24, "This is motivated": 14, "These may be": 10, "This illustrates the": 17, "The flow is": 16, "Tsai 's scheme": 12, "Therefore , taking": 20, "The model assumes": 18, "This helps to": 12, "The nonlinear operator": 13, "The limiting distribution": 10, "The objectives of": 11, "These results provide": 11, "This is sufficient": 11, "They use the": 15, "Tevatron and LHC": 20, "The DO Collaboration": 10, "The above equations": 17, "Thus in the": 22, "This allows to": 28, "This is often": 19, "The _MATH_ function": 19, "To estimate _MATH_": 28, "The simulations are": 20, "The expected number": 25, "The inequality is": 12, "Two examples of": 15, "To justify the": 14, "The global stability": 11, "The first point": 15, "The radio emission": 14, "The requirement that": 20, "The scaling factor": 12, "The main features": 26, "The first contribution": 12, "The domain _MATH_": 23, "These transformations are": 10, "They can not": 14, "This result indicates": 13, "This is proved": 13, "They have a": 12, "The values in": 20, "The previous section": 18, "To carry out": 21, "The same process": 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"The disadvantage of": 14, "The second derivative": 13, "Theorem _REF_ establishes": 10, "To optimize the": 15, "The left hand": 13, "This allows one": 43, "The noise level": 16, "The system can": 31, "The left and": 11, "The proposed solution": 13, "This paper presented": 13, "Then _MATH_ _MATH_": 14, "Therefore , assume": 10, "The expressions (": 11, "The fit is": 10, "The resulting algorithm": 11, "The choice _MATH_": 22, "Thus , applying": 17, "The other one": 16, "Then , all": 22, "To minimize the": 24, "This relationship is": 15, "The motivation behind": 12, "The critic network": 12, "This was first": 21, "Thus the total": 11, "This technique can": 10, "The variations in": 12, "The ratios of": 16, "The input _MATH_": 12, "The regularity of": 11, "The user is": 16, "The system then": 11, "The _MATH_ dependence": 13, "The Nash equilibrium": 10, "Therefore , due": 16, "The failure of": 12, "The numbers _MATH_": 18, "These results ,": 14, "The base case": 11, "This simplifies the": 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"The main source": 12, "The following assertion": 10, "The moments of": 10, "Then every solution": 12, "The reason behind": 16, "Thus , up": 12, "The stability problem": 10, "The Lie algebra": 20, "Then we write": 11, "This operation is": 19, "That is :": 10, "The cause of": 14, "The measurements of": 19, "Theorem can be": 10, "The main interest": 14, "The integral _MATH_": 14, "Two of the": 24, "The proof given": 10, "The height of": 41, "This is clear": 18, "The explicit forms": 11, "This rule is": 10, "To summarize the": 13, "This generalizes the": 11, "This change is": 12, "The covariance matrix": 19, "This problem arises": 10, "The third component": 10, "The phase space": 16, "The PID controller": 10, "The model presented": 19, "The second issue": 24, "The two terms": 14, "The response of": 30, "This constraint is": 11, "There is evidence": 10, "To understand how": 10, "To represent the": 17, "The temporal variation": 10, "The histogram of": 14, "The condition of": 36, "This is 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"Then the optimal": 13, "The Markov chain": 12, "The root of": 12, "The log-likelihood function": 14, "This will result": 11, "To distinguish the": 16, "TeV scale ,": 17, "Turing machine (": 12, "Tevatron Run II": 10, "Theorem 4 .": 26, "The top right": 10, "The reader will": 13, "There was an": 10, "The standard deviations": 17, "The closed -loop": 15, "To obtain this": 19, "There is one": 41, "The Lagrangian is": 13, "These could be": 11, "These are all": 12, "Then the proof": 12, "The expression above": 10, "The ( _MATH_": 11, "The authors declare": 13, "The Netherlands .": 10, "Theorem _MATH_ in": 11, "This reduction is": 10, "The first group": 18, "This assumption can": 15, "The reliability of": 11, "Taking the difference": 11, "The explanation for": 11, "The profile of": 16, "Then we present": 12, "This is repeated": 14, "The fit of": 11, "Theorem _REF_ ;": 29, "They proved the": 10, "The shift of": 12, "The protocol is": 17, "Types 1 and": 11, "The model predicts": 10, "Toolbox 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"The setup is": 11, "Thus the _MATH_": 10, "The posterior distribution": 17, "They are defined": 17, "To select the": 12, "The holographic bound": 11, "The method proposed": 15, "The setting of": 10, "The flow equation": 13, "The energy dependence": 16, "T Tauri stars": 21, "They satisfy the": 10, "To prove _MATH_": 16, "Then _MATH_ will": 15, "These are not": 13, "The present model": 12, "Therefore , its": 17, "Theorem 4 in": 11, "The discretization of": 12, "The algorithm terminates": 10, "The result obtained": 10, "The first results": 10, "The error of": 15, "The EM algorithm": 16, "To confirm this": 12, "The worst case": 15, "Turing machine and": 11, "This makes sense": 12, "Then with the": 10, "The second contribution": 15, "The key issue": 12, "The matrix _MATHDISP_": 11, "The performance evaluation": 10, "This concept is": 23, "The estimate for": 13, "The structure is": 11, "The expression (": 17, "Therefore , without": 10, "Then the process": 13, "The physical meaning": 11, "This reduction in": 16, "The suppression of": 12, "Torun and Ond": 13, "The interest of": 11, "This work focuses": 12, "The histograms of": 10, "Tx and Rx": 13, "This leaves the": 13, "The Hamiltonian _MATH_": 21, "The second factor": 13, "The incidence matrix": 10, "The execution time": 15, "These algorithms are": 17, "Then we use": 23, "Taking the Fourier": 11, "The trajectory of": 20, "The phase shift": 11, "To preserve the": 10, "The second important": 11, "The last expression": 13, "This function _MATH_": 11, "These relations are": 10, "The Green 's": 14, "To the author": 10, "Thus , considering": 13, "The algorithm has": 18, "The present results": 10, "Through the use": 10, "The same problem": 15, "Theorem _REF_ when": 11, "The sufficient conditions": 13, "The total cross": 17, "This error is": 11, "The uncertainty of": 13, "The random variables": 29, "The limit _MATH_": 13, "The Friedmann equation": 10, "The model equations": 10, "The characteristic of": 11, "This proves 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which extent": 24, "true if the": 30, "the item responses": 13, "the response process": 11, "the effective number": 35, "the Laplacian operator": 31, "the spectrum and": 25, "the surfaces of": 40, "they are stable": 12, "the PWF method": 17, "to the analysis": 191, "the active region": 436, "the 171 \u00c5": 43, "temporal cadence of": 14, "these data to": 15, "the data ,": 343, "to confirm this": 15, "the work of": 537, "the experiments were": 17, "that they have": 115, "the films .": 10, "the horizontality condition": 19, "the nilpotent (": 22, "the fields of": 92, "that emerge from": 19, "then , the": 130, "the large-scale magnetic": 41, "the Sun has": 17, "the Sun 's": 223, "toroidal magnetic field": 41, "the 11-year solar": 30, "the toroidal magnetic": 24, "the Sun is": 93, "toroidal magnetic fields": 14, "the foreseeable future": 16, "the definitions of": 244, "that the generalized": 47, "the generalized inverse": 19, "the model shows": 12, "the notion that": 31, "the null model": 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's": 228, "the experimental situation": 13, "the last century": 24, "this situation ,": 181, "terms of some": 17, "the code of": 27, "the KP hierarchy": 14, "the Plucker relations": 13, "the hierarchy .": 22, "that this does": 43, "that the set": 381, "there exist vectors": 22, "the derivative _MATH_": 76, "therefore , by": 33, "the assumption made": 18, "the segment _MATH_": 117, "the coherence length": 23, "to uncover the": 18, "the scalar meson": 12, "the two- and": 16, "the expected value": 196, "the _MATH_-value of": 14, "that _MATH_ belongs": 106, "the Minkowski inequality": 10, "theorem follows .": 30, "to achieve a": 247, "to be aligned": 21, "to make use": 79, "the free boundary": 31, "that the free": 39, "time tends to": 13, "to the CPU": 26, "the simulation for": 14, "the GPU ,": 30, "time step .": 112, "that the code": 12, "that reflect the": 13, "the public education": 13, "to _MATH_ )": 461, "that by assumption": 10, "the area of": 541, "the determination of": 518, "to react to": 27, "the most appropriate": 70, "the subsequent sections": 35, "they are used": 34, "to get the": 422, "the tail asymptotics": 47, "tail asymptotics of": 30, "the first or": 25, "the label of": 48, "the chain _MATH_": 76, "the sink bitangent": 11, "this method the": 12, "the dispersion relation": 178, "the curl of": 24, "the operator norm": 52, "typical example of": 51, "transition from state": 17, "this case there": 49, "there exists no": 70, "that _MATH_ starts": 11, "two phases ,": 30, "the time from": 27, "the period from": 74, "the current direction": 11, "the columns of": 164, "that we need": 116, "the composition of": 194, "the same code": 15, "type , the": 42, "then combined to": 10, "to produce an": 66, "the last equation": 113, "the theorem .": 302, "to the LHC": 18, "the LHC ,": 123, "the hierarchy problem": 52, "to solve this": 166, "treated as a": 187, "the fine-tuning problem": 11, "to overcome these": 27, "the littlest Higgs": 14, "to the electroweak": 30, "to develop the": 77, "the LH model": 40, "that the top": 38, "that the homogeneous": 11, "the corresponding energy": 21, "the following series": 17, "that _MATH_ where": 92, "this result by": 20, "the list _MATH_": 35, "the decision of": 30, "this question ,": 75, "the Central Committee": 29, "the case the": 11, "to depend on": 118, "that can take": 20, "take an arbitrary": 14, "the master equations": 14, "the capacity of": 108, "the example of": 168, "typically lead to": 12, "to _MATH_ where": 56, "then the positive": 13, "the positive equilibrium": 121, "the study on": 32, "this problem in": 75, "to compute the": 1155, "the documents .": 13, "the previous method": 21, "the model 's": 74, "the window is": 13, "those cases ,": 28, "to compute and": 27, "time domain ,": 42, "the underlying process": 28, "that would otherwise": 17, "the limits of": 133, "time of writing": 29, "the possibilities of": 42, "to switch from": 20, "to the high": 154, "the high number": 22, "to _MATH_ would": 17, "the results is": 37, "this point .": 109, "the additional constraint": 19, "the dummy adversary": 53, "time of _MATH_": 222, "that does not": 347, "the polynomial _MATH_": 220, "thus we have": 49, "that Condition (": 11, "the following relations": 163, "the assumptions that": 46, "that the sunspot": 18, "the sunspot is": 20, "to the quiet": 31, "the quiet Sun": 355, "the strong magnetic": 17, "the waves are": 22, "the cardinality _MATH_": 10, "the subsets of": 32, "the subset of": 184, "that in this": 450, "the mapping function": 12, "terms ( see": 15, "the kernel is": 31, "that the classical": 42, "time goes to": 17, "technique has been": 75, "the wave equation": 126, "time using the": 16, "then _MATHDISP_ holds": 10, "the black holes": 34, "the gravitational field": 69, "that it was": 93, "the presence and": 33, "to decide the": 37, "the vacuum energy": 67, "the cosmological constant": 165, "the phantom energy": 44, "then have _MATHDISP_": 98, "the _MATH_ which": 20, "the _MATH_ for": 82, "the action of": 615, "that since _MATH_": 141, "two hash function": 10, "the load ,": 13, "the proposed scheme": 183, "the registration center": 19, "the server can": 11, "the computational load": 50, "the signing oracle": 23, "than 0 ,": 10, "then there is": 267, "the success probability": 48, "there is still": 121, "to simulate the": 197, "that the probability": 267, "the rising and": 10, "there appears to": 22, "than 20 %": 29, "to 15 %": 14, "thinking about the": 14, "the integral curves": 29, "the divergence is": 14, "the components of": 516, "the first fundamental": 11, "the outward normal": 27, "the divergence in": 13, "the divergence of": 95, "the Laplace-Beltrami operator": 46, "the following piecewise": 11, "terms , a": 19, "the environment (": 34, "the short term": 15, "term , the": 62, "to the mentioned": 12, "the elasticity of": 75, "tax policy .": 10, "to the equilibrium": 107, "the dynamic response": 32, "the interior of": 384, "the exterior of": 45, "two edges _MATH_": 13, "the fit is": 26, "to the interval": 74, "the transition probability": 108, "these cases are": 14, "the numerical values": 62, "the fractal dimension": 53, "the input _MATH_": 163, "the auxiliary input": 19, "that for (": 12, "the previous experiment": 11, "the zero set": 18, "to the cubic": 17, "the cubic equation": 17, "then problem (": 34, "that _MATH_ are": 394, "that ( 2.2": 18, "that _MATHDISP_ Thus": 28, "then we can": 345, "that ( 1.1": 13, "the propulsion system": 21, "the ones of": 69, "the asymptotic mean-square": 19, "trivial solution of": 198, "the geometry of": 321, "the first order": 312, "that , out": 11, "the _MATH_ components": 38, "the curvature tensor": 31, "tensor is _MATHDISP_": 12, "the convergence in": 88, "the details ,": 29, "to the proofs": 16, "then _MATHDISP_ ,": 442, "to implement this": 24, "the design is": 25, "the hardware and": 13, "the more general": 224, "the gravitational action": 10, "the interval in": 11, "the metric _MATH_": 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which": 81, "to the operator": 47, "to _MATH_ defined": 42, "the almost sure": 48, "the identity operator": 56, "that _MATH_ converges": 227, "twisted flux tubes": 20, "this using the": 10, "the rotation rate": 81, "the same method": 143, "the original image": 159, "that the density": 80, "the very definition": 15, "the neutral line": 138, "to influence the": 58, "the global field": 11, "that results in": 60, "the spherical harmonic": 36, "the field is": 142, "to the rotation": 52, "the field .": 92, "the models for": 20, "tilt of the": 42, "the streamer belt": 63, "the active regions": 98, "the model for": 112, "the displacement of": 88, "to Figure _REF_": 84, "the necessity of": 101, "this paper uses": 12, "theoretical results are": 29, "theoretical results ,": 21, "the joint probability": 97, "the Bayes rule": 34, "them to the": 117, "the `` real": 20, "the smoothness of": 111, "this with the": 68, "the long exact": 10, "the following commutative": 19, "to the optical": 79, "the _MATH_ direction": 241, "that a small": 60, "the authors considered": 37, "that the smallest": 24, "the smallest eigenvalue": 50, "to infinity as": 36, "these conditions ,": 129, "the conditions on": 59, "the Michelson Doppler": 48, "the Solar and": 113, "the Sun .": 471, "the observations in": 61, "time periods .": 28, "the general solution": 151, "this case is": 231, "to fulfill the": 47, "that the higher": 60, "the faster the": 20, "the universe expands": 20, "the largest _MATH_": 49, "this reason the": 20, "the abundance of": 59, "the two main": 42, "then be obtained": 32, "the abundances of": 23, "than expected .": 17, "the discrepancy between": 73, "the large uncertainties": 10, "the differential of": 36, "the PH system": 28, "the above method": 27, "the numerical value": 24, "this method of": 28, "the auxiliary function": 22, "translated into a": 21, "the absolute value": 210, "the conclusion .": 53, "that this function": 25, "the theta series": 11, "the quadratic forms": 18, 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"the main points": 13, "the light of": 121, "to the Earth": 72, "the notion of": 904, "to quantify the": 165, "the resolution of": 198, "that in many": 28, "the inner and": 71, "to a factor": 62, "that the definition": 61, "they are either": 15, "type II bursts": 98, "to the Sun": 265, "the driver of": 14, "the shock ,": 39, "the ICME center": 12, "the Sun and": 207, "the next three": 34, "to be larger": 75, "than the local": 25, "the spacecraft .": 51, "the _MATH_ energy": 17, "the _MATH_ factor": 55, "the energy of": 418, "the electron beam": 40, "the _MATH_ -beam": 13, "the laser energy": 25, "the laser beam": 158, "the photons are": 12, "three generations of": 14, "too small for": 21, "the one used": 116, "time of observation": 15, "the signal strength": 18, "the radial distance": 54, "the Sun ,": 365, "the power of": 308, "the density .": 22, "to 1 ,": 253, "to an increased": 25, "the gain in": 32, "to reduce by": 11, "to get a": 321, "the sample for": 11, "that _MATH_ ;": 268, 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"this happens ,": 42, "the equilibrium in": 19, "the index set": 60, "the variables .": 41, "then the corresponding": 89, "that _MATHDISP_ since": 29, "the mass conservation": 18, "the next order": 15, "to point _MATH_": 27, "terms : the": 20, "the matrix representation": 35, "that one is": 31, "the numerical point": 11, "the integration by": 23, "the channel 's": 16, "to three different": 17, "the same service": 15, "the detection threshold": 11, "these models ,": 99, "this may not": 41, "to compute .": 43, "to be measured": 79, "time is measured": 11, "these steps ,": 12, "the simplest model": 32, "to the SM": 102, "the SM particles": 39, "terms are given": 13, "to : _MATHDISP_": 78, "the redshift of": 13, "the frequency ratio": 10, "the new time": 13, "the angular momentum": 182, "the angular velocity": 173, "the rotating mass": 12, "the centre of": 184, "two methods of": 11, "the following characteristic": 16, "the Carrington rotation": 14, "the solar activity": 148, "the real 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activation energy": 33, "the pressure in": 22, "the other the": 13, "to the tuning": 13, "to be crucial": 15, "the enhancement of": 59, "the reputation of": 18, "to play a": 67, "the corresponding result": 37, "the ocean current": 14, "the riser and": 10, "the damping coefficient": 41, "the riser ,": 13, "the boundary control": 23, "the vessel ,": 16, "then Eq .": 101, "the discrete time": 49, "true that _MATH_": 39, "the reset control": 76, "the base linear": 18, "to a direct": 22, "to illustrate that": 26, "the performance degradation": 27, "the schedule of": 10, "the group action": 25, "to the _MATH_-axis": 98, "the _MATH_-axis and": 55, "to the _MATH_-plane": 13, "that the rotation": 39, "the rotation matrix": 59, "the unit vectors": 32, "to the group": 78, "the values given": 17, "the application in": 19, "the setting of": 150, "that the simulation": 35, "the simulation of": 210, "the instances of": 30, "that the only": 160, "to the hybrid": 11, "the stable steady": 11, "to the 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"that all _MATH_": 76, "the region around": 25, "the sample standard": 16, "the estimator _MATH_": 72, "the ODE _MATHDISP_": 16, "the scalar function": 26, "to apply this": 33, "this technique to": 41, "the image space": 26, "then it can": 76, "the agents '": 18, "the balance equations": 20, "transmitted from _MATH_": 19, "to its parent": 22, "this ensures that": 18, "that the flow": 64, "the flow on": 18, "the tree is": 38, "the input rate": 10, "that acts on": 18, "the _MATH_ axes": 10, "to the experimental": 119, "the theoretical curve": 12, "the semi-tensor product": 53, "then , using": 26, "that the sign": 39, "test statistics _MATH_": 15, "the one based": 15, "the NPMLE .": 12, "the sample sizes": 13, "the dual polar": 21, "the polar space": 13, "the kinematic constraint": 11, "the contact forces": 38, "the former ,": 69, "the _MATH_-distribution with": 24, "the above model": 40, "the random effect": 18, "the logistic and": 10, "the maximal and": 14, "that in Fig": 38, "time 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no such": 12, "the sample holder": 18, "the drift term": 12, "term _MATH_ for": 11, "to generate new": 25, "the wavelet coefficients": 53, "the tree are": 10, "the foundation of": 30, "that they can": 195, "to apply in": 16, "the formulas _MATH_": 13, "the Euclidean median": 22, "time scales ,": 66, "time and spatial": 13, "the neutron counts": 10, "the peak and": 19, "through the heliosphere": 17, "the heliosphere ,": 30, "the constraints imposed": 28, "the _MATH_ discrete": 17, "the Wilson flux": 14, "the four-dimensional theory": 13, "the linear combinations": 15, "the states at": 13, "the quadratic cost": 12, "the weight on": 16, "the system states": 54, "the positive definite": 46, "the control effort": 24, "the stabilizing controller": 11, "tries to find": 25, "the location and": 64, "to the execution": 20, "the query ,": 21, "the result to": 51, "the assumptions for": 11, "thanks to a": 17, "that measures the": 44, "the regular and": 16, "to the linear": 185, "that is present": 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"However it is": 15, "However , compared": 13, "Hence _MATHDISP_ and": 14, "However , (": 15, "However , given": 39, "However , considering": 18, "He II 304": 21, "Higgs field _MATH_": 16, "However , increasing": 13, "Higgs doublets _MATH_": 11, "High-Energy Solar Spectroscopic": 10, "However , any": 18, "Hopf bifurcations ,": 20, "Hessian matrix .": 10, "However , two": 19, "Hopf bifurcations at": 20, "H1 ) _MATH_": 10, "Here we study": 30, "However , within": 12, "Having obtained the": 12, "Hasse diagram of": 11, "Huairou Solar Observing": 10, "Higgs fields in": 10, "Hamiltonian is the": 10, "Hurwitz polyzeta functions": 33, "Hence we conclude": 15, "However , few": 12, "Hz ) ,": 12, "He ii 4685.7\u00c5": 14, "Higgs boson _CITE_": 16, "H3 ) and": 11, "Hardy space _MATH_": 14, "Hamilton-Jacobi-Bellman ( HJB": 11, "Hamiltonian systems .": 12, "Here , however": 29, "Here we used": 32, "Hopf bifurcation in": 23, "Higgs couplings to": 14, "Hence , at": 19, "HER2 and EGFR": 11, "Hamilton 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"Higgs fields _MATH_": 10, "Hilbert spaces _MATH_": 15, "H1 and ZEUS": 12, "Here , each": 15, "He ( _MATH_": 16, "He , _MATH_": 15, "Hence , letting": 10, "Hamiltonian systems with": 13, "However , several": 23, "Hamiltonian path of": 12, "HMM for affective": 13, "Hence , condition": 10, "Hausdorff error function": 10, "Hypothesis _REF_ .": 13, "However , once": 32, "Hardy 's inequality": 12, "Howard et al.": 12, "Hardy and Ramanujan": 17, "Here are the": 15, "Hence , every": 11, "Hamiltonian has the": 10, "Higgs vacuum expectation": 15, "H_MATH_ line .": 15, "Hence we see": 13, "Hz ] ,": 17, "Hamiltonian systems ,": 10, "Hardy-type integral operator": 12, "However , so": 12, "Hence _MATH_ has": 16, "Higgs mass ,": 16, "Hamiltonian _MATHDISP_ ,": 24, "Henkin 's question": 12, "Hodge theory .": 12, "Higgs mechanism is": 11, "Here , since": 11, "Hamiltonian function (": 11, "H7 ) ,": 12, "Hilbert series of": 10, "Hurvich , Moulines": 12, "Human Pacman ,": 11, "Hernandez et al": 10, 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The": 133, "_REF_ summarizes the": 139, "_MATH_ the _MATH_": 98, "_MATH_ for which": 719, "_CITE_ , hence": 13, "_MATH_ ) the": 213, "_MATH_ and by": 276, "_CITE_ the following": 25, "_MATH_ and any": 387, "_MATH_ , on": 249, "_MATH_ forms a": 131, "_REF_ , the": 3354, "_CITE_ , for": 406, "_MATH_ values .": 148, "_MATH_ are all": 306, "_MATH_ values (": 20, "_MATH_ value ,": 45, "_MATH_ corresponding to": 653, "_REF_ ) to": 1224, "_REF_ ( b": 1421, "_REF_ ) are": 1680, "_MATH_ , note": 57, "_MATH_ is simply": 138, "_CITE_ , and": 3558, "_MATH_ describe the": 44, "_MATH_ describes the": 179, "_MATH_ , by": 1219, "_MATH_ ) and": 2447, "_MATH_ ) ;": 290, "_MATH_ can also": 205, "_MATH_ are given": 983, "_MATHDISP_ , _MATHDISP_": 5282, "_MATH_ denotes the": 3475, "_REF_ ) -": 2727, "_MATH_ when _MATH_": 884, "_MATH_ at _MATH_": 1143, "_MATH_ are _MATH_": 488, "_MATH_ and _MATHDISP_": 1114, "_MATHDISP_ then the": 74, "_MATH_ defined by": 1016, "_REF_ , _REF_": 2470, "_REF_ converges to": 20, "_REF_ in the": 408, "_REF_ we have": 428, "_MATHDISP_ we have": 41, "_MATH_ depend on": 147, "_MATH_ and have": 60, "_MATHDISP_ , with": 2245, "_MATH_ not depending": 13, "_REF_ there exists": 37, "_MATHDISP_ we get": 29, "_MATH_ by using": 226, "_MATH_ in addition": 28, "_MATH_ such as": 52, "_MATH_ are sufficient": 10, "_MATH_ belongs to": 669, "_MATH_ for certain": 23, "_MATH_ but not": 116, "_MATH_ , thus": 417, "_MATH_ ; therefore": 144, "_MATH_ of Section": 10, "_MATH_ is limited": 17, "_CITE_ , on": 33, "_REF_ shows the": 2401, "_MATH_ and select": 11, "_MATH_ , choose": 71, "_MATH_ from the": 1272, "_REF_ ) is": 7021, "_MATH_ as the": 1519, "_REF_ ) (": 499, "_MATH_ about _MATH_": 28, "_MATH_ for every": 913, "_MATH_ ; (": 545, "_MATH_ and its": 637, "_MATH_ are evaluated": 28, "_MATH_ : if": 43, "_MATH_ is chosen": 499, "_MATH_ is being": 11, "_MATH_ is evaluated": 50, "_MATH_ are those": 39, "_MATH_ ; moreover": 58, "_CITE_ and _CITE_": 2330, "_MATH_ is continuous": 907, "_MATH_ , Equation": 57, "_REF_ ) holds": 930, "_CITE_ , (": 72, "_MATH_ are used": 162, "_MATH_ and they": 43, "_REF_ , where": 727, "_MATH_ can be": 7207, "_MATH_ matrix ,": 105, "_REF_ ) such": 143, "_MATH_ , say": 184, "_MATHDISP_ or _MATHDISP_": 129, "_REF_ ) satisfying": 51, "_REF_-_REF_ , we": 74, "_MATH_ and 2": 27, "_MATHDISP_ , and": 6053, "_MATH_ satisfy the": 466, "_REF_ ) has": 1141, "_MATH_ with the": 1950, "_REF_ are satisfied": 136, "_MATH_ Equation (": 16, "_CITE_ provides a": 57, "_MATH_ are said": 67, "_MATH_ is proportional": 208, "_MATH_ of the": 5808, "_MATH_ is as": 247, "_MATH_ ( _MATH_": 3388, "_MATH_ ) ,": 5329, "_MATH_ are not": 558, "_MATH_ converges absolutely": 14, "_REF_ we see": 101, "_MATH_ space ,": 54, "_MATH_ is represented": 149, "_MATH_ has three": 46, "_MATH_ at each": 131, "_REF_ we know": 64, "_MATHDISP_ where _MATH_": 5290, "_REF_ ) _MATH_": 171, "_MATH_ and (": 362, "_MATHDISP_ are given": 10, "_MATH_ first .": 14, "_REF_ ) into": 974, "_REF_ ) yields": 507, "_REF_ ) tends": 32, "_MATHDISP_ which ,": 46, "_MATHDISP_ and thus": 75, "_REF_ ) we": 1610, "_REF_ ) of": 444, "_REF_ ) then": 104, "_MATH_ in (": 1805, "_REF_ ) can": 2298, "_REF_ ) together": 95, "_MATHDISP_ is a": 363, "_MATH_ ; for": 128, "_MATH_ iff _MATH_": 173, "_MATH_ ( with": 387, "_MATH_ and all": 469, "_MATH_ are determined": 190, "_MATH_-rays in the": 16, "_MATH_ is defined": 2705, "_MATHDISP_ , to": 82, "_MATH_- and _MATH_-axes": 18, "_MATH_ are _MATHDISP_": 180, "_MATH_ , equivalently": 29, "_MATHDISP_ for all": 1022, "_MATH_ generated by": 235, "_MATH_ near _MATH_": 81, "_MATH_ for some": 1755, "_MATH_ so that": 888, "_MATH_ returns _MATH_": 18, "_MATH_ of points": 47, "_MATH_ consists of": 449, "_MATH_ is contained": 300, "_MATH_ around the": 103, "_URL_ ) .": 122, "_REF_ we present": 179, "_MATH_ % of": 50, "_MATH_ % .": 50, "_MATH_ degrees of": 121, "_MATH_ defines the": 153, "_MATH_ or on": 19, "_MATH_ ; thus": 139, "_MATH_ is null": 18, "_CITE_ for an": 134, "_MATH_ increases ,": 233, "_MATH_ the family": 16, "_MATH_ the corresponding": 123, "_MATH_ for any": 1222, "_MATH_ reads _MATHDISP_": 60, "_MATH_ scale .": 17, "_MATH_ model .": 71, "_REF_ , a": 341, "_MATH_ ( to": 53, "_MATH_ is connected": 209, "_MATH_ is observed": 69, "_MATH_ is obtained": 718, "_MATH_ is expressed": 155, "_MATHDISP_ using the": 16, "_MATH_ ) of": 557, "_MATH_ becomes _MATHDISP_": 109, "_MATH_ is equal": 624, "_REF_ is a": 343, "_REF_ , two": 33, "_MATH_ is composed": 75, "_MATH_ _CITE_ .": 1509, "_REF_ ) as": 922, "_MATH_ is associated": 114, "_MATH_ and is": 548, "_MATH_ means the": 127, "_CITE_ ; see": 129, "_CITE_ , as": 291, "_CITE_ , by": 97, "_MATH_ is its": 185, "_MATH_ are their": 23, "_MATH_ ; in": 215, "_MATH_ is similar": 116, "_MATH_ as time": 16, "_MATH_ is necessarily": 62, "_MATH_ will be": 1257, "_MATH_ is introduced": 108, "_MATHDISP_ where the": 599, "_MATH_ is equivalent": 392, "_MATH_ and to": 213, "_MATH_ and every": 207, "_MATHDISP_ , from": 220, "_MATH_ is equicontinuous": 45, "_MATH_ is also": 1092, "_MATH_ produces the": 25, "_CITE_ reported that": 31, "_MATH_ the estimate": 12, "_CITE_ , including": 47, "_CITE_ ) where": 14, "_MATH_ and time": 75, "_MATH_ , whose": 280, "_MATH_ is determined": 444, "_MATH_ is unique": 101, "_MATH_ _MATH_ )": 72, "_MATH_ ) is": 1494, "_MATH_ is much": 139, "_MATH_ with respect": 1472, "_MATH_ , an": 324, "_MATH_ is said": 699, "_MATH_ takes into": 22, "_MATH_ ( including": 38, "_MATH_ , he": 25, "_MATH_ and replacing": 17, "_MATH_ by _MATH_": 1723, "_MATH_ times ,": 91, "_MATH_ ) when": 53, "_REF_ , if": 168, "_MATH_ should be": 609, "_MATH_ in direction": 21, "_MATH_ of _MATH_": 4466, "_MATH_ , i.e.": 1914, "_MATH_ , is": 3035, "_MATH_ as _MATHDISP_": 879, "_MATH_ fulfill the": 14, "_MATH_ , integrating": 44, "_MATH_ and applying": 69, "_REF_ ) provides": 87, "_REF_ ) with": 2397, "_MATH_ in Equation": 222, "_MATH_ implies that": 578, "_MATH_ increases .": 175, "_MATH_ , (": 861, "_REF_ ) results": 60, "_CITE_ _MATHDISP_ .": 427, "_MATH_ and of": 232, "_MATH_ vanish ,": 15, "_MATHDISP_ , while": 239, "_MATH_ requires the": 20, "_MATH_ vanishes ,": 44, "_REF_ ) gives": 477, "_MATH_ is explicitly": 20, "_MATHDISP_ with some": 32, "_MATH_ we first": 12, "_MATHDISP_ , which": 3971, "_MATH_ yields _MATHDISP_": 225, "_MATH_ does not": 1703, "_MATH_ we may": 51, "_MATHDISP_ is an": 80, "_REF_ ( i.e.": 14, "_REF_ and boundary": 10, "_REF_ , with": 247, "_REF_ , given": 30, "_MATH_ is important": 20, "_MATH_ are positive": 431, "_MATH_ is interpreted": 54, "_MATH_ as a": 1603, "_REF_ , can": 55, "_MATH_ , defined": 434, "_REF_ , are": 98, "_MATH_ using the": 369, "_MATH_ for a": 867, "_MATH_ , but": 1490, "_MATH_ as well": 563, "_REF_ has two": 21, "_MATH_ and 10": 13, "_MATH_ are calculated": 105, "_MATH_ , with": 2980, "_MATH_ values were": 17, "_MATH_ depending only": 85, "_CITE_ claimed that": 11, "_REF_ and Table": 102, "_MATH_ if it": 128, "_MATH_ is reached": 61, "_MATH_ at the": 1144, "_MATH_ intersects the": 64, "_REF_ above )": 15, "_MATH_ described in": 25, "_REF_ , together": 91, "_MATH_ , give": 17, "_MATH_ , are": 1378, "_MATH_ , i.e": 1218, "_REF_ ) still": 43, "_MATH_ , that": 2056, "_MATH_ tend to": 101, "_CITE_ ) for": 101, "_MATH_ is multiplicative": 32, "_MATH_ and pressure": 12, "_MATH_ are defined": 674, "_MATH_ ( a": 154, "_MATH_ , of": 717, "_MATH_ from a": 182, "_MATH_ , as": 2352, "_MATH_ ( see": 2306, "_REF_ shows a": 420, "_MATH_ and no": 61, "_MATH_ depends only": 166, "_MATH_ ( Fig": 250, "_MATH_ ) with": 295, "_MATHDISP_ ; (": 69, "_MATH_ is shown": 275, "_CITE_ on the": 105, "_MATH_ if and": 1180, "_MATH_ be two": 409, "_CITE_ that a": 46, "_MATH_ , ...": 371, "_MATH_ represents the": 1293, "_MATH_ , provided": 227, "_MATH_ with an": 141, "_MATH_ with a": 827, "_MATH_-dependence of _MATH_": 24, "_MATH_ from _MATH_": 998, "_MATH_ with increasing": 26, "_MATH_ decreases with": 52, "_MATH_ values ,": 92, "_MATH_ , assuming": 101, "_MATH_ and those": 49, "_REF_ to be": 49, "_MATH_ are expected": 20, "_MATH_ between _MATH_": 197, "_MATH_ being the": 588, "_MATH_ and node": 19, "_MATH_ represent the": 443, "_MATH_ to represent": 78, "_MATH_ at time": 522, "_MATH_ represents a": 216, "_MATH_ among the": 40, "_MATH_ as an": 234, "_MATH_ have a": 192, "_MATH_ according to": 497, "_MATH_ are associated": 34, "_MATH_ ( for": 445, "_MATH_ for different": 149, "_MATH_ over time": 12, "_CITE_ is the": 93, "_MATH_ is treated": 22, "_REF_ can be": 1027, "_MATH_ from _REF_": 144, "_REF_ , and": 2191, "_REF_ , _MATHDISP_": 642, "_MATHDISP_ , i.e.": 200, "_CITE_ ) and": 459, "_MATH_ parameterized by": 16, "_MATH_ represents _MATH_": 15, "_MATH_ or any": 16, "_MATHDISP_ , the": 664, "_MATH_ depends on": 574, "_MATH_ and not": 121, "_MATH_ given _MATH_": 199, "_MATH_ to account": 16, "_MATH_ is called": 1518, "_MATH_ is strongly": 126, "_MATH_ data points": 41, "_MATH_ yields the": 137, "_MATH_ is best": 10, "_MATH_ of each": 113, "_MATH_ we are": 37, "_REF_ is given": 142, "_MATH_ the space": 65, "_MATH_ one has": 117, "_MATH_ for each": 1002, "_MATH_ , defining": 24, "_CITE_ ; _CITE_": 1877, "_MATH_ is more": 141, "_REF_ ) converges": 73, "_CITE_ , an": 165, "_REF_ illustrates the": 308, "_MATH_ in _CITE_": 156, "_CITE_ can be": 256, "_MATH_ are both": 255, "_MATH_ for fixed": 58, "_MATH_ follows from": 184, "_MATH_ denote a": 175, "_MATH_ of integers": 10, "_MATH_ threshold .": 17, "_MATH_ where the": 309, "_MATHDISP_ , using": 76, "_MATH_ steps ,": 64, "_MATH_ steps .": 58, "_MATH_ , select": 11, "_MATH_ is full": 35, "_MATH_ onto _MATH_": 214, "_MATHDISP_ , giving": 30, "_MATHDISP_ , showing": 30, "_MATH_ is onto": 10, "_MATH_ ( resp.": 180, "_MATH_ ) be": 150, "_REF_ ) for": 1490, "_MATH_ must satisfy": 104, "_REF_ , but": 171, "_MATH_ are two": 346, "_REF_ , one": 317, "_MATH_ bits of": 61, "_REF_ above ,": 31, "_MATH_ with no": 63, "_MATH_ points .": 95, "_MATH_ denote ,": 53, "_MATH_ coordinates ,": 29, "_MATH_ , using": 370, "_MATH_ in _MATHDISP_": 21, "_MATHDISP_ when _MATH_": 39, "_MATH_ has to": 322, "_MATH_ must be": 962, "_REF_ does not": 148, "_MATH_ indicates the": 179, "_MATH_ was determined": 19, "_REF_ is similar": 33, "_MATH_ at a": 248, "_MATH_ whenever _MATH_": 205, "_MATH_ be an": 1531, "_MATH_ and we": 415, "_MATH_ ) in": 469, "_CITE_ , which": 1745, "_MATH_ to 1": 48, "_MATH_ and calculate": 23, "_MATH_ which are": 343, "_CITE_ is applied": 21, "_MATH_ is increased": 132, "_MATH_ to problem": 15, "_MATH_ satisfies _MATHDISP_": 414, "_REF_ for the": 537, "_MATHDISP_ and _MATH_": 474, "_MATH_ are called": 211, "_MATH_ and a": 1871, "_MATH_ admits an": 21, "_MATH_ , regardless": 30, "_CITE_ to prove": 25, "_REF_ reveals that": 34, "_MATH_ ; see": 408, "_MATH_ contains a": 250, "_MATH_ tends to": 439, "_MATH_ being an": 50, "_MATH_ with constant": 34, "_MATH_ and _MATH_-": 329, "_MATH_ ; this": 181, "_CITE_ is that": 70, "_MATH_ ; hence": 201, "_MATHDISP_ does not": 22, "_CITE_ is not": 43, "_MATH_ that are": 406, "_REF_ below .": 143, "_REF_ below )": 117, "_MATH_ ; otherwise": 104, "_MATH_ , or": 1270, "_MATH_ , centered": 25, "_MATH_ , will": 128, "_MATHDISP_ in the": 123, "_MATH_ is some": 207, "_MATH_ , satisfying": 241, "_MATH_ the number": 208, "_REF_ is satisfied": 183, "_MATH_ is conservative": 18, "_MATH_ needs to": 108, "_CITE_ using a": 34, "_MATH_ ) for": 394, "_MATH_ , to": 586, "_MATH_ and set": 116, "_MATH_ ) by": 144, "_MATH_ and if": 141, "_MATH_ and that": 624, "_MATH_ into _MATH_": 715, "_MATH_ given by": 991, "_MATH_ is then": 396, "_MATH_ starting at": 43, "_MATH_ , from": 619, "_MATH_ exists and": 123, "_CITE_ and for": 67, "_MATH_ have been": 324, "_MATH_ has been": 609, "_MATH_ of data": 23, "_MATH_ TeV _CITE_": 15, "_MATH_ is essentially": 61, "_REF_ ) shows": 253, "_MATH_ , gives": 79, "_MATH_ is suppressed": 17, "_MATH_ to produce": 25, "_MATH_ solves the": 83, "_MATH_ as _MATH_": 2648, "_MATH_ is nonnegative": 117, "_MATH_ is even": 322, "_MATH_ is odd": 303, "_MATHDISP_ defines the": 10, "_MATH_ has two": 129, "_MATH_ , correspond": 13, "_REF_ contains a": 36, "_MATH_ and using": 310, "_REF_ holds with": 34, "_MATH_ _MATH_ .": 690, "_MATH_ , since": 952, "_CITE_ , _MATH_": 339, "_MATH_ is relatively": 133, "_MATH_ is played": 18, "_MATH_ derived from": 50, "_CITE_ where the": 128, "_REF_ and its": 35, "_MATH_ there exist": 116, "_MATH_ consisting of": 162, "_MATH_ points ,": 66, "_MATH_ defined on": 239, "_MATH_ there are": 107, "_MATH_ _MATH_ ,": 809, "_MATH_ , define": 495, "_MATH_ m ,": 74, "_MATH_ we can": 278, "_MATHDISP_ where _MATHDISP_": 890, "_MATH_ are a": 93, "_MATH_ by a": 400, "_CITE_ for details": 275, "_CITE_ , i.e.": 75, "_MATH_ ) can": 237, "_MATH_ since otherwise": 11, "_MATH_ be as": 200, "_MATH_ and let": 757, "_MATHDISP_ , _MATH_": 452, "_CITE_ , who": 421, "_CITE_ and have": 27, "_MATH_ is mapped": 56, "_MATH_ ) via": 10, "_MATH_ in a": 882, "_MATH_ , uniformly": 34, "_MATH_ and independent": 22, "_MATH_ need not": 64, "_MATH_ vectors in": 16, "_MATH_ is based": 52, "_MATH_ ) between": 48, "_MATH_ is taken": 233, "_REF_b ) .": 172, "_REF_ ) becomes": 599, "_MATHDISP_ Using the": 61, "_MATH_ gravity .": 42, "_CITE_ for the": 657, "_REF_ ) :": 840, "_MATHDISP_ which implies": 70, "_REF_ ) _MATHDISP_": 386, "_MATH_ into four": 14, "_MATH_ satisfies the": 1189, "_MATHDISP_ , if": 108, "_MATH_ are disjoint": 88, "_MATH_ we deduce": 20, "_MATHDISP_ holds for": 118, "_REF_ , there": 424, "_MATH_ satisfies (": 270, "_REF_ ) implies": 539, "_REF_ and let": 18, "_MATH_ be given": 258, "_MATHDISP_ , that": 315, "_MATH_ there is": 279, "_MATH_ is surjective": 68, "_MATH_ possesses a": 57, "_MATH_ and charge": 15, "_MATH_ and it": 211, "_MATHDISP_ , is": 408, "_MATH_ admits a": 107, "_MATH_ is _MATH_": 1871, "_MATH_ and then": 453, "_MATH_ takes _MATH_": 20, "_MATH_ units of": 104, "_MATH_ is only": 141, "_MATH_ corresponds to": 861, "_MATH_ ( and": 542, "_REF_ displays the": 166, "_REF_ ; _MATH_": 11, "_MATH_ ; _MATH_": 1199, "_REF_ ; and": 14, "_MATH_ be some": 52, "_MATH_ , because": 411, "_MATH_ ) at": 137, "_MATH_ be any": 361, "_MATH_ coordinates .": 36, "_MATH_ onto the": 147, "_MATH_ are in": 369, "_MATH_ is either": 216, "_MATH_ , namely": 447, "_REF_ , will": 17, "_MATH_ to a": 450, "_MATH_ , equals": 18, "_MATH_ , while": 1200, "_MATH_ for (": 54, "_MATH_ along the": 359, "_MATH_ are constants": 290, "_REF_ ) the": 480, "_MATHDISP_ Finally ,": 51, "_REF_ ) back": 10, "_MATHDISP_ Thus ,": 131, "_REF_ ) satisfies": 201, "_MATH_ , one": 1481, "_MATH_ is non-negative": 34, "_MATHDISP_ and _MATHDISP_": 2020, "_REF_ ) ]": 302, "_MATH_ leads to": 302, "_CITE_ _CITE_ .": 145, "_MATH_ of (": 498, "_MATH_ by its": 66, "_MATHDISP_ Similarly ,": 56, "_MATH_-norm of a": 14, "_MATH_ _MATH_ is": 284, "_MATH_ is generally": 46, "_MATH_ as shown": 179, "_REF_ ( ii": 117, "_MATH_ ( e.g": 69, "_MATH_ has no": 342, "_MATH_ is disconnected": 12, "_MATH_ values are": 100, "_MATH_ is replaced": 251, "_MATH_ admits the": 47, "_MATHDISP_ and ,": 203, "_MATH_ to any": 39, "_MATH_ after _MATH_": 43, "_MATH_ the potential": 15, "_MATH_ ) denotes": 58, "_CITE_ and references": 345, "_MATH_ in Theorem": 219, "_MATH_ pixels ,": 39, "_MATH_ pixels .": 45, "_MATH_ ( Table": 27, "_CITE_ have studied": 29, "_MATH_ the condition": 17, "_MATH_ is true": 145, "_MATH_ is still": 153, "_MATH_ in two": 65, "_MATH_ times the": 139, "_CITE_ ( Fig": 23, "_MATH_ when there": 16, "_MATH_ is negative": 217, "_MATH_ the following": 139, "_MATH_ shows a": 35, "_REF_ be satisfied": 63, "_REF_ on _MATH_": 81, "_MATH_ implies _MATH_": 399, "_MATH_ also holds": 18, "_MATH_ which indicates": 12, "_MATH_ _MATHDISP_ .": 632, "_MATH_ shows that": 108, "_MATH_ are invertible": 23, "_MATH_ are non-zero": 19, "_MATH_ presented in": 23, "_MATH_ are satisfied": 70, "_REF_ ) that": 1136, "_MATH_ of an": 168, "_MATH_ goes to": 218, "_CITE_ and thus": 16, "_MATH_ under the": 438, "_MATH_ ] ,": 262, "_MATH_ . Hence": 13, "_MATH_ is bigger": 22, "_REF_ ) correspond": 35, "_MATH_ is globally": 128, "_REF_ ) suggests": 28, "_REF_ ) should": 103, "_MATH_ or the": 166, "_MATHDISP_ ( note": 18, "_MATH_ is increasing": 225, "_CITE_ ; and": 70, "_MATH_ be such": 463, "_MATH_ and a.e": 16, "_MATH_ is differentiable": 80, "_MATH_ iff for": 10, "_MATH_and _MATH_ ,": 130, "_MATH_ is Lipschitz": 73, "_MATH_ ( shown": 13, "_REF_ ) a": 57, "_MATH_ , seen": 10, "_MATH_ , shown": 40, "_MATH_ indicates that": 117, "_MATH_ control problem": 55, "_REF_ based on": 24, "_MATH_ ( recall": 89, "_MATH_ satisfying (": 234, "_MATH_ is nonsingular": 148, "_REF_ ) hold": 198, "_MATH_ when it": 54, "_MATH_ as functions": 47, "_MATH_ at low": 38, "_MATH_ at high": 24, "_CITE_ are shown": 15, "_MATH_ ( cf": 309, "_REF_ , shows": 33, "_MATH_ , taken": 19, "_MATH_ becomes positive": 15, "_MATH_ and 1": 88, "_REF_ that this": 23, "_CITE_ , one": 180, "_REF_ illustrates how": 32, "_MATH_ ) if": 146, "_MATH_ , both": 212, "_MATH_ is positive": 605, "_MATH_th iteration of": 14, "_MATH_ will have": 108, "_CITE_ ) is": 127, "_MATH_ vertices and": 37, "_MATH_ edges .": 33, "_MATH_ time per": 17, "_MATH_ is removed": 41, "_MATH_ and scalars": 19, "_CITE_ 's _CITE_": 20, "_MATH_ 's (": 29, "_MATH_ 's )": 27, "_MATH_ converges strongly": 30, "_MATH_ weakly converges": 21, "_MATH_ converges weakly": 86, "_REF_ with _REF_": 62, "_MATH_ is convex": 233, "_MATH_ we obtain": 388, "_REF_ ) or": 292, "_REF_ , _MATH_": 1253, "_MATHDISP_ Replacing _MATH_": 12, "_MATHDISP_ Substituting the": 16, "_MATH_ are arbitrary": 143, "_MATH_ between two": 69, "_MATH_ induces a": 78, "_MATH_ is solved": 25, "_MATH_ is dual": 14, "_CITE_ , let": 21, "_MATH_ to vertex": 15, "_REF_ together with": 93, "_MATH_ are reduced": 16, "_REF_ presents the": 297, "_MATH_ , consisting": 44, "_MATH_ representing the": 110, "_MATH_ equal to": 185, "_REF_ gives an": 69, "_REF_ and Sect": 21, "_MATH_ of a": 890, "_MATH_ satisfying _MATH_": 566, "_MATH_ range over": 13, "_MATH_ in order": 314, "_MATH_ case ,": 85, "_MATH_ , during": 19, "_CITE_ , only": 28, "_MATH_ is sufficiently": 313, "_MATH_ in our": 178, "_MATH_ : the": 192, "_MATH_ is uniquely": 109, "_MATH_ respectively ,": 107, "_MATHDISP_ Applying the": 19, "_REF_ shows that": 681, "_MATH_ converges to": 435, "_MATH_ is close": 187, "_REF_ to this": 18, "_MATH_ has maximal": 13, "_MATH_ vertices .": 86, "_MATH_ since _MATH_": 342, "_MATH_ are shown": 250, "_REF_ and Theorem": 192, "_MATH_ , converges": 21, "_REF_ ( 2": 29, "_MATH_ , denoted": 380, "_CITE_ , but": 605, "_MATH_ filter design": 19, "_MATH_ performance .": 20, "_CITE_ described a": 25, "_CITE_ described the": 11, "_MATH_ gives a": 119, "_MATHDISP_ is the": 299, "_MATH_ or ,": 88, "_MATH_-measurable function _MATH_": 10, "_MATH_ is of": 767, "_MATH_ is adapted": 19, "_MATH_ with values": 83, "_MATH_ contains _MATH_": 159, "_MATH_ via _MATH_": 77, "_MATH_ to itself": 30, "_MATH_ is dependent": 31, "_REF_ , however": 32, "_MATH_ which gives": 31, "_CITE_ : _MATH_": 66, "_MATH_ for this": 111, "_MATH_ is invertible": 201, "_CITE_ of the": 146, "_MATH_ _MATHDISP_ which": 14, "_CITE_ ; a": 17, "_MATH_ is referred": 54, "_MATH_ are now": 46, "_MATH_ so as": 36, "_MATHDISP_ . Note": 94, "_MATH_ in Eq": 658, "_MATHDISP_ _MATH_ is": 66, "_MATH_ modulo _MATH_": 69, "_MATHDISP_ . _MATH_": 99, "_MATH_ constraints .": 13, "_MATH_ part of": 40, "_MATH_ , let": 1474, "_MATHDISP_ , when": 72, "_MATH_ or when": 15, "_MATH_ be defined": 226, "_URL_ . )": 18, "_REF_ shows an": 232, "_MATH_ is thus": 95, "_CITE_ _MATHDISP_ ,": 626, "_MATH_ production and": 23, "_MATH_ is their": 17, "_MATH_ and Equation": 14, "_MATHDISP_ , provided": 114, "_MATHDISP_ , Eq": 20, "_MATH_ can have": 59, "_MATH_ , consequently": 22, "_MATH_ and there": 178, "_MATH_ we will": 54, "_REF_ , (": 136, "_CITE_ or _CITE_": 202, "_MATH_ ) or": 254, "_MATH_ only has": 16, "_CITE_ or by": 38, "_REF_ ) below": 75, "_MATH_ given that": 26, "_REF_ illustrates an": 22, "_MATH_ , requires": 10, "_MATH_ we need": 37, "_MATH_ is aligned": 12, "_MATH_ is part": 16, "_MATH_ ( or": 629, "_MATH_ higher than": 31, "_MATH_ that contains": 96, "_MATH_ is nonempty": 136, "_MATH_ and has": 139, "_CITE_ and ``": 14, "_CITE_ is an": 78, "_MATH_ are IO-compatible": 11, "_MATH_ ( called": 46, "_MATH_ as required": 33, "_MATH_ it follows": 153, "_MATH_ is just": 148, "_MATH_ would not": 50, "_MATH_ is regular": 142, "_MATH_ may contain": 24, "_MATH_ is finite": 440, "_MATH_ is closed": 209, "_MATH_ is injective": 83, "_MATH_ if necessary": 28, "_MATH_ into (": 136, "_MATHDISP_ holds .": 68, "_REF_ ) must": 103, "_MATH_ will denote": 89, "_MATHDISP_ denotes the": 22, "_MATH_ is inside": 28, "_MATH_ ( resp": 472, "_MATH_ the concentration": 13, "_MATH_ maps the": 33, "_MATH_ axis .": 84, "_MATH_ and shape": 10, "_MATHDISP_ . This": 31, "_MATH_ contains only": 49, "_MATH_ through _MATH_": 133, "_MATH_ have two": 10, "_MATHDISP_ , we": 1047, "_MATH_ , provides": 15, "_MATHDISP_ , being": 24, "_MATH_ together with": 182, "_MATH_ at position": 16, "_MATH_ are introduced": 48, "_MATH_ and vanishes": 10, "_REF_ we only": 11, "_MATH_ vanishes identically": 16, "_MATH_ , has": 252, "_MATH_ _MATH_ such": 46, "_MATH_ with index": 11, "_MATHDISP_ _MATHDISP_ _MATHDISP_": 1518, "_MATHDISP_ _MATHDISP_ .": 830, "_MATH_ ( i.e": 317, "_MATH_ ( first": 10, "_MATH_ that can": 138, "_REF_ ) on": 254, "_MATH_ could be": 259, "_MATH_ , obtained": 82, "_CITE_ ) ;": 112, "_MATH_ follows by": 26, "_MATH_ be its": 167, "_CITE_ proposed to": 48, "_REF_ is equivalent": 136, "_REF_ ) according": 21, "_REF_ ( in": 31, "_MATH_ ) it": 31, "_MATH_ sufficiently small": 100, "_MATH_ small enough": 219, "_MATH_ are fixed": 125, "_MATH_ are also": 227, "_CITE_ or the": 92, "_MATH_ has only": 102, "_REF_ ) does": 237, "_REF_ and Fig": 230, "_MATH_ is _MATHDISP_": 911, "_MATH_ is monotone": 87, "_MATH_ expansion of": 10, "_CITE_ used the": 111, "_MATH_ is almost": 106, "_MATH_ ) then": 44, "_MATH_ to belong": 15, "_MATH_ given the": 83, "_MATH_ km )": 19, "_REF_ where _MATH_": 39, "_MATH_ are equal": 169, "_MATH_ and hence": 449, "_MATH_ in reading": 16, "_MATH_ which would": 11, "_MATHDISP_ is continuous": 19, "_REF_ and Proposition": 110, "_REF_ to Eq": 12, "_MATH_ as depicted": 11, "_CITE_ ) which": 38, "_MATH_ are constant": 183, "_MATH_ , into": 51, "_MATH_ group .": 20, "_MATH_ over _MATH_": 432, "_MATH_ are governed": 12, "_MATH_ is smooth": 112, "_MATH_ the linear": 24, "_MATH__MATH_ , _MATH_": 11, "_MATH_ , contains": 28, "_REF_ , this": 297, "_MATHDISP_ . Thus": 114, "_MATH_ since the": 126, "_MATHDISP_ and in": 26, "_MATHDISP_ which means": 23, "_MATH_ from 0": 48, "_MATH_ implies _MATHDISP_": 79, "_MATH_ have negative": 26, "_MATH_ gauge boson": 10, "_MATH_ ; and": 383, "_CITE_ proposed a": 298, "_CITE_ ; the": 84, "_MATH_ ( over": 19, "_MATH_ is zero": 188, "_MATH_ containing _MATH_": 170, "_MATH_ and fixed": 26, "_MATH_ , set": 156, "_MATH_ equals to": 13, "_MATH_ is deterministic": 33, "_MATH_ is constant": 316, "_MATH_ is exactly": 101, "_MATH_ one gets": 19, "_REF_ ) but": 79, "_CITE_ , this": 232, "_MATH_ is below": 47, "_REF_ ( top": 43, "_MATH_ ( bottom": 26, "_REF_ that _MATH_": 326, "_MATH_ we get": 282, "_MATH_ with at": 42, "_CITE_ , it": 557, "_REF_ that we": 22, "_MATH_ then _MATH_": 483, "_REF_ ) was": 171, "_MATH_ was found": 42, "_CITE_ , in": 480, "_CITE_ . )": 170, "_MATH_ ( Figure": 95, "_REF_ , for": 459, "_MATH_ , our": 106, "_MATH_ into Eq": 53, "_MATH_ for both": 105, "_MATH_ are constructed": 21, "_CITE_ have given": 12, "_MATH_ is used": 452, "_REF_ hold and": 14, "_MATHDISP_ has a": 81, "_MATH_ occurs in": 27, "_REF_ if and": 27, "_CITE_ has been": 130, "_REF_ ) indicates": 40, "_CITE_ , Li": 15, "_MATH_ and consequently": 71, "_REF_ ) makes": 23, "_MATH_ the inverse": 18, "_MATH_ , condition": 59, "_CITE_ and later": 47, "_MATH_ but are": 14, "_CITE_ use the": 31, "_REF_ are shown": 35, "_REF_ by _MATH_": 117, "_MATH_ and summing": 24, "_MATH_ to ensure": 47, "_MATH_ share a": 15, "_MATH_ contained in": 69, "_MATH_ is correctly": 13, "_REF_ show the": 248, "_MATH_ is parallel": 37, "_MATH_ to indicate": 46, "_MATH_ form a": 155, "_MATH_ that _MATHDISP_": 248, "_MATH_ the diagonal": 10, "_MATH_ for an": 162, "_MATH_- of _MATH_": 17, "_MATH_ is abelian": 33, "_MATH_ has _MATH_": 236, "_MATH_ of its": 86, "_MATH_ and when": 26, "_MATH_ ) plane": 26, "_MATH_ , instead": 77, "_REF_ to the": 186, "_MATH_ has in": 10, "_MATH_ denotes an": 80, "_MATH_ introduces a": 11, "_MATH_ that computes": 12, "_MATH_ multiplied by": 24, "_MATH_ _MATH_ for": 146, "_MATH_ iff it": 12, "_REF_ ( c": 569, "_MATH_ are identified": 30, "_MATH_ are selected": 40, "_REF_ and Corollary": 104, "_REF_ . )": 129, "_MATH_ holds true": 24, "_MATH_ gives _MATHDISP_": 140, "_MATH_-_MATH_ hold .": 14, "_REF_ has a": 222, "_MATH_ by _MATHDISP_": 813, "_MATH_ satisfies _REF_": 109, "_MATH_ satisfies _MATH_": 500, "_MATHDISP_ _MATHDISP_ ,": 493, "_REF_ contains the": 82, "_MATH_ in probability": 58, "_MATH_ with zero": 29, "_CITE_ leads to": 20, "_MATH_ conditional on": 39, "_MATH_ is computed": 274, "_REF_ shows this": 29, "_CITE_ extended the": 53, "_MATH_ , called": 155, "_MATH_ gives the": 271, "_MATH_ if there": 186, "_MATH_ and scalar": 17, "_MATH_ that realizes": 15, "_MATH_ that is": 684, "_MATH_ is reactively": 17, "_MATHDISP_ and consider": 18, "_MATH_ as our": 19, "_MATH_ , equation": 60, "_MATH_ and note": 61, "_MATH_ increases in": 24, "_MATH_ and therefore": 219, "_MATHDISP_ if _MATH_": 76, "_MATH_ is concave": 78, "_REF_ ( d": 278, "_MATH_ _CITE_ ,": 542, "_CITE_ , or": 368, "_CITE_ , other": 11, "_MATH_ is calculated": 220, "_MATH_ is approximately": 75, "_MATH_ ( i.e.": 545, "_MATH_ ) indicates": 12, "_MATH_ indicates a": 40, "_REF_ for details": 68, "_MATH_ is now": 134, "_MATH_ as long": 70, "_MATH_ are adjacent": 51, "_MATH_ and their": 163, "_MATH_ , possibly": 24, "_MATH_ the sequence": 18, "_MATH_ is well-defined": 21, "_MATH_ unless the": 12, "_MATH_ from equation": 11, "_MATH_ nor _MATH_": 85, "_MATH_ starts with": 11, "_MATH_ with components": 17, "_REF_ that _MATHDISP_": 245, "_CITE_ and will": 17, "_CITE_ in the": 373, "_MATH_ production at": 30, "_CITE_ use a": 39, "_MATH_ hours of": 13, "_MATH_ hours (": 13, "_MATH_ was chosen": 58, "_MATH_ with overwhelming": 27, "_MATH_ simulates _MATH_": 12, "_MATH_ and at": 104, "_MATH_ instances of": 11, "_MATH_ and each": 187, "_MATH_ that does": 46, "_MATH_ is uniformly": 286, "_MATH_ satisfying the": 370, "_MATHDISP_ , or": 405, "_MATH_ is such": 316, "_CITE_ , have": 74, "_MATH_ , denote": 181, "_MATH_ which satisfies": 142, "_CITE_ and our": 22, "_CITE_ as follows": 49, "_MATH_ provides a": 77, "_MATH_ which can": 127, "_MATH_ correspond to": 299, "_MATH_ are exactly": 37, "_MATHDISP_ . Hence": 85, "_MATH_ no longer": 12, "_MATH_ guarantees that": 39, "_REF_ , since": 83, "_MATH_ is that": 186, "_MATH_ then _MATHDISP_": 67, "_MATH_ is denoted": 379, "_MATH_ and zero": 53, "_MATH_ , these": 157, "_MATH_ are chosen": 167, "_MATH_ are normalized": 32, "_MATH_ . (": 97, "_MATH_ when the": 254, "_MATH_ , subject": 54, "_MATH_ satisfy _MATHDISP_": 123, "_MATHDISP_ . It": 25, "_MATHDISP_ Combining (": 34, "_MATH_ are bounded": 317, "_MATH_and _MATH_ .": 69, "_REF_ ) imply": 176, "_MATH_ , at": 301, "_REF_ , Lemma": 49, "_MATH_ , having": 59, "_MATH_ in an": 168, "_MATH_ are typically": 15, "_MATH_ with UC": 13, "_MATH_ and call": 22, "_MATH_ dB ,": 14, "_REF_ , Figure": 16, "_REF_ , respectively": 416, "_MATH_ is discussed": 23, "_CITE_ to provide": 10, "_MATH_ which converges": 20, "_MATH_ converges almost": 23, "_MATH_ ) converges": 13, "_MATHDISP_ , it": 204, "_REF_ ( the": 46, "_MATH_ arises from": 23, "_CITE_ for examples": 17, "_MATH_ induces the": 21, "_MATH_ holds .": 227, "_MATH_ are closed": 31, "_MATH_ direction ,": 84, "_CITE_ indicates that": 18, "_MATH_ is compactly": 29, "_REF_ ) will": 259, "_MATH_ was a": 23, "_MATH_ ) :": 328, "_MATHDISP_ implies that": 26, "_MATHDISP_ of the": 63, "_MATH_ using Eq": 20, "_MATH_ from _CITE_": 26, "_MATH_ decreases from": 22, "_MATH_ ( actually": 14, "_MATH_ lead to": 65, "_MATH_ is related": 196, "_MATH_ , around": 19, "_REF_ ) )": 1346, "_MATH_ can only": 112, "_MATH_ , this": 1013, "_MATH_ reaches its": 37, "_MATH_ which satisfy": 53, "_MATH_ converges in": 164, "_REF_ , show": 20, "_REF_ ) may": 208, "_MATH_ intersect at": 19, "_MATH_ is derived": 86, "_MATH_ because _MATH_": 188, "_MATHDISP_ with the": 371, "_MATH_ gravity with": 21, "_MATH_ ) than": 26, "_CITE_ , a": 681, "_MATH_ , setting": 40, "_MATH_ MHz ,": 22, "_MATH_ vanishes on": 33, "_MATH_ , unless": 37, "_MATH_ variables .": 42, "_MATH_ with coefficients": 30, "_MATH_ a point": 14, "_MATH_ must vanish": 25, "_MATH_ ) are": 749, "_MATH_ are quite": 20, "_MATH_ for example": 16, "_CITE_ , there": 160, "_MATH_-valued process _MATH_": 16, "_MATH_ is one": 139, "_MATH_ ) such": 164, "_MATH_ starting from": 84, "_MATH_ by (": 151, "_MATHDISP_ , together": 48, "_MATH_ before _MATH_": 29, "_MATH_ , also": 120, "_MATH_ ) that": 140, "_MATH_ may take": 10, "_MATH_ ) _CITE_": 141, "_REF_ that in": 21, "_MATH_ to hold": 12, "_MATH_ factor ,": 11, "_MATH_ , its": 237, "_CITE_ , each": 38, "_CITE_ , also": 45, "_REF_ : _MATHDISP_": 253, "_REF_ where the": 63, "_MATH_ is set": 270, "_CITE_ that the": 331, "_MATH_ , satisfies": 83, "_CITE_ , that": 145, "_MATH_ we see": 85, "_MATH_ lies in": 232, "_MATH_ , i.": 30, "_MATH_ with all": 60, "_MATHDISP_ is satisfied": 35, "_MATH_ to satisfy": 64, "_MATH_ implies the": 83, "_MATHDISP_ , so": 683, "_CITE_ consider the": 25, "_MATH_ and run": 10, "_MATH_ , yielding": 76, "_MATH_ , they": 211, "_MATHDISP_ and finally": 10, "_MATH_ is satisfied": 194, "_REF_ , Eq": 42, "_REF_ as _MATHDISP_": 105, "_MATH_ as given": 88, "_MATH_ only if": 69, "_MATH_ equally spaced": 14, "_MATH_ , not": 126, "_MATH_ close to": 130, "_MATH_ serves as": 22, "_MATH_ expansion .": 12, "_REF_ is used": 62, "_MATH_ ; if": 131, "_REF_ by applying": 12, "_MATH_ matrix _MATH_": 264, "_MATH_ is variable": 10, "_CITE_ ) Suppose": 19, "_CITE_ , with": 180, "_MATH_ , can": 522, "_MATH_ only )": 10, "_MATH_ , different": 24, "_MATH_ iterations ,": 30, "_MATH_ that guarantees": 10, "_MATH_ are different": 78, "_REF_ , system": 12, "_MATH_ if ,": 60, "_MATH_ is _MATH_-integrable": 12, "_REF_ ; in": 17, "_MATH_ where _MATHDISP_": 111, "_MATH_ denotes a": 303, "_MATH_ ; the": 459, "_MATH_ eV )": 18, "_MATH_ ( defined": 54, "_MATHDISP_ . Equation": 28, "_REF_ with _MATH_": 540, "_MATH_ : in": 26, "_MATH_ are separated": 22, "_MATH_ _MATHDISP_ ,": 415, "_MATH_ outside the": 31, "_MATH_ runs over": 56, "_MATH_ , including": 56, "_CITE_ , whereas": 70, "_MATH_ and found": 13, "_MATHDISP_ if and": 48, "_MATH_ ) given": 25, "_MATHDISP_ and for": 96, "_MATH_ and suppose": 113, "_MATH_ with any": 30, "_MATH_ by adding": 78, "_MATH_ come from": 21, "_CITE_ , ``": 23, "_MATH_ within the": 133, "_MATH_ in _REF_": 769, "_REF_ is the": 252, "_REF_ as a": 125, "_MATH_ due to": 393, "_MATH_ ( which": 459, "_MATH_ ) only": 16, "_MATH_ remains invariant": 24, "_MATHDISP_ , can": 43, "_CITE_ _CITE_ ,": 99, "_MATH_ , all": 332, "_MATH_ SUSY Yang-Mills": 16, "_MATH_ space .": 50, "_REF_ ) since": 44, "_MATH_ while _MATH_": 78, "_MATH_ are usually": 28, "_MATH_ ) decreases": 11, "_CITE_ and was": 27, "_MATH_ Mm .": 47, "_MATH_ and associated": 21, "_MATH_ of size": 195, "_CITE_ implies that": 49, "_MATH_ preprocessing time": 15, "_MATH_ points of": 82, "_MATH_ is invariant": 202, "_REF_ possesses a": 48, "_REF_ is trivial": 12, "_REF_ is derived": 15, "_REF_ corresponding to": 29, "_REF_ ) become": 71, "_REF_ , to": 125, "_MATH_ plus the": 36, "_REF_ ( i": 141, "_CITE_ as well": 133, "_CITE_ have been": 174, "_MATH_ is isotropic": 12, "_MATH_ are linearly": 123, "_CITE_ is more": 15, "_MATH_ is required": 114, "_MATH_ is eventually": 27, "_MATH_ sufficiently large": 134, "_MATH_ is decreasing": 163, "_MATH_ while the": 110, "_MATH_ ( then": 10, "_REF_ ) admits": 138, "_MATH_ time (": 13, "_MATH_ is well": 309, "_MATH_ time .": 163, "_MATH_ , determine": 20, "_MATH_ is fixed": 294, "_MATH_ is understood": 26, "_MATH_ form the": 24, "_MATH_ are completely": 18, "_MATH_ is stable": 217, "_REF_ when _MATH_": 71, "_MATH_ and small": 36, "_REF_ implies the": 38, "_MATH_ matrices ,": 49, "_MATH_ satisfying _REF_": 97, "_REF_ hold .": 86, "_MATH_ , hence": 340, "_MATH_ is ``": 72, "_REF_ is to": 51, "_MATH_ is necessary": 60, "_MATH_ that correspond": 19, "_MATH_ instead of": 518, "_MATH_ ) will": 68, "_MATH_ passing through": 46, "_MATH_ are invariant": 33, "_MATH_ are found": 56, "_MATH_ extracted from": 25, "_CITE_ ( see": 495, "_MATH_ of closed": 10, "_REF_ is defined": 30, "_MATH_ belonging to": 114, "_MATH_ becomes _MATH_": 50, "_MATHDISP_ can be": 94, "_MATH_ to construct": 16, "_MATH_ to obtain": 305, "_MATH_ even if": 31, "_MATH_ be in": 71, "_CITE_ computed the": 10, "_CITE_ provided a": 41, "_REF_ and Lemma": 160, "_MATH_ are directly": 16, "_MATH_ and vice": 34, "_MATH_th root of": 13, "_MATH_ is different": 90, "_MATH_ when we": 28, "_MATH_ by defining": 23, "_MATH_ are martingales": 10, "_MATH_ are included": 36, "_MATH_ control the": 12, "_MATH_ ( in": 394, "_MATH_ allows us": 61, "_REF_ ) allows": 78, "_MATH_ matrices _MATH_": 47, "_REF_ ) equals": 45, "_MATH_ , exactly": 29, "_MATH_ linear equations": 23, "_CITE_ to be": 51, "_REF_b ) and": 18, "_REF_ ) leads": 203, "_REF_c ) and": 16, "_MATH_ will give": 20, "_MATH_ is low": 47, "_REF_ ) corresponds": 88, "_CITE_ investigated a": 13, "_MATH_ is closable": 13, "_MATH_ , does": 59, "_CITE_ by considering": 12, "_REF_ describes the": 164, "_REF_ shows our": 13, "_MATH_ parameter .": 27, "_REF_ ) without": 45, "_MATH_ takes the": 187, "_MATH_ given as": 20, "_MATH_ nodes ,": 51, "_MATH_ in Fig": 286, "_MATH_ into three": 23, "_MATH_ centered on": 12, "_MATH_ vary in": 18, "_MATH_ under a": 31, "_MATH_ and service": 24, "_MATH_ are allowed": 38, "_MATH_ to refer": 22, "_MATH_ ] are": 27, "_REF_ for each": 33, "_CITE_ is one": 21, "_CITE_ , respectively": 155, "_MATH_ is valid": 118, "_REF_ ) coincides": 44, "_MATH_ in .": 16, "_CITE_ and the": 943, "_MATH_ is performed": 36, "_REF_ ) yield": 75, "_MATH_ identity matrix": 108, "_MATH_ can lead": 18, "_MATH_ ) have": 61, "_MATH_ are integers": 63, "_MATH_ , any": 123, "_CITE_ as a": 108, "_CITE_ and then": 37, "_MATH_ ( where": 360, "_MATH_ and define": 227, "_CITE_ , are": 91, "_REF_ ) take": 26, "_MATH_ defined as": 245, "_REF_ ) give": 73, "_MATH_ of all": 204, "_MATH_ , equipped": 27, "_CITE_ and others": 43, "_MATH_ , over": 51, "_MATH_ it is": 209, "_REF_ yields the": 65, "_REF_ should be": 26, "_REF_ , namely": 53, "_REF_ , Fig": 32, "_REF_ , after": 24, "_REF_ ( f": 68, "_REF_ ( h": 23, "_MATH_ , remain": 10, "_MATH_ acts by": 17, "_MATH_ or in": 33, "_MATH_ of Fig": 16, "_REF_ is _MATH_": 59, "_MATH_ have to": 101, "_MATH_ GeV .": 233, "_REF_ shows two": 53, "_REF_ ) under": 182, "_MATH_ ) during": 18, "_REF_ present the": 16, "_CITE_ , _MATHDISP_": 369, "_MATH_ independently of": 21, "_REF_ are the": 55, "_MATH_ are similar": 62, "_MATH_ have the": 425, "_MATH_ and one": 124, "_MATH_ , meaning": 86, "_MATH_ of convex": 11, "_MATH_ we let": 14, "_REF_ to _REF_": 177, "_MATH_ vertices ,": 76, "_CITE_ ) was": 29, "_REF_ allows us": 43, "_MATH_ is typically": 63, "_MATH_-sparse signal _MATH_": 16, "_MATHDISP_ in which": 98, "_MATH_ is high": 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"_MATH_ elements in": 30, "_MATH_ ; that": 124, "_MATH_ ( otherwise": 54, "_REF_ , it": 916, "_CITE_ and by": 79, "_MATH_ value and": 12, "_MATH_ the phase": 14, "_MATH_ ( ii": 49, "_MATH_ ( iii": 32, "_REF_ ) _CITE_": 115, "_CITE_ to obtain": 49, "_MATH_ can then": 72, "_MATH_ must have": 107, "_MATH_ and sets": 22, "_REF_ is due": 20, "_CITE_ for _MATH_": 79, "_MATH_ performance _MATH_": 36, "_MATH_ is characterized": 63, "_MATH_ are ,": 238, "_MATH_ given in": 304, "_MATH_ encodes the": 18, "_MATH_ ) do": 17, "_MATH_ , each": 290, "_MATH_ the radius": 16, "_MATH_ is strictly": 367, "_MATH_ term ,": 38, "_MATH_ term .": 33, "_MATH_ term is": 46, "_MATH_ almost surely": 115, "_REF_ in _MATH_": 55, "_MATH_ have at": 16, "_MATH_ holds and": 41, "_MATH_ , follows": 26, "_MATH_ ; all": 21, "_MATH_ are taken": 75, "_MATH_ odd ,": 34, "_MATHDISP_ and therefore": 40, "_MATH_ by considering": 30, "_MATH_ are real": 218, "_REF_ and by": 39, "_REF_ , p.": 203, "_MATHDISP_ . Applying": 28, "_MATHDISP_ or ,": 94, "_MATHDISP_ so that": 138, "_MATH_ to _REF_": 43, "_MATH_ ; we": 212, "_MATH_s and _MATH_s": 11, "_MATH_s , the": 11, "_CITE_ and Theorem": 25, "_MATHDISP_ ; _MATHDISP_": 207, "_MATHDISP_ such that": 154, "_REF_ that there": 42, "_MATH_ states in": 14, "_MATH_ into a": 219, "_CITE_ , if": 69, "_MATH_ the process": 28, "_MATH_ is Markovian": 18, "_MATH_ and initial": 59, "_MATH_ _MATH_ the": 26, "_MATH_ is in": 941, "_MATH_ from 1": 34, "_MATH_ than the": 54, "_MATH_ MK )": 54, "_MATH_ for short": 29, "_MATH_ system in": 14, "_MATH_ , may": 69, "_MATH_ contains an": 54, "_MATH_ with ,": 13, "_MATH_ considering the": 14, "_MATH_ ) was": 70, "_MATHDISP_ for a": 77, "_REF_ , while": 93, "_MATH_ the result": 19, "_MATH_ of dimension": 108, "_MATH_ composed of": 23, "_MATH_ is linearly": 105, "_MATH_ of degree": 155, "_MATH_ and combining": 10, "_MATH_ because it": 35, "_MATH_ and back": 10, "_MATH_ are distinct": 91, "_MATH_ are simply": 18, "_MATH_ in general": 72, "_MATH_ of simple": 12, "_MATHDISP_ , are": 110, "_MATH_ are finite": 86, "_MATH_ exists ,": 116, "_MATH_ for large": 198, "_CITE_ ) provides": 14, "_MATH_ and with": 212, "_MATH_ observations ,": 14, "_MATHDISP_ _MATHDISP_ Thus": 20, "_MATH_ , 2": 63, "_MATH_ is depicted": 40, "_MATH_ are complex": 64, "_MATH_ requires a": 24, "_MATH_ . It": 18, "_CITE_ ) that": 214, "_MATH_ the unique": 29, "_MATH_ norm ,": 42, "_MATHDISP_ for the": 177, "_MATH_ denoting the": 176, "_MATH_ the length": 26, "_REF_ , several": 12, "_MATH_ of order": 163, "_MATH_ MK ,": 29, "_MATH_ is unbounded": 91, "_MATH_ ( such": 28, "_CITE_ proposed that": 33, "_CITE_ found the": 24, "_MATH_ are saddle": 12, "_MATH_ , two": 117, "_REF_ we show": 244, "_MATH_ . If": 13, "_MATH_ starts at": 19, "_MATH_ is same": 21, "_REF_ ) describe": 25, "_MATH_ is Planck": 14, "_MATH_ has an": 288, "_MATH_ ) gives": 20, "_MATH_ nonzero entries": 12, "_MATH_ commutes with": 59, "_MATH_ of functions": 29, "_MATH_ , computing": 11, "_MATH_ , imply": 10, "_MATH_ . )": 483, "_MATH_ parallel to": 36, "_MATH_ refer to": 57, "_REF_ ] .": 87, "_MATHDISP_ , satisfying": 24, "_MATH_ , consider": 225, "_MATH_ determined by": 72, "_MATH_ we define": 71, "_MATH_ and being": 11, "_MATH_ is false": 11, "_REF_ we get": 115, "_MATH_ , _REF_": 160, "_MATH_ is to": 270, "_MATH_ , those": 21, "_MATH_ 's output": 14, "_MATH_ is statistically": 20, "_MATH_ is unramified": 10, "_MATH_ that _MATH_": 232, "_MATHDISP_ i.e .": 21, "_MATHDISP_ and by": 35, "_MATH_ , differentiating": 11, "_MATH_ all _MATH_": 12, "_MATH_ positive integers": 11, "_MATH_ the sum": 14, "_MATH_ the collection": 19, "_MATH_ is compact": 310, "_MATH_ when they": 12, "_REF_ leads to": 76, "_MATH_ model in": 14, "_MATH_ have no": 78, "_MATH_ with period": 35, "_MATH_ and output": 42, "_CITE_ , is": 257, "_REF_ _CITE_ .": 64, "_MATH_ range .": 15, "_MATHDISP_ which is": 268, "_MATH_ at zero": 33, "_MATH_ ( hence": 33, "_MATH_ ; cf": 32, "_MATH_ decreases (": 11, "_MATH_ specified by": 12, "_MATH_ may be": 732, "_REF_ which shows": 17, "_REF_ ( right": 137, "_MATH_ , noting": 23, "_REF_ ) reduce": 38, "_CITE_ can not": 41, "_MATH_- in (": 14, "_CITE_ investigate the": 16, "_MATH_ are restricted": 15, "_MATH_ , described": 21, "_MATH_ is completely": 144, "_MATH_ in their": 26, "_MATH_ , given": 423, "_MATH_ ; namely": 24, "_MATHDISP_ , be": 29, "_MATH_ lines in": 16, "_MATH_ ( because": 64, "_MATH_ lies on": 114, "_MATH_ were computed": 19, "_MATH_ as above": 136, "_MATH_ and plot": 16, "_MATH_ is minimized": 48, "_MATH_ , pick": 12, "_MATH_ ] as": 22, "_MATH_ ] and": 104, "_MATH_ ] .": 164, "_MATH_ , between": 65, "_MATH_ exists .": 87, "_REF_ ) show": 77, "_MATH_ matrix in": 15, "_MATH_ , etc": 183, "_CITE_ ( _MATH_": 33, "_CITE_ implemented a": 12, "_REF_ ) ;": 393, "_MATH_ are coefficients": 11, "_CITE_ _MATH_ ,": 11, "_CITE_ for a": 603, "_MATH_ are computed": 99, "_MATH_ , under": 103, "_REF_ on the": 105, "_MATH_ or vice": 15, "_CITE_ showed how": 16, "_MATHDISP_ , in": 444, "_MATH_ be fixed": 96, "_MATH_ ( respectively": 253, "_MATH_- and _MATH_-": 76, "_MATH_ _MATH_ _MATH_": 584, "_MATH_ is stochastically": 37, "_MATH_ , followed": 43, "_MATH_ decay modes": 12, "_MATH_ decays to": 19, "_MATH_ are much": 32, "_MATH_ decay mode": 26, "_MATHDISP_ and let": 39, "_MATH_ is locally": 214, "_MATH_ , symmetric": 22, "_MATHDISP_ . Then": 60, "_MATH_ are continuous": 218, "_REF_ we briefly": 20, "_MATH_ is continuously": 125, "_MATH_ equals the": 146, "_MATH_ and sufficiently": 38, "_MATH_ is separated": 22, "_MATH_ containing the": 73, "_CITE_ based on": 111, "_MATH_ into its": 21, "_MATH_ the root": 11, "_MATH_ the positive": 11, "_MATH_ for arbitrary": 36, "_MATH_ , taking": 99, "_MATH_ sufficiently close": 25, "_MATH_ 's to": 21, "_REF_ ( e": 124, "_MATH_ induced by": 140, "_REF_ , have": 10, "_MATH_ in place": 88, "_REF_ ( 4": 11, "_MATH_ algorithm .": 25, "_MATH_ ( this": 145, "_MATH_ via the": 98, "_MATH_ and assume": 151, "_MATH_ constant and": 12, "_MATH_ satisfies condition": 61, "_MATH_ if for": 88, "_MATH_ ) from": 99, "_MATH_ bosons ,": 13, "_MATH_ , compute": 38, "_MATH_ from this": 34, "_MATH_ , results": 19, "_MATH_ depending on": 161, "_MATH_ states that": 14, "_MATH_ are scalar": 16, "_MATH_ are nonnegative": 104, "_MATH_ be denoted": 35, "_REF_ in order": 41, "_REF_ is devoted": 106, "_MATH_ , defines": 14, "_CITE_ may be": 29, "_MATH_ are homogeneous": 23, "_MATH_ if we": 57, "_MATH_ points in": 158, "_MATH_ ; as": 37, "_MATH_ is _MATH_-stable": 15, "_MATH_ the set": 366, "_REF_ as well": 47, "_REF_ for two": 20, "_CITE_ found that": 136, "_MATH_ and input": 14, "_MATH_ from which": 46, "_MATHDISP_ from (": 11, "_MATH_ ( while": 13, "_MATH_ the usual": 16, "_MATH_ the mass": 32, "_MATH_ and substituting": 34, "_MATH_ coefficients ,": 13, "_MATH_ is very": 216, "_MATHDISP_ with probability": 14, "_MATHDISP_ almost surely": 15, "_CITE_ and ,": 65, "_MATH_ , corresponds": 33, "_REF_ we study": 18, "_MATH_ is generated": 225, "_MATH_ 's for": 26, "_MATH_ into one": 11, "_MATH_ if the": 334, "_MATH_ space and": 20, "_MATH_ are uniformly": 76, "_MATH_ into _MATHDISP_": 18, "_MATH_ without changing": 18, "_REF_ ) constitute": 16, "_MATHDISP_ when the": 11, "_CITE_ , especially": 29, "_REF_ and _CITE_": 41, "_MATH_ the Banach": 15, "_CITE_ state that": 19, "_MATH_ that maximizes": 40, "_MATHDISP_ . One": 22, "_MATH_ ; or": 39, "_MATH_ bound state": 13, "_MATH_ exhibits a": 16, "_MATH_ follows the": 58, "_MATHDISP_ subject to": 116, "_MATHDISP_ _MATHDISP_ where": 286, "_MATH_ and weight": 15, "_REF_ since _MATH_": 12, "_CITE_ extends the": 10, "_MATH_ , be": 354, "_MATHDISP_ , uniformly": 25, "_MATH_ are referred": 16, "_CITE_ ) _MATHDISP_": 207, "_MATH_ , expressed": 24, "_CITE_ propose an": 32, "_CITE_ where it": 24, "_MATH_ only depend": 17, "_MATH_ , without": 73, "_MATH_ is nested": 10, "_MATH_ -- is": 13, "_MATHDISP_ for some": 402, "_MATH_ V ,": 16, "_REF_ illustrates that": 15, "_MATH_ being a": 210, "_MATH_ that lies": 15, "_MATH_ at which": 127, "_MATH_ '' .": 79, "_MATH_ remains unchanged": 24, "_MATH_ in Proposition": 53, "_MATHDISP_ , a": 111, "_MATH_ uniformly converges": 13, "_MATH_ includes all": 16, "_MATH_ between the": 271, "_MATH_ ( except": 26, "_MATH_ in Algorithm": 11, "_MATH_ in Example": 29, "_MATH_ matrix of": 67, "_MATH_ has not": 59, "_MATH_ from Table": 10, "_MATH_ is irreducible": 124, "_REF_ , in": 255, "_MATHDISP_ , In": 27, "_MATH_ in case": 76, "_CITE_ was the": 32, "_MATH_ is _MATH_-connected": 39, "_MATH_ of elements": 20, "_MATH_ changes with": 10, "_MATH_ km .": 35, "_MATH_ in each": 105, "_MATH_ ) shows": 14, "_REF_ ) because": 48, "_MATH_ below the": 34, "_MATH_ shows the": 44, "_MATH_ as soon": 19, "_MATH_ filtering problem": 109, "_MATH_ are dimensionless": 27, "_MATH_ coincides with": 217, "_MATH_ , see": 518, "_MATH_ are zeros": 10, "_MATHDISP_ , such": 124, "_MATH_ dominates the": 15, "_MATH_ is non-empty": 36, "_REF_ ) ensure": 23, "_REF_ can also": 40, "_REF_ ( for": 27, "_REF_ in this": 29, "_MATH_ of gyrotriangle": 15, "_MATH_ , Fig": 65, "_REF_ yields that": 34, "_REF_ suggest that": 19, "_MATH_ to (": 65, "_MATH_ the mean": 25, "_CITE_ ) with": 42, "_MATH_ by means": 72, "_MATH_ with bounded": 38, "_REF_ holds for": 145, "_REF_ , suppose": 19, "_MATH_ through the": 198, "_MATH_ by one": 24, "_MATH_ increases to": 46, "_MATH_ decreases to": 27, "_MATH_ as explained": 12, "_MATH_ is mainly": 17, "_MATH_ , means": 13, "_MATH_ and apply": 32, "_MATH_ is diagonal": 57, "_MATH_ and obtain": 93, "_MATH_ for various": 41, "_CITE_ ) have": 63, "_REF_ to a": 32, "_REF_ left )": 10, "_MATHDISP_ , hence": 95, "_MATH_ obeys the": 34, "_MATH_ state .": 38, "_MATH_- of the": 13, "_MATH_ is less": 221, "_MATH_ are set": 69, "_MATH_ are randomly": 24, "_MATH_ distribution .": 60, "_MATH_ was set": 44, "_MATHDISP_ . Based": 15, "_MATH_ passes through": 59, "_REF_ shows one": 13, "_REF_ , is": 253, "_MATH_ , _MATH__MATH_": 14, "_MATH_ or so": 11, "_CITE_ , though": 23, "_MATH_ is random": 26, "_MATH_ items .": 13, "_MATH_ ; at": 10, "_MATH_ with support": 32, "_MATH_ and rewrite": 18, "_REF_ that the": 383, "_MATH_ be _MATH_": 157, "_MATH_-space _MATH_ ,": 11, "_MATH_ possesses the": 48, "_MATH_ transition .": 20, "_MATH_ , making": 57, "_MATH_ ] is": 104, "_MATH_ to generate": 27, "_MATH_ - and": 56, "_CITE_ or to": 20, "_MATHDISP_ , thus": 76, "_REF_ reports the": 54, "_MATH_ , do": 36, "_MATHDISP_ and to": 17, "_MATH_ _MATH_ (": 61, "_MATH_ _MATH_ on": 16, "_MATHDISP_ for which": 18, "_MATHDISP_ the following": 10, "_MATH_ -- see": 12, "_MATH_ lie on": 60, "_MATH_ to our": 10, "_MATH_ of edges": 15, "_MATH_ to those": 16, "_REF_ , let": 116, "_REF_ , as": 148, "_MATH_ with corresponding": 22, "_REF_ still holds": 16, "_MATH_ are vectors": 39, "_MATHDISP_ for large": 31, "_REF_ ) which": 209, "_MATH_ is nonoscillatory": 35, "_MATH_ , denoting": 20, "_MATH_ and letting": 43, "_MATH_ stand for": 92, "_CITE_ as _MATHDISP_": 57, "_REF_ , some": 40, "_MATH_ _MATH_ or": 13, "_MATH_ starts from": 15, "_MATH_ changes the": 34, "_MATH_ replaced by": 213, "_MATHDISP_ Thus the": 39, "_MATH_ maps a": 26, "_MATHDISP_ together with": 18, "_REF_ demonstrates the": 47, "_MATH_ is one-to-one": 21, "_MATH_ faithfully realizes": 21, "_MATH_ takes a": 35, "_MATH_ is unity": 10, "_REF_ ) could": 55, "_MATH_ exceeds a": 14, "_MATH_ ( Eq": 65, "_MATH_ vanishes at": 38, "_MATH_ that corresponds": 36, "_MATH_ and setting": 45, "_MATH_ as .": 13, "_MATH_ using _MATH_": 62, "_MATH_ , first": 33, "_MATH_ is correct": 15, "_MATH_ : number": 17, "_MATH_ is selected": 112, "_MATH_ for positive": 18, "_MATH_ is always": 288, "_REF_ ) an": 14, "_MATH_ which has": 87, "_MATH_ contains the": 278, "_MATH_ divided by": 27, "_MATH_ has finite": 61, "_MATH_ algorithm ,": 21, "_MATH_ time complexity": 20, "_CITE_ in order": 96, "_CITE_ indicated that": 11, "_CITE_ uses a": 41, "_REF_ can not": 71, "_MATH_ , except": 135, "_MATH_ is never": 34, "_MATH_ level .": 25, "_MATH_ is constrained": 26, "_MATH_ states .": 56, "_MATH_ that the": 102, "_MATH_ then the": 188, "_MATH_ only when": 22, "_MATH_-_MATH_ phase difference": 12, "_MATH_ containing a": 24, "_MATH_ up to": 297, "_MATH_ , yields": 84, "_MATH_ is considerably": 14, "_MATH_ constant matrix": 12, "_MATH_ , generated": 32, "_MATH_ nodes of": 10, "_REF_ are used": 23, "_MATH_ relative to": 164, "_MATH_ ; 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"_MATH_ as being": 34, "_MATH_ is discontinuous": 25, "_MATH_ and consider": 184, "_MATH_ converge in": 19, "_MATH_ : for": 43, "_MATH_ GeV_MATH_ ,": 51, "_MATH_ bits for": 17, "_MATH_ which have": 32, "_MATH_ become _MATHDISP_": 13, "_MATH_ is solvable": 28, "_MATH_ has this": 14, "_MATH_ form factors": 23, "_MATH_ under consideration": 12, "_MATH_ performance of": 18, "_MATH_ is robustly": 17, "_MATH_ exist in": 14, "_CITE_ for all": 12, "_MATH_ are identically": 20, "_MATHDISP_ then (": 10, "_MATH_ and real": 19, "_REF_ or _REF_": 92, "_CITE_ develop a": 12, "_MATH_ messages to": 14, "_MATH_ message ,": 19, "_MATH_ state and": 18, "_MATH_ the probability": 43, "_MATH_ times for": 12, "_MATH_ '' denotes": 21, "_CITE_ and is": 120, "_CITE_ have demonstrated": 12, "_CITE_ ) on": 37, "_MATH_ matrix and": 45, "_MATH_ are either": 41, "_MATH_ has all": 26, "_MATH_ is Hurwitz": 57, "_MATH_ is totally": 27, "_MATH_ control problems": 14, "_MATH_ appear to": 10, "_MATH_ takes its": 24, "_MATH_ maps _MATH_": 79, "_MATH_ characterize the": 10, "_REF_ we conclude": 35, "_MATH_ has stationary": 16, "_REF_ ) completes": 13, "_MATH_ was proved": 12, "_MATH_ we know": 24, "_MATHDISP_ . 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Combining": 19, "_MATH_ and again": 18, "_MATH_ is updated": 55, "_MATH_ represent ,": 14, "_MATH_ is omitted": 25, "_MATH_ is Poisson": 18, "_CITE_ , p.": 130, "_MATH_ allow us": 14, "_MATH_ point .": 12, "_MATH_ is free": 40, "_MATH_ induces an": 31, "_MATH_ directions ,": 41, "_MATH_ of this": 114, "_MATH_ _MATHDISP_ and": 45, "_REF_ ) described": 11, "_MATH_ is formed": 49, "_MATH_ are small": 66, "_MATH_ appears as": 25, "_MATH_ is closely": 20, "_REF_ by means": 19, "_REF_ is shown": 36, "_MATH_ may also": 42, "_MATH_ of at": 12, "_MATH_ parties ,": 11, "_MATH_ is honest": 36, "_MATH_ are at": 53, "_MATH_ is completed": 18, "_MATH_ as claimed": 12, "_MATH_ in antighost": 10, "_REF_ ) ensures": 40, "_MATH_ MK and": 14, "_MATH_ T ,": 12, "_MATH_ m_MATH_ ,": 19, "_MATH_ are lower": 16, "_MATH_ gauge symmetry": 32, "_CITE_ demonstrated that": 44, "_MATH_ which only": 11, "_MATHDISP_ and _REF_": 11, "_MATH_and _MATH_ (": 10, "_MATH_ ; its": 14, "_MATH_ be continuously": 13, "_MATH_ are state": 14, "_REF_ we define": 19, "_MATH_ the equation": 17, "_MATH_ model reduction": 12, "_MATH_ above .": 31, "_CITE_ , such": 85, "_MATH_ Mm )": 35, "_REF_ , different": 11, "_MATH_th node in": 10, "_MATH_ for system": 35, "_MATH_ or more": 27, "_MATH_ vector _MATH_": 34, "_MATH_ ( compare": 21, "_REF_ ) differs": 14, "_MATH_ are 0": 20, "_REF_ is now": 30, "_CITE_ has also": 16, "_CITE_ proposes a": 50, "_CITE_ is described": 14, "_MATH_ has units": 10, "_MATH_ _CITE_ (": 25, "_CITE_ ( and": 37, "_MATH_ to control": 16, "_CITE_ for additional": 17, "_MATHDISP_ , all": 13, "_REF_ may be": 81, "_MATHDISP_ , corresponding": 10, "_MATH_th entry of": 30, "_REF_ are _MATHDISP_": 27, "_MATH_ is observable": 26, "_REF_ ) contain": 14, "_MATH_ are approximated": 21, "_MATH_ varies in": 59, "_MATHDISP_ . For": 24, "_MATH_ and even": 34, "_MATH_and _MATH_ such": 23, "_MATHDISP_ , also": 17, "_MATH_ . _MATH_": 126, "_MATH_ 's satisfy": 10, "_MATH_ on top": 17, "_MATH_ to show": 22, "_CITE_ that for": 37, "_MATH_ described above": 19, "_MATH_ ways .": 13, "_CITE_ had a": 11, "_MATH_ , above": 16, "_MATH_ cm )": 10, "_CITE_ of a": 24, "_CITE_ and of": 38, "_MATH_ with normal": 13, "_MATH_ is located": 44, "_MATH_ changes from": 27, "_MATH_ changes its": 16, "_MATH_ , according": 136, "_MATH_ , becomes": 34, "_REF_ with some": 15, "_MATH_ which represent": 13, "_MATH_ is attached": 15, "_MATH_ that vanishes": 10, "_REF_ ) undergoes": 33, "_MATH_ then there": 48, "_MATH_ . For": 12, "_MATH_ and almost": 17, "_REF_ page _REF_": 47, "_REF_ and taking": 16, "_REF_ then yields": 13, "_CITE_ describe a": 24, "_MATH_ , belongs": 11, "_MATH_ to its": 73, "_REF_ , Chapter": 12, "_MATH_ obtained using": 10, "_MATH_ remains the": 16, "_MATH_ contribute to": 12, "_MATH_ is joined": 11, "_MATH_ vertices of": 29, "_MATH_ satisfies all": 36, "_MATH_ has at": 268, "_MATH_ is done": 26, "_CITE_ , all": 28, "_MATH_ has probability": 14, "_MATHDISP_ due to": 34, "_MATH_ in equation": 68, "_REF_ c )": 18, "_MATH_ are regarded": 12, "_REF_ indicate the": 13, "_MATH_ _MATH_ has": 24, "_REF_ ) along": 42, "_MATH_ and/or _MATH_": 63, "_MATH_ , what": 20, "_MATH_ , how": 14, "_MATH_ , being": 103, "_REF_ illustrates this": 28, "_MATH_ bounds the": 10, "_MATH_ ) whose": 12, "_MATH_ are correlated": 20, "_MATHDISP_ which yields": 31, "_MATH_ be of": 30, "_MATH_ if both": 10, "_MATH_ is studied": 17, "_MATHDISP_ are the": 58, "_MATH_ appears .": 12, "_MATH_ solutions .": 20, "_MATH_ diagonal block": 10, "_MATH_ that minimizes": 71, "_MATH_ are parameters": 48, "_MATH_ follow a": 15, "_MATH_ reflect the": 15, "_MATH_ time units": 75, "_MATH_ leading to": 39, "_REF_ , Corollary": 20, "_MATH_ , similar": 45, "_MATH_ for several": 18, "_MATH_ statistic ,": 12, "_MATH_ be three": 25, "_MATH_ defining the": 15, "_CITE_ , will": 12, "_MATHDISP_ Substituting (": 47, "_MATHDISP_ by the": 45, "_MATHDISP_ by (": 52, "_MATH_ satisfies conditions": 25, "_MATH_ a.s. ,": 37, "_MATH_ pair .": 11, "_MATH_ TeV .": 47, "_MATH_ and momentum": 18, "_MATH_ and energy": 11, "_MATH_ norm _MATH_": 11, "_CITE_ presents a": 42, "_MATHDISP_ implies _MATHDISP_": 13, "_MATH_ is semisimple": 13, "_MATH_ then ,": 43, "_MATH_ by Proposition": 32, "_MATH_ is somewhat": 12, "_MATH_ colors .": 26, "_MATH_ has already": 40, "_MATH_ is sampled": 16, "_MATH_ is itself": 42, "_REF_ admits a": 32, "_MATHDISP_ , leads": 12, "_MATH_ fails to": 41, "_MATH_ from below": 19, "_MATH_ and where": 79, "_MATH_ are ``": 16, "_MATH_ and ``": 23, "_MATH_ function is": 32, "_MATH_ ; 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Minimize": 46, "_MATH_ messages in": 11, "_MATH_ is nonzero": 92, "_CITE_ used an": 16, "_CITE_ improved the": 27, "_MATH_ and maps": 12, "_MATH_ , giving": 104, "_MATH_ are larger": 16, "_CITE_ ] .": 55, "_MATH_ ( here": 93, "_MATH_ is superadditive": 10, "_REF_ ) runs": 10, "_MATH_ vertex .": 11, "_MATHDISP_ Hence ,": 84, "_MATH_ are derived": 40, "_MATH_ will never": 22, "_MATH_ is polynomial-time": 18, "_MATH_ is guaranteed": 45, "_REF_ ) involves": 30, "_MATH_ by another": 10, "_MATH_ , still": 29, "_MATH_ becomes zero": 13, "_MATH_ columns .": 12, "_REF_ and Figure": 81, "_MATH_ standing for": 18, "_CITE_ _CITE_ )": 39, "_MATH_ discussed in": 23, "_MATH_ cm_MATH_ )": 23, "_MATH_ and measurable": 10, "_MATH_ is prime": 43, "_MATH_ were chosen": 10, "_MATHDISP_ Set _MATHDISP_": 11, "_MATH_ becomes larger": 32, "_REF_ show ,": 13, "_REF_ , middle": 14, "_MATH_ fulfills _REF_": 18, "_MATH_ of Player": 11, "_MATH_ that has": 101, "_MATH_ are transformed": 12, "_MATH_ itself .": 70, "_MATH_ only on": 12, "_MATH_ ) because": 25, "_MATH_ is affine": 37, "_MATHDISP_ ; 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but": 11, "_MATH_ keeps the": 14, "_MATHDISP_ Obviously ,": 22, "_MATH_ increases as": 25, "_MATHDISP_ . Taking": 28, "_MATHDISP_ Consider the": 29, "_MATHDISP_ then _MATHDISP_": 24, "_MATH_ , suppose": 71, "_REF_ ( 1": 45, "_MATH_ the associated": 30, "_MATH_-_MATH_ ) ,": 11, "_REF_a and b": 20, "_MATH_ , n": 10, "_REF_ ) degenerates": 10, "_MATH_ to which": 27, "_MATH_ meson is": 19, "_MATH_ _MATH_ decay": 20, "_MATH_ decay is": 22, "_MATH_ : this": 26, "_MATH_ is nondecreasing": 122, "_MATH_ , other": 16, "_MATH_ are control": 12, "_CITE_ , under": 20, "_MATH_ on machine": 22, "_MATH_ the time": 40, "_REF_ , leads": 14, "_MATH_ is one-dimensional": 21, "_MATH_ are treated": 16, "_MATH_m , which": 12, "_MATH_ ) contains": 15, "_MATH_ -- in": 11, "_MATH_ directly ,": 13, "_MATH_ and height": 10, "_CITE_ noted that": 30, "_MATH_ runs through": 15, "_MATH_ are oscillatory": 11, "_REF_ of Lemma": 13, "_REF_ and Equation": 11, "_MATH_ of index": 11, "_MATH_ , would": 27, "_MATH_ calculated for": 13, "_REF_ , obtaining": 10, "_MATH_ for given": 20, "_MATH_ in any": 57, "_REF_ ) arise": 10, "_MATH_ as solution": 12, "_MATH_ is Euler": 16, "_MATH_ are unstable": 10, "_REF_b , the": 17, "_MATH_ under which": 15, "_MATH_ phase ,": 15, "_MATH_ we found": 10, "_MATH_ follow from": 18, "_REF_ ( v": 10, "_REF_ ; however": 14, "_MATHDISP_ . Proof": 21, "_MATH_ should have": 31, "_MATH_ and ending": 21, "_MATH_ matrix is": 33, "_MATH_ in powers": 21, "_MATH_ ) versus": 11, "_CITE_ instead of": 15, "_MATHDISP_ and denote": 14, "_MATH_ kHz ,": 11, "_MATH_ to test": 10, "_MATH_ was _MATH_": 18, "_REF_ ) this": 38, "_MATH_ where ,": 15, "_REF_ , including": 22, "_MATH_ is non-decreasing": 33, "_MATHDISP_ and there": 10, "_MATH_ and show": 47, "_CITE_ , gives": 11, "_REF_ ) turns": 29, "_MATH_ ( so": 86, "_MATH_-dimensional Riemannian manifold": 10, "_MATH_ points are": 19, "_MATH_ and integrate": 49, "_MATH_ surface .": 10, "_MATH_ 30 _MATH_": 10, "_MATH_ AU )": 10, "_MATH_ are negligible": 14, "_REF_ and Example": 11, "_MATH_ component of": 69, "_MATH_ data .": 19, "_MATH_ transforms the": 17, "_MATH_ has constant": 27, "_MATH_ is illustrated": 26, "_MATH_ is time": 36, "_MATH_ will remain": 28, "_MATH_ as on": 33, "_MATH_ with weight": 16, "_MATH_ if :": 14, "_MATH_ that represents": 28, "_REF_ , showing": 27, "_MATH_ would lead": 17, "_CITE_ , along": 17, "_MATH_ iff _MATHDISP_": 10, "_MATH_ min )": 12, "_MATH_ and satisfying": 43, "_MATH_ are periodic": 23, "_MATH_ must equal": 10, "_MATH_ states are": 23, "_MATH_ is most": 17, "_MATH_ state with": 11, "_MATH_ ) associated": 17, "_MATH_ will also": 41, "_MATH_ which depends": 30, "_CITE_ ) but": 22, "_MATH_ with parameters": 18, "_MATH_-valued random variables": 41, "_MATH_ that there": 26, "_MATH_ has four": 14, "_MATH_ , requiring": 10, "_MATH_ clock cycles": 17, "_MATHDISP_ , leading": 23, "_MATH_ odd .": 16, "_MATH_ ) distributions": 10, "_REF_ to show": 21, "_MATH_ is non-zero": 40, "_MATH_ is primitive": 23, "_MATH_ for random": 13, "_CITE_ showed a": 10, "_MATH_ the numbers": 10, "_MATH_ gauge groups": 12, "_MATH_ and fix": 18, "_MATH_- and _MATH_-channel": 17, "_MATH_ axis and": 27, "_MATHDISP_ , given": 22, "_MATHDISP_ , yielding": 26, "_REF_ requires that": 12, "_REF_-_REF_ can be": 19, "_MATH_ or 1": 38, "_REF_ for both": 24, "_MATH_ if this": 14, "_MATH_ decreases ,": 51, "_REF_ ) always": 20, "_CITE_ for their": 13, "_MATH_ is too": 70, "_MATH_ and compute": 31, "_MATH_ of genus": 20, "_MATH_ ( equivalent": 11, "_MATH_ by their": 28, "_MATH_ and increases": 12, "_MATH_ system with": 18, "_MATH_ case is": 14, "_REF_ give the": 30, "_MATH_-coordinate of _MATH_": 10, "_CITE_ ) )": 18, "_MATH_ ) model": 34, "_MATH_ as compared": 24, "_MATH_ by performing": 18, "_MATH_ processes ,": 12, "_MATH_ [ or": 10, "_MATH_ is modified": 21, "_MATH_-axis and the": 25, "_MATH_ in degree": 10, "_MATH_ is algebraically": 21, "_MATHDISP_ . Consider": 19, "_MATH_ and does": 33, "_MATH_ is covered": 35, "_MATHDISP_ . Recall": 14, "_CITE_ , suggesting": 13, "_MATH_ cm_MATH_ ,": 35, "_CITE_ that we": 13, "_CITE_ that it": 18, "_REF_ ( respectively": 13, "_MATH_ explicitly .": 20, "_MATH_ , lead": 11, "_MATH_ ( See": 13, "_MATH_ and over": 13, "_MATH_ is undefined": 11, "_MATH_ from left": 12, "_MATH_ simultaneously .": 15, "_MATH_ is viewed": 15, "_CITE_ argued that": 23, "_MATH_ parameter is": 23, "_MATH_ directions .": 20, "_MATH_ is nontrivial": 12, "_MATH_ the eigenvalues": 13, "_MATH_ or 2": 42, "_MATH_ is conserved": 19, "_MATH_ kHz .": 19, "_MATHDISP_ Also ,": 15, "_MATH_ lines ,": 15, "_MATH_ 's can": 18, "_MATH_ acting in": 12, "_MATH_ and functions": 19, "_MATH_ are its": 14, "_MATH_ may vary": 11, "_MATH_ with two": 44, "_CITE_ we find": 17, "_CITE_ , except": 19, "_REF_ could be": 14, "_REF_ be given": 12, "_MATH_ to avoid": 24, "_MATH_ and odd": 14, "_REF_ , see": 37, "_REF_ ( when": 16, "_MATH_ edges and": 14, "_MATH_ that depend": 14, "_MATH_ that includes": 17, "_MATH_ is produced": 23, "_MATHDISP_ ; where": 39, "_MATH_ ; so": 47, "_MATH_ is shifted": 19, "_MATH_ satisfying condition": 16, "_MATH_ by removing": 37, "_MATH_ , known": 25, "_MATH_ _REF_ ,": 14, "_MATH_ ( even": 20, "_MATH_ , some": 48, "_MATH_ sector ,": 14, "_MATH_ are generally": 20, "_MATH_ components are": 15, "_MATH_ , increases": 19, "_REF_ under the": 30, "_MATH_ times larger": 11, "_MATH_ , combining": 19, "_MATH_ works as": 17, "_MATH_ 0 ,": 10, "_MATH_ meson and": 13, "_MATH_ is deleted": 21, "_MATH_ , node": 16, "_MATH_ for suitable": 17, "_REF_ , every": 22, "_REF_ takes the": 27, "_MATH_ becomes negative": 14, "_MATH_ values )": 20, "_MATH_ axis )": 23, "_MATH_ , ''": 13, "_MATH_ . ''": 21, "_REF_ that ,": 43, "_MATH_ while keeping": 19, "_MATH_ and scale": 16, "_MATH_ is likely": 20, "_REF_ to conclude": 33, "_MATH_ value )": 16, "_MATH_ sends the": 17, "_MATH_ - the": 46, "_MATH_ ms .": 20, "_REF_ are based": 13, "_MATH_ behaves like": 19, "_MATH_ are displayed": 19, "_MATH_ GeV in": 15, "_MATH_ GeV at": 17, "_MATH_ pair production": 15, "_CITE_ , taking": 18, "_MATH_ since there": 11, "_MATH_ is URGAOS": 13, "_MATHDISP_ . Define": 20, "_MATH_ contains both": 13, "_MATH_ ) within": 17, "_MATH_ is nothing": 23, "_REF_ we use": 43, "_MATH_ which was": 18, "_MATH_ is far": 27, "_MATH_ implies a": 30, "_MATH_th moment of": 22, "_CITE_ , two": 23, "_MATH_ to see": 14, "_MATH_ in three": 18, "_MATH_ diagonal matrix": 50, "_MATH_ GeV )": 75, "_MATH_ or even": 21, "_MATH_ is embedded": 48, "_MATH_ modeling the": 11, "_MATH_ governs the": 12, "_MATH_ introduced in": 66, "_MATH_ is kinematically": 13, "_MATH_ the scalar": 10, "_REF_ ( or": 33, "_CITE_ ( Theorem": 14, "_CITE_ in this": 18, "_MATH_ using _REF_": 13, "_REF_ gives us": 19, "_MATH_ have an": 24, "_MATH_ the surface": 14, "_MATH_ days .": 23, "_MATH_ in ,": 16, "_MATHDISP_ _MATHDISP_ (": 30, "_MATH_ applied to": 25, "_REF_ has at": 45, "_MATH_ pairs of": 47, "_MATH_ is incident": 21, "_MATH_ decays .": 71, "_CITE_ within the": 22, "_MATH_ the point": 20, "_MATH_ are uncorrelated": 33, "_MATH_ in image": 30, "_MATH_ are collinear": 37, "_MATH_ as function": 18, "_CITE_ ) show": 10, "_MATH_ and denoted": 20, "_MATH_ we shall": 12, "_MATH_ provided _MATH_": 26, "_MATH_ follows directly": 15, "_MATH_ are mapped": 29, "_MATHDISP_ Denote _MATHDISP_": 11, "_MATH_ _CITE_ with": 11, "_MATH_ to all": 54, "_MATH_ converges ,": 15, "_MATH_ ( iv": 13, "_MATH_-dimensional star graph": 11, "_MATH_ faulty edges": 13, "_MATH_ be functions": 19, "_MATH_ in discrete": 12, "_CITE_ gives the": 18, "_MATH_ , makes": 13, "_MATH_ queries ,": 15, "_MATH_ is upper-bounded": 14, "_CITE_ : ``": 21, "_MATH_ were derived": 13, "_MATHDISP_ under the": 25, "_REF_ ( which": 19, "_MATH_ are new": 17, "_CITE_ and Section": 13, "_CITE_ , e.g.": 15, "_MATH_ are represented": 43, "_MATH_ by introducing": 17, "_MATH_ are differentiable": 17, "_MATHDISP_ . Substituting": 55, "_MATH_ , ensures": 10, "_MATH_ ) means": 27, "_MATH_ and uses": 13, "_MATH_-periodic solution .": 12, "_MATHDISP_ _MATHDISP_- _MATHDISP_": 18, "_MATHDISP_- _MATHDISP_ _MATHDISP_": 14, "_CITE_ discuss the": 15, "_MATH_ is expanded": 18, "_REF_ that when": 11, "_MATH_ sense ,": 10, "_MATH_ meson ,": 29, "_REF_ : the": 32, "_MATH_ vanish .": 22, "_MATH_ guaranteed cost": 32, "_MATH_ mentioned in": 10, "_MATH_ of about": 15, "_CITE_ etc .": 29, "_MATH_ is attained": 42, "_MATH_ were the": 11, "_CITE_ concerning the": 12, "_MATH_ bounded by": 20, "_REF_ of Theorem": 23, "_MATH_ to conclude": 23, "_MATH_ are precisely": 17, "_MATH_ have opposite": 15, "_MATHDISP_ Based on": 23, "_MATH_ is a.s.": 21, "_MATHDISP_ has been": 11, "_CITE_ is employed": 13, "_REF_ ) equal": 20, "_MATH_ , simply": 14, "_CITE_ that an": 10, "_REF_ shows four": 15, "_MATH_ mass ,": 19, "_CITE_ in _MATH_": 15, "_MATH_ constructed by": 10, "_MATH_ the free": 15, "_MATH_ ; 2": 23, "_REF_ to hold": 20, "_MATH_ and defining": 17, "_CITE_-_CITE_ and the": 15, "_CITE_-_CITE_ ) .": 26, "_MATH_ be closed": 13, "_MATH_ which correspond": 16, "_MATH_ , no": 91, "_MATH_ to estimate": 26, "_CITE_ , different": 15, "_MATH_ ; i.e": 19, "_MATH_ inherits the": 16, "_MATHDISP_ ( see": 117, "_MATH_-stable random variable": 11, "_MATH_ crosses _MATH_": 22, "_MATH_ pairwise disjoint": 15, "_MATH_ _MATH_-a.s. and": 11, "_MATH_ share the": 14, "_REF_ ( iv": 25, "_CITE_ , may": 10, "_MATHDISP_ to the": 25, "_MATH_ signifies the": 11, "_MATH_ are approximately": 25, "_REF_ shows results": 12, "_MATH_-valued _MATH_-Wiener process": 19, "_MATH_ , completing": 10, "_MATH_ dual to": 13, "_CITE_ which has": 12, "_CITE_ has the": 11, "_MATH_ the values": 19, "_MATH_ are integration": 18, "_CITE_ , several": 25, "_MATH_ leaves _MATH_": 14, "_MATH_ with boundary": 32, "_MATH_ are admissible": 23, "_MATH_ and both": 29, "_MATH_ owing to": 16, "_MATHDISP_ is bounded": 28, "_CITE_ ) as": 51, "_CITE_ has used": 10, "_CITE_ to give": 10, "_REF_ is chosen": 10, "_CITE_ : we": 10, "_REF_ ) form": 37, "_MATH_ has zero": 29, "_MATH_ , calculated": 18, "_MATH_ are free": 44, "_MATH_ at small": 12, "_MATH_ of node": 13, "_CITE_ ) also": 11, "_MATH_ will yield": 10, "_REF_ with Theorem": 10, "_CITE_ and can": 47, "_MATH_ is fitted": 10, "_MATH_ runs in": 31, "_REF_ , though": 11, "_MATH_ is diagonalizable": 17, "_MATH_ was first": 18, "_MATH_ only in": 23, "_MATH_ the coefficient": 13, "_MATH_ _MATHDISP_ is": 14, "_MATH_ in Section": 67, "_MATH_ is simplified": 13, "_MATH_ above ,": 29, "_CITE_ , its": 17, "_MATH_ 's view": 28, "_MATH_ is indistinguishable": 12, "_MATHDISP_ . Set": 10, "_MATH_ ( on": 22, "_CITE_ provides an": 21, "_REF_ do not": 38, "_MATH_ is marked": 18, "_REF_ is completed": 11, "_MATH_ component and": 11, "_REF_ is presented": 11, "_MATH_ '' stands": 14, "_MATH_ matrix such": 10, "_MATH_ G in": 10, "_MATHDISP_ . By": 28, "_MATH_ is proposed": 13, "_MATH_th order _MATH_": 15, "_CITE_ _MATHDISP_ and": 24, "_MATH_ norms of": 14, "_CITE_ deals with": 10, "_MATH_ occurs .": 19, "_REF_ ) asymptotically": 21, "_REF_ ) based": 27, "_MATH_-almost all _MATH_": 26, "_MATH_ a solution": 18, "_MATHDISP_ which gives": 31, "_MATH_ needed for": 11, "_MATH_ times faster": 12, "_MATH_ statistic is": 16, "_MATH_ of finite": 40, "_MATH_ the density": 30, "_MATH_ the velocity": 17, "_MATH_ the pressure": 14, "_MATH_ is Type": 10, "_MATH_ is algebraic": 18, "_MATH_ , normalized": 18, "_REF_ , top": 50, "_MATH_ and three": 30, "_MATH_ . We": 51, "_MATH_ of Eqs": 10, "_MATH_- can be": 36, "_MATH_ fraction of": 19, "_REF_ is always": 11, "_MATH_ from its": 46, "_MATH_ is sparse": 19, "_MATH_ rows in": 10, "_REF_ ; we": 18, "_MATH_ , typically": 17, "_CITE_ consists of": 26, "_MATH_ be bounded": 37, "_MATH_ '' (": 12, "_CITE_ , without": 12, "_MATH_ in these": 49, "_CITE_ analyzed the": 53, "_MATH_ iterations .": 34, "_REF_ ) states": 22, "_MATH_ , obtain": 14, "_MATH_ minimizing the": 11, "_MATH_ is analogous": 26, "_CITE_ provide a": 28, "_CITE_ ) has": 26, "_CITE_ assume that": 11, "_MATH_ vectors ,": 10, "_MATH_ is cash": 12, "_MATH_ given above": 15, "_MATH_ during a": 17, "_MATH_ as suggested": 10, "_MATH_ may differ": 11, "_MATH_ members of": 13, "_MATH_ grid points": 28, "_CITE_ as _MATH_": 12, "_REF_ instead of": 16, "_MATH_ ( possibly": 20, "_MATH_ is 0-1": 13, "_REF_ is strictly": 10, "_MATH_ direction (": 16, "_MATH_-_MATH_ plane .": 22, "_MATHDISP_ and from": 19, "_MATHDISP_ with an": 18, "_CITE_ when _MATH_": 12, "_MATH_ , appears": 12, "_MATH_ is stabilizable": 22, "_MATH_ has occurred": 11, "_MATH_ at every": 28, "_MATH_ applies to": 18, "_MATH_ cross sections": 49, "_CITE_ generalized this": 13, "_MATH_ uniformly in": 66, "_MATH_ has density": 18, "_MATH_ 's is": 49, "_MATH_ gives that": 20, "_MATH_ the matrix": 37, "_MATH_ with Neumann": 10, "_MATH_ choices for": 12, "_MATH_ having _MATH_": 32, "_REF_ of Section": 29, "_MATH_ is readily": 12, "_MATH_ function with": 13, "_MATH_ satisfy _REF_": 43, "_MATH_ a continuous": 10, "_CITE_ and they": 20, "_MATH_ minimizes _MATH_": 12, "_MATH_ are from": 20, "_MATH_ solutions to": 10, "_MATH_ from Theorem": 17, "_REF_ provide a": 14, "_MATHDISP_ . Further": 11, "_CITE_ points out": 16, "_REF_ ) tend": 12, "_REF_ introduces a": 14, "_MATH_ is sometimes": 15, "_MATH_ to each": 93, "_MATHDISP_ . Noting": 11, "_REF_ as the": 64, "_MATH_ ) remains": 11, "_REF_ ) determines": 27, "_MATH_ has positive": 20, "_MATH_ terms ,": 36, "_MATH_ _MATH_-converges to": 11, "_MATHDISP_ , satisfies": 15, "_MATH_ ( Section": 14, "_MATH_ nm (": 16, "_MATH_ fields ,": 13, "_MATH_ plays a": 42, "_MATH_ a bounded": 13, "_MATH_and _MATH_ for": 22, "_REF_ presents an": 25, "_MATH_ account for": 10, "_MATHDISP_ ( 2": 10, "_MATH_ have not": 19, "_MATH_ are conditionally": 19, "_CITE_ and this": 14, "_MATH_ again .": 26, "_MATH_-deformed phase space": 13, "_MATH_ provides the": 51, "_MATH_ is with": 22, "_MATH_ minutes ,": 15, "_MATH_ used to": 40, "_MATH_ satisfy one": 11, "_MATH_ to destination": 13, "_MATH_ function in": 18, "_REF_a shows a": 12, "_MATH_ is horizontal": 11, "_MATH_ onto a": 25, "_MATH_ since we": 27, "_MATH_ , up": 58, "_MATH_ all have": 11, "_MATH_ and between": 12, "_MATH_ images .": 13, "_MATH_ plays according": 12, "_MATH_ will only": 14, "_MATH_ th element": 17, "_MATH_ functions are": 11, "_MATH_ they are": 17, "_MATH_ , forms": 12, "_CITE_ have also": 27, "_MATH_ satisfying a": 12, "_CITE_ and an": 17, "_MATH_ and eventually": 10, "_MATH_ , assumed": 22, "_MATH_ only depends": 48, "_MATH_ ) so": 17, "_MATH_ mod _MATH_": 37, "_REF_ ) between": 21, "_REF_ ( resp.": 18, "_MATH_ vertices in": 36, "_MATH_ are necessary": 13, "_MATH_ , separately": 19, "_MATH_ at most": 31, "_MATH_ are excluded": 11, "_MATH_ represent respectively": 11, "_MATH_ is Hermitian": 19, "_MATH_ is probably": 13, "_MATH_ , exists": 17, "_MATH_ function for": 10, "_MATH_ is half": 16, "_MATH_ is varied": 38, "_MATH_-direction , and": 10, "_MATH_ is spatially": 11, "_MATH_ is controllable": 26, "_REF_ where we": 38, "_MATH_ quark .": 11, "_MATH_ ) should": 28, "_MATH_ elements _MATH_": 16, "_MATH_ is pure": 16, "_MATH_ filtering design": 11, "_REF_ deals with": 44, "_MATH_ ; while": 15, "_CITE_ , Wang": 19, "_MATH_ rad ,": 16, "_MATH_ with frame": 12, "_MATH_ are vertices": 14, "_MATH_ and large": 48, "_CITE_ to compute": 24, "_MATH_ theory can": 12, "_MATH_ solves _MATHDISP_": 12, "_MATH_ parameters of": 11, "_MATH_ becomes more": 15, "_MATH_ enters the": 22, "_CITE_ or even": 10, "_MATH_ are polynomial": 16, "_REF_ ) having": 11, "_MATH_ of nonnegative": 13, "_REF_B ) .": 12, "_REF_ ) coincide": 13, "_MATH_ to reach": 18, "_MATH_ at pixel": 12, "_MATH_ groups of": 10, "_MATH_ times _MATH_": 18, "_MATH_ cm_MATH_ for": 13, "_REF_ for all": 54, "_MATHDISP_ , was": 21, "_MATH_ approaches infinity": 13, "_MATH_-stopping time _MATH_": 17, "_MATH_ are pairwise": 40, "_REF_ again ,": 25, "_MATH_ the optimal": 19, "_MATH_ between them": 14, "_MATH_ and low": 13, "_REF_ ) tells": 14, "_MATH_ grows large": 10, "_MATH_ makes a": 19, "_MATH_ of cardinality": 28, "_MATH_ to achieve": 16, "_MATH_ , solving": 10, "_MATH_ vector fields": 15, "_MATH_ [ resp.": 12, "_REF_ and to": 13, "_MATH_ a.s. as": 12, "_MATH_-out-of-_MATH_ : F": 21, "_MATH_ were used": 34, "_MATH_ AU .": 30, "_MATH_ drawn from": 17, "_MATHDISP_ , completing": 13, "_MATH_ in comparison": 24, "_MATH_ occur in": 11, "_MATH_ terminals in": 10, "_MATH_ is needed": 62, "_MATH_ affect the": 14, "_MATH_ ( dashed": 33, "_MATH_ are strongly": 18, "_MATH_ couplings ,": 11, "_MATH_ of _MATHDISP_": 22, "_MATH_- such that": 11, "_MATH_ becomes an": 20, "_MATH_ is ergodic": 26, "_MATH_ performs the": 11, "_MATH_ between a": 15, "_MATH_ with transition": 21, "_CITE_ , various": 10, "_MATH_ quarks ,": 13, "_REF_ we summarize": 20, "_MATH_ ] that": 17, "_MATH_ and make": 22, "_CITE_ , here": 22, "_MATH_-module _MATH_ .": 13, "_MATH_ in conjunction": 12, "_MATH_ of 0": 14, "_MATH_ minutes .": 13, "_MATH_ ) correspond": 11, "_MATHDISP_ [ cf": 12, "_MATH_ representing a": 25, "_CITE_ in two": 13, "_MATH_ messages ,": 14, "_REF_ are all": 16, "_MATH_ contains exactly": 42, "_MATH_ isomorphic to": 21, "_MATH_ we infer": 10, "_REF_ details the": 14, "_MATH_ of Lemma": 33, "_REF_ we explain": 11, "_CITE_ give a": 17, "_REF_ we compare": 49, "_REF_SM Higgs boson": 13, "_MATH_ at 95": 16, "_MATH_ because we": 10, "_MATH_ where it": 21, "_MATH_ the maximal": 16, "_MATH_ that would": 15, "_MATH_ gives us": 29, "_MATH_ , obtaining": 48, "_MATH_ is naturally": 18, "_MATH_ be associated": 10, "_MATH_ is perfectly": 12, "_REF_ , on": 24, "_MATH_ for general": 11, "_CITE_ , cf": 13, "_MATH_ incident to": 29, "_MATHDISP_ where in": 23, "_MATHDISP_ . 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is perfect": 16, "_MATH_ will decrease": 12, "_MATH_ from Assumption": 12, "_MATH_ also depends": 12, "_MATH_ runs from": 14, "_MATH_ and 5": 14, "_REF_ one sees": 11, "_MATH_ more than": 12, "_REF_ there exist": 11, "_MATH_ kHz and": 14, "_MATH_ given a": 16, "_REF_ and obtain": 14, "_MATHDISP_ to obtain": 15, "_MATH_ atoms .": 18, "_MATH_ atoms ,": 10, "_MATH_ rows .": 11, "_REF_ and thus": 14, "_MATH_ to study": 13, "_MATH_ has eigenvalues": 18, "_MATH_ _CITE_ for": 14, "_MATH_ -dependence of": 10, "_CITE_ or in": 25, "_MATH_ boson mass": 40, "_MATH_ ) [": 13, "_REF_ is applicable": 12, "_MATH_ in equations": 10, "_MATH_ , else": 18, "_CITE_ it has": 21, "_MATH_ agrees with": 26, "_MATH_ and order": 11, "_MATH_ seconds ,": 28, "_MATH_ and linear": 14, "_MATH_ is properly": 12, "_MATH_ supported by": 21, "_MATH_ to increase": 21, "_MATH_ and condition": 14, "_MATH_ covariance matrix": 17, "_MATH_ is stochastic": 11, "_MATH_ is generic": 12, "_REF_ _CITE_ ,": 12, "_MATH_ are nearly": 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Let": 15, "_REF_ with Fig": 10, "_CITE_ but also": 13, "_MATH_-a.s. for all": 10, "_CITE_ , Lemma": 23, "_MATH_ then by": 16, "_MATH_ iff the": 20, "_MATH_ are measured": 20, "_MATH_ cells ,": 17, "_MATH_ partial waves": 11, "_MATH_ a real": 17, "_MATH_ during an": 12, "_MATH_ making the": 11, "_MATH_ ( usually": 10, "_CITE_ assumed that": 15, "_MATH_ of maximal": 10, "_MATH_-fold covering of": 18, "_REF_ by setting": 12, "_MATH_ pairs in": 17, "_MATHDISP_ in (": 14, "_MATH_ present in": 14, "_MATH_ vanishes for": 19, "_CITE_ and as": 17, "_MATHDISP_ is oscillatory": 16, "_MATH_ large jobs": 10, "_MATH_ is distance": 10, "_CITE_ assumes that": 12, "_CITE_ that any": 12, "_MATH_ violation in": 16, "_MATH_ be protocols": 13, "_MATH_ will become": 18, "_MATH_ centred at": 14, "_MATH_ are vector": 15, "_MATH_ , If": 11, "_MATH_ i.e. ,": 29, "_MATH_ , acts": 10, "_REF_ become _MATHDISP_": 11, "_MATH_ ( marked": 11, "_MATH_ , most": 13, "_MATH_ mm and": 25, "_MATH_ a contradiction": 12, "_MATH_ _MATH_ :": 43, "_MATH_ ( positive": 10, "_REF_ , I": 10, "_MATH_ the coefficients": 10, "_MATH_ as for": 25, "_MATH_ constant ,": 16, "_MATH_ ) direction": 17, "_MATH_ mag .": 12, "_MATH_ satisfy condition": 10, "_MATH_ ) plus": 10, "_MATH_ plus _MATH_": 13, "_MATH_ increases by": 19, "_MATH_ run over": 15, "_MATH_ are optimal": 14, "_MATHDISP_ , Hence": 10, "_MATH_ ) corresponding": 13, "_MATH_ vertices (": 10, "_CITE_ introduce the": 14, "_MATH_ remains a": 17, "_REF_ we apply": 12, "_MATHDISP_ Thus _MATH_": 14, "_MATH_ computes a": 13, "_MATH_ pixels and": 13, "_MATH_ [ Hz": 28, "_MATH_ , holds": 13, "_MATH_ system (": 12, "_CITE_ in Fig": 11, "_MATH_ which makes": 12, "_REF_ is indeed": 11, "_MATH_ cases .": 11, "_REF_ , ,": 11, "_REF_ reviews the": 11, "_MATH_ '' dimensional": 23, "_MATH_ frames .": 10, "_MATH_ a _MATH_": 21, "_MATH_ ) values": 21, "_MATHDISP_ uniformly on": 26, "_REF_ ) amounts": 16, "_CITE_ ) _MATH_": 16, "_MATH_ : then": 10, "_REF_ is related": 13, "_MATH_ planes .": 11, "_MATH_ asymptotically .": 13, "_MATH_-even Higgs boson": 12, "_MATH_ pixels for": 13, "_REF_ to calculate": 11, "_MATH_ is exact": 13, "_MATH_ contains points": 11, "_MATH_ with random": 10, "_MATHDISP_ so ,": 16, "_REF_ ] -": 11, "_MATH_ functions .": 24, "_MATH_ remains bounded": 13, "_MATH_ of pairs": 10, "_MATH_ after a": 15, "_MATH_ molecular states": 13, "_MATH_ '' to": 13, "_MATH_ are relevant": 10, "_MATHDISP_ Eq .": 11, "_MATH_ supported on": 12, "_MATH_ uses a": 12, "_MATH_ the elements": 12, "_MATH_ ratio ,": 13, "_MATH_ is better": 22, "_MATH_ at times": 10, "_CITE_ has studied": 11, "_MATH_ total cross": 15, "_MATH_ simultaneously ,": 13, "_MATH_ possible values": 14, "_MATH_ mass .": 14, "_MATH_ accordingly .": 11, "_MATH_ with equality": 17, "_MATH_ to change": 10, "_MATH_ the differential": 10, "_MATH_ uses the": 34, "_REF_ of Appendix": 10, "_MATH_ invokes _MATH_": 13, "_MATH_ 's input": 44, "_MATH_ mentioned above": 16, "_MATH_ , functions": 11, "_MATH_ the difference": 11, "_MATH_ , evaluated": 11, "_MATH_ , presented": 12, "_MATH_ values is": 16, "_MATH_ N ,": 11, "_MATH_ , mass": 10, "_MATH_ points from": 12, "_REF_ , whose": 16, "_MATH_ remains constant": 28, "_MATH_ is distinct": 15, "_MATH_ when _MATHDISP_": 15, "_MATH_ multiplications and": 21, "_MATHDISP_ and define": 21, "_MATH_ and orientation": 11, "_MATH_ for real": 11, "_MATH_ has coordinates": 10, "_MATH_ alone ,": 14, "_MATHDISP_ ( for": 20, "_REF_ , has": 23, "_MATH_ retrial queue": 17, "_MATH_ decomposes into": 11, "_ MATH_ .": 19, "_MATH_ it has": 16, "_MATH_ . ]": 20, "_MATH_ will stand": 12, "_MATH_ axes .": 11, "_REF_ is asymptotically": 13, "_MATH_ parameters .": 25, "_MATHDISP_ Here the": 12, "_MATH_ are 1": 19, "_MATHDISP_ , contradicting": 11, "_MATH_ clusters ,": 11, "_MATH_ than to": 16, "_CITE_ aims to": 10, "_MATH_ nm is": 10, "_MATH_ boson with": 10, "_MATHDISP_ for almost": 21, "_MATH_-_MATH_ are satisfied": 10, "_MATH_ with edge": 13, "_MATH_ from Proposition": 14, "_MATH_ to mode": 10, "_REF_ , now": 12, "_MATHDISP_ Thus we": 14, "_REF_ plot the": 13, "_MATH_ is by": 39, "_MATH_ is maintained": 11, "_MATH_ performance index": 26, "_MATH_ with these": 11, "_REF_ means that": 23, "_MATH_for all _MATH_": 20, "_MATH_ is dominant": 11, "_MATH_ and volatility": 12, "_MATH_ seconds for": 19, "_MATH_ problem is": 15, "_MATH_ at _MATHDISP_": 11, "_MATH_ background .": 14, "_MATH_ are continuously": 19, "_CITE_ describe the": 10, "_MATH_ taking values": 27, "_MATH_ and conclude": 11, "_CITE_ were able": 16, "_MATH_ is regarded": 27, "_MATH_ is flat": 10, "_MATH_ and conditional": 10, "_MATH_ that could": 12, "_MATH_ are proportional": 30, "_MATH_ security of": 10, "_MATH_ separation case": 10, "_MATH_ transitions of": 10, "_MATH_ , recall": 22, "_MATH_ is substituted": 19, "_MATH_ . Therefore": 11, "_MATH_ is non-degenerate": 18, "_REF_ ) relates": 14, "_MATH_ nearest neighbor": 11, "_REF_ and compared": 11, "_MATH_ ) into": 28, "_MATH_ which belongs": 11, "_MATH_ equals zero": 23, "_MATHDISP_ will be": 12, "_MATHDISP_ and suppose": 10, "_MATHDISP_ , valid": 12, "_MATH_ samples ,": 18, "_MATH_ , higher": 10, "_MATH_ the identity": 14, "_REF_ ] and": 11, "_MATH_ is influenced": 12, "_MATH_ is alternating": 10, "_MATHDISP_ exists and": 10, "_MATH_ ( data": 18, "_MATHDISP_ then ,": 16, "_MATH_ between 1": 13, "_MATH_ modular exponentiations": 10, "_MATH_ in model": 24, "_CITE_ study the": 26, "_CITE_ and Wang": 11, "_MATH_ crosses the": 30, "_MATH_ and length": 12, "_CITE_ provided an": 13, "_REF_ to find": 21, "_MATH_ the speed": 13, "_MATH_ and was": 10, "_REF_ ) vanish": 11, "_MATH_ of prime": 12, "_MATH_ and current": 15, "_CITE_ are a": 13, "_MATH_ and labour": 10, "_CITE_ suggest to": 12, "_MATH_ , nor": 22, "_MATH_ to model": 10, "_REF_ defines a": 18, "_MATH_ is divergent": 12, "_REF_ lead to": 13, "_MATH_ varies ,": 22, "_REF_ ) says": 13, "_REF_ indicates the": 17, "_MATH_ is verified": 17, "_MATH_ are involved": 11, "_MATHDISP_ is well": 16, "_MATH_ indicates whether": 12, "_MATH_ is like": 11, "_MATH_ \u00c5 .": 18, "_MATH_ ; indeed": 25, "_MATH_ m )": 21, "_MATH_ 's :": 15, "_MATH_ K _CITE_": 13, "_MATH_ models with": 11, "_MATH_ hits _MATH_": 14, "_MATH_ the average": 22, "_CITE_ consider a": 21, "_MATH_ is undirected": 17, "_MATH_ Yang-Mills theory": 17, "_CITE_ are two": 11, "_MATH_ is minimally": 11, "_MATH_ theories ,": 14, "_REF_ ) even": 16, "_MATH_ that make": 11, "_MATH_ which describes": 18, "_CITE_ , many": 15, "_CITE_ ; they": 14, "_MATH_ as illustrated": 12, "_MATH_ computed from": 17, "_MATH_ th-ranked element": 27, "_MATH_ is secure": 12, "_MATH_ decreases and": 12, "_MATH_ gets large": 12, "_MATH_ are matrices": 24, "_MATH_ , temperature": 10, "_MATHDISP_ leads to": 14, "_MATH_ days (": 12, "_MATH_such that _MATH_": 11, "_MATH_ is Borel": 18, "_MATH_ when (": 11, "_MATH_ that take": 13, "_MATH_ that appears": 17, "_REF_a , b": 22, "_MATH_ while for": 13, "_MATH_ only contains": 10, "_MATHDISP_ by _MATHDISP_": 10, "_REF_-_REF_ , respectively": 12, "_MATH_ is commutative": 15, "_MATH_ scattering .": 19, "_MATHDISP_ , This": 13, "_MATH_ satisfies Eq": 20, "_REF_ can now": 11, "_MATH_ is _MATH_-linear": 14, "_MATH_ were _MATH_": 10, "_MATH_ where a": 15, "_MATH_ to depend": 13, "_MATH_ : there": 11, "_MATH_ to two": 11, "_MATH_ we construct": 16, "_MATH_ is triangular": 10, "_MATH_ together .": 10, "_MATH_ , density": 16, "_MATH_ for more": 13, "_MATH_ are _MATH_-dimensional": 10, "_MATH_ variables are": 12, "_CITE_ have investigated": 22, "_MATHDISP_ which leads": 26, "_MATH_ shown on": 10, "_MATH_ is ignored": 13, "_MATH_ are thus": 13, "_MATH_ constitute the": 11, "_MATH_ is ultimately": 13, "_MATH_ makes sense": 13, "_MATH_ taken from": 13, "_MATH_-transform of _MATH_": 11, "_MATH_ if either": 10, "_MATH_-_MATH_ , and": 15, "_MATH_ , termed": 10, "_MATH_ denote all": 12, "_CITE_ , just": 11, "_MATH_ rows ,": 13, "_CITE_ with an": 14, "_MATH_ is homeomorphic": 18, "_MATH_ m/s .": 13, "_MATH_ point vortices": 10, "_MATH_ satisfy that": 10, "_MATH_ ( after": 15, "_MATH_ ) over": 22, "_CITE_ applied to": 12, "_MATH_ are deleted": 10, "_MATH_ and arbitrary": 16, "_MATH_ are standard": 19, "_REF_- ( ii": 12, "_MATH_ for _REF_": 16, "_REF_ is identical": 10, "_MATH_ are primitive": 11, "_MATH_ are scheduled": 11, "_REF_ over the": 12, "_MATH_ MHz and": 13, "_REF_ ) goes": 12, "_CITE_ suggested the": 11, "_REF_ we observe": 16, "_CITE_ ( Chapter": 11, "_MATHDISP_ . Clearly": 11, "_MATH_ and estimate": 13, "_CITE_ can also": 13, "_MATH_ is derivable": 11, "_MATH_ one by": 10, "_MATH_ at both": 21, "_MATH_ is integer": 16, "_REF_ ) up": 17, "_MATH_ , initial": 17, "_ MATH_ ,": 18, "_MATH_ were taken": 10, "_MATH_ a partition": 11, "_CITE_ , Zhang": 12, "_MATH_ which ensures": 12, "_MATH_ process at": 11, "_MATH_-_MATH_ collisions at": 10, "_MATHDISP_ as well": 17, "_MATHDISP_ Define _MATH_": 10, "_REF_ considers the": 12, "_MATH_ , allows": 15, "_MATH_ by requiring": 10, "_CITE_ proposed another": 10, "_MATH_ ( black": 10, "_MATH_ are joined": 10, "_MATH_ of codimension": 11, "_MATH_ degrees ,": 10, "_MATH_ running in": 10, "_MATH_ region is": 11, "_MATH_ was derived": 17, "_MATH_ we then": 10, "_MATH_ of side": 13, "_MATH_ measured at": 11, "_MATH_ ; using": 10, "_REF_ , note": 20, "_MATH_ are applied": 15, "_MATHDISP_ , namely": 29, "_MATH_ by substituting": 11, "_REF_ : for": 12, "_MATH_ ( Figs": 15, "_CITE_ ; here": 13, "_CITE_ has a": 17, "_MATH_ is strong": 10, "_CITE_ ( hereafter": 17, "_MATHDISP_ , Then": 13, "_MATH_ is outside": 17, "_MATH_ that minimize": 10, "_MATHDISP_ belongs to": 15, "_MATH_ is aperiodic": 10, "_CITE_ _MATH_ is": 17, "_MATH_ AU and": 11, "_MATH_ precedes _MATH_": 13, "_MATH_ ( still": 12, "_REF_ in Theorem": 11, "_CITE_ because the": 12, "_CITE_ was proposed": 11, "_MATH_ decays into": 15, "_MATH_ even .": 14, "_MATH_- step linear": 10, "_MATH_ is Lipschitzian": 10, "_MATH_ . Let": 10, "_MATH_ confidence interval": 28, "_MATH_ resulting in": 13, "_MATH_ the resulting": 12, "_MATH_ found in": 21, "_MATH_ were defined": 11, "_REF_ ( a1": 12, "_REF_ , too": 10, "_MATH_ processes .": 13, "_MATH_ are essentially": 10, "_CITE_ is presented": 12, "_MATH_ rounds of": 13, "_REF_ ) than": 13, "_CITE_ consists in": 12, "_MATH_ structure .": 13, "_MATH_ and nonnegative": 14, "_CITE_ performed a": 19, "_MATH_ the largest": 13, "_MATH_ are unique": 17, "_CITE_ , Corollary": 13, "_MATH_ data sets": 11, "_MATH_-enhancement can make": 11, "_REF_ to compute": 13, "_MATH_ TeV )": 13, "_MATH_ are decreasing": 13, "_MATH_ are Gaussian": 14, "_MATH_ time algorithm": 11, "_MATH_ is implemented": 15, "_MATH_ case )": 11, "_CITE_-_CITE_ , _CITE_": 23, "_MATH_ is Hamiltonian": 21, "_MATH_ when a": 14, "_MATH_ must divide": 10, "_URL_ ) and": 11, "_CITE_ in his": 10, "_MATH_ ) represent": 14, "_REF_ ) result": 10, "_MATH_ the pair": 10, "_MATH_ contains three": 17, "_CITE_ was a": 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and smaller": 12, "_MATH_ is Newton": 10, "_REF_ ( b1": 11, "_MATH_ ( Proposition": 18, "_MATH_ functions ,": 20, "_MATH_ using this": 10, "_MATH_ elements with": 16, "_MATH_ problem ,": 18, "_MATH_ are easily": 14, "_MATH_ , remains": 15, "_MATHDISP_ hold for": 11, "_MATH_ are modified": 12, "_MATH_ is _MATH_-weakly": 13, "_MATH_ we recover": 19, "_MATH_ values to": 10, "_MATH_-periodic solutions of": 16, "_MATH_ at node": 13, "_CITE_ from a": 11, "_MATHDISP_ satisfies _MATHDISP_": 11, "_CITE_ or ,": 15, "_MATH_ keV )": 12, "_MATH_ is _MATH_-sparse": 10, "_MATH_-sided Bohm-Bawerk assignment": 10, "_MATH_ are Lagrange": 10, "_CITE_ , considering": 10, "_MATH_ verifies _MATH_": 13, "_MATH_ were assumed": 10, "_MATH_ to converge": 11, "_MATH_ then yields": 11, "_MATH_ is super": 12, "_MATH_ can compute": 11, "_MATH_ and remains": 10, "_MATH_ is dropped": 15, "_REF_ , hence": 11, "_MATH_ becomes unstable": 13, "_MATH_ _MATH_ -": 12, "_MATH_ ( 2": 12, "_MATH_ parameter in": 10, "_MATH_ , 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for given": 60, ", while in": 425, ", which does": 206, ", this will": 115, ", an arbitrary": 26, ", therefore ,": 1228, ", we require": 162, ", for simplicity": 140, ", described above": 11, ", the use": 355, ", _REF_ ,": 1654, ", and rotation": 10, ", the second": 682, ", without the": 92, ", it becomes": 204, ", when the": 1502, ", the measurement": 89, ", we get": 3984, ", we can": 10291, ", depending only": 47, ", such that": 2394, ", which appears": 77, ", we conclude": 1064, ", it was": 836, ", we introduce": 1155, ", such a": 444, ", only the": 535, ", after the": 212, ", the lower": 231, ", we do": 765, ", the studies": 15, ", we adopt": 239, ", and allows": 51, ", the dynamic": 148, ", the proposed": 536, ", and to": 677, ", an estimate": 33, ", implies that": 214, ", while the": 3211, ", by means": 125, ", in fact": 468, ", for any": 2306, ", and they": 767, ", the case": 205, ", hence the": 208, ", we comment": 15, ", there exists": 3224, ", on which": 70, ", the 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", 1994 ;": 86, ", 2000 ;": 121, ", 2001 ;": 122, ", 2005 )": 350, ", an accurate": 16, ", _MATH_ as": 386, ", the mass": 194, ", _MATH_ will": 364, ", either in": 36, ", and has": 228, ", from which": 494, ", we claim": 110, ", this number": 34, ", with zero": 22, ", a very": 113, ", of the": 790, ", assuming the": 89, ", _CITE_ reported": 27, ", using the": 1426, ", and found": 67, ", and set": 128, ", making it": 139, ", and perhaps": 38, ", and one": 482, ", whose elements": 23, ", represented by": 104, ", and in": 1590, ", using a": 360, ", we derived": 34, ", and so": 1954, ", respectively :": 103, ", and more": 200, ", which gives": 486, ", which indicates": 213, ", an effect": 23, ", corresponding to": 762, ", because the": 976, ", the local": 247, ", we write": 440, ", then ,": 565, ", the integral": 198, ", the middle": 37, ", first ,": 77, ", he can": 21, ", the secret": 15, ", and due": 37, ", a possible": 37, ", the other": 258, ", together with": 1105, ", provided that": 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", and when": 190, ", a product": 12, ", this allows": 56, ", the monotonicity": 17, ", a larger": 66, ", the histogram": 17, ", the properties": 74, ", the master": 45, ", this means": 251, ", we carry": 43, ", or in": 178, ", the mappings": 21, ", giving the": 74, ", which shows": 480, ", showing that": 199, ", the conclusion": 78, ", and relative": 20, ", are in": 50, ", _MATH_ )": 2261, ", then it": 840, ", but these": 117, ", and should": 44, ", as illustrated": 310, ", but they": 494, ", the samples": 38, ", the conventional": 38, ", recall that": 137, ", assume that": 593, ", called the": 330, ", one will": 32, ", Ch .": 21, ", the lowest": 60, ", of all": 23, ", using only": 40, ", not necessarily": 59, ", the quotient": 22, ", for otherwise": 15, ", which may": 708, ", this idea": 14, ", but on": 70, ", it turns": 167, ", meaning that": 310, ", cf .": 395, ", let alone": 22, ", the static": 44, ", the two": 671, ", we specify": 54, ", as described": 346, ", a detailed": 76, ", 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", it must": 264, ", the fluctuation": 35, ", from left": 12, ", _MATH_ such": 221, ", for three": 16, ", a corresponding": 18, ", one of": 569, ", including those": 45, ", the equation": 298, ", and other": 311, ", the induction": 13, ", and summing": 14, ", the conservation": 28, ", the sparse": 10, ", so one": 43, ", we directly": 31, ", letting _MATH_": 151, ", say _MATH_": 573, ", the constant": 96, ", see _CITE_": 1166, ", since in": 154, ", or _MATH_": 614, ", the small": 73, ", or at": 76, ", we call": 250, ", we omit": 92, ", since otherwise": 61, ", the adversary": 124, ", a case": 17, ", by replacing": 38, ", _REF_ and": 393, ", ( iii": 158, ", large amplitude": 11, ", 1992 ;": 53, ", 1994 )": 105, ", 1984 )": 38, ", in two": 33, ", satisfying the": 109, ", plus a": 27, ", as indicated": 153, ", the growth": 96, ", produces a": 15, ", making use": 68, ", a ray": 12, ", which focuses": 18, ", below we": 16, ", considering _MATH_": 40, ", provides the": 23, ", being _MATH_": 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", the DM": 19, ", by fixing": 10, ", higher than": 13, ", weighted by": 24, ", the score": 35, ", we demonstrate": 173, ", a number": 184, ", by assumption": 37, ", are often": 24, ", the dynamical": 71, ", the heavy": 31, ", which needs": 36, ", it remains": 183, ", as predicted": 45, ", is very": 59, ", the coefficients": 168, ", the equilibrium": 180, ", a Hopf": 17, ", the conclusions": 44, ", _REF_ )": 274, ", referred to": 111, ", and of": 199, ", it reflects": 10, ", under certain": 34, ", an approximation": 22, ", the methods": 76, ", especially when": 227, ", a huge": 10, ", updating the": 11, ", and ii": 36, ", because these": 36, ", which measure": 11, ", which play": 17, ", the theory": 114, ", 13 ,": 33, ", _MATH_ if": 378, ", to address": 11, ", we introduced": 74, ", while their": 38, ", _CITE_ and": 503, ", when one": 51, ", in principle": 220, ", this corresponds": 57, ", and make": 47, ", the power": 194, ", the Fourier": 62, ", the client": 28, ", the equality": 57, ", the latent": 10, ", the shortest": 26, ", the one-dimensional": 15, ", is required": 20, ", _MATH_ being": 255, ", the required": 89, ", as required": 125, ", a series": 56, ", allowing to": 22, ", this mechanism": 16, ", for certain": 35, ", the bandwidth": 34, ", thus enabling": 28, ", _REF_ has": 46, ", bounded ,": 33, ", are the": 240, ", the projected": 19, ", with one": 75, ", affects the": 13, ", the discounted": 10, ", while there": 48, ", namely _MATH_": 357, ", information about": 20, ", which results": 287, ", plays a": 26, ", we explore": 94, ", adapted to": 20, ", which controls": 20, ", and all": 429, ", also _MATH_": 37, ", we treat": 75, ", and discuss": 60, ", one for": 176, ", starting with": 116, ", the horizontal": 51, ", the net": 67, ", as with": 38, ", systems with": 13, ", Liu and": 15, ", they have": 213, ", so ,": 91, ", applying Lemma": 37, ", we infer": 116, ", including a": 76, ", a comparison": 60, ", Section _REF_": 182, ", Wu et": 13, ", changing 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", _MATH_ since": 50, ", by introducing": 67, ", where all": 159, ", _MATH_ holds": 106, ", the inner": 62, ", p. _REF_": 204, ", _MATHDISP_ so": 34, ", the largest": 98, ", the user": 247, ", are very": 29, ", while not": 26, ", denoted as": 132, ", it takes": 77, ", must be": 116, ", to deal": 13, ", see Table": 55, ", we check": 93, ", the resolution": 36, ", studying the": 22, ", from these": 12, ", education ,": 21, ", and retirement": 26, ", we computed": 86, ", they can": 409, ", the real": 169, ", 1 ,": 102, ", _MATH_ on": 116, ", the truncation": 14, ", solid lines": 10, ", the AR": 14, ", the periods": 25, ", by increasing": 25, ", the decrease": 44, ", the damping": 57, ", we want": 296, ", one more": 18, ", we evaluated": 38, ", and network": 26, ", if only": 39, ", but all": 57, ", the radial": 83, ", to describe": 31, ", the fuzzy": 36, ", and extend": 18, ", and compared": 29, ", the tracking": 53, ", the coupled": 37, ", by which": 73, ", the parameters": 233, ", may 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", is expressed": 14, ", computing _MATH_": 13, ", the MSE": 15, ", and variance": 16, ", _MATH_ a": 110, ", the convex": 44, ", where 0": 18, ", and call": 24, ", the interpretation": 34, ", either because": 15, ", again by": 35, ", the equilibria": 16, ", are obtained": 49, ", _MATH_ defined": 43, ", the center": 77, ", _MATH_ :": 199, ", as mentioned": 170, ", the electrical": 26, ", the restricted": 16, ", we substitute": 52, ", and solving": 25, ", : _MATHDISP_": 27, ", compute the": 40, ", we proceed": 150, ", each _MATH_": 108, ", each edge": 15, ", results in": 97, ", thus being": 10, ", the vector": 258, ", using both": 18, ", and inverse": 12, ", is considered": 66, ", it reduces": 33, ", among other": 78, ", reliability ,": 17, ", we review": 134, ", Sec .": 22, ", which satisfies": 173, ", and two": 244, ", and low": 35, ", we summarize": 93, ", defines an": 10, ", almost all": 53, ", and management": 15, ", the matrices": 56, ", consequently ,": 224, ", the matrix": 330, ", 1999 )": 177, ", Ireland ,": 11, ", 2000 ,": 32, ", _MATH_ its": 37, ", coincides with": 26, ", the design": 140, ", since some": 18, ", when compared": 47, ", with input": 10, ", the unknown": 45, ", the dimension": 64, ", not a": 45, ", they were": 76, ", we study": 687, ", and line": 15, ", as there": 80, ", the synthesis": 21, ", B )": 21, ", by observing": 11, ", one knows": 13, ", the current": 228, ", or only": 15, ", much of": 18, ", 5 and": 15, ", the applied": 23, ", while for": 326, ", using _MATH_": 158, ", the de": 17, ", corresponds to": 106, ", equal to": 79, ", and minimum": 17, ", the detection": 55, ", it converges": 13, ", positively homogeneous": 10, ", the quark": 32, ", the numerical": 174, ", a variant": 20, ", defined on": 57, ", 2005 ,": 60, ", and proposed": 18, ", the independence": 22, ", both for": 78, ", was first": 13, ", 3 ]": 10, ", equations (": 43, ", where any": 17, ", _MATH_ should": 140, ", a fast": 30, ", or ``": 46, ", or on": 48, ", from 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", thus confirming": 10, ", which improves": 29, ", the entry": 21, ", ACE and": 13, ", the explicit": 59, ", were generated": 10, ", the light": 85, ", the papers": 10, ", color ,": 14, ", the outputs": 21, ", we formulate": 104, ", the start": 17, ", the supremum": 14, ", the penalty": 18, ", the property": 36, ", actually ,": 15, ", hence _MATHDISP_": 50, ", the norm": 63, ", each agent": 18, ", the private": 11, ", reaching the": 13, ", the intrinsic": 29, ", the order": 124, ", is set": 17, ", and almost": 20, ", this point": 15, ", Astrophys .": 11, ", requires the": 17, ", although they": 83, ", the odd": 10, ", after each": 10, ", we tried": 24, ", the techniques": 27, ", then those": 10, ", which says": 21, ", an exponential": 22, ", one important": 13, ", and electric": 14, ", _REF_ are": 11, ", especially of": 10, ", we drop": 29, ", although not": 52, ", i. e.": 64, ", in section": 39, ", again the": 18, ", thus creating": 21, ", thus producing": 18, ", the scheme": 57, ", 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", which constructs": 10, ", the routing": 16, ", where as": 22, ", the responses": 14, ", using Eq": 41, ", a protocol": 17, ", pressure and": 16, ", the toroidal": 10, ", and models": 11, ", to study": 47, ", one recovers": 19, ", existence and": 11, ", for (": 14, ", is more": 55, ", we exhibit": 22, ", those who": 10, ", one does": 31, ", we run": 41, ", the longest": 10, ", in more": 16, ", one expects": 60, ", 20 ,": 35, ", and c": 24, ", whether they": 13, ", when (": 15, ", a widely": 11, ", _MATH_ attains": 16, ", one ,": 16, ", the respective": 29, ", where their": 10, ", sunspots ,": 10, ", _MATH_-a.s .": 10, ", but unlike": 15, ", each particle": 15, ", it works": 12, ", and within": 26, ", in essence": 15, ", the death": 11, ", and radio": 16, ", and correspondingly": 21, ", type III": 11, ", 1976 ;": 20, ", Karlicky ,": 18, ", we described": 20, ", field lines": 16, ", in phase": 10, ", and local": 31, ", we developed": 75, ", we indicate": 26, ", integrating by": 16, ", 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significant modeling": 14, ", until it": 18, ", the Web": 22, ", we characterize": 39, ", by measuring": 12, ", and additionally": 15, ", the message": 46, ", which computes": 13, ", which transform": 10, ", play a": 10, ", also with": 15, ", the star": 24, ", a variation": 15, ", 9 ,": 50, ", 12 ,": 42, ", but of": 34, ", more precisely": 59, ", he showed": 12, ", a bound": 24, ", the generalization": 12, ", a pair": 47, ", the signal-to-noise": 10, ", the topic": 11, ", Liu et": 36, ", as time": 11, ", the slave": 13, ", the kink": 13, ", whereby _MATH_": 12, ", to decide": 11, ", the welfare": 13, ", our strategy": 10, ", the approximated": 14, ", many papers": 13, ", the analytic": 25, ", then define": 12, ", maximizing the": 17, ", we tend": 13, ", a message": 11, ", in light": 16, ", by integrating": 18, ", mass ,": 26, ", a potential": 22, ", by studying": 10, ", and general": 13, ", a penalty": 11, ", the sampled": 10, ", with more": 30, ", since at": 26, ", and analysis": 13, ", its corresponding": 15, ", the GPU": 18, ", since only": 28, ", we reconstruct": 23, ", the creation": 17, ", the kinematics": 15, ", then such": 17, ", some numerical": 21, ", since with": 11, ", the attacker": 29, ", just to": 24, ", until now": 21, ", a measurement": 11, ", differences between": 11, ", the missing": 32, ", the restriction": 62, ", if every": 18, ", is greater": 14, ", by looking": 14, ", energy ,": 20, ", the regular": 25, ", also for": 22, ", the monitoring": 11, ", with mean": 23, ", once it": 14, ", death ,": 13, ", _MATHDISP_ since": 20, ", the fastest": 13, ", we got": 13, ", rather it": 10, ", ( II": 13, ", the relativistic": 19, ", V_MATH_ ,": 10, ", are included": 17, ", which compares": 17, ", the cyclic": 19, ", when combined": 22, ", the straight": 13, ", it suggests": 15, ", as found": 23, ", the cascade": 13, ", it sets": 18, ", the strings": 13, ", observed by": 17, ", using ,": 18, ", so our": 20, ", regarded as": 13, ", including both": 32, ", and 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designed for": 12, ", because their": 34, ", the later": 11, ", is investigated": 15, ", we indeed": 14, ", a consistent": 20, ", since an": 24, ", this formula": 29, ", there does": 40, ", otherwise .": 30, ", which provided": 15, ", our definition": 11, ", of (": 13, ", and surface": 21, ", an adversary": 23, ", it changes": 13, ", though they": 32, ", replace _MATH_": 20, ", the residuals": 22, ", our first": 14, ", _MATH_ an": 33, ", neglecting the": 19, ", which breaks": 11, ", which as": 20, ", the character": 12, ", ( 2.4": 10, ", by simple": 15, ", the bifurcating": 22, ", problem _REF_": 25, ", we carefully": 10, ", which act": 13, ", the probe": 15, ", the large-scale": 16, ", and reduces": 14, ", a type": 12, ", this restriction": 16, ", we established": 22, ", the gravitino": 17, ", but given": 11, ", the arguments": 20, ", can still": 13, ", also using": 11, ", the RMS": 10, ", and although": 22, ", as all": 26, ", _MATH_ -": 37, ", a narrow": 11, ", a clear": 31, ", which 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19, ", mostly because": 14, ", occurs when": 10, ", we place": 19, ", by abuse": 11, ", which contributes": 21, ", we agree": 10, ", usually the": 24, ", the fractal": 13, ", and into": 11, ", Lin et": 12, ", the terminal": 28, ", although these": 23, ", respectively in": 11, ", thereby increasing": 12, ", plus an": 11, ", and 304": 16, ", without using": 14, ", A ,": 13, ", and could": 37, ", the _MATH_-dimensional": 36, ", our claim": 13, ", Figure 4": 10, ", _MATHDISP_ _MATH_": 17, ", a computer": 10, ", towards the": 14, ", a standard": 47, ", the fractional-order": 12, ", our conclusions": 12, ", the separation": 50, ", selection of": 14, ", and Proposition": 25, ", then if": 19, ", to allow": 24, ", by removing": 10, ", we move": 24, ", they might": 22, ", the usage": 15, ", separately .": 21, ", the proposal": 14, ", we truncate": 10, ", observed at": 12, ", are considered": 34, ", several works": 10, ", we view": 15, ", we vary": 32, ", gives _MATH_": 27, ", we assess": 11, ", is plotted": 16, ", the assertion": 53, ", the coordinate": 30, ", is only": 22, ", consider _MATHDISP_": 13, ", in Theorem": 35, ", because any": 10, ", and satisfying": 15, ", the suppression": 19, ", we subtract": 18, ", is constructed": 14, ", which relates": 35, ", and sleep": 11, ", 24 ,": 13, ", is one": 56, ", the viral": 10, ", by decreasing": 11, ", i )": 13, ", iv )": 16, ", we collected": 11, ", containing only": 14, ", race ,": 11, ", we identified": 28, ", this defines": 10, ", we readily": 15, ", is depicted": 14, ", construct a": 18, ", and expressed": 10, ", architecture principles": 10, ", and energy": 49, ", because every": 12, ", because that": 10, ", for details": 24, ", the predator": 14, ", this fact": 37, ", we summarise": 10, ", since from": 13, ", the remainder": 19, ", who reported": 12, ", no other": 21, ", our framework": 24, ", angular momentum": 31, ", the operating": 13, ", section _REF_": 18, ", forming the": 21, ", a line": 21, ", measuring the": 29, ", and 19": 15, ", for arbitrary": 32, ", returning to": 10, ", suggest that": 24, ", to each": 35, ", closely related": 11, ", the template": 17, ", _MATH_ extends": 11, ", the peaks": 21, ", which forms": 21, ", this issue": 22, ", especially ,": 32, ", a statistical": 17, ", the saddle": 11, ", the gains": 10, ", the vorticity": 19, ", this raises": 10, ", composition and": 13, ", with reference": 17, ", and estimated": 10, ", the prey": 19, ", ( e": 24, ", the degradation": 11, ", in those": 12, ", the variations": 30, ", we noted": 12, ", obtaining _MATH_": 10, ", and right": 15, ", no more": 22, ", even a": 39, ", where I": 10, ", all eigenvalues": 11, ", fear ,": 11, ", the swarm": 11, ", evolution ,": 12, ", for systems": 16, ", because our": 24, ", energy and": 18, ", the understanding": 14, ", cost ,": 14, ", shape and": 18, ", which typically": 28, ", denotes the": 31, ", because at": 16, ", performed by": 11, ", we gain": 10, ", 2012 ;": 18, ", and mathematical": 12, ", 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", it assumes": 13, ", which combined": 16, ", to capture": 10, ", gives ,": 11, ", solutions to": 16, ", Theorem 4.1": 13, ", function _MATH_": 22, ", for brevity": 14, ", are taken": 15, ", the extremal": 19, ", demonstrating that": 29, ", among many": 14, ", Subsection _REF_": 19, ", spanned by": 12, ", _MATH_ km": 14, ", this control": 10, ", and asymptotic": 11, ", often called": 24, ", it decreases": 21, ", when applying": 12, ", we typically": 15, ", the laws": 12, ", the vast": 13, ", since both": 46, ", this translates": 10, ", choose the": 16, ", a quantity": 14, ", using integration": 10, ", the rejection": 14, ", computed by": 14, ", thus explaining": 11, ", the demand": 14, ", at all": 16, ", the public": 17, ", after having": 17, ", with any": 15, ", two and": 11, ", create a": 12, ", and reduce": 14, ", coronal holes": 16, ", a spectral": 10, ", an interaction": 14, ", and combined": 12, ", their method": 22, ", there might": 24, ", holds for": 42, ", relating the": 12, ", it performs": 11, ", a data": 24, ", so an": 20, ", whether a": 17, ", _MATH_ values": 15, ", to account": 25, ", a modification": 12, ", the subset": 21, ", who have": 20, ", aside from": 14, ", the coverage": 27, ", can we": 30, ", are associated": 16, ", we return": 23, ", the formulae": 11, ", its solution": 10, ", passing through": 13, ", separating the": 11, ", we offer": 13, ", these algorithms": 20, ", _MATH_ respectively": 13, ", the variety": 12, ", parallel ,": 10, ", -2 )": 15, ", one finally": 10, ", which produces": 57, ", the tradeoff": 10, ", the formalism": 12, ", the circuit": 36, ", the electromagnetic": 28, ", an object": 14, ", mainly the": 10, ", several models": 11, ", the latest": 15, ", the early": 13, ", and 15": 27, ", with characteristic": 14, ", and build": 10, ", [ _CITE_": 11, ", they suggest": 10, ", Theorem 2.1": 21, ", and certain": 13, ", their results": 19, ", _CITE_ ]": 22, ", more efficient": 13, ", we classified": 11, ", estimate (": 21, ", and 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"Now , from": 59, "Now we have": 73, "Notice that in": 93, "Now , the": 244, "Notice , however": 24, "Next , for": 50, "Nevertheless , in": 78, "Now we assume": 28, "Next , _MATH_": 24, "Note that for": 328, "Note first that": 22, "Now if _MATH_": 40, "Next , define": 14, "Numerical results show": 11, "Namely , for": 34, "Now we turn": 41, "Now we shall": 30, "Now _MATH_ is": 40, "Now , by": 139, "Next , let": 73, "Nevertheless , since": 15, "Noticing that _MATHDISP_": 20, "Now , assume": 56, "NLO and NNLO": 30, "Now , in": 62, "Note that every": 23, "Note that a": 154, "Notice that we": 49, "Now consider a": 34, "Newton 's method": 59, "Note that even": 35, "Now , if": 156, "N - S": 22, "Note that by": 102, "Now we use": 45, "National Geophysical Data": 12, "Now , using": 66, "Next , using": 33, "Note that such": 47, "Note that unlike": 10, "Notice that this": 75, "Nash equilibrium ,": 35, "Nash equilibrium .": 46, "Namely , _MATH_": 56, "Namely , the": 111, "Now assume that": 84, "Now we show": 51, "Nevertheless , there": 42, "Note that under": 25, "Nonetheless , the": 54, "Newton polyhedra of": 11, "Note that Eq": 21, "Nevertheless , these": 31, "Now we need": 21, "Note that to": 21, "Note that an": 35, "Now , recall": 10, "Notice that when": 18, "Note that if": 293, "Note that while": 25, "NM station .": 11, "Now we are": 105, "Namely , there": 10, "Notably , the": 12, "Now we will": 45, "NMPC closed -loop": 11, "Note that it": 88, "Noether quasisymmetry transformation": 12, "Needless to say": 35, "Next , _MATHDISP_": 16, "Noting that _MATH_": 141, "Navier-Stokes equations .": 36, "Navier-Stokes equations for": 20, "Next , to": 15, "Next , it": 13, "Note that some": 21, "Now consider the": 104, "Now for _MATH_": 19, "Now it is": 42, "Now , _MATHDISP_": 74, "Now , define": 23, "N is the": 25, "Notice that there": 24, "Nevertheless , a": 37, "Now , consider": 77, "Notice that for": 63, "Now fix _MATH_": 10, "Now we introduce": 28, "Navier-Stokes equations (": 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III": 15, "Since _MATH_ can": 38, "SEP ) events": 20, "Similarly for _MATH_": 11, "Stirling 's formula": 32, "Since it is": 83, "Steps 2 and": 12, "Standard Model is": 13, "Space D *": 19, "Section _REF_ for": 235, "Section 2 ,": 455, "Schrodinger equation _MATHDISP_": 18, "Schrodinger equations with": 17, "Schrodinger equation with": 32, "Schrodinger equation is": 13, "Section _REF_ below": 48, "Schrodinger equation in": 17, "Secretary of the": 13, "Section _REF_ .": 2938, "Sun ) .": 18, "Section _REF_ contains": 88, "So , by": 105, "Section 3 we": 92, "Schrodinger equation _REF_": 10, "Section 3.2 )": 17, "Since _MATH_ has": 124, "Sections _REF_ and": 379, "Set _MATH_ and": 89, "Show that _MATH_": 38, "So far ,": 207, "Spectrometer ( EIS": 19, "Since _MATH_ is": 2173, "So , we": 368, "Subsection _REF_ ,": 106, "Suppose first that": 38, "Substituting the above": 26, "Suppose _MATH_ is": 183, "Semantic Web Service": 15, "So , it": 125, "Schur complement formula": 17, "Shapley value for": 20, "Set _MATH_ is": 14, "Similarly , _MATH_": 221, "Suppose that there": 225, "Section 2 the": 11, "Section 3 the": 11, "Section 4 is": 38, "Section 5 ,": 116, "Some concluding remarks": 11, "Section 6 .": 86, "Suppose that ,": 34, "Substituting _MATH_ into": 85, "Since , in": 22, "Specifically , the": 248, "Standard Model and": 15, "Substituting Eqs .": 50, "Since there are": 119, "Sun during the": 25, "Since all these": 10, "SU ( 2": 185, "So _MATH_ .": 80, "Section _REF_ are": 59, "Set _MATH_ ,": 137, "Sun has been": 10, "Sufficient conditions for": 29, "Science of the": 10, "Similarly , one": 50, "Strong Unforgeability _REF_": 14, "Similarly , _MATHDISP_": 107, "Similarly to Theorem": 10, "Section 4 .": 204, "Section 5 .": 145, "Solar and Heliospheric": 136, "SOHO ) ,": 17, "SN Ia data": 10, "Sloan Digital Sky": 15, "Sun and in": 10, "Sun , _MATH_": 24, "Second , we": 263, "So , _MATH_": 237, "Sylow 2-subgroup of": 10, "Since for any": 20, "Since the number": 66, "Section _REF_ ;": 42, "Since we have": 110, "Suppose _MATH_ .": 86, "Solar Observatory (": 64, "Section _REF_ by": 19, "Sky Survey (": 12, "Survey ( SDSS": 11, "Since the magnetic": 15, "So , each": 10, "Section _REF_ reviews": 21, "Section _REF_ describes": 164, "Section _REF_ shows": 42, "Section _REF_ presents": 201, "Section _REF_ with": 56, "Smith et al": 26, "Similarly , as": 16, "Step _REF_ .": 11, "System ( _REF_": 161, "Suppose that an": 26, "Similarly to the": 197, "Section 3.1 .": 18, "Since _MATH_ by": 38, "So we can": 114, "Similar results were": 19, "Similarly , when": 44, "Simulation results show": 37, "Since the length": 12, "Subsequently , the": 99, "Such an example": 10, "Section 3 ,": 391, "Since the sequence": 27, "Some of these": 146, "Similarly , in": 84, "Section _REF_ can": 52, "Section _REF_ gives": 77, "So we get": 49, "SI and SS": 37, "SU ( 3": 148, "Solution of the": 11, "Sheeley et al": 17, "Sect . 3.2": 11, "Suppose _MATH_ ,": 82, "Set _MATH_ .": 209, "Sec . 2": 33, "Sec . 5": 17, "Section _REF_ in": 34, "Section _REF_ is": 248, "Starting from the": 86, "Show that for": 14, "Show that if": 16, "Some examples are": 20, "Sobolev 's embedding": 11, "See _CITE_ for": 144, "Substituting this expression": 22, "Section V .": 10, "So , according": 12, "Sect . IV": 14, "Separating the real": 15, "Since _MATH_ are": 47, "STEREO spacecraft ,": 23, "Since _MATH_ contains": 24, "Section 2.1 ,": 11, "Step 3 of": 13, "Section 2 is": 22, "Since all the": 35, "Section 4.1 .": 10, "So _MATH_ is": 118, "Since Eq .": 12, "Step 1 .": 116, "Sect . 2": 188, "Sect . 3": 194, "Suppose there is": 16, "So far we": 58, "Section _REF_ focuses": 15, "Since _MATHDISP_ ,": 301, "Sudakov form factor": 22, "Section _REF_ to": 112, "Sun ( _MATH_": 12, "STEREO-A and STEREO-B": 24, "Similarly , let": 49, "So by the": 17, "Secondly , we": 131, "Solving this equation": 12, "Since both _MATH_": 36, "Since _MATH_ (": 59, "Section 3 )": 48, "Since the process": 16, "Similarly , there": 25, "Support Vector Machine": 15, "Supersymmetry ( SUSY": 11, "Similarly , for": 145, "Substituting the general": 10, "See for example": 12, "Section 2.2 ,": 12, "Suppose that for": 48, "S/m , _MATH_": 13, "Step 2 :": 66, "Specifically , _MATH_": 39, "Solar Cycle 23": 87, "Section _REF_ a": 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"Sobolev spaces .": 21, "Section 2 .": 165, "Section _REF_ as": 15, "Since _MATH_ as": 58, "Similarly to Section": 13, "STEREO spacecraft .": 26, "Since _MATH_ for": 228, "Since the coefficients": 20, "Section 8 .": 12, "SM , and": 11, "Schauder fixed point": 29, "Sun _CITE_ .": 39, "Since we are": 174, "STEREO B and": 19, "STEREO A was": 14, "STEREO A ,": 30, "Solar Observatory ,": 23, "Set _MATHDISP_ .": 106, "Since ( _REF_": 75, "Schwarzschild black hole": 118, "Since the matrix": 20, "Since these are": 13, "Schur 's complement": 55, "SC 23 period": 16, "Section 6 ,": 46, "Since _MATH_ in": 56, "Standard Model (": 84, "Since the _MATH_": 52, "Summarizing , we": 37, "So , there": 50, "Sturm-Liouville boundary value": 18, "Substituting this value": 11, "Substituting _MATH_ and": 27, "STEREO A and": 59, "SEP events in": 15, "Suppose that _MATHDISP_": 55, "Step 2 of": 21, "Sun in the": 34, "Sun and the": 58, "Since the two": 24, "Section 5 discusses": 12, "Since we can": 31, "SM ) of": 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"It is evident": 173, "It is desired": 14, "In regard to": 23, "If we know": 17, "Indeed , even": 13, "In the ``": 40, "In the upper": 28, "II , and": 34, "In our first": 15, "It also provides": 10, "If either _MATH_": 23, "IP type II": 14, "II bursts ,": 16, "II bursts are": 15, "In the standard": 48, "In light of": 70, "Intuitively , a": 22, "In this review": 25, "Institute of Physics": 10, "It was assumed": 19, "I.V . 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"large uncertainties .": 12, "level from the": 10, "linear force-free fields": 10, "line joining the": 15, "linear regime ,": 11, "leads to similar": 11, "luma and chroma": 11, "loops , where": 12, "linear model with": 10, "limit of an": 13, "line segment is": 14, "likely to contain": 12, "linearization of (": 15, "low degree of": 13, "least-squares fit to": 11, "least two distinct": 13, "length of commitment": 16, "linear with the": 11, "line element of": 15, "line bundles _MATH_": 10, "lateral and top": 13, "local minima and": 13, "local existence and": 14, "limited only by": 16, "latent class models": 11, "least-squares method .": 10, "larger in magnitude": 11, "lines shown in": 12, "lower boundary .": 11, "leader and the": 12, "large uncertainties in": 18, "laser power density": 10, "list in the": 12, "law as _MATH_": 20, "lower bound _REF_": 10, "latently infected cells": 16, "lines may be": 10, "locally in the": 10, "level _MATH_ at": 12, "lag synchronization of": 11, "lagged 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)": 30, "; cf .": 111, "; _MATH_ ;": 239, "; this is": 290, "; a more": 12, "; let _MATH_": 54, "; in particular": 223, "; see ,": 388, "; and the": 210, "; e.g .": 32, "; ( 2": 248, "; ( 3": 141, "; see _CITE_": 523, "; i.e. ,": 289, "; we will": 77, "; ( b": 93, "; ( c": 46, "; it will": 18, "; hence ,": 324, "; they have": 16, "; then _MATH_": 141, "; _MATH_ with": 12, "; in both": 13, "; _MATH_ and": 244, "; see Figure": 156, "; see Chapter": 16, "; _MATH_ _MATH_": 111, "; the first": 45, "; the second": 78, "; the average": 11, "; but ,": 15, "; however ,": 1023, "; that is": 493, "; the only": 25, "; see (": 55, "; we only": 12, "; _MATHDISP_ .": 92, "; then the": 126, "; finally ,": 39, "; _MATH_ are": 63, "; on the": 101, "; thus ,": 335, "; hence the": 60, "; it may": 13, "; the reader": 15, "; _MATH_ ,": 299, "; instead ,": 48, "; see e.g": 66, "; we shall": 20, "; as a": 50, "; the two": 19, "; here we": 39, "; then ,": 176, "; in other": 88, "; this implies": 15, "; additionally ,": 10, "; Fig .": 42, "; at the": 24, "; there is": 46, "; for more": 17, "; during the": 11, "; equivalently ,": 14, "; _CITE_ ,": 251, "; see Section": 77, "; it also": 19, "; for details": 30, "; also see": 15, "; then we": 100, "; in that": 12, "; as well": 10, "; Li et": 12, "; ( _MATH_": 18, "; this shows": 10, "; see _REF_": 28, "; _MATH_ represents": 41, "; and it": 18, "; here ,": 32, "; furthermore ,": 60, "; if the": 75, "; see the": 121, "; this can": 41, "; since _MATH_": 29, "; it was": 29, "; i.e .": 78, "; thus the": 57, "; whereas ,": 13, "; see [": 46, "; and a": 30, "; more precisely": 28, "; otherwise it": 27, "; in Section": 23, "; where the": 11, "; and references": 19, "; and ,": 56, "; we can": 48, "; and this": 17, "; third ,": 12, "; we also": 26, "; indeed ,": 91, "; the model": 12, "; the value": 12, "; the main": 15, "; specifically ,": 19, "; one can": 21, "; _REF_ )": 13, "; the other": 56, "; see Table": 39, "; De Moortel": 13, "; namely ,": 94, "; and when": 20, "; nevertheless ,": 47, "; it can": 64, "; accordingly ,": 13, "; the results": 22, "; this follows": 13, "; and for": 37, "; _MATH_ (": 32, "; one is": 19, "; the remaining": 19, "; the resulting": 15, "; ( iv": 60, "; we call": 25, "; if _MATH_": 176, "; for any": 17, "; in the": 197, "; and therefore": 10, "; 2 )": 79, "; 3 )": 30, "; these are": 45, "; hence _MATHDISP_": 13, "; similarly ,": 33, "; or (": 14, "; such a": 20, "; this gives": 13, "; with _MATH_": 13, "; we are": 20, "; so the": 20, "; so we": 14, "; but it": 13, "; this will": 31, "; in our": 20, "; refer to": 11, "; then for": 15, "; in general": 19, "; then by": 13, "; also ,": 32, "; the case": 16, "; we have": 73, "; otherwise the": 22, "; and we": 34, "; when the": 21, "; especially ,": 19, "; the corresponding": 38, "; among them": 12, "; here _MATH_": 52, "; see Eq": 19, "; when _MATH_": 72, "; all other": 17, "; we use": 22, "; _MATH_ satisfies": 13, "; etc .": 13, "; and so": 14, "; in fact": 97, "; this has": 12, "; so _MATH_": 13, "; ( 4": 57, "; ( 5": 23, "; Maximize _MATH_": 103, "; Minimize _MATH_": 46, "; this value": 10, "; _MATHDISP_ ;": 109, "; the proof": 25, "; this means": 41, "; we say": 11, "; an example": 12, "; so ,": 63, "; in addition": 33, "; for a": 65, "; they can": 30, "; the general": 12, "; Gopalswamy et": 15, "; then _MATHDISP_": 61, "; 4 )": 13, "; _MATH_ .": 125, "; but this": 16, "; the latter": 56, "; ii )": 66, "; iii )": 28, "; there are": 25, "; hence _MATH_": 47, "; consequently ,": 63, "; Wang et": 23, "; see Lemma": 19, "; the time": 12, "; therefore we": 19, "; b )": 31, "; conversely ,": 19, "; the lower": 12, "; the same": 28, "; and then": 14, "; if there": 13, "; see Proposition": 17, "; and iii": 12, "; one of": 17, "; and if": 48, "; see Remark": 15, "; Wang ,": 15, "; Zhang ,": 10, "; for each": 16, "; and that": 16, "; by the": 20, "; some of": 22, "; ( vi": 10, "; since the": 28, "; the notation": 10, "; _MATH_ if": 32, "; in such": 12, "; in case": 11, "; _MATHDISP_ ,": 38, "; in Fig": 11, "; where _MATH_": 35, "; if not": 15, "; see Sect": 18, "; Figure _REF_": 20, "; so that": 12, "; therefore the": 25, "; Liu et": 15, "; it has": 32, "; we then": 19, "; when it": 10, "; ( _REF_": 15, "; secondly ,": 18, "; only the": 22, "; it would": 12, "; _MATH_ :": 56, "; let us": 15, "; while in": 12, "; ( v": 20, "; and in": 29, "; ( d": 22, "; rather ,": 31, "; here the": 12, "; _MATH_ there": 24, "; we take": 14, "; see Theorem": 36, "; the _MATH_": 48, "; see below": 15, "; if we": 15, "; for this": 33, "; again ,": 12, "; hence it": 16, "; _MATH_ for": 39, "; then it": 17, "; see Appendix": 32, "; otherwise we": 13, "; it follows": 19, "; this leads": 14, "; the CME": 10, "; we assume": 13, "; in _CITE_": 21, "; in contrast": 12, "; see Example": 11, "; the number": 36, "; as the": 14, "; Zhang et": 14, "; the system": 15, "; Section _REF_": 18, "; the data": 12, "; the mean": 10, "; see for": 59, "; we denote": 15, "; thus it": 14, "; if it": 25, "; Zhang and": 11, "; first ,": 10, "; in a": 10, "; or _MATH_": 11, "; and _MATHDISP_": 32, "; each of": 13, "; as we": 16, "; see Figs": 16, "; and 3": 14, "; it does": 23, "; then a": 13, "; c )": 12, "; we do": 18, "; otherwise _MATH_": 17, "; then in": 10, "; the difference": 10, "; to be": 10, "; the result": 15, "; in order": 16, "; see Equation": 11, "; whereas the": 10, "; then there": 20, "; while for": 16, "; _MATH_ in": 15, "; such an": 10, "; ( 6": 11, "; with a": 10, "; and also": 11, "; we write": 13, "; therefore _MATH_": 23, "; both are": 11, "; while the": 17, "; see_REF_ .": 16, "; due to": 11, "; the last": 14, "; but the": 16, "; notice that": 14, "; at _MATH_": 10, "; and _CITE_": 11, "; this was": 12, "; thus a": 10, "; using the": 11, "; _MATH_ from": 11, "; _MATH_ the": 14, "; in practice": 10, "; _MATH_ so": 12}, "C": {"Combining this with": 66, "Clearly , this": 86, "Compared with the": 149, "Cheng et al": 32, "Clearly , since": 11, "Clearly , such": 15, "Clearly , _MATH_": 435, "Ca ii 8542": 36, "Cartesian product _MATH_": 13, "Coronal Explorer (": 38, "Chen , and": 11, "CME leading edge": 40, "CMEs have been": 14, "CME in the": 39, "CP violating phase": 11, "CP violation ,": 11, "Currently , there": 19, "Correspondingly , the": 60, "Consequently , it": 78, "Consider now the": 137, "C ) ,": 36, "Clearly , if": 70, "Conjecture _REF_ is": 11, "Clearly , the": 374, "Ca ii H": 44, "Consequently , the": 629, "Consider the system": 106, "Chen et al": 97, "Chapter _REF_ .": 261, "Case 1 ,": 34, "Corollary _REF_ .": 207, "CP violating phases": 17, "CP violation in": 26, "Carlo simulation of": 17, "Consider the following": 576, "Consider , for": 76, "Considering that the": 50, "Chaplygin gas (": 37, "CFC elements in": 12, "Coxeter groups .": 12, "Consider a sequence": 35, "Comparing the coefficients": 24, "Currently , the": 40, "Consequently , _MATHDISP_": 146, "Consider the set": 43, "Comparisons 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"Consider a solution": 16, "Consider the function": 35, "Case 2 .": 58, "Corollary _REF_ that": 31, "Corollary _REF_ with": 18, "Claim _REF_ ,": 32, "C is a": 12, "Consider the first": 23, "Corollary 2 .": 22, "Chomsky normal form": 14, "Clearly , _REF_": 10, "Choudhury et al": 10, "Close to the": 20, "CME source regions": 20, "Consider _MATH_ ,": 39, "C and D": 18, "Choose _MATH_ such": 38, "Compared to the": 134, "Comparing Fig .": 11, "CME as a": 16, "CMEs and their": 15, "CMEs , which": 20, "Coronal Diagnostic Spectrometer": 13, "Consider the control": 11, "CPU and GPU": 14, "Clearly , we": 47, "Chaplygin gas model": 22, "Chapter 2 .": 13, "Clearly , each": 10, "Combining the previous": 12, "Carrington rotation (": 15, "Composition Explorer (": 29, "Consequently , one": 18, "Contrary to the": 59, "CME was observed": 22, "CME , and": 20, "Cauchy sequence in": 45, "Cholesky decomposition of": 13, "CPU time .": 20, "CME , which": 18, "Consider the map": 13, "C2 field of": 11, "Cycle 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,": 11, "CME _CITE_ .": 13, "Cauchy inequality ,": 10, "Comparing Eq .": 21, "Convergence Theorem ,": 12, "Consequently , to": 16, "Consider _MATHDISP_ ,": 20, "Clearly , it": 24, "CME speed .": 10, "Color online )": 11, "Choi et al": 14, "Corollary 1 ,": 17, "C_REF_ ) ,": 13, "Christiansen ( 2011": 10, "Conditions ( _REF_": 21, "Compared to previous": 11, "Criterion ( BIC": 14, "CPU and the": 39, "Correspondingly , we": 10, "COR2 A and": 11, "COR1 and COR2": 29, "Considering the above": 11, "Comparison with the": 16, "Cycle 23 and": 13, "Consider the sequence": 16, "Consider any _MATH_": 21, "Corollary 3.1 .": 11, "CME , the": 17, "Clifford Fourier transform": 10, "Choose _MATH_ .": 23, "Conversely , given": 15, "Chapter 6 of": 10, "Chapter 6 .": 10, "CMOS technology .": 10, "Central Committee .": 11, "COP ( _REF_": 11, "CMEs ) and": 12, "Chapter 8 of": 10, "CME is a": 10, "Case 1 )": 11, "Case 2 )": 14, "CM energy of": 16, "Cartesian stiffness matrix": 15, "C.L . )": 15, "CME 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"Coulomb friction .": 10, "Consequently , an": 19, "Corollary of Theorem": 10, "Chapter 5 )": 13, "Caputo fractional derivatives": 11, "Cycle 23 (": 14, "Computer Science in": 10, "Coxeter group ,": 11, "Consider next the": 12, "Consequently , our": 18, "CESE method in": 10, "CEP stabilization of": 15, "Condition _MATH_ ,": 11, "CPU time in": 12, "Clearly , as": 11, "CMEs during the": 13, "Chapter 4 )": 12, "Conclusions are given": 10, "C3 ) .": 11, "Chapter 7 )": 12, "CCD camera (": 23, "Conversely , it": 12, "Coulomb potential ,": 10, "Case _MATH_ :": 11, "CMEs , but": 10, "CME can be": 18, "CMCK and CK": 10, "CME ) ,": 12, "Claim _REF_ )": 11, "Consider a set": 13, "Chaplygin gas _CITE_": 15, "Chapter 3 .": 12, "Condition ( i": 15, "Consider the switched": 12, "Consider the problem": 24, "Consider a pair": 11, "Consider the point": 10, "Consequently , since": 13, "Csorgo _CITE_ .": 11, "Cohen 's _MATH_": 10, "Control Lyapunov Function": 10, "Clearly _MATH_ ,": 10, "C_MATH_ ) ,": 10, "Clearly , when": 16, "Chapter _REF_ (": 17, "C ( Er_MATH_S_MATH_": 10, "Carlo simulation .": 10, "Chen 's algorithm": 18, "Chaplin et al": 16, "Cu ( 110": 10, "CMB power spectrum": 11, "Claim _REF_ .": 16, "Cloud node 1": 12, "CME and shock": 10, "CSD multiplier coefficient": 10, "Cressie , 1993": 11, "Charbonneau ( 1999": 10, "Conformal Geometric Algebra": 10}, "(": {"( 2002 )": 451, "( where the": 144, "( e.g. ,": 3159, "( _REF_ )": 84459, "( as in": 259, "( 2012b )": 14, "( CT )": 18, "( see also": 838, "( 1973 )": 56, "( 1995 )": 260, "( 2004 )": 594, "( 2007 )": 589, "( a )": 3875, "( c )": 1696, "( see e.g": 478, "( 1 )": 3084, "( Fig .": 2271, "( see _REF_": 208, "( we use": 42, "( i.e. ,": 3511, "( 2.14 )": 32, "( SH )": 11, "( recall _MATH_": 10, "( b )": 3649, "( or both": 23, "( Note that": 234, "( here _MATH_": 79, "( ii )": 3340, "( 2.6 )": 100, "( LDA )": 22, "( see the": 769, "( the _MATH_": 78, "( and ,": 102, "( _MATH_ )": 12928, "( upper right": 17, "( cf .": 1862, 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Let": 11, ") with the": 795, ") _CITE_ and": 208, ") _CITE_ .": 1109, ") and use": 31, ") , we": 7738, ") , which": 2488, ") , and": 7777, ") _MATHDISP_ _MATHDISP_": 31, ") and there": 19, ") , choosing": 12, ") argues that": 17, ") find that": 24, ") are shown": 123, ") - (": 4051, ") , respectively": 747, ") are similar": 24, ") in the": 1839, ") by _MATH_": 404, ") and (": 9448, ") , can": 148, ") is based": 76, ") , let": 112, ") by considering": 18, ") of a": 235, ") it follows": 252, ") and _REF_": 147, ") for (": 18, ") is of": 146, ") provided a": 11, ") for all": 172, ") result in": 17, ") of each": 43, ") ) ,": 653, ") do not": 143, ") and therefore": 45, ") suggests that": 50, ") leading to": 13, ") _CITE_ ,": 785, ") ; this": 70, ") show that": 200, ") _MATH_ for": 201, ") Given a": 11, ") The function": 24, ") holds .": 433, ") are employed": 10, ") such that": 429, ") , _MATH_": 2214, ") satisfying (": 18, ") , then": 1083, ") has a": 623, ") , _MATHDISP_": 1024, ") Let _MATH_": 413, ") that can": 61, ") _MATH_ and": 327, ") _MATH_ .": 478, ") _MATH_ ,": 858, ") into (": 557, ") yields _MATHDISP_": 329, ") tends to": 49, ") is just": 38, ") , is": 516, ") is proved": 63, ") of Lemma": 148, ") , (": 4700, ") we see": 100, ") can be": 3126, ") we may": 21, ") and using": 183, ") and the": 3140, ") together with": 139, ") proposed that": 18, ") , as": 601, ") reads _MATHDISP_": 56, ") , one": 781, ") , an": 153, ") becomes _MATHDISP_": 494, ") If _MATH_": 570, ") provides the": 52, ") of _MATH_": 442, ") to approximate": 12, ") as a": 344, ") as follows": 223, ") and _MATH_": 1449, ") is defined": 161, ") the ``": 10, ") provides a": 76, ") and by": 122, ") in their": 30, ") holds ,": 239, ") has at": 177, ") when _MATH_": 192, ") with initial": 96, ") is equivalent": 392, ") is not": 421, ") results in": 84, ") gives the": 163, ") we have": 684, ") we obtain": 430, ") gives _MATHDISP_": 228, ") instead of": 77, ") rather than": 38, ") has been": 399, ") and a": 477, ") , these": 81, ") is uniformly": 29, ") , with": 559, ") is written": 47, ") is presented": 41, ") into the": 254, ") , a": 687, ") and are": 73, ") for any": 106, ") with _MATH_": 1303, ") is that": 147, ") and 2": 30, ") show the": 152, ") depicts the": 30, ") describes the": 70, ") is obtained": 172, ") of the": 1941, ") and three": 26, ") with two": 26, ") , every": 13, ") given the": 13, ") , it": 1508, ") is also": 218, ") , or": 511, ") , suggesting": 31, ") is proposed": 35, ") , although": 105, ") are equivalent": 101, ") , note": 33, ") on _MATH_": 175, ") for the": 1165, ") , for": 573, ") and from": 59, ") with an": 70, ") and get": 18, ") consists of": 76, ") is said": 117, ") and b": 17, ") of Theorem": 230, ") , since": 180, ") in _CITE_": 212, ") and in": 174, ") , that": 358, ") , such": 164, ") at the": 348, ") during the": 67, ") , could": 11, ") , their": 29, ") shows that": 372, ") , Eq": 83, ") to get": 68, ") is satisfied": 390, ") is shown": 116, ") There are": 15, ") , whose": 82, ") , but": 902, ") or the": 158, ") and let": 61, ") via a": 11, ") , where": 971, ") between the": 113, ") because the": 40, ") also shows": 13, ") : _MATHDISP_": 1730, ") _MATHDISP_ ,": 507, ") when the": 128, ") and _MATHDISP_": 123, ") implies _MATH_": 87, ") is composed": 16, ") method .": 43, ") in Section": 54, ") implies that": 433, ") will be": 280, ") is fulfilled": 67, ") is first": 11, ") for a": 272, ") region ,": 12, ") is made": 12, ") is directly": 11, ") is used": 257, ") it is": 236, ") to the": 650, ") is positive": 61, ") satisfies the": 110, ") is exponentially": 52, ") , provide": 10, ") and that": 133, ") display the": 10, ") is complete": 16, ") distribution .": 18, ") data ,": 14, ") through the": 59, ") instrument onboard": 12, ") onboard the": 94, ") follows .": 82, ") denotes the": 75, ") , whereas": 162, ") ] ,": 107, ") For _MATH_": 129, ") than the": 103, ") which is": 181, ") that _MATH_": 395, ") , in": 516, ") gives a": 51, ") correspond to": 77, ") should be": 178, ") and consider": 19, ") by the": 249, ") we get": 230, ") hold with": 24, ") holds with": 83, ") of Fig": 52, ") are denoted": 12, ") if for": 32, ") is difficult": 10, ") is a": 1208, ") graph _MATH_": 10, ") , while": 498, ") with time-varying": 17, ") results from": 17, ") or Eq": 10, ") _CITE_ is": 113, ") , using": 166, ") , this": 378, ") _MATH_ as": 42, ") that _MATHDISP_": 598, ") data from": 14, ") and 1": 33, ") and response": 17, ") are in": 59, ") , so": 355, ") and it": 69, ") , though": 31, ") and applying": 27, ") is then": 102, ") or ,": 23, ") has exactly": 13, ") there exists": 82, ") and separating": 11, ") must hold": 13, ") with respect": 352, ") It is": 28, ") developed by": 12, ") is considered": 72, ") on the": 463, ") and comparing": 16, ") obtained from": 29, ") ; and": 131, ") ; see": 132, ") according to": 83, ") does not": 384, ") ( also": 14, ") cross section": 18, ") , set": 12, ") is related": 28, ") is an": 299, ") _MATHDISP_ and": 49, ") that there": 66, ") suggest that": 49, ") by using": 102, ") _MATH_ (": 310, ") each _MATH_": 10, ") but with": 37, ") illustrates the": 44, ") that the": 395, ") up to": 58, ") _CITE_ )": 36, ") _CITE_ has": 23, ") indicates that": 82, ") _MATH_ ;": 291, ") ) .": 1409, ") for different": 42, ") _CITE_ for": 43, ") satisfies (": 18, ") satisfies _MATH_": 49, ") is globally": 96, ") _MATH_ in": 35, ") , except": 51, ") BRST symmetry": 98, ") Abelian 1-form": 12, ") with (": 229, ") ; for": 49, ") is robustly": 39, ") for _MATH_": 842, ") with fixed": 10, ") is rewritten": 61, ") , showing": 22, ") in two": 22, ") , high": 14, ") and then": 173, ") becomes a": 50, ") model _CITE_": 71, ") are given": 157, ") In this": 12, ") number of": 50, ") In case": 10, ") belongs to": 27, ") has no": 102, ") are obtained": 75, ") ; it": 44, ") imply that": 132, ") is actually": 23, ") , together": 70, ") , setting": 15, ") can then": 36, ") in which": 115, ") the state": 12, ") gauge transformations": 11, ") data _CITE_": 12, ") holds for": 258, ") has to": 61, ") that is": 113, ") undergoes a": 41, ") and consequently": 14, ") and substituting": 22, ") Suppose that": 112, ") is negative": 28, ") above ,": 44, ") accounts for": 19, ") comes from": 31, ") and can": 69, ") satisfies _MATHDISP_": 51, ") in terms": 155, ") are used": 102, ") as well": 245, ") , has": 73, ") given by": 66, ") is replaced": 53, ") ) are": 54, ") since the": 50, ") become _MATHDISP_": 56, ") model ,": 81, ") Assume that": 68, ") admits a": 82, ") could be": 100, ") ) _MATHDISP_": 86, ") _MATHDISP_ .": 596, ") and negative": 17, ") we will": 15, ") Show that": 27, ") , was": 49, ") ( i": 25, ") ( iii": 12, ") ; (": 105, ") into account": 24, ") allows us": 65, ") If we": 24, ") , also": 69, ") and equating": 26, ") and Eq": 180, ") leads to": 295, ") as :": 12, ") if the": 110, ") corresponds to": 185, ") found that": 78, ") , will": 30, ") , each": 97, ") where the": 116, ") ) in": 36, ") by applying": 18, ") between _MATH_": 21, ") to model": 24, ") is nonoscillatory": 59, ") is linear": 22, ") coincides with": 57, ") shows the": 505, ") yield the": 26, ") from the": 297, ") have the": 73, ") can not": 198, ") take the": 25, ") give _MATHDISP_": 38, ") amounts to": 25, ") are not": 144, ") of Ref": 37, ") ) ;": 45, ") ; we": 54, ") using the": 207, ") using a": 65, ") under hypotheses": 55, ") then the": 32, ") , all": 83, ") was used": 98, ") hold for": 58, ") is autonomous": 10, ") gives _MATH_": 66, ") as _MATH_": 159, ") is equal": 104, ") algorithm is": 31, ") yields that": 15, ") and obtain": 56, ") with their": 11, ") with its": 15, ") contains the": 20, ") to be": 228, ") with _MATHDISP_": 89, ") and Lemma": 132, ") and thus": 70, ") ( _REF_": 42, ") to make": 26, ") is given": 456, ") is only": 43, ") to (": 210, ") has the": 250, ") equal to": 37, ") and also": 74, ") is similar": 63, ") and is": 142, ") at different": 13, ") is about": 31, ") as an": 59, ") will give": 12, ") presents a": 15, ") model .": 85, ") hold ,": 106, ") must be": 159, ") _MATH_ satisfies": 18, ") systems .": 26, ") have shown": 46, ") algorithm .": 32, ") approach ,": 21, ") being the": 11, ") is ,": 53, ") observed in": 12, ") ( or": 67, ") ) is": 114, ") describe the": 28, ") condition ,": 16, ") is strictly": 14, ") Consider the": 29, ") such as": 30, ") are solved": 26, ") component of": 23, ") , who": 176, ") imply _MATHDISP_": 57, ") , there": 474, ") shows a": 126, ") reduce to": 47, ") method ,": 30, ") are small": 10, ") have been": 313, ") in (": 186, ") , i.e.": 225, ") and Fig": 68, ") This is": 11, ") Finally ,": 15, ") ; _MATH_": 127, ") to a": 139, ") consider the": 16, ") with zero": 14, ") implies _MATHDISP_": 107, ") and with": 74, ") yield _MATHDISP_": 45, ") , if": 266, ") are satisfied": 184, ") ) to": 42, ") the sum": 12, ") _MATH_ :": 55, ") in [": 15, ") was introduced": 26, ") was observed": 26, ") or an": 16, ") allow us": 18, ") are also": 109, ") ) the": 17, ") is much": 42, ") in some": 17, ") provide a": 22, ") along the": 57, ") , because": 86, ") in order": 143, ") is expressed": 31, ") have negative": 23, ") , magnetic": 11, ") under the": 117, ") contains a": 31, ") values of": 32, ") if _MATH_": 371, ") are considered": 52, ") ) for": 33, ") ) which": 18, ") ) can": 22, ") , provides": 14, ") might be": 30, ") by assuming": 10, ") before the": 13, ") so that": 121, ") that are": 112, ") because of": 50, ") is solved": 65, ") of an": 41, ") depict the": 10, ") and an": 109, ") is as": 47, ") in our": 42, ") of these": 18, ") components of": 12, ") by _MATHDISP_": 65, ") by a": 113, ") is represented": 28, ") is extended": 14, ") , some": 40, ") ; the": 215, ") is oscillatory": 179, ") are nonoscillatory": 10, ") have to": 41, ") or its": 18, ") is introduced": 22, ") to evaluate": 28, ") is quite": 41, ") followed by": 17, ") , derived": 11, ") and finally": 20, ") over the": 73, ") have a": 76, ") , define": 33, ") _MATH_ is": 591, ") ] .": 190, ") at _MATH_": 166, ") obtained with": 14, ") in an": 55, ") to each": 31, ") requires that": 35, ") represents the": 112, ") is reduced": 67, ") but the": 25, ") , of": 62, ") and Theorem": 63, ") holds and": 49, ") as the": 253, ") found a": 21, ") If the": 52, ") that ,": 80, ") , Lemma": 26, ") technique to": 10, ") is calculated": 39, ") are the": 262, ") was proposed": 23, ") BRST transformations": 21, ") , into": 14, ") if and": 147, ") in a": 276, ") obtained in": 15, ") is small": 18, ") in this": 96, ") can have": 17, ") in conjunction": 18, ") ( ii": 16, ") pointed out": 32, ") and magnetic": 19, ") has an": 97, ") the effective": 10, ") model of": 29, ") , two": 65, ") ; however": 57, ") in equation": 14, ") to eliminate": 13, ") For the": 60, ") we note": 11, ") has property": 25, ") ; that": 29, ") ' and": 11, ") ' ,": 15, ") is _MATHDISP_": 362, ") , are": 214, ") of _CITE_": 141, ") follows from": 254, ") or _MATH_": 91, ") for some": 58, ") , similarly": 11, ") and for": 122, ") to reduce": 15, ") and 5": 32, ") , gives": 64, ") as in": 46, ") for an": 61, ") may be": 273, ") and time": 15, ") given in": 35, ") is exactly": 28, ") is minimized": 19, ") for these": 22, ") to generate": 28, ") has two": 92, ") _CITE_ that": 16, ") are those": 15, ") ) :": 69, ") were also": 18, ") numerically .": 14, ") to study": 22, ") reduces to": 292, ") is stable": 62, ") is plotted": 18, ") by setting": 23, ") since it": 14, ") investigated the": 24, ") are known": 32, ") _MATH_ contains": 14, ") for every": 52, ") defining the": 11, ") and hence": 59, ") to solve": 31, ") to obtain": 180, ") against the": 13, ") ( i.e.": 23, ") is slightly": 12, ") is one": 62, ") , when": 136, ") . )": 65, ") be a": 63, ") , indicating": 40, ") ) and": 188, ") corresponding to": 119, ") whereas the": 12, ") in Lemma": 66, ") are more": 21, ") , corresponding": 50, ") provided that": 15, ") obtained the": 12, ") studied the": 57, ") depend on": 28, ") are plotted": 26, ") is no": 28, ") and setting": 18, ") _MATH_ are": 41, ") , thus": 93, ") , from": 111, ") we find": 156, ") there is": 99, ") ) with": 34, ") of that": 16, ") used the": 30, ") aboard the": 13, ") are found": 29, ") is :": 15, ") are defined": 61, ") are generated": 14, ") , i.e": 182, ") : _MATH_": 189, ") ( for": 43, ") under a": 17, ") are asymptotically": 10, ") is chaotic": 13, ") models .": 22, ") model and": 11, ") _CITE_ can": 13, ") is applied": 73, ") ( b": 15, ") extended the": 14, ") and assuming": 17, ") note that": 12, ") with a": 333, ") will become": 10, ") satisfying the": 34, ") where _MATH_": 91, ") but also": 43, ") associated with": 78, ") inside the": 16, ") theory .": 12, ") , more": 15, ") of two": 19, ") that in": 20, ") is modified": 21, ") is nothing": 13, ") and Figure": 19, ") and considering": 19, ") or (": 262, ") Fig .": 17, ") are chosen": 16, ") and system": 11, ") was chosen": 13, ") were used": 43, ") is straightforward": 19, ") are written": 13, ") for each": 136, ") , denoted": 35, ") _MATH_ with": 35, ") magnetic field": 40, ") due to": 130, ") techniques ,": 16, ") takes the": 140, ") denote the": 45, ") are clearly": 12, ") and only": 19, ") since _MATH_": 24, ") , making": 23, ") There exist": 89, ") approach _CITE_": 25, ") refers to": 32, ") into a": 72, ") there exist": 39, ") , yielding": 19, ") systems are": 10, ") , imply": 10, ") within a": 17, ") _CITE_ was": 10, ") the same": 25, ") , however": 89, ") , etc": 59, ") at low": 14, ") yields _MATH_": 55, ") to _MATHDISP_": 53, ") shows how": 15, ") Note that": 26, ") implies the": 63, ") , show": 17, ") , on": 69, ") , consistent": 13, ") , even": 50, ") is greater": 14, ") limit ,": 10, ") For all": 34, ") : for": 27, ") , allowing": 14, ") lead to": 49, ") are to": 14, ") while _MATH_": 11, ") by _CITE_": 13, ") and two": 71, ") to find": 46, ") is usually": 30, ") defined on": 22, ") that were": 21, ") need to": 30, ") between two": 19, ") solutions of": 10, ") process with": 23, ") defined by": 26, ") guarantees that": 37, ") and after": 25, ") depends on": 77, ") we deduce": 35, ") holds true": 37, ") is well": 57, ") , no": 30, ") The following": 17, ") has three": 27, ") ; also": 11, ") simultaneously .": 17, ") for two": 31, ") There is": 37, ") by taking": 23, ") we can": 202, ") are related": 27, ") coordinate system": 11, ") , assuming": 24, ") into Eq": 175, ") is valid": 105, ") where a": 19, ") is asymptotically": 216, ") one can": 64, ") then we": 14, ") , to": 195, ") is very": 62, ") even if": 13, ") for which": 68, ") , by": 195, ") using an": 18, ") , its": 64, ") to conclude": 12, ") satisfy _MATHDISP_": 13, ") were not": 13, ") _MATH_ to": 15, ") , among": 51, ") is regular": 19, ") of our": 24, ") is expected": 25, ") algorithm ,": 21, ") is implied": 15, ") we use": 32, ") becomes ,": 13, ") -dimensional supermanifold": 27, ") technique _CITE_": 25, ") the value": 23, ") of Table": 28, ") than those": 14, ") , may": 21, ") introduced in": 13, ") , both": 68, ") , defined": 39, ") over a": 37, ") ensures that": 47, ") was obtained": 21, ") is depicted": 14, ") in Fig": 66, ") ; otherwise": 11, ") that allows": 13, ") as _MATHDISP_": 398, ") the time": 12, ") and dividing": 11, ") near the": 30, ") ; therefore": 32, ") are listed": 12, ") _CITE_ :": 50, ") From (": 11, ") , according": 29, ") and Eqs": 17, ") because they": 10, ") are depicted": 11, ") / (": 14, ") is passive": 18, ") , they": 114, ") hold .": 212, ") from 0": 24, ") is identically": 10, ") and of": 83, ") is discussed": 16, ") at a": 90, ") into _MATHDISP_": 26, ") possesses a": 14, ") is feasible": 18, ") to illustrate": 10, ") can also": 117, ") _MATHDISP_ where": 57, ") is transformed": 41, ") into Equation": 29, ") and Remark": 10, ") and ``": 27, ") is achieved": 30, ") converge to": 18, ") , namely": 104, ") is automatically": 13, ") were first": 12, ") for details": 24, ") in Appendix": 21, ") , implies": 70, ") is _MATH_": 223, ") model is": 40, ") is negligible": 10, ") is to": 116, ") admits the": 14, ") are consistent": 15, ") and _CITE_": 48, ") equation is": 10, ") are much": 14, ") ; thus": 38, ") are referred": 12, ") and references": 29, ") is always": 41, ") observed by": 12, ") is assumed": 48, ") subject to": 42, ") is true": 119, ") _MATH_ has": 67, ") process .": 29, ") and ,": 184, ") which have": 15, ") , implying": 26, ") we present": 14, ") BRST and": 25, ") co-BRST symmetry": 37, ") has one": 16, ") becomes the": 52, ") provided by": 20, ") and any": 11, ") yields a": 50, ") the following": 50, ") holds in": 32, ") are present": 14, ") and compared": 11, ") proposed a": 49, ") that we": 47, ") is smaller": 23, ") follows immediately": 26, ") which has": 40, ") simplifies to": 34, ") is .": 10, ") , being": 28, ") ( see": 230, ") from (": 64, ") plays an": 14, ") indicate that": 41, ") and its": 180, ") , see": 86, ") is needed": 22, ") proposed to": 15, ") : (": 41, ") which represents": 14, ") equations .": 13, ") in its": 22, ") to an": 35, ") exhibits a": 13, ") ( and": 32, ") because it": 23, ") or with": 15, ") is proportional": 34, ") is continuous": 10, ") than _MATH_": 15, ") if there": 59, ") When the": 26, ") which can": 38, ") and define": 20, ") is different": 24, ") is found": 35, ") above .": 28, ") or by": 40, ") , provided": 51, ") or in": 40, ") to _MATH_": 135, ") vanishes ,": 16, ") ) of": 31, ") defines a": 41, ") of this": 67, ") is violated": 20, ") satellite ,": 11, ") is clearly": 14, ") is still": 42, ") we first": 11, ") is either": 12, ") over _MATH_": 74, ") is applicable": 13, ") allow one": 11, ") to have": 20, ") but is": 11, ") , having": 15, ") discussed the": 11, ") process ,": 32, ") ( anti-": 11, ") ghost fields": 27, ") defined in": 14, ") are feasible": 10, ") , suppose": 25, ") , considering": 18, ") has only": 55, ") , given": 71, ") resulting from": 11, ") , ``": 22, ") and on": 46, ") for both": 38, ") above the": 17, ") distribution of": 18, ") follows by": 32, ") to show": 27, ") , shows": 23, ") part of": 37, ") because we": 11, ") and not": 31, ") is solvable": 26, ") are presented": 54, ") showed that": 143, ") ; they": 16, ") and Proposition": 30, ") imply the": 22, ") yields (": 17, ") across the": 19, ") only for": 10, ") and to": 101, ") to Eq": 25, ") and collecting": 18, ") , number": 10, ") , total": 12, ") through by": 11, ") from Eq": 14, ") yields the": 140, ") in Theorem": 105, ") along with": 59, ") at time": 29, ") to fit": 13, ") is called": 154, ") would be": 69, ") is guaranteed": 16, ") if we": 29, ") and we": 91, ") can only": 21, ") in Sect": 11, ") of Definition": 82, ") admits an": 35, ") , guarantees": 10, ") _MATH_ or": 23, ") condition .": 14, ") increases with": 15, ") we write": 14, ") to measure": 12, ") is due": 33, ") appears to": 26, ") is symmetric": 12, ") guarantee that": 19, ") from which": 17, ") in Definition": 17, ") from _MATH_": 89, ") the total": 19, ") via the": 25, ") ] are": 11, ") ] and": 43, ") in _MATH_": 225, ") , _REF_": 43, ") , yields": 47, ") if it": 54, ") close to": 17, ") to hold": 23, ") are of": 39, ") we are": 16, ") is generated": 24, ") black hole": 15, ") this is": 19, ") is realized": 12, ") the system": 22, ") : the": 95, ") is responsible": 15, ") models for": 12, ") and where": 11, ") of (": 38, ") is unstable": 32, ") problem ,": 19, ") is referred": 16, ") by choosing": 19, ") ( the": 25, ") method _CITE_": 52, ") one finds": 32, ") are then": 25, ") has shown": 20, ") has also": 14, ") argue that": 19, ") shows an": 24, ") is approximated": 14, ") ) as": 25, ") developed a": 29, ") is larger": 15, ") and without": 16, ") to prove": 14, ") imply _MATH_": 12, ") and has": 43, ") are ,": 25, ") seems to": 20, ") is associated": 18, ") around the": 31, ") , here": 17, ") is determined": 43, ") or at": 16, ") , our": 71, ") We have": 26, ") On the": 12, ") starting from": 19, ") _MATH_ of": 53, ") to derive": 32, ") in eq": 20, ") is consistent": 35, ") are described": 21, ") _MATH_ can": 22, ") again ,": 13, ") are only": 21, ") is set": 18, ") phase .": 10, ") representation of": 14, ") Suppose _MATH_": 19, ") model with": 18, ") , leads": 32, ") of all": 41, ") are _MATHDISP_": 75, ") with Eq": 25, ") that a": 33, ") matrix _MATH_": 17, ") , very": 14, ") is located": 11, ") is approximately": 17, ") one gets": 18, ") and high": 29, ") that (": 12, ") functions ,": 11, ") [ l": 20, ") or to": 35, ") of Figure": 38, ") concluded that": 23, ") models ,": 20, ") is developed": 12, ") and have": 30, ") can now": 25, ") completes the": 13, ") is essentially": 14, ") , consisting": 11, ") and higher": 14, ") , due": 34, ") and make": 10, ") , especially": 29, ") are determined": 27, ") for further": 16, ") _CITE_ _MATHDISP_": 15, ") _CITE_ proposed": 11, ") for our": 18, ") the model": 16, ") is often": 18, ") gauge group": 11, ") than for": 18, ") are compared": 21, ") examined the": 11, ") and subsequently": 11, ") , assume": 28, ") onboard SOHO": 13, ") are all": 33, ") or on": 12, ") are taken": 29, ") is highly": 14, ") of about": 11, ") is bounded": 70, ") based on": 151, ") relies on": 12, ") to provide": 30, ") model for": 20, ") ; hence": 26, ") which are": 74, ") is characterized": 20, ") ) that": 37, ") have no": 13, ") , under": 43, ") at some": 10, ") are applied": 17, ") in that": 13, ") solution to": 10, ") , were": 29, ") is finite": 42, ") that satisfies": 11, ") we need": 21, ") ; a": 15, ") as it": 18, ") fails to": 16, ") are close": 11, ") and 6": 12, ") includes the": 18, ") described in": 17, ") the magnetic": 13, ") in general": 11, ") , similar": 20, ") is described": 43, ") and definition": 17, ") , meaning": 16, ") differs from": 22, ") are based": 19, ") studied a": 11, ") assumes the": 20, ") implies (": 64, ") is denoted": 24, ") functions _MATH_": 13, ") that have": 12, ") , Figure": 10, ") ; then": 51, ") with parameters": 25, ") to this": 11, ") as described": 13, ") The matrix": 12, ") gives rise": 22, ") becomes :": 21, ") and may": 17, ") represent the": 40, ") , Li": 11, ") Using the": 10, ") needed to": 11, ") and some": 20, ") If there": 23, ") system ,": 28, ") about _MATH_": 10, ") , written": 10, ") , Equation": 18, ") in Equation": 24, ") compared with": 15, ") and Assumption": 12, ") illustrate the": 10, ") makes the": 15, ") , providing": 15, ") and take": 17, ") there are": 50, ") systems ,": 18, ") , e.g.": 14, ") , following": 17, ") in case": 14, ") we show": 36, ") arising from": 11, ") to compute": 57, ") ( in": 28, ") is unique": 27, ") is mean-square": 13, ") structure .": 18, ") , inequality": 11, ") requires the": 20, ") and write": 12, ") ( cf": 27, ") converges to": 52, ") is another": 12, ") give the": 35, ") , at": 78, ") are constant": 11, ") because _MATH_": 14, ") while the": 50, ") arises from": 12, ") , e.g": 20, ") was first": 24, ") are expressed": 12, ") respectively ,": 11, ") associated to": 24, ") , results": 11, ") algorithm _CITE_": 52, ") , taking": 36, ") demonstrated that": 21, ") , starting": 18, ") Let us": 37, ") case ,": 18, ") we observe": 20, ") and if": 21, ") are called": 20, ") is completely": 24, ") below )": 22, ") have studied": 15, ") be _MATH_": 12, ") is thus": 26, ") is in": 98, ") seem to": 21, ") need not": 10, ") the condition": 10, ") : we": 11, ") , hence": 37, ") below .": 39, ") There exists": 90, ") analyzed the": 17, ") are an": 10, ") gives us": 30, ") one has": 37, ") ) by": 18, ") assumes that": 18, ") is possible": 10, ") and one": 59, ") _MATHDISP_ ;": 13, ") those with": 12, ") ; 2": 10, ") ; 3": 10, ") instrument _CITE_": 12, ") : if": 21, ") , ii": 12, ") will not": 34, ") are available": 13, ") or not": 27, ") , Fig": 17, ") , called": 18, ") with different": 24, ") , say": 11, ") , containing": 10, ") into _MATH_": 31, ") blows up": 15, ") one obtains": 48, ") present a": 10, ") and performing": 14, ") also holds": 19, ") still holds": 27, ") are negative": 10, ") was also": 17, ") with output": 11, ") follows directly": 15, ") stands for": 21, ") turns out": 16, ") and suppose": 25, ") is known": 45, ") induced by": 19, ") then _MATH_": 33, ") was found": 23, ") and such": 20, ") to improve": 15, ") to compare": 16, ") , he": 13, ") in Proposition": 28, ") we consider": 18, ") the set": 20, ") and even": 14, ") into Eqs": 31, ") in Figure": 56, ") are introduced": 14, ") simulations .": 11, ") needs to": 31, ") that when": 14, ") the first": 31, ") problem .": 24, ") in Eq": 35, ") presents the": 19, ") For a": 12, ") is converted": 12, ") are respectively": 11, ") , have": 52, ") did not": 19, ") system _CITE_": 13, ") that for": 73, ") and noting": 18, ") black holes": 11, ") that all": 12, ") and calculate": 10, ") , integrating": 10, ") Since _MATH_": 36, ") vector of": 16, ") ( _MATH_": 86, ") , must": 10, ") For any": 76, ") at any": 10, ") below ,": 16, ") ensure that": 21, ") now follows": 14, ") in one": 15, ") and this": 37, ") is necessary": 30, ") process is": 20, ") processes ,": 15, ") are fulfilled": 27, ") define the": 27, ") the number": 55, ") , _CITE_": 72, ") embedded in": 13, ") and will": 20, ") ( Fig": 29, ") satisfy the": 31, ") is available": 16, ") with that": 10, ") the main": 12, ") methods .": 13, ") is finite-time": 13, ") used a": 18, ") equals _MATH_": 20, ") Consider a": 11, ") be the": 74, ") for this": 50, ") , Theorem": 34, ") we take": 17, ") are true": 10, ") proposed in": 17, ") requires a": 13, ") equation .": 18, ") field .": 18, ") field ,": 10, ") defined as": 21, ") along _MATH_": 10, ") on a": 73, ") to use": 11, ") First ,": 18, ") , about": 11, ") which ,": 17, ") and multiplying": 12, ") in all": 21, ") In the": 67, ") and show": 19, ") expresses the": 14, ") and temporal": 11, ") and found": 13, ") when a": 11, ") evaluated at": 17, ") parameter _MATH_": 15, ") and find": 14, ") obtained by": 34, ") used to": 14, ") , thereby": 16, ") into an": 22, ") - the": 11, ") and large": 12, ") the distribution": 11, ") give a": 11, ") , system": 31, ") , without": 40, ") if _MATHDISP_": 34, ") _CITE_ in": 23, ") follows the": 15, ") that it": 17, ") is invariant": 36, ") through (": 25, ") are :": 15, ") by introducing": 16, ") represents a": 52, ") and no": 15, ") is performed": 38, ") is specified": 11, ") may have": 14, ") or as": 14, ") data .": 32, ") was solved": 10, ") as shown": 37, ") is compared": 13, ") tells us": 18, ") determine the": 18, ") is zero": 41, ") means that": 91, ") with constant": 19, ") , obtained": 24, ") we compare": 10, ") to take": 13, ") is simply": 18, ") states that": 54, ") level of": 11, ") holds if": 46, ") allows one": 20, ") uses the": 17, ") tend to": 38, ") reveals that": 37, ") Under the": 20, ") w.r.t .": 13, ") _MATH_ converges": 11, ") present the": 10, ") contain the": 10, ") are evaluated": 12, ") are _MATH_": 38, ") hold and": 26, ") only .": 10, ") into Equations": 14, ") in time": 15, ") consists in": 11, ") _CITE_ ;": 22, ") is trivial": 10, ") : Consider": 15, ") of Proposition": 70, ") What is": 14, ") , after": 65, ") images .": 16, ") assuming that": 11, ") and Equation": 20, ") has become": 11, ") at which": 12, ") ( which": 25, ") ; each": 10, ") can lead": 11, ") is verified": 35, ") the second": 11, ") is locally": 28, ") are associated": 13, ") turns into": 19, ") it can": 30, ") also implies": 11, ") and showed": 10, ") and assume": 27, ") of class": 10, ") and 4": 30, ") are derived": 24, ") function _MATH_": 26, ") are two": 15, ") , including": 46, ") and their": 84, ") from one": 12, ") is designed": 17, ") set of": 39, ") and small": 14, ") are usually": 10, ") are invariant": 10, ") , time": 12, ") model has": 10, ") proposed the": 22, ") to estimate": 39, ") , only": 54, ") propose a": 13, ") instrument on": 11, ") are widely": 10, ") waves .": 10, ") since we": 10, ") vanishes in": 16, ") the function": 18, ") described by": 17, ") The system": 11, ") and 8": 14, ") and more": 15, ") We can": 12, ") , along": 40, ") and solving": 26, ") and Definition": 11, ") is required": 29, ") should also": 10, ") has infinitely": 11, ") is at": 30, ") _CITE_ with": 11, ") presented a": 26, ") presented in": 17, ") within the": 50, ") is less": 37, ") was considered": 18, ") shown in": 22, ") and rearranging": 16, ") near _MATH_": 10, ") scheme ,": 10, ") , followed": 34, ") to all": 10, ") until the": 21, ") When _MATH_": 53, ") ( _CITE_": 21, ") is divided": 20, ") hold true": 14, ") related to": 14, ") that was": 20, ") which satisfies": 15, ") or a": 73, ") are within": 10, ") _MATH_ at": 17, ") are computed": 29, ") , four": 14, ") ( 1": 13, ") _CITE_ or": 46, ") appear in": 13, ") method for": 16, ") and at": 49, ") was developed": 12, ") system .": 34, ") are included": 21, ") and those": 23, ") , any": 23, ") are quite": 10, ") from a": 45, ") ; these": 15, ") in each": 28, ") admits at": 18, ") Set _MATH_": 13, ") are needed": 13, ") we arrive": 11, ") through a": 14, ") and 7": 10, ") and when": 13, ") relative to": 27, ") , Proposition": 13, ") : a": 29, ") have found": 17, ") _CITE_ to": 38, ") region .": 12, ") suggested that": 33, ") is computed": 34, ") is obviously": 10, ") ; in": 67, ") are mutually": 11, ") , ,": 16, ") images ,": 11, ") model to": 13, ") . We": 17, ") but not": 22, ") used in": 33, ") is now": 34, ") gives that": 13, ") we know": 40, ") is quadratically": 15, ") behaves as": 12, ") for large": 12, ") We first": 10, ") coordinates .": 12, ") determines the": 23, ") without any": 12, ") to give": 21, ") is optimal": 11, ") and these": 10, ") we assume": 14, ") are provided": 10, ") will have": 28, ") _MATH_ if": 32, ") derived from": 15, ") they are": 29, ") or for": 14, ") , during": 12, ") involves the": 19, ") , subject": 20, ") on each": 11, ") of different": 12, ") with probability": 11, ") is widely": 14, ") having a": 14, ") are bounded": 24, ") is independent": 36, ") coincide with": 13, ") and set": 23, ") produces the": 11, ") , applying": 11, ") is identical": 15, ") Find the": 16, ") _MATH_ does": 12, ") derived the": 11, ") defines the": 25, ") , resulting": 45, ") , those": 12, ") ( with": 47, ") and data": 12, ") _MATHDISP_ with": 18, ") For each": 54, ") _MATH_ _MATH_": 30, ") at each": 32, ") are often": 12, ") proposed by": 23, ") shows two": 10, ") theory ,": 11, ") used for": 12, ") can achieve": 10, ") about the": 24, ") that this": 26, ") ) we": 14, ") plus the": 13, ") has _MATH_": 24, ") and another": 15, ") versus the": 18, ") , does": 15, ") or only": 10, ") algorithm to": 13, ") equals _MATHDISP_": 16, ") which were": 10, ") into two": 20, ") is chosen": 29, ") suggested a": 10, ") , many": 15, ") were observed": 10, ") out of": 14, ") indicate the": 10, ") to see": 13, ") than that": 22, ") converges absolutely": 10, ") is formed": 11, ") plots the": 11, ") to achieve": 17, ") gauge theories": 14, ") onboard Hinode": 11, ") are identical": 17, ") is present": 15, ") , instead": 24, ") provides an": 21, ") is attained": 13, ") is taken": 39, ") , through": 12, ") serves as": 13, ") value of": 28, ") solution of": 23, ") respectively .": 21, ") only depends": 10, ") and our": 17, ") on board": 30, ") with some": 14, ") Proposition :": 20, ") was not": 15, ") is added": 15, ") of its": 15, ") form a": 33, ") it was": 17, ") BRST invariance": 13, ") BRST invariant": 16, ") models _CITE_": 10, ") has not": 19, ") , depending": 27, ") is adopted": 12, ") ; but": 13, ") and SU": 14, ") and second": 13, ") is indeed": 20, ") to determine": 45, ") gives an": 21, ") will also": 12, ") to calculate": 35, ") was the": 19, ") and 3": 22, ") without the": 22, ") be an": 11, ") are at": 10, ") implies a": 17, ") compared to": 55, ") is studied": 11, ") stability of": 13, ") that corresponds": 10, ") ( a": 20, ") ( respectively": 12, ") considered the": 28, ") and taking": 62, ") satisfying _MATHDISP_": 17, ") located in": 10, ") the corresponding": 15, ") can easily": 12, ") as functions": 10, ") following the": 17, ") ; moreover": 13, ") , different": 13, ") asymptotically stabilizing": 11, ") are equal": 29, ") is termed": 12, ") and all": 24, ") in addition": 12, ") were obtained": 32, ") is more": 63, ") are estimated": 12, ") Assume _MATH_": 15, ") appear to": 10, ") is significantly": 13, ") by means": 40, ") is large": 12, ") For every": 39, ") are very": 30, ") we also": 21, ") is generally": 15, ") and unstable": 10, ") set _MATH_": 14, ") : it": 12, ") The proof": 12, ") and other": 24, ") only the": 12, ") by replacing": 15, ") , several": 13, ") makes it": 13, ") is easily": 14, ") be satisfied": 19, ") and others": 16, ") method is": 31, ") after the": 27, ") , should": 10, ") are exactly": 12, ") holds as": 21, ") or from": 22, ") into equation": 16, ") depends only": 10, ") and apply": 11, ") are required": 13, ") with each": 13, ") and derive": 10, ") case .": 14, ") then becomes": 17, ") _CITE_ (": 22, ") random variables": 19, ") is included": 14, ") all the": 21, ") are a": 35, ") generates a": 10, ") , adding": 13, ") for one": 11, ") and eq": 13, ") are displayed": 13, ") to produce": 15, ") the expression": 12, ") , 2": 17, ") in _REF_": 12, ") show a": 22, ") equation _CITE_": 13, ") equation ,": 15, ") the _MATH_": 38, ") are calculated": 30, ") , consider": 28, ") possesses the": 13, ") _MATHDISP_ is": 15, ") _CITE_ which": 13, ") lies in": 10, ") were introduced": 14, ") are replaced": 18, ") that has": 14, ") framework ,": 10, ") and integrating": 32, ") eigenvalues of": 10, ") have at": 12, ") than in": 19, ") version of": 19, ") and so": 32, ") vanishes .": 19, ") ; if": 16, ") displays the": 18, ") , introduced": 12, ") to its": 19, ") outside the": 10, ") we must": 10, ") is sufficient": 16, ") would lead": 10, ") , not": 28, ") in powers": 10, ") _MATHDISP_ for": 16, ") in such": 23, ") waves in": 10, ") and neglecting": 10, ") is constructed": 16, ") is displayed": 10, ") , first": 26, ") at least": 16, ") describes a": 27, ") passing through": 10, ") includes a": 10, ") where we": 10, ") from those": 10, ") in Ref": 17, ") , again": 13, ") is correct": 11, ") are positive": 20, ") we compute": 13, ") is almost": 17, ") , low": 14, ") and four": 10, ") in Table": 22, ") from _CITE_": 19, ") by (": 25, ") in both": 18, ") says that": 28, ") and letting": 10, ") are assumed": 29, ") is relatively": 13, ") with time": 11, ") is employed": 20, ") using _MATH_": 19, ") the existence": 13, ") equipped with": 10, ") where _MATHDISP_": 10, ") gives (": 11, ") to identify": 11, ") ( where": 13, ") should not": 13, ") in Corollary": 16, ") follow from": 25, ") , three": 14, ") allows the": 14, ") , up": 17, ") with increasing": 10, ") are valid": 22, ") values for": 15, ") are as": 22, ") by an": 24, ") clearly shows": 13, ") in any": 11, ") and they": 23, ") to satisfy": 10, ") and simplifying": 23, ") are well": 18, ") ; 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": that the": 17, ": we are": 16, ": _MATHDISP_ Notice": 31, ": `` It": 13, ": _MATHDISP_ that": 22, ": in Section": 45, ": _MATHDISP_ Thus": 24, ": _MATHDISP_ in": 47, ": in order": 16, ": at the": 23, ": _MATH_ _CITE_": 23, ": in fact": 23, ": _MATH_ has": 20, ": Section _REF_": 36, ": e.g. ,": 16, ": _MATHDISP_ Hence": 26, ": there exists": 28, ": firstly ,": 27, ": Consider a": 37, ": _MATHDISP_ Note": 35, ": _MATH_ implies": 12, ": when _MATH_": 27, ": _URL_ .": 14, ": the total": 20, ": 1 .": 14, ": _MATHDISP_ Therefore": 12, ": the use": 11, ": _MATHDISP_ then": 28, ": as the": 10, ": Let _MATH_": 35, ": the set": 18, ": if it": 14, ": _MATH_ which": 12, ": _MATHDISP_ One": 13, ": _MATH_ can": 20, ": for every": 27, ": _MATH_ in": 38, ": _MATH_ are": 14, ": given _MATH_": 18, ": the higher": 19, ": F system": 15, ": the initial": 12, ": _MATH_ '": 29, ": if one": 10, ": the original": 10, ": Find _MATH_": 12, ": Is it": 11, ": as a": 11, ": one can": 18, ": _MATHDISP_ if": 11, ": Using the": 18, ": ( A": 14, ": Consider an": 10, ": from the": 20, ": one of": 15, ": _MATHDISP_ from": 14, ": _MATH_ km": 11, ": _MATH_ denotes": 15, ": one in": 10, ": there are": 34, ": one for": 27, ": _MATHDISP_ so": 16, ": _MATH_ be": 16, ": ( )": 15, ": either a": 10, ": according to": 10, ": Fix _MATH_": 10, ": a ``": 12, ": Based on": 14, ": Er :": 41, ": MgO (": 30, ": either _MATH_": 11, ": they can": 12, ": _MATHDISP_ Moreover": 18, ": since the": 11, ": Sapphire laser": 12, ": _MATHDISP_ Finally": 11, ": _MATHDISP_ Equation": 11, ": indeed ,": 30, ": `` In": 13, ": Find a": 18, ": all the": 17, ": _MATHDISP_ Similarly": 13, ": the position": 11, ": the process": 12, ": see _CITE_": 12, ": for a": 33, ": the problem": 10, ": in section": 13, ": _MATH_ such": 10, ": first we": 11, ": we first": 14, ": _MATH_ as": 20, ": Notice that": 12, ": _MATHDISP_ Applying": 12, ": _MATHDISP_ the": 13, ": _CITE_ ,": 46, ": It is": 13, ": one to": 10, ": `` I": 10, ": _MATHDISP_ we": 10, ": set of": 16, ": it would": 11, ": even if": 10, ": the one": 13, ": how to": 15, ": _MATH_ there": 10, ": we assume": 12, ": _MATH_ from": 12, ": _MATHDISP_ as": 13, ": `` ...": 12, ": in a": 15, ": given the": 10, ": G system": 16, ": _MATHDISP_ Figure": 10, ": in _CITE_": 10, ": YVO_MATH_ laser": 10, ": _MATH_ -": 11, ": while the": 17, ": IF _MATH_": 11, ": it can": 14, ": _MATHDISP_ has": 11, ": suppose that": 10, ": _MATH_ at": 10, ": in our": 11, ": production of": 12}, "F": {"Finally , by": 106, "For example ,": 5437, "Fig . _REF_": 17754, "For a discussion": 21, "Figure _REF_ for": 232, "Fan et al": 23, "From Fig .": 261, "Furthermore , since": 127, "Figs . _REF_": 892, "Fig . _REF_.a": 31, "Fig . _REF_.b": 30, "For _MATH_ ,": 3030, "For this ,": 326, "First , notice": 19, "Following the approach": 17, "From the theoretical": 11, "For convenience of": 19, "Figure _REF_ summarizes": 27, "Figure _REF_ ,": 1664, "First , it": 167, "From _REF_ we": 42, "Finally , after": 15, 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"Figure 7 .": 28, "Figure 4 )": 50, "Figure 4 ,": 43, "Finally , and": 10, "Finally , _CITE_": 29, "Figs . _MATH_": 11, "Fundamental Theorem of": 19, "For more details": 158, "For practical reasons": 14, "From the previous": 51, "Figure 2 of": 19, "For simplicity we": 55, "From Proposition _REF_": 70, "For the continued": 36, "For that reason": 43, "Formally , we": 46, "Fatou 's lemma": 54, "For the second": 155, "Figure 4 .": 64, "Figures 5 (": 15, "From the numerical": 15, "For any function": 25, "Figure 8 (": 15, "For a general": 66, "Fig . _REF_c": 139, "For the two": 58, "For the former": 20, "Further , assume": 18, "Further , this": 18, "Figures _REF_c and": 19, "Further note that": 12, "For a partition": 14, "For that ,": 56, "Furthermore , our": 41, "For any nonnegative": 11, "For each vertex": 37, "For the special": 50, "For more information": 44, "Finally , if": 103, "Fix _MATH_ .": 110, "For the time": 36, "Fig . 2a": 30, "Fig . 2b": 19, "Figure _REF_ provides": 25, "Fourier 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.": 59, "Firstly , it": 46, "Fourth , we": 11, "Figure _REF_d ,": 10, "For even _MATH_": 10, "Focusing on the": 21, "Fe i _MATH_": 22, "FARIMA ( _MATH_": 42, "Finally , (": 27, "Figure 2 ,": 81, "From the results": 58, "Following the standard": 17, "For these cases": 13, "From this equation": 25, "Figures 3 and": 34, "Figs . 7": 13, "Fresnel transmission ratio": 14, "Figure _REF_ compares": 74, "Further details on": 20, "First , this": 14, "First we prove": 22, "Figure _REF_ clearly": 20, "From the second": 25, "For the initial": 39, "Fig . _REF_d": 67, "For the nonlinear": 15, "First we introduce": 10, "Find _MATH_ ,": 11, "From Equation (": 44, "Following _CITE_ and": 15, "For _MATH_ is": 13, "From the experimental": 24, "For each pixel": 29, "Furthermore , due": 25, "For the proof": 75, "Fourier series with": 14, "For all other": 20, "From the simulation": 18, "For the moment": 32, "For the data": 20, "For the evaluation": 13, "From Theorem _REF_": 137, "For _MATH_ this": 26, 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(": 28, "For _MATH_ there": 20, "For an _MATH_": 15, "For the next": 21, "Fourier coefficients _MATH_": 23, "Friedmann-Robertson-Walker ( FRW": 38, "FRW universe ,": 10, "First let _MATH_": 12, "Fourier transform can": 11, "For each such": 15, "Figure _REF_a ,": 38, "Figure _REF_b ,": 36, "For the last": 51, "For notational convenience": 35, "Furthermore , define": 12, "Figure _REF_ suggests": 11, "From the properties": 16, "Fig . 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each": 27, "First , define": 13, "F.1 ) ,": 10, "Figure _REF_ to": 30, "Frechet differentiable ,": 13, "Figure 6 shows": 38, "First , to": 16, "Further , _MATH_": 85, "From the viewpoint": 30, "For the reader": 24, "Fourier transform on": 11, "Finally , since": 69, "From ( 3.2": 11, "Finally , conclusions": 32, "Finally , with": 22, "Finally , this": 38, "Finally we have": 11, "Friedmann equation (": 18, "For a node": 11, "For the definition": 11, "For the matrix": 11, "From the hypothesis": 13, "For values of": 21, "Furthermore , under": 13, "Figure _REF_d )": 45, "For each fixed": 46, "Follows from Item": 44, "Figure _REF_ confirms": 11, "Figs . 2": 51, "FWHM of the": 40, "For such _MATH_": 13, "For a finite": 28, "For _MATH_ GeV": 12, "Figure 4 shows": 59, "For illustration purposes": 10, "For such an": 10, "From left to": 10, "For this problem": 21, "For an example": 23, "From this theorem": 10, "FOV ) of": 14, "For the values": 10, "For simplicity of": 40, "From the expression": 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"Fourier series ,": 19, "For this value": 13, "For systems with": 14, "For example the": 18, "For more detailed": 12, "From these results": 30, "Figure _REF_ corresponds": 16, "From another point": 10, "For both cases": 19, "Fourier coefficients .": 21, "For the function": 18, "First , when": 14, "From Lemmas _REF_": 12, "For many years": 12, "Formally , this": 13, "For _MATH_ or": 19, "For a simple": 25, "Figure _REF_d .": 16, "FRW ) metric": 15, "For given _MATH_": 53, "For the proposed": 16, "For _MATH_ :": 18, "Fang et al": 12, "For all the": 62, "For illustrative purposes": 13, "First assume that": 19, "Figure _REF_ ]": 12, "Feigin-Stoyanovsky 's type": 12, "Furthermore , even": 12, "First we assume": 13, "Figure 6 ,": 32, "For a generic": 21, "For the charged": 12, "Fourier transformation of": 16, "Finally , Sect": 33, "For almost all": 11, "From the given": 14, "For further discussion": 10, "For a large": 34, "Fourier transform in": 23, "First and foremost": 11, "From Equations 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"Fig . _MATH_": 16, "Finally , each": 16, "For instance in": 13, "First , they": 28, "Figures _REF_ to": 31, "For each integer": 11, "For illustration ,": 34, "Firstly , there": 10, "Fermi level ,": 15, "For _REF_ ,": 10, "For any point": 18, "Fe i 525.02": 13, "For larger _MATH_": 12, "Fourier domain .": 13, "For the example": 34, "For an edge": 10, "Figure 7 ,": 29, "From the comparison": 21, "Figure _REF_ on": 13, "First we show": 34, "Figure 10 (": 22, "Fermi level .": 24, "For _MATH_ odd": 13, "For calculating the": 12, "Fast Fourier Transform": 24, "From the general": 12, "For a subset": 18, "Furthermore , at": 10, "FIL random oracle": 11, "First let us": 21, "Feynman diagrams in": 10, "From Lemma 1": 16, "Following the ideas": 11, "For more than": 12, "From the linear": 12, "For the larger": 12, "Figure _REF_ a": 21, "Figure _REF_ below": 15, "For sake of": 19, "For consistency ,": 13, "Figures _REF_ -": 43, "Fourier transforms .": 16, "Furthermore , based": 12, "Figure _REF_c 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"Fig . 3b": 15, "From Section _REF_": 11, "Feynman diagrams are": 12, "For every fixed": 13, "For that we": 15, "For the stochastic": 11, "From the continuity": 10, "Fig . _REF__MATH_": 35, "Fu et al": 10, "From equation (": 45, "Further , using": 14, "Fourier coefficients are": 18, "Fig._REF_ and Fig._REF_": 12, "For this work": 12, "For the situation": 11, "Formally , let": 15, "For the input": 11, "For the process": 12, "Figure 9 ,": 14, "For a specific": 23, "For a further": 12, "Figure 12 shows": 11, "From this one": 12, "Fortunately , in": 10, "For our model": 12, "For simplicity in": 12, "For an illustration": 13, "For any finite": 12, "Finally , assume": 11, "For each time": 16, "Figure _REF_ right": 11, "For the solution": 27, "Fig._REF_ ( a": 19, "Figs . _REF_b": 15, "Fig . _REF_D": 10, "Finally , they": 21, "Figure 9 (": 12, "From this result": 20, "For this type": 15, "From Theorem 1": 14, "For a real": 18, "Figure 9 )": 17, "For a quantitative": 10, "Formally , 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.": 30, "Lyapunov functional candidate": 18, "LMIs : _MATHDISP_": 13, "Laplacian of a": 10, "Lemma _REF_ will": 14, "Lebesgue measure .": 47, "LE and EP": 13, "LEs and EPs": 12, "Linear Collider (": 18, "Laplace transform _MATHDISP_": 10, "Lyapunov exponents are": 22, "LS estimate of": 11, "Lemma _REF_ gives": 36, "Lorenz canonical form": 10, "Let _MATH_ represent": 54, "Lie subgroup of": 13, "Lipschitz in _MATH_": 25, "Let also _MATH_": 23, "Let us give": 41, "Lipschitz constant of": 26, "Lemma _REF_ hold": 19, "Lemma , we": 20, "Lemma _REF_ follows": 12, "Last , we": 12, "Lagrange multiplier method": 17, "Lorentz -force changes": 23, "Lyapunov functions .": 18, "LN : Fe": 14, "Let ( _MATH_": 11, "LMI ( _REF_": 53, "Lemma 3.2 .": 21, "Liu et al.": 14, "Let us compute": 23, "Laplacian spectrum of": 17, "Let us state": 12, "Lagrangian is _MATHDISP_": 15, "Lemma 3 ,": 31, "Lyapunov functionals .": 12, "Lagrangian function _MATH_": 12, "Laplace transforms of": 26, "Let us observe": 39, 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spectroscopy .": 11, "Remark that _MATH_": 18, "Recall Example _REF_": 14, "Remark 5 .": 17, "Ref . 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Liljeback ,": 14, "Problem ( _REF_": 119, "Poisson random measure": 21, "Proposition _REF_ implies": 51, "Proposition _REF_ _MATH_": 12, "Proof : First": 22, "Poisson process _MATH_": 22, "Proof : _MATH_": 27, "Practical Dynamic Cone": 11, "Proposition _REF_ for": 24, "Proof of the": 15, "Parisian knock-in call": 10, "Poisson processes ,": 19, "Previous studies have": 18, "Pauli matrices .": 15, "Poisson point process": 34, "Particle Data Group": 15, "Pecora and Carroll": 18, "P2P streaming applications": 23, "P2P streaming systems": 22, "Poisson equation ,": 12, "Perhaps the most": 32, "Poisson 's ratio": 34, "Particularly , the": 33, "Passing to the": 38, "PPLive and PPStream": 13, "Proposition _REF_ gives": 21, "Proof Let _MATH_": 15, "Prior to the": 28, "Poincare inequality ,": 12, "Planck mass .": 17, "Poisson processes with": 19, "Poincare group ,": 12, "Paper I )": 52, "Problem _REF_ .": 36, "Poisson distribution with": 21, "Poisson process and": 19, "Pedersen et al": 10, "Parikh and Wilczek": 14, "Planck constant _MATH_": 12, "Petri net model": 20, "Proposition 1 ,": 19, "Piovan et al": 20, "PCA ) _CITE_": 15, "Pontryagin 's maximum": 11, "Proposition 2 .": 22, "Provided that the": 19, "Proof The proof": 11, "Proof : Using": 12, "PS and APS": 15, "Poincare group .": 11, "Park black hole": 15, "Poisson process of": 17, "PEM fuel cells": 10, "Plugging _MATH_ into": 12, "P.L . Kapitsa": 29, "Positioning System (": 10, "Player _MATH_ ,": 15, "Planck scale ,": 25, "Pach and Toth": 10, "Planck mass ,": 18, "Probably the most": 10, "Proposition _REF_ applies": 11, "Poisson 's equation": 11, "Poisson impulses .": 13, "PDF of the": 32, "Poisson processes .": 19, "Part 1 .": 14, "Part ( ii": 10, "PID controllers .": 11, "PID controller (": 15, "PID controller ,": 21, "PID controller .": 33, "Processing Container .": 11, "Proposition _REF_ of": 11, "Part I )": 12, "Proposition _REF_ as": 16, "PPT w.r.t .": 21, "PDEs ( _REF_": 11, "PWS of Eq": 10, "Proof Note that": 10, "Prove that if": 12, "Poisson distribution .": 12, "Proposition 2 ,": 13, "PSO algorithms .": 10, "Proposition _REF_ :": 15, "Pop III stars": 25, "Proceeding in this": 11, "Problem _MATH_ can": 11, "Planck constant .": 10, "Parkinson 's disease": 11, "P ) ,": 15, "Proposition _REF_ ;": 13, "PID control .": 10, "Platonov and Fleishman": 11, "Problem _REF_ ,": 35, "Property _REF_ ,": 31, "PI and PID": 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"quantity in the": 20, "quite well the": 14, "query _MATH_ to": 11, "quality , the": 18, "quadratic APN function": 12, "quite complicated .": 10, "quite a lot": 11, "quantities , _MATH_": 13, "quarks and leptons": 46, "questions related to": 16, "quantity _MATH_ denotes": 10, "quite small .": 20, "quantities related to": 11, "quantum dots on": 10, "questions to be": 19, "quantum numbers as": 15, "quadratic Lyapunov functions": 27, "quantum gravity ,": 15, "quantum number .": 13, "quite similar .": 21, "queue length of": 10, "quarks , respectively": 12, "quark propagator in": 12, "quark and a": 10, "quantities , the": 17, "quarks can be": 10, "quite interesting to": 10, "quantization of a": 11, "queue length and": 12, "question in this": 12, "quark model (": 10, "question arises whether": 17, "quality and the": 16, "quadrant of the": 21, "queueing systems with": 13, "quadratic form _MATHDISP_": 15, "question arises :": 10, "quality of these": 10, "queue length is": 19, "quantum number 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Let _MATH_": 97, ". _REF_ .": 6431, ". _REF_ ,": 5028, ". _REF_ (": 2713, ". _CITE_ .": 1807, ". ) are": 47, ". _CITE_ showed": 43, ". if _MATH_": 31, ". _REF_ )": 3470, ". _CITE_ and": 489, ". ( _REF_": 12093, ". on _MATH_": 80, ". _CITE_ developed": 44, ". Fig .": 208, ". ( 2004": 197, ". ( 2007": 225, ". ( 1999": 114, ". ( 2010": 157, ". ( 2006": 218, ". _REF_ we": 456, ". random variables": 112, ". _CITE_ ,": 1475, ". 6 (": 43, ". ( 1997": 74, ". 2 and": 53, ". 4 ,": 168, ". 5 ,": 105, ". _MATH_ ,": 498, ". Section _REF_": 209, ". _REF_ with": 178, ". , if": 43, ". _CITE_ established": 11, ". ( 12": 32, ". _REF_ and": 1551, "... , _MATH_": 377, ". 2 (": 140, ". 1 )": 119, ". _CITE_ )": 1178, ". ( 2000": 107, ". ( 2003": 169, ". _REF_ for": 482, ". Definition _REF_": 43, ". _REF_ is": 530, ". , from": 14, ". _MATH_ )": 662, ". ) ,": 203, ". , the": 489, ". _CITE_ ;": 149, ". _REF_b )": 139, ". 1 ,": 146, ". , _MATHDISP_": 177, ". ( 2002": 132, ". 1 (": 127, ". _CITE_ also": 55, ". _MATH_ has": 12, ". _MATHDISP_ ,": 119, ". ( 2008": 172, ". _CITE_ reported": 13, ". Hence ,": 87, ". 6 ,": 64, ". 8 .": 37, ". _MATHDISP_ .": 226, ". _REF_ shows": 541, ". Appendix _REF_": 15, ". _REF_ that": 187, ". _REF_ the": 215, ". It is": 60, ". _MATH_ and": 207, ". _MATH_ ;": 16, ". _REF_ gives": 41, ". _REF_ by": 95, ". to the": 25, ". _REF_ in": 126, ". _REF_ are": 214, ". Note that": 138, ". _MATH_ is": 219, ". when the": 35, ". _MATH_ .": 522, ". ( 19": 23, ". _CITE_ or": 31, ". In Section": 22, ". ( 10": 47, ". _CITE_ analyzed": 16, ". _CITE_ investigated": 57, ". _CITE_ used": 99, ". 5 (": 81, ". in _CITE_": 140, ". _CITE_ proposed": 251, ". it is": 45, ". _CITE_ have": 179, ". _REF_ illustrates": 64, ". _CITE_ use": 45, ". 2001 )": 25, ". 1 .": 208, ". studied the": 23, ". _REF_-_REF_ ,": 44, ". _CITE_ where": 25, ". 4 .": 159, ". ( a": 75, ". _REF_C )": 20, ". , _MATH_": 622, ". Equation _REF_": 11, ". ( 11": 44, ". _REF_ at": 28, ". 3 ,": 188, ". , their": 11, ". _CITE_ provided": 18, ". _REF_ where": 59, ". 2008 ;": 12, ". 2010 )": 26, ". , (": 10, ". 2003 )": 31, ". _CITE_ the": 56, ". We have": 31, ". ( 1998": 78, ". _CITE_ which": 19, ". _CITE_ can": 13, ". ( 2012": 73, ". 5 .": 115, ". If _MATH_": 40, ". 's .": 12, ". _REF_ _CITE_": 47, ". _REF_a and": 31, ". Eq .": 73, ". _REF_ which": 31, ". _REF_ on": 32, ". 7 .": 64, ". We define": 12, ". 12 ,": 16, ". 12 (": 11, ". ( 2008a": 10, ". 3 )": 51, ". 's _MATH_": 15, ". 2 ,": 223, ". 2002 ;": 19, ". [ 2": 20, ". ( 2": 105, ". III ,": 23, ". IV ,": 12, ". _CITE_ propose": 73, ". , _CITE_": 150, ". Define _MATH_": 10, ". Suppose that": 13, ". Then the": 25, ". ) .": 327, ". 3 (": 154, ". _REF_ to": 141, ". Based on": 26, ". [ 10": 14, ". ( 2011": 63, ". Here ,": 77, ". 2006 )": 61, ". 1988 )": 12, "... , and": 27, ". at _MATH_": 18, ". , a": 120, ". 3 .": 172, ". _MATH_ in": 33, ". ( 2005": 197, ". 2 .": 206, ". for the": 45, ". _REF_ concludes": 11, ". _CITE_ for": 258, ". in a": 17, ". 9 .": 26, ". ( i": 151, ". _REF_ as": 123, ". 6 and": 18, ". 7 ,": 32, ". , without": 13, ". in the": 90, ". _REF_ becomes": 32, ". ( _CITE_": 89, ". _REF_ compares": 22, ". 5 )": 51, ". _CITE_ with": 17, ". _REF_ show": 70, ". _CITE_ in": 66, ". _REF_c ,": 18, ". the number": 24, ". _REF_b and": 18, "... ) .": 21, ". sequence of": 19, "... , F_p_MATH_": 10, ". Obviously ,": 23, ". Thus ,": 121, ". ( 25": 31, ". Eqs .": 12, ". 9 ,": 24, ". _MATH_ are": 15, ". 2000 ;": 26, ". 2005 )": 51, ". _CITE_ as": 30, ". ) of": 33, ". 10 ,": 16, ". in _MATH_": 53, ". , that": 31, ". found that": 10, ". 2002 )": 20, ". ( 13": 42, ". 10 .": 17, ". 11 .": 13, ". ( 2001": 109, ". ( 42": 14, ". ( 48": 11, ". _REF_a ,": 62, ". _REF_ describes": 21, ". Consequently ,": 23, ". , see": 15, ". First ,": 38, ". when _MATH_": 30, ". Finally ,": 53, ". ( 1996": 53, ". Here _MATH_": 88, ". can be": 16, ". ( 16": 54, ". ( 21": 23, ". 2 for": 11, ". _CITE_ applied": 23, ". ( 1990": 15, ". ( 2009": 155, ". _REF_ ;": 81, ". that _MATH_": 22, ". ( 1989": 14, ". ( 1994": 34, ". 2007 )": 45, ". energy _MATH_": 10, ". , it": 36, ". _REF_ a": 52, ". Theorem _REF_": 48, ". _CITE_ considered": 27, ". , to": 25, ". , of": 10, ". 6 )": 23, ". Moreover ,": 67, ". Using (": 15, ". _REF_ :": 138, ". ( 2.1": 15, ". 7 (": 49, ". _CITE_ that": 58, ". _REF_- (": 42, ". We also": 15, ". 2008 )": 37, ". ( 33": 20, ". Figure _REF_": 76, ". 1 and": 55, ". ) can": 16, ". _CITE_ introduced": 52, ". ) is": 44, ". _REF_ leads": 15, ". _REF_ will": 19, ". 2 )": 93, ". at the": 15, ". , for": 56, ". ) and": 74, ". for _MATH_": 57, ". , and": 24, ". _REF_ can": 172, ". 's method": 30, ". [ 27": 15, ". Applying the": 15, ". 4 is": 14, ". Again ,": 12, ". ( 6": 78, ". _REF_ contains": 20, ". 1996 )": 21, ". _CITE_ it": 30, ". 3 in": 13, ". 8 (": 45, ". 1 shows": 27, ". _MATHDISP_ where": 10, ". On the": 19, ". with the": 14, ". ( 1995": 61, ". 6 .": 93, ". ( 1991": 39, ". ( 7": 74, ". Then we": 12, ". In the": 27, ". , [": 14, ". the discussion": 10, ". For the": 14, ". Then ,": 29, ". 7 and": 19, ". _CITE_ is": 62, ". _REF_a )": 161, ". 1995 ;": 11, ". 2004 )": 42, ". , its": 13, ". _CITE_ describe": 17, ". to _MATH_": 12, ". also _CITE_": 29, ". _CITE_ using": 20, ". _MATH_ if": 17, ". see _CITE_": 14, ". _CITE_ (": 101, ". _CITE_ to": 81, ". _REF_ into": 37, ". _REF_ yields": 24, ". ( ii": 31, ". ( iii": 10, ". _REF_ has": 99, ". have shown": 11, ". ( 9": 64, ". , 2004": 10, ". _REF_ when": 19, ". Lemma _REF_": 32, ". ( 20": 48, ". _REF_ it": 33, ". ( 1": 177, ". _REF_d )": 36, ". _CITE_ obtained": 13, ". from the": 17, ". of (": 57, ". ) to": 16, ". _CITE_ has": 34, ". of the": 83, ". ( 4": 94, ". in terms": 12, ". ( 1993": 38, ". _REF_ one": 22, ". One can": 19, ". where _MATH_": 12, ". _MATH_ for": 77, ". _REF_ below": 35, ". e.g .": 34, ". of _MATH_": 19, ". Indeed ,": 16, "... '' .": 12, ". Chapter _REF_": 20, ". ! (": 11, ". Then _MATH_": 29, ". Therefore ,": 124, ". ( _REF_-_REF_": 46, ". _REF_ were": 22, ". _REF_e )": 10, ". _REF_ reveals": 15, ". _CITE_ we": 37, ". , by": 44, ". ( see": 52, ". _REF_ correspond": 13, ". , in": 49, ". with _MATH_": 17, ". propose a": 13, ". of _REF_": 18, ". II ,": 27, ". IV .": 14, ". _REF_.b )": 10, ". _REF_ was": 31, ". ( 17": 28, ". ( 18": 44, ". Exercise _REF_": 10, ". according to": 13, ". Assume that": 30, ". This is": 41, ". For any": 13, ". : _MATHDISP_": 29, ". ( 40": 11, ". _REF_ reduces": 16, ". 9 (": 30, ". ( 1.1": 45, ". independent of": 10, ". ) if": 15, ". _REF_ does": 15, ". [ 4": 11, ". _CITE_ improved": 14, ". ( 31": 10, ". for all": 13, ". _CITE_ further": 15, ". ( 37": 14, ". 7 )": 24, ". proposed a": 50, ". _CITE_ first": 15, ". ( 14": 51, ". ( 15": 35, "... ) ,": 22, ". ( 1.3": 16, ". , an": 26, ". showed that": 13, ". _CITE_ shows": 12, ". _REF_ may": 18, ". Ref .": 33, ". _CITE_ studied": 85, ". 1 in": 12, ". , those": 15, ". _REF_ or": 15, ". _CITE_ present": 41, ". _CITE_ extend": 10, ". _REF_c )": 78, ". Table _REF_": 39, ". have been": 10, ". ( 26": 14, ". 4 (": 101, ". _REF_ have": 19, ". ( 43": 16, ". , when": 41, ". _REF_a shows": 10, ". _REF_b .": 53, ". _REF_d .": 14, ". the first": 10, ". ( 36": 20, ". ( 8": 64, ". Remark _REF_": 24, ". Thus _MATH_": 11, ". _MATH_ where": 11, ". , we": 37, ". [ _REF_": 22, ". _CITE_ suggested": 17, ". _REF_ using": 21, ". there is": 25, ". ( 1987": 18, ". 1 is": 11, ". Observe that": 10, ". _CITE_ demonstrated": 12, ". ( _MATH_": 27, ". 4 shows": 16, ". is the": 16, ". Notice that": 29, ". [ 7": 17, ". 2 shows": 22, ". 3 and": 41, ". _CITE_ are": 31, ". _REF_-a .": 10, ". _REF_c .": 29, ". [ 8": 14, ". 1995 )": 16, ". Using the": 49, ". if the": 26, ". ( 1986": 12, ". 's (": 16, ". 5 and": 28, ". ) in": 24, ". For example": 12, ". _CITE_ extended": 21, ". section _REF_": 12, ". Also ,": 19, ". Figs .": 21, ". 3 is": 10, ". _CITE_ who": 23, ". 2004 ;": 37, ". _CITE_ introduce": 14, ". _REF_b ,": 50, ". However ,": 32, ". and _MATH_": 24, ". Sect .": 19, ". Proof .": 17, ". For _MATH_": 23, ". 's _CITE_": 22, ". 5 shows": 14, ". Consider the": 30, ". Recall that": 17, ". [ 11": 17, ". _MATH_ (": 34, ". _REF_a .": 76, ". _MATH_ :": 28, ". case ,": 11, ". '' (": 19, ". we have": 20, ". the _MATH_": 30, ". _MATH_ of": 11, ". _REF_-_REF_ .": 78, ". The first": 11, ". _REF_ from": 18, ". _CITE_ show": 22, ". In this": 27, ". standard normal": 19, ". ( 28": 21, ". 2000 )": 30, ". 1998 )": 19, ". ( 2006a": 16, ". 2009 )": 37, ". Taking _MATH_": 14, ". _REF_ of": 29, ". degree in": 12, ". _CITE_ presented": 99, ". Similarly ,": 31, ". They are": 17, ". Refs .": 18, ". _REF_ ]": 26, ". ( 29": 14, ". ( 2008b": 10, ". _REF_ displays": 23, ". _REF_ also": 25, ". the set": 14, ". _MATH_ can": 13, ". ( 2013": 16, ". ( 1988": 16, ". ( 44": 12, ". Here we": 19, ". _REF_ summarizes": 10, ". , as": 13, ". _REF_B )": 18, ". due to": 19, ". _REF_ presents": 42, ". _REF_ demonstrates": 15, ". _CITE_ observed": 14, ". ) ;": 15, ". ( 3": 80, ". _MATH_ with": 15, ". , there": 28, ". , with": 24, ". presented a": 27, ". _REF_-_REF_ )": 18, ". _CITE_ :": 44, ". copies of": 11, ". _REF_ implies": 11, ". Sec .": 14, ". ( 24": 25, ". ; see": 18, ". ( 1983": 16, ". _CITE_ found": 15, ". [ 6": 14, ". _CITE_ provide": 17, ". on the": 22, ". _REF_-_REF_ and": 13, ". _CITE_ by": 21, ". 2011 )": 14, ". _CITE_ give": 12, ". ( 2.6": 10, ". al .": 29, ". ( 1992": 38, ". as _MATH_": 11, ". ( 1982": 13, ". _CITE_ on": 15, ". ( 5": 70, ". 8 )": 18, ". if and": 14, ". 2 of": 13, ". [ 14": 13, ". _REF_ together": 17, ". Thus we": 15, ". , where": 11, ". This means": 13, ". , one": 11, ". _CITE_ a": 11, ". 2009 ;": 13, ". Taking the": 14, ". '' )": 11, ". Here the": 16, ". the one": 13, ". in Computer": 11, ". 9 )": 15, ". 3 shows": 19, ". using the": 11, ". energy of": 15, ". 2005 ;": 13, ". _REF_ plots": 18, ". 1999 )": 22, ". _MATH_ or": 15, ". present a": 14, ". where the": 17, ". Corollary _REF_": 14, ". eq .": 11, ". _CITE_ were": 22, ". 1 of": 12, ". [ 13": 19, ". 4 and": 39, ". Clearly ,": 15, ". [ 5": 11, ". 1989 )": 10, ". and the": 13, ". Then _MATHDISP_": 13, ". the probability": 12, ". 2012 )": 18, ". ( 3.2": 20, ". [ 1": 10, ". _REF_ depicts": 29, ". If the": 13, ". Equation (": 29, ". ( 47": 16, ". ( 50": 11, ". ( 59": 13, ". 8 ,": 25, ". 11 ,": 19, ". 2 in": 12, ". ( 46": 12, ". ) _MATH_": 11, ". ( b": 40, ". with a": 20, ". with respect": 11, ". Proof :": 12, ". Since _MATH_": 19, ". proposed to": 11, ". number of": 11, ". developed a": 11, ". We can": 18, ". We will": 14, ". ) :": 10, ". _MATH_ as": 10, ". ( c": 21, ". that the": 20, ". ( d": 10, ". _REF_ represents": 27, ". 4 )": 55, ". , no": 18, ". We then": 12, ". _REF_ provides": 14, ". _REF__MATH_ )": 14, ". 1998 ;": 16, ". _REF_ represent": 13, ". _REF_ indicates": 19, ". Proposition _REF_": 26, ". ( 22": 21, ". which is": 10, ". sample of": 10, ". [ 3": 13, ". Substituting (": 18, ". _REF_c and": 14, ". _CITE_ employed": 14, ". 4.1 .": 10, ". they are": 12, ". 11 (": 12, ". 13 (": 15, ". negative )": 20, ". , at": 12, ". ( cf": 13, ". the proof": 14, ". _REF_ b": 25, ". Then there": 11, ". When _MATH_": 14, ". ( 34": 12, ". Let _MATHDISP_": 10, ". _REF_ c": 16, ". 2001 ;": 16, ". ( 3.6": 10, ". 1987 )": 10, ". ) that": 10, ". 2 we": 15, ". _CITE_ define": 13, ". 3 we": 10, ". ( 2.4": 10, ". _CITE_ consider": 19, ". Example _REF_": 26, ". there exists": 11, ". _MATH_- )": 10, ". ( [": 10, ". 1997 ;": 22, ". 10 (": 12, ". _CITE_ _CITE_": 13, ". _CITE_ study": 12, ". 's ,": 12, ". _CITE_ defined": 12, ". of Eq": 18, ". there are": 12, ". Further ,": 11, ". _CITE_ proposes": 12, ". Furthermore ,": 12, ". for a": 10, ". 4 of": 18, ". ) for": 17, ". ( 1984": 12, ". , they": 24, ". _REF_ holds": 15, ". _CITE_ was": 11, ". 2006 ;": 17, ". _REF_ _MATH_": 18, ". _REF_.a )": 10, ". 1994 )": 12, ". 2003 ;": 28, ". _CITE_ described": 13, ". we can": 11, ". [ 18": 11, ". _REF__MATH_ ,": 12, ". _CITE_ proved": 21, ". ) as": 15, ". cit .": 10, ". ( 23": 32, ". 1997 )": 13, ". [ 17": 11, ". 13 ,": 10, ". _CITE_ gave": 17, ". Define the": 11, ". _REF_ -": 10, ". Set _MATH_": 11, ". ( 27": 12, ". _MATH_ _MATH_": 10, ". It follows": 12, ". _REF_ corresponds": 10, ". 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