diff --git a/data/corpus_n=1.json b/data/corpus_n=1.json
new file mode 100644
index 0000000000000000000000000000000000000000..0c54b97d40a59d582efcf5a3f6badc5c80700ff1
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+++ b/data/corpus_n=1.json
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of": 203, "This is simply": 23, "Thus there exists": 70, "To avoid the": 80, "The polynomial _MATH_": 34, "To show that": 138, "Then _MATH_ with": 19, "The effects of": 171, "There are numerous": 29, "This technique has": 18, "To reduce the": 108, "The definition of": 217, "The constants _MATH_": 52, "The following inequality": 10, "That is we": 207, "Thus for all": 38, "Then _MATH_ can": 96, "Therefore the number": 33, "This is similar": 78, "Therefore we can": 271, "The non vanishing": 13, "Throughout this paper": 166, "The results for": 147, "The inverse problem": 13, "To deal with": 87, "Therefore since _MATH_": 39, "The error bars": 24, "The proposed method": 125, "Theorem 3 END": 61, "The theoretical results": 18, "To show the": 102, "The model parameters": 27, "The training set": 10, "Thus by the": 61, "The Helioseismic and": 16, "The lower bound": 59, "The coefficients are": 12, "This together with": 149, "The integration over": 10, "This solution is": 46, "There is an": 171, "Tables _REF_ and": 233, "This is why": 98, "This comes from": 19, "The direction of": 48, "This difference in": 10, "These include a": 10, "Thus if _MATHDISP_": 12, "The real time": 23, "This implies by": 11, "Therefore _MATH_ must": 17, "The dimension of": 53, "This difference is": 37, "They are also": 43, "This case is": 64, "The other case": 17, "They can be": 148, "The energy _MATH_": 11, "Thus _MATH_ satisfies": 18, "These methods are": 51, "Therefore when the": 30, "This choice is": 36, "The lemma is": 72, "The Monte Carlo": 36, "Thus according to": 25, "To check this": 15, "Table 1 END": 296, "Table 1 the": 25, "This might be": 65, "This leads to": 563, "The user can": 33, "This follows directly": 13, "Table _REF_ by": 10, "Table _REF_ illustrates": 19, "This is called": 90, "Then _MATH_ forms": 17, "The investigation of": 35, "This paper presents": 131, "This algorithm is": 69, "The resolution of": 34, "The non perturbative": 14, "This phenomenon is": 70, "The Lyapunov function": 15, "The flux rope": 33, "The transition probabilities": 18, "Then according to": 70, "There are many": 307, "There might be": 13, "The mean field": 20, "The inverse of": 33, "The phenomenon of": 29, "Therefore the data": 10, "To implement the": 30, "There has been": 97, "The question of": 72, "That is to": 155, "The special case": 32, "There were no": 22, "Theorem 3 1": 338, "This indicates that": 224, "The magnetic energy": 15, "This proves that": 84, "This in turn": 175, "These models are": 53, "The approach presented": 12, "TeV scale END": 25, "The key to": 44, "Therefore by the": 57, "Table _REF_ presents": 92, "The data from": 26, "This contradicts _MATH_": 19, "The most popular": 33, "This suggests that": 241, "This phenomenon has": 21, "The speed of": 50, "This technique is": 63, "The input data": 16, "Thus we consider": 34, "Theorem _REF_ hold": 68, "The results obtained": 134, "This is more": 35, "Table _REF_ where": 69, "The drag force": 10, "The distance between": 84, "Then _MATHDISP_ where": 279, "Then we study": 13, "Taking _MATH_ and": 51, "Theorem 3 4": 57, "The polynomials _MATH_": 17, "The class of": 84, "The following example": 86, "The results in": 152, "Theorem 2 of": 24, "The corresponding eigenvalues": 11, "The product _MATH_": 22, "This is in": 263, "The kinetic energy": 34, "Thus we expect": 19, "To understand the": 98, "To this aim": 56, "The support of": 13, "The sequence of": 72, "The first way": 11, "The plot of": 26, "The following relations": 11, "This may explain": 16, "Theorem END END": 197, "Then for all": 212, "This problem can": 66, "To start with": 22, "The result is": 307, "Thus _MATHDISP_ which": 39, "Therefore our results": 11, "The factor of": 14, "The treatment of": 21, "Then Eqs _REF_": 13, "The spectrum of": 71, "The problem has": 14, "To compute the": 119, "The latter is": 183, "This result is": 329, "This feature is": 53, "The advantage is": 19, "The main motivation": 28, "To get a": 50, "That means the": 18, "Theorems 1 2": 21, "To motivate the": 13, "Taylor coefficients _MATH_": 15, "The mean value": 43, "This explains the": 47, "This is impossible": 21, "This approach is": 193, "The problem was": 15, "The following simple": 13, "Thus _MATH_ are": 10, "Then for _MATH_": 335, "The following results": 24, "This is consistent": 164, "This is particularly": 102, "Therefore it is": 465, "The proposed scheme": 24, "The starting point": 83, "The most probable": 13, "The center of": 36, "The elements _MATH_": 13, "The data set": 61, "The locations of": 28, "The travel time": 24, "The matrices _MATH_": 85, "This step is": 42, "The idea here": 15, "The proposed approach": 93, "These constraints are": 15, "Therefore there exist": 25, "The comparison of": 90, "Table _REF_ for": 171, "The elements of": 77, "The upper bound": 49, "The total number": 122, "The proposed technique": 17, "The selection of": 58, "The initial conditions": 80, "The coefficients in": 16, "Then _MATHDISP_ is": 35, "Table _REF_ summarizes": 111, "Theorem 1 in": 64, "The shape of": 94, "The expectation of": 13, "Then there are": 69, "To do so": 168, "The integration of": 38, "Therefore if we": 60, "Therefore we also": 15, "The amount of": 123, "This allowed us": 18, "Therefore we will": 45, "The deviation of": 20, "This process is": 139, "The first of": 61, "To realize the": 12, "To be more": 117, "The control objective": 36, "Ti sapphire laser": 34, "The phase difference": 14, "The next proposition": 39, "This follows from": 136, "Thus the proof": 37, "This condition is": 79, "The chapter is": 37, "The first example": 35, "The unique solution": 21, "Thus we use": 22, "There exist two": 37, "The phase portrait": 26, "The increase in": 38, "Theorem 1 is": 35, "The form of": 77, "This value is": 89, "The next step": 148, "The interaction between": 47, "There is another": 29, "The coupling constant": 12, "The Hamiltonian _REF_": 10, "Taking the _MATH_": 18, "Taking the time": 15, "The accuracy of": 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_MATH_": 70, "The same situation": 11, "The optimization problem": 41, "The difficulty of": 24, "The discussion of": 26, "This system has": 29, "The stability analysis": 23, "The control of": 29, "The main contributions": 32, "Table _REF_ as": 22, "The usual way": 11, "The minimum value": 13, "The sum of": 110, "Theorem 1 we": 67, "Table _REF_ in": 61, "The difference from": 13, "The transformation is": 12, "Theorem 2 2": 122, "Table _REF_ have": 12, "Then since _MATH_": 73, "The optimal control": 39, "To estimate the": 155, "The spaces _MATH_": 16, "The sample is": 16, "The reason for": 277, "Then the probability": 40, "This does not": 92, "The last section": 45, "This result will": 11, "This definition of": 15, "The orientation of": 41, "This is of": 73, "The indices _MATH_": 16, "This is END": 11, "To determine the": 185, "The following two": 63, "The expressions for": 38, "The algorithm is": 103, "This fact is": 62, "The second term": 196, "Thus the function": 22, "The remainder of": 249, "To cope with": 35, "This is achieved": 167, "The details can": 15, "Theorem 4 2": 67, "The steady state": 82, "Thus we suggest": 13, "The vector _MATH_": 103, "The organization of": 76, "Then it follows": 151, "The results on": 18, "The symbols _MATH_": 14, "The depth of": 22, "Then by Corollary": 12, "The conclusions of": 11, "Table _REF_ are": 95, "Then we are": 11, "The action of": 87, "The last equation": 25, "To have a": 31, "The solution of": 268, "Then the corresponding": 41, "The main conclusion": 22, "Therefore for all": 31, "Therefore _MATH_ has": 37, "Thus _MATH_ in": 18, "This is accomplished": 49, "Then let us": 14, "The maximum number": 24, "The matrix of": 19, "The proof follows": 88, "Therefore we shall": 15, "This result can": 63, "The result for": 46, "This is so": 53, "The most important": 142, "This should be": 40, "These are the": 135, "To be able": 53, "To find a": 23, "This notion of": 12, "Then we define": 52, "The top panel": 43, "The change in": 68, "The most recent": 34, "To calculate the": 120, "Therefore if _MATH_": 133, "The near field": 10, "This concludes the": 139, "There is therefore": 14, "The efficiency of": 58, "Theorem _REF_ can": 148, "The pulse duration": 17, "The _MATH_ can": 13, "The first term": 257, "Therefore the proposed": 18, "The dual of": 23, "The model is": 154, "They are related": 15, "The process _MATH_": 110, "The potential _MATH_": 19, "This behavior is": 86, "The divergence of": 12, "This line of": 10, "Theorem _REF_ since": 23, "Therefore we do": 24, "They found that": 124, "The performances of": 22, "The main results": 94, "This was the": 53, "Then _MATH_ END": 483, "The parameters are": 38, "The vector field": 28, "Table _REF_ reports": 55, "The table shows": 14, "This is essentially": 18, "The equation is": 22, "The solutions to": 18, "That means that": 33, "Throughout the paper": 93, "This was later": 11, "To get the": 56, "The appearance of": 71, "The theory of": 116, "There is little": 10, "The linearization of": 26, "Thus we will": 30, "Thus the transformation": 16, "To derive the": 73, "The notion of": 137, "There are five": 17, "The spectra of": 19, "This conclusion is": 48, "Then _MATH_ implies": 19, "The restriction of": 24, "Therefore we propose": 30, "There exist a": 59, "Theorem 2 we": 21, "The non linear": 28, "To demonstrate this": 20, "The frequency response": 22, "The maximum value": 31, "This enables us": 49, "Thus the total": 39, "These events are": 13, "This is still": 17, "The equality is": 14, "The left hand": 107, "The majority of": 71, "Table _REF_ the": 216, "The simulation of": 22, "The element _MATH_": 30, "This is however": 39, "To overcome this": 146, "This opens up": 10, "The models are": 17, "Then the set": 52, "The last condition": 11, "Theorem _REF_ _MATH_": 259, "The resulting _MATH_": 32, "To avoid this": 76, "This effect has": 10, "The introduction of": 77, "This behaviour is": 20, "The correlation between": 54, "The analysis in": 22, "The addition of": 45, "The first observation": 21, "These variables are": 12, "The only difference": 116, "This restriction is": 13, "Table 3 END": 88, "That is if": 104, "The full conditional": 19, "The field equation": 10, "Table _REF_ indicates": 14, "The data that": 11, "The procedure is": 64, "To show this": 48, "This interpretation is": 18, "The latter can": 47, "This will also": 14, "Taylor expansion of": 91, "The novelty of": 29, "The constraints of": 12, "This result suggests": 22, "The advantage of": 258, "Then there is": 149, "Theorem _REF_ b": 36, "The parameters _MATH_": 146, "The last term": 80, "The case _MATH_": 158, "Theorem 2 5": 33, "Then the point": 11, "The set _MATH_": 233, "The property of": 22, "Therefore as _MATH_": 14, "To study the": 141, "The percentage of": 23, "The network is": 23, "Therefore from _REF_": 33, "This part of": 24, "The task is": 18, "The output of": 117, "The first and": 101, "This corresponds to": 204, "The second and": 58, "The third term": 49, "The process starts": 11, "The time _MATH_": 11, "The time interval": 26, "The triple _MATH_": 11, "The latter case": 21, "This approach has": 80, "The figure shows": 88, "The free energy": 26, "Theorem _REF_ also": 32, "The model was": 23, "The convergence rate": 16, "This yields a": 46, "Thus END END": 25, "Thus they are": 14, "The increase of": 53, "TDP END END": 20, "Thus given _MATH_": 12, "Then applying the": 17, "This process can": 28, "The region of": 22, "Then _MATHDISP_ for": 69, "The above mentioned": 46, "To implement this": 12, "Therefore there are": 43, "This happens when": 16, "This is reasonable": 15, "This result may": 24, "Then if _MATH_": 86, "There are some": 126, "Therefore we need": 45, "This is supported": 17, "The key feature": 18, "The time resolution": 12, "Thus in the": 137, "The boundary of": 35, "The components _MATH_": 13, "Theorem _REF_ i": 58, "The _MATH_ END": 87, "The input output": 25, "The estimator _MATH_": 12, "The adaptation of": 11, "The average power": 10, "That is an": 13, "The threshold value": 16, "This theory is": 12, "Then we propose": 10, "The main purpose": 79, "T_MATH_ END END": 20, "Taylor series approximation": 10, "The agreement between": 39, "To test this": 22, "The conclusion follows": 16, "Then in Section": 49, "The _MATH_ mode": 14, "The amplitudes of": 25, "Therefore the problem": 23, "The integral in": 28, "The resulting expression": 11, "Therefore _MATH_ for": 57, "The resulting model": 19, "These processes are": 13, "The general idea": 21, "This figure shows": 59, "Theorem 1 1": 214, "Therefore we only": 35, "The other is": 55, "The angle of": 15, "The technique is": 23, "There are no": 88, "Theorem 3 2": 148, "The third and": 21, "The results can": 33, "Throughout this section": 73, "Then in order": 15, "This allows a": 19, "The proofs are": 16, "To show _REF_": 18, "The first inequality": 33, "Thus for the": 73, "The results reported": 18, "The group of": 21, "The value of": 461, "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, "Then _REF_ is": 44, "The first is": 188, "The transformation matrix": 12, "This section discusses": 29, "Then system _REF_": 25, "Theorem _REF_ this": 41, "There are mainly": 11, "The other way": 12, "The process of": 105, "The distributions of": 32, "The area of": 44, "The integration is": 11, "The good visibility": 10, "This contribution is": 17, "The two cases": 11, "The graph _MATH_": 27, "The main goal": 72, "Then _MATH_ if": 50, "Table _REF_ lists": 100, "The same is": 82, "To give a": 30, "To increase the": 43, "The virtual work": 15, "Then the solution": 60, "To handle the": 16, "The absence of": 54, "The first case": 53, "The second case": 34, "The mass of": 50, "The main conclusions": 16, "The details of": 146, "To evaluate the": 127, "Theory END END": 33, "The first phase": 14, "The second phase": 16, "The data are": 79, "This approach was": 49, "Then on the": 15, "Taylor s expansion": 19, "Theorem 3 3": 74, "To allow for": 24, "They assumed that": 14, "The time required": 11, "The running time": 27, "This proves the": 153, "The idea of": 225, "Transform END END": 12, "The columns of": 20, "Table 1 shows": 39, "There exist an": 13, "Therefore _MATHDISP_ where": 56, "The reason that": 25, "The conditional probability": 23, "The cases _MATH_": 20, "Then all the": 21, "T b rhodesiense": 10, "This paper considers": 43, "This behavior was": 12, "The asymptotic distribution": 22, "This yields _MATHDISP_": 76, "The tree level": 18, "They are _MATHDISP_": 12, "The above results": 29, "The top row": 13, "The cosmological constant": 18, "Table 2 where": 10, "Type III burst": 17, "The most general": 40, "This model can": 37, "Theorem _REF_ will": 40, "The contribution of": 124, "This results in": 260, "Therefore the optimal": 15, "Thus if the": 76, "The discovery of": 57, "Therefore the equation": 16, "Theorem _REF_ or": 42, "The conditions _MATH_": 17, "The partition function": 13, "Therefore the total": 30, "The total time": 18, "Two types of": 52, "This is one": 69, "The propagation of": 31, "The evaluation of": 62, "The latter may": 11, "Tab _REF_ END": 64, "Thus if _MATH_": 147, "The sets _MATH_": 25, "The most likely": 14, "This gives an": 23, "The second one": 116, "The term _MATH_": 183, "The derivative of": 81, "Taking the limit": 56, "This coincides with": 14, "Tables _REF_ _REF_": 124, "The first thing": 19, "The knowledge of": 38, "To be precise": 82, "The same holds": 57, "Then as _MATH_": 37, "The square of": 17, "This way a": 12, "This is always": 14, "The potential energy": 16, "Therefore the system": 28, "The proof will": 30, "The set _MATHDISP_": 18, "Theorem _REF_ yields": 54, "Theorem _REF_ holds": 65, "The results confirm": 12, "To achieve this": 125, "This shows the": 39, "Therefore _MATH_ in": 15, "Theorem _REF_ it": 166, "Then the linear": 18, "This representation is": 19, "The previous results": 14, "To complete the": 148, "Theorem _REF_ _MATHDISP_": 86, "The proposed algorithm": 54, "The generation of": 34, "The significance of": 39, "Then let _MATH_": 22, "Thus from _REF_": 30, "This amounts to": 37, "Then we obtain": 131, "The result now": 16, "That is _MATHDISP_": 204, "Thus for _MATH_": 127, "The following assumptions": 17, "This choice of": 22, "The operation of": 29, "The point _MATH_": 74, "This chapter focuses": 11, "The constant _MATH_": 114, "The output power": 10, "Thus the algorithm": 14, "This trend is": 22, "Then the function": 48, "Therefore we get": 42, "Therefore if the": 52, "Then _MATH_ contains": 20, "This paper addresses": 35, "This notion is": 14, "The main drawback": 39, "The following lemma": 191, "The complement of": 17, "The temporal evolution": 21, "This approximation is": 33, "The approximation of": 23, "The first set": 31, "To find the": 136, "The other part": 11, "Therefore the state": 12, "Therefore we apply": 10, "This is obtained": 18, "Then the error": 29, "Theorem 1 the": 38, "The initial values": 29, "Tab _REF_ and": 15, "The experiments were": 27, "This could be": 95, "This signal is": 10, "The variation in": 26, "Therefore we choose": 15, "The solution is": 92, "Then from the": 63, "There are of": 12, "The proportion of": 20, "This reflects the": 24, "The principle of": 57, "The boundary conditions": 84, "The end result": 11, "The main difficulty": 46, "The influence of": 141, "Therefore the time": 17, "There are six": 16, "The claim follows": 16, "The conclusions are": 25, "The code was": 10, "This motivates us": 32, "This is precisely": 27, "Thus the set": 27, "This fact and": 12, "To solve this": 83, "Then it can": 38, "To resolve this": 24, "This lemma is": 20, "The main advantage": 102, "The width of": 72, "Therefore the following": 37, "There exist _MATH_": 96, "The law of": 31, "These can be": 59, "Therefore only the": 14, "Therefore there exists": 90, "Thus by _REF_": 38, "Then _REF_ holds": 14, "The main problem": 53, "Thus we must": 26, "Therefore in view": 24, "Then the two": 16, "The objective is": 113, "To obtain _MATH_": 18, "The effect is": 33, "Then for every": 136, "This scenario is": 27, "Thus at least": 10, "Therefore at the": 11, "This is useful": 29, "That is why": 130, "The assumption of": 58, "This term is": 32, "The bottom panel": 38, "Table II END": 20, "Then _REF_ _REF_": 11, "The consequence of": 23, "To summarize we": 30, "Therefore system _REF_": 13, "This section provides": 22, "The sizes of": 16, "The upper panel": 24, "The middle panel": 12, "The lower panel": 18, "The distribution is": 11, "Th END END": 37, "This paper investigates": 44, "The case study": 11, "The first column": 45, "Table 3 and": 10, "The magnitude of": 115, "Table _REF_ that": 66, "The development of": 110, "The strength of": 63, "Then _MATHDISP_ which": 39, "This leads us": 51, "This task is": 18, "This number is": 22, "Thus it follows": 62, "The key idea": 83, "The denominator is": 11, "The upper and": 27, "The same happens": 17, "The robustness of": 20, "The properties of": 88, "Then the sequence": 49, "Then we write": 15, "Table _REF_ compares": 31, "This and the": 21, "The list of": 25, "The value for": 17, "The rate of": 91, "The algorithm then": 14, "The final solution": 11, "Thus the number": 44, "The connection between": 35, "The best fit": 57, "They concluded that": 52, "The time difference": 16, "The modeling of": 18, "Therefore it has": 11, "The expression _MATH_": 20, "To verify this": 19, "To discuss the": 20, "The size of": 247, "The origin of": 94, "This upper bound": 12, "The so called": 71, "The second group": 12, "This procedure is": 96, "Theorem 2 7": 23, "Thus we present": 10, "The conditions _REF_": 10, "Therefore we use": 37, "The Hausdorff distance": 10, "The degrees of": 16, "They also showed": 21, "This implies _MATHDISP_": 59, "The difference is": 77, "To state the": 11, "The momentum factor": 14, "Therefore we may": 55, "Thus if we": 89, "The last inequality": 41, "The converse is": 21, "To improve the": 80, "To conclude we": 25, "The amplitude _MATH_": 26, "The first type": 39, "The second type": 38, "The second reason": 19, "This issue is": 36, "This chapter introduces": 14, "Then Equation _REF_": 12, "The assignment of": 11, "The first algorithm": 18, "Thus while the": 10, "The _MATH_ factor": 10, "Therefore the first": 27, "The contribution from": 30, "TRACE 173 \u00c5": 13, "The period of": 30, "There then exists": 12, "The first stage": 43, "This comparison is": 13, "To characterize the": 19, "The continuous time": 23, "Theorem _REF_ then": 48, "These measurements are": 14, "The bulk of": 14, "This study was": 14, "This information can": 26, "The vectors _MATH_": 33, "To identify the": 34, "Then the time": 27, "This paper proposes": 64, "The most significant": 26, "They have been": 46, "This system of": 15, "To facilitate the": 28, "This is our": 26, "The theorem follows": 13, "This question is": 36, "The edges of": 16, "The derivation of": 80, "This is caused": 23, "TeV END END": 146, "This motivates the": 42, "The final result": 32, "The question is": 62, "The model used": 17, "They are in": 10, "Theorem _REF_ provides": 38, "The fundamental idea": 10, "This approach however": 12, "To compute a": 12, "The main disadvantage": 15, "The _MATH_ and": 122, "The dark energy": 16, "The data used": 22, "The experiment was": 17, "To make this": 26, "The generalization of": 24, "The region where": 12, "The intensity of": 41, "The test statistic": 15, "The present work": 53, "The stability of": 107, "The motivation for": 46, "This is much": 15, "TRACE 1600 \u00c5": 18, "This provides the": 26, "The last part": 16, "The authors of": 82, "The spectra were": 11, "Then we consider": 40, "Thus if there": 10, "This was not": 21, "There is only": 32, "The above discussion": 20, "This is to": 58, "Therefore we take": 14, "This chapter is": 79, "The results 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"The complex _MATH_": 12, "To prove _REF_": 44, "The conclusion of": 29, "Theorem _REF_ now": 15, "To be clear": 10, "The calculation of": 114, "The article is": 41, "The occurrence of": 49, "This modification is": 12, "The next section": 68, "The final section": 18, "The estimate _REF_": 18, "Table _REF_ this": 16, "The entries of": 21, "Therefore there must": 12, "This is different": 42, "This of course": 26, "These conditions are": 40, "This proves _REF_": 23, "The following corollary": 35, "The index of": 19, "This is defined": 11, "The results shown": 22, "The interaction of": 42, "The theory is": 17, "There are other": 58, "Then the system": 59, "The first model": 23, "This section briefly": 10, "Table _REF_ gives": 95, "The random variable": 24, "Throughout this chapter": 15, "The present paper": 95, "The service time": 13, "The constraints are": 12, "The models of": 10, "Theorem _MATH_ END": 16, "Theorem we have": 13, "The discriminant of": 16, "Thus _MATH_ if": 19, "This is 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"The resulting time": 10, "This simple model": 15, "The choice of": 228, "The experiments are": 18, "The third order": 18, "The second order": 72, "The first derivative": 11, "To illustrate the": 163, "Therefore we END": 11, "The details are": 33, "Thus the result": 18, "Thus we note": 11, "Then one can": 68, "The semantics of": 13, "This will not": 15, "This will give": 17, "Theorem _REF_ gives": 62, "This formula can": 14, "Therefore we conclude": 69, "To remove the": 16, "The states of": 12, "Thus one needs": 11, "Therefore _MATH_ which": 24, "The substitution of": 18, "Then if the": 28, "The average values": 14, "The average _MATH_": 13, "The argument is": 18, "The Doppler velocity": 18, "These values are": 86, "The framework of": 15, "This difference can": 12, "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, "The DAE _REF_": 12, "The log likelihood": 34, "Table _REF_ 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lists": 12, "The methodology is": 17, "The proposed algorithms": 10, "Thus we could": 14, "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": 58, "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, "Therefore we must": 28, "The next two": 37, "The expression for": 85, "This represents a": 27, "This subsection presents": 10, "The idea behind": 64, "The symbol _MATH_": 78, "The calculations are": 21, "Two cases are": 16, "This point of": 14, "Then the equations": 14, "Table 6 END": 16, "There are different": 51, "This assumes that": 11, "Theorem _REF_ implies": 99, "This article is": 44, "These are used": 12, "This has the": 51, "This is well": 17, "The critical points": 13, "T S fuzzy": 88, "To do that": 20, "The state of": 50, "To prove this": 93, "Turing machine is": 20, "This paper will": 16, "The real and": 22, "These terms are": 14, "The transformation _MATH_": 25, "The final step": 37, "The results presented": 72, "These estimates are": 16, "Take _MATHDISP_ END": 10, "This seems to": 36, "The power of": 40, "Then the same": 13, "Therefore under the": 12, "To make a": 13, "The vertex _MATH_": 16, "This occurs when": 11, "The cost function": 34, "The predictions of": 13, "The joint distribution": 13, "They may be": 18, "That is any": 12, "The joint probability": 17, "Then the joint": 11, "This expression is": 48, "The intuition behind": 30, "The electric field": 38, "The condition for": 37, "Then with probability": 15, "The number _MATH_": 57, "They correspond to": 17, "The probability that": 65, "This property of": 13, "The composition of": 26, "The condition is": 12, "The way to": 16, "The angle between": 24, "This is related": 30, "The energy momentum": 17, "This set is": 31, "The characteristics of": 58, "This is shown": 105, "The limit of": 14, "The two parameters": 12, "The proof can": 25, "Therefore we introduce": 24, "The spatial distribution": 24, "This enables the": 24, "There is now": 10, "The energy flux": 11, "Theorem 1 it": 18, "The equation _MATH_": 22, "TV and TV": 10, "TV series channels": 49, "The rotation of": 24, "The Lorentz force": 10, "This is demonstrated": 31, "The level of": 41, "The probability _MATH_": 25, "The problem with": 44, "The likelihood of": 20, "Then the family": 12, "Then we describe": 15, "This can lead": 12, "This is illustrated": 132, "The Euclidean distance": 10, "Therefore we consider": 33, "The Hamiltonian function": 15, "These studies have": 14, "Then one has": 46, "The following statements": 27, "The solar wind": 56, "The cross correlation": 34, "This was also": 18, "The second stage": 27, "Table _REF_ it": 44, "Turing machine _MATH_": 32, "The remaining part": 26, "Therefore Theorem _REF_": 14, "This statement is": 18, "This action is": 10, "Then the number": 23, "The solid lines": 32, "The convexity of": 11, "Then _MATH_ where": 71, "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, "Therefore we present": 11, "Two sets of": 12, "The total energy": 36, "This equation is": 80, "The _MATH_ parameter": 29, "The outline of": 65, "Table I END": 38, "Then the _MATH_": 66, "Thus the condition": 14, "The system of": 81, "The total power": 10, "The upper limit": 20, "The main properties": 11, "The last example": 14, "The time derivative": 66, "To describe the": 72, "The subject of": 21, "The estimates of": 26, "The incorporation of": 11, "To ensure the": 33, "The critical value": 24, "The first equality": 23, "The interested reader": 53, "To compensate for": 20, "This results from": 13, "The above system": 20, "The theoretical analysis": 22, "The impact of": 66, "Then as in": 18, "Th M Rassias": 13, "The gradient of": 21, "This chapter provides": 34, "The second level": 10, "The method was": 21, "The equality _MATH_": 19, "There will be": 30, "This paper deals": 44, "There is of": 13, "The frequency range": 11, "The extent to": 13, "Therefore the set": 19, "The reader can": 36, "This value was": 12, "This so called": 13, "Then taking into": 24, "Then from Lemma": 15, "The extension to": 28, "Then _REF_ becomes": 17, "To make the": 113, "The final expression": 21, "The curvature of": 14, "This however is": 23, "To limit the": 10, "The name of": 12, "This map is": 13, "Thus _MATHDISP_ and": 56, "The sliding mode": 11, "The control system": 12, "The aim is": 66, "This method has": 60, "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, "Thus _MATH_ which": 22, "The initial and": 12, "The high resolution": 20, "These features are": 27, "The case where": 35, "Theorem _REF_ tells": 16, "They consist of": 14, "The architecture is": 11, "Theorem 2 in": 43, "The growth rate": 24, "Table _REF_ _CITE_": 14, "The transformation from": 11, "The model can": 35, "These parameters are": 46, "This brings us": 11, "The system under": 11, "This observation is": 50, "These results show": 57, "This points to": 13, "This is referred": 19, "Test _MATH_ and": 21, "Theorem _REF_ c": 11, "Then as the": 10, "This implies _MATH_": 96, "The share of": 12, "The result then": 15, "The number density": 11, "This suggests a": 20, "The value function": 14, "The scalar field": 22, "These results have": 24, "This allows the": 56, "The method uses": 22, "The method is": 158, "The coupling between": 22, "This allows 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"Theorem _REF_ states": 14, "The estimate of": 30, "The key difference": 16, "The coordinates of": 32, "Table END END": 23, "Therefore for the": 47, "This paper provides": 24, "They are given": 20, "Theorem _REF_ says": 15, "Therefore according to": 31, "Then in view": 37, "The simplest case": 15, "The relation _MATH_": 48, "These quantities are": 29, "Therefore _MATH_ if": 18, "Table 4 END": 39, "The vector of": 28, "The unknown parameters": 11, "The straight line": 13, "The integral over": 21, "The only way": 33, "This approach to": 14, "Theorem _REF_ with": 101, "Then _MATHDISP_ with": 30, "The minus sign": 12, "These parameters can": 13, "The assumption that": 46, "Therefore by using": 18, "The method of": 93, "Thus the value": 15, "The first problem": 21, "The integration in": 12, "These correspond to": 17, "The motion of": 69, "Therefore the value": 14, "The above equation": 48, "To overcome these": 27, "Then from _MATH_": 11, "TErrestrial RElations Observatory": 26, "Therefore 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"That _MATH_ is": 18, "To generate the": 20, "TRACE 1550 \u00c5": 15, "Then _MATH_ defined": 12, "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, "Table 1 that": 10, "The system uses": 12, "The approach is": 59, "This is obvious": 15, "The _MATH_ are": 66, "This chapter has": 22, "The function _MATHDISP_": 20, "This can also": 41, "The difference of": 53, "This follows by": 11, "This holds for": 22, "The non trivial": 14, "The current state": 12, "The algorithm for": 34, "This would imply": 15, "The weight _MATH_": 27, "To prove Theorem": 33, "This work is": 75, "The analysis and": 17, "The sets of": 17, "Thus _REF_ and": 13, "Thus the proposed": 23, "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, "Then the vector": 14, "This plot shows": 11, "The normal form": 12, "The displacement of": 13, "This study is": 22, "This claim is": 16, "The methods presented": 12, "Theorem 5 4": 18, "T END END": 68, "This gives _MATH_": 29, "The proof that": 23, "This is analogous": 26, "Then we find": 54, "The unit cell": 13, "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, "Theorem 5 5": 18, "This idea is": 31, "This definition is": 26, "This is explained": 19, "The time series": 33, "The first few": 15, "The remaining _MATH_": 24, "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, "Therefore _MATH_ converges": 11, "The path _MATH_": 12, "The next result": 51, "This translates to": 10, "The equations for": 26, "The proof relies": 23, "Theorem _REF_ page": 14, "The creation of": 21, "The higher the": 30, "The energy conservation": 13, "This implies a": 32, "Type II censored": 15, "They found a": 10, "Then _MATH_ _MATH_": 133, "The main advantages": 16, "Then the equation": 33, "To circumvent this": 18, "There is much": 15, "The main objective": 67, "The field is": 13, "Thus at the": 25, "The problem _MATH_": 11, "The results we": 12, "The analysis shows": 23, "The specification of": 20, "This gives _MATHDISP_": 61, "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, "The variance of": 44, "Then problem _REF_": 17, "This explains why": 49, "The other important": 12, "Therefore as the": 14, "The work of": 53, "Thus there are": 51, "The results from": 45, "The _MATH_ function": 28, "To define the": 35, "The basic reproduction": 14, "This case has": 10, "Then given _MATH_": 13, "Then considering the": 12, "The low energy": 16, "The skin friction": 17, "The Nusselt number": 12, "The following are": 46, "The best known": 34, "The relevance of": 25, "Then the result": 15, "The asymptotic variance": 12, "The component _MATH_": 13, "Theorem 5 2": 30, "The power law": 31, "The second set": 27, "The interest in": 26, "Thus the problem": 31, "Table _REF_ has": 10, "To handle this": 10, "Then by definition": 20, "The explicit form": 31, "The convergence of": 52, "Therefore the probability": 26, "This method was": 36, "This algorithm has": 15, "The probabilities _MATH_": 13, "This establishes the": 19, "The analysis is": 44, "Theorem _REF_ when": 20, "The validity of": 62, "This is what": 57, "Therefore we should": 18, "The metric of": 16, "Therefore the design": 12, "The initial state": 33, "Then with the": 24, "Then we compute": 23, "The first section": 14, "Taylor series _MATHDISP_": 12, "The above analysis": 19, "The phase of": 15, "These results can": 36, "They used the": 16, "The CME was": 18, "The time dependent": 26, "This yields END": 14, "They observed that": 15, "This demonstrates the": 18, "The correctness of": 16, "Therefore in this": 89, "The frequency of": 45, "This result was": 53, "Taylor problem in": 12, "The results suggest": 20, "Theorem _REF_ under": 14, "The field of": 46, "The order of": 73, "The algorithm starts": 16, "Then the algorithm": 19, "The second is": 61, "Table 1 presents": 11, "To account for": 71, "They are the": 49, "The first _MATH_": 24, "The computation is": 17, "To find out": 12, "Therefore _REF_ is": 27, "Then based on": 40, "This chapter describes": 30, "This way we": 41, "Theorem B END": 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, "Table _REF_ were": 23, "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, "Torrance Sparrow model": 15, "TI END END": 21, "They are very": 12, "This result follows": 12, "To quantify the": 46, "This can easily": 16, "The general expression": 16, "The algorithm can": 18, "The conditions on": 12, "The ability to": 60, "The method presented": 20, "This means _MATH_": 21, "Table 2 for": 10, "Tevatron _CITE_ END": 14, "This yields that": 20, "The union of": 30, "This paper aims": 19, "Therefore the energy": 10, "The same procedure": 31, "The data for": 32, "The paper ends": 20, "This space is": 16, "This mode is": 11, "The angle _MATH_": 34, "The square root": 13, "There are _MATH_": 97, "Therefore _MATHDISP_ and": 64, "The monotonicity of": 14, "The main reason": 99, "The matrix elements": 22, "The following is": 89, "To facilitate this": 10, "The inclusion _MATH_": 14, "The filtration _MATH_": 12, "Thus it can": 41, "Theorem _REF_ together": 20, "These values can": 11, "Thus Proposition _REF_": 11, "This also implies": 24, "To accomplish this": 40, "Then we discuss": 20, "The _MATH_ model": 19, "The discussion in": 12, "This information is": 45, "The temperature is": 13, "Theorem 3 of": 14, "These bounds are": 10, "The latter approach": 11, "This metric is": 12, "The continuity equation": 11, "The equation _MATHDISP_": 15, "The reason why": 45, "The authors in": 50, "This makes it": 53, "The time scale": 14, "The work by": 21, "The theorem is": 78, "To match the": 11, "This yields an": 15, "To clarify this": 10, "Then under the": 35, "This is confirmed": 60, "Table _REF_ with": 51, "This chapter presents": 46, "Thus one of": 13, "The approach in": 12, "Then in a": 16, "This implies for": 10, "The index _MATH_": 41, "To investigate this": 18, "The observations were": 16, "The dimensions of": 13, "This _MATH_ is": 29, "The model that": 12, "The lower limit": 12, "This induces a": 10, "TeV and _MATH_": 32, "This case corresponds": 11, "The time varying": 18, "Theorem _REF_ at": 14, "The change of": 69, "The wave functions": 13, "The representation of": 20, "The main challenge": 17, "This limits the": 14, "Theorem _REF_ follows": 42, "The part of": 17, "The first line": 20, "The transition matrix": 16, "To produce the": 10, "The effect on": 13, "The angular velocity": 15, "These data were": 15, "Therefore the solution": 21, "To verify the": 58, "The fourth column": 12, "Table _REF_ show": 53, "This strategy is": 16, "Theorem 2 END": 123, "Theorem _REF_ on": 28, "Then by Lemma": 74, "The interpretation of": 60, "This ends the": 27, "The most commonly": 42, "Three types of": 20, "Therefore both the": 11, "There it is": 10, "This justifies the": 18, "To illustrate how": 19, "Throughout this book": 11, "To build a": 11, "Theorem _REF_ 3": 20, "The proposed framework": 13, "The effectiveness of": 39, "The dispersion relation": 20, "The comparison with": 23, "The uniqueness of": 41, "The most well": 14, "The density is": 14, "The changes in": 29, "The transition to": 12, "The distance of": 12, "There are basically": 13, "Theorem 7 1": 10, "Then the total": 18, "Thus _MATHDISP_ where": 78, "The corresponding time": 10, "The essence of": 21, "These imply that": 12, "The Dirac equation": 11, "The right panel": 46, "The detection of": 42, "Theorem _REF_ p": 38, "The source of": 26, "To check that": 12, "The _MATH_ distribution": 15, "The last column": 22, "Then _REF_ and": 28, "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, "Thus by Theorem": 21, "The _MATH_ terms": 15, "To finish the": 24, "The second method": 35, "The controller is": 18, "The point of": 49, "The _MATH_ in": 15, "To begin we": 18, "Table 3 we": 15, "The characterization of": 23, "This formulation is": 10, "Taking _MATH_ _MATH_": 13, "The vertices of": 29, "The second statement": 15, "The dependence on": 36, "To take into": 21, "Then we conclude": 11, "The measure of": 10, "TSP END END": 15, "The differential equations": 16, "This is only": 33, "This fact was": 13, "The control law": 17, "Thus due to": 18, "These results indicate": 35, "This value of": 15, "The activation functions": 11, "This contradicts the": 78, "To clarify the": 16, "This is clear": 19, "The waiting time": 11, "The product of": 34, "The approach taken": 10, "The approach of": 28, "This form of": 27, "Table 2 shows": 23, "The model takes": 11, "There was also": 11, "Then there must": 13, "Terrestrial Relations Observatory": 43, "This example is": 33, "The work in": 30, "Turing machine END": 33, "The proposed circuit": 14, "To achieve the": 36, "These equations can": 28, "The next to": 15, "The procedure for": 23, "Their approach is": 15, "The model for": 26, "The stability and": 10, "The general form": 48, "The observed data": 10, "Therefore the two": 19, "This in particular": 21, "The lower the": 12, "These expressions are": 13, "The overall system": 10, "Type III like": 47, "Type III bursts": 31, "The availability of": 33, "The three dimensional": 58, "The improvement in": 10, "Then Theorem _REF_": 28, "Theorem _REF_ reduces": 11, "The model we": 23, "These kinds of": 28, "The collection of": 37, "They are based": 20, "To date the": 12, "The state transition": 17, "The state and": 14, "The one step": 10, "The second equality": 32, "Therefore it seems": 16, "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_": 11, "The above condition": 13, "Taylor coefficients of": 16, "Taylor series END": 11, "This procedure can": 15, "The contributions from": 19, "Thus _MATHDISP_ _MATHDISP_": 26, "This suggests the": 26, "Table _REF_ column": 10, "The price of": 16, "The intuition is": 19, "The only thing": 19, "This may not": 11, "The well known": 47, "Thus the time": 16, "The observations of": 27, "The minimum of": 18, "Theorem 4 4": 24, "This tells us": 14, "This turns out": 16, "The average number": 24, "The problem can": 34, "To distinguish between": 10, "Table 2 END": 133, "This proves _MATH_": 12, "The computational cost": 14, "The approach we": 23, "The identification of": 37, "Thus we find": 36, "They did not": 14, "Then _MATH_ in": 32, "This argument is": 18, "The obtained values": 12, "This implies _REF_": 10, "The latter are": 46, "The challenge is": 18, "There are at": 34, "Thus _MATHDISP_ for": 34, "Theorem 2 4": 45, "This illustrates that": 10, "Therefore although the": 11, "The first approach": 34, "The following set": 10, "Therefore the results": 13, "The last relation": 10, "The reduced order": 13, "The first condition": 32, "Taking this into": 20, "The consistency of": 18, "The characteristic polynomial": 19, "Table 2 and": 12, "The top left": 24, "The first was": 14, "The two other": 14, "This requires the": 25, "Thus in a": 22, "The system parameters": 16, "Theorem 1 and": 54, "The present study": 34, "The obtained results": 57, "The basic tool": 11, "Table 1 we": 38, "The graphs in": 10, "The first test": 12, "Therefore if one": 12, "Therefore the overall": 19, "To model this": 16, "The simplest example": 21, "To apply the": 38, "Then _MATH_ as": 47, "The primary objective": 10, "The numbers of": 28, "The following lemmas": 16, "The comparison between": 45, "The two main": 27, "Thanks to _REF_": 12, "The components of": 71, "The scalar product": 19, "Then _MATH_ which": 12, "The most striking": 12, "The parameters for": 21, "This immediately implies": 21, "Throughout the proof": 10, "This means in": 17, "The calculation is": 15, "The conclusion is": 42, "This theorem is": 25, "This fact can": 28, "This time we": 19, "This appears to": 13, "The plasma density": 13, "The points in": 11, "There exists an": 85, "The electron density": 26, "Therefore _MATHDISP_ _MATHDISP_": 18, "Theorem _REF_ as": 52, "This procedure was": 11, "This parameter is": 19, "The issue of": 46, "The contents of": 17, "The larger _MATH_": 14, "The basis functions": 10, "The main theorem": 15, "The sum _MATH_": 17, "That means _MATH_": 12, "That is they": 16, "The values are": 25, "The family _MATH_": 14, "The work presented": 20, "They find that": 26, "The result shows": 24, "Taylor series in": 14, "Therefore _MATH_ can": 35, "Therefore the main": 13, "The relation _REF_": 15, "Traveling Salesman Problem": 18, "Thus the second": 16, "The lengths of": 11, "The spectral index": 10, "Therefore we assume": 26, "The question arises": 28, "Therefore we believe": 10, "Theorem 2 are": 11, "There may be": 31, "Then and _MATH_": 14, "To explain this": 17, "Theorem _REF_ asserts": 12, "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, "The transition function": 10, "Thus instead of": 22, "To reach this": 12, "These values of": 13, "The high frequency": 22, "The subset of": 10, "This result shows": 23, "Theorem 3 and": 13, "That is in": 54, "The closed loop": 79, "The key property": 10, "The expansion of": 27, "Taking the derivative": 44, "The uncertainties are": 13, "Then starting from": 14, "The fraction of": 37, "This extension is": 11, "Therefore _MATH_ satisfies": 11, "The history of": 14, "TCP END END": 27, "The remaining parameters": 11, "The values for": 38, "The kernel of": 25, "Therefore since the": 10, "Thus Eq _REF_": 33, "The numerical value": 10, "The fractal dimension": 12, "The system has": 36, "To validate the": 17, "Therefore when _MATH_": 34, "They showed that": 88, "Therefore _MATH_ _MATH_": 25, "The total magnetic": 14, "Therefore it follows": 51, "The field equations": 14, "The Euler Lagrange": 20, "This means the": 24, "Then _REF_ implies": 27, "Thus we get": 95, "The latter two": 23, "Table _REF_ indicate": 11, "The underlying idea": 23, "This estimate is": 16, "Then the process": 20, "The energy density": 31, "This paper discusses": 18, "The notions of": 15, "The other type": 11, "This is essential": 12, "The spectral density": 16, "Thus with a": 12, "The total decay": 11, "Then the trivial": 23, "The same arguments": 14, "These assumptions are": 20, "This possibility is": 10, "This not only": 11, "Table _REF_ but": 15, "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 assumption _MATH_": 21, "This is now": 11, "Tevatron END END": 31, "The corresponding _MATH_": 30, "The method used": 22, "The vertical axis": 10, "Thus for every": 27, "The simulated results": 11, "This causes a": 12, "Take _MATH_ END": 41, "The observations are": 13, "The differences in": 33, "The argument for": 12, "This would allow": 25, "These points are": 13, "The discrete time": 27, "The other parameters": 27, "To illustrate this": 81, "The active region": 31, "The wave function": 19, "The main differences": 15, "Thus the phase": 12, "This section contains": 15, "This will allow": 30, "The differences are": 10, "Thus the use": 10, "Thus the method": 13, "The subscripts _MATH_": 12, "The partial derivatives": 17, "Then the Cauchy": 11, "The obtained result": 11, "The above two": 37, "To summarize the": 42, "Then if we": 25, "Table 1 it": 10, "To compute _MATH_": 40, "Thus it seems": 11, "Thus by using": 17, "The correlation coefficient": 23, "Thus _MATH_ so": 10, "Table 1 summarizes": 14, "Thus for example": 36, "The adjacency matrix": 12, "This also means": 19, "To this purpose": 38, "The comparison shows": 13, "The profiles of": 19, "Thus we need": 59, "The velocity field": 12, "Then by Theorem": 59, "This method does": 16, "This finding is": 27, "TPC W benchmark": 12, "Theorem 6 4": 16, "The first equation": 34, "Thus without loss": 10, "Theorem _REF_ a": 51, "This requirement is": 18, "The vertex set": 11, "The reduction in": 17, "Theorem _REF_ let": 30, "The criteria for": 10, "The factors _MATH_": 11, "Therefore we first": 12, "The Lyapunov exponents": 11, "The experimental data": 21, "The critical path": 14, "The actuarial present": 11, "To solve _REF_": 10, "The Lagrangian of": 27, "The order _MATH_": 11, "The paper also": 14, "The open loop": 24, "The lemma follows": 23, "The matrix function": 12, "Two Phase I": 19, "The most notable": 12, "This set of": 57, "The system consists": 12, "Theorem _REF_ cannot": 16, "Therefore _MATH_ where": 11, "The initial value": 48, "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": 17, "Take _MATH_ and": 38, "This is actually": 13, "The same result": 25, "Thus as the": 16, "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, "The second equation": 28, "The convergence in": 11, "There are however": 34, "The vanishing of": 14, "The cardinality of": 13, "The neural network": 15, "This is made": 14, "The bandwidth of": 16, "The samples were": 15, "The laser system": 10, "The key observation": 19, "Thus the corresponding": 15, "This reveals the": 10, "There also exists": 10, "The states _MATH_": 11, "The state _MATH_": 14, "Theorem and the": 10, "The signal to": 19, "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": 36, "Theorem 1 4": 30, "This will help": 10, "Then _MATH_ so": 29, "Thus the solution": 36, "The case with": 14, "The one loop": 27, "Thus far we": 10, "Then the initial": 11, "There exist several": 21, "Therefore the result": 16, "To begin with": 66, "To simplify notation": 20, "The plots of": 13, "The relative error": 10, "Theorem _REF_ requires": 14, "This result could": 10, "The dotted line": 16, "The second example": 34, "The third example": 10, "Then we set": 18, "The proof given": 11, "Thus we shall": 13, "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, "The outcome of": 29, "The optimal policy": 14, "To prevent the": 16, "The masses of": 26, "The integer _MATH_": 11, "The usefulness of": 14, "The proof uses": 17, "Taylor s series": 11, "The line of": 19, "The form factor": 19, "There was no": 12, "To perform this": 10, "Two examples are": 17, "Then the control": 17, "T cells END": 17, "The cut off": 12, "The formula for": 31, "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, "The _MATH_ dependence": 30, "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": 15, "This case can": 12, "This relation is": 26, "To explain the": 43, "Turing Hopf bifurcation": 14, "The fractional order": 14, "Theorem _REF_ every": 14, "To consider the": 22, "The coupling of": 23, "Theorem 5 1": 50, "This is easy": 17, "To sum up": 28, "Then the second": 22, "This confirms that": 23, "The bound of": 11, "The uncertainty on": 10, "The current version": 12, "The main point": 30, "Then we see": 12, "To design the": 14, "The critical temperature": 11, "The problem that": 10, "This completes our": 11, "This is partly": 19, "Thus the initial": 17, "Therefore instead of": 14, "The most prominent": 22, "Thus we take": 12, "There are in": 12, "To alleviate the": 11, "This section will": 14, "These data are": 41, "The most simple": 13, "The large number": 20, "This is necessary": 20, "The input is": 11, "The correlation function": 10, "The decay width": 11, "This data set": 37, "The last step": 44, "These authors found": 15, "Then _REF_ follows": 12, "The two models": 13, "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": 23, "The results have": 22, "Theorem _REF_ see": 32, "Thus it suffices": 18, "The task of": 35, "The differential equation": 26, "The heavy quark": 12, "The eigenvalues _MATH_": 28, "Then we say": 11, "The reconstruction of": 20, "Thus if a": 17, "Thus it remains": 12, "This mapping is": 14, "The null hypothesis": 18, "The strategy of": 16, "The assertion follows": 13, "This result implies": 14, "T F units": 12, "The finite time": 12, "This section also": 17, "This END END": 25, "The inequality _MATH_": 26, "TV END END": 12, "This solution can": 11, "The consideration of": 20, "The technique of": 20, "The pair of": 18, "The two components": 11, "The operation _MATH_": 20, "The other cases": 11, "The frequency domain": 13, "This is based": 32, "The branching ratios": 11, "The parameters in": 17, "To further improve": 13, "The decomposition of": 21, "Time END END": 10, "The worst case": 27, "Then passing to": 11, "The algorithm _MATH_": 12, "The second point": 12, "This means _MATHDISP_": 10, "The strong coupling": 16, "The following section": 12, "The necessity of": 14, "The value _MATH_": 79, "The _MATH_ of": 15, "The fact is": 11, "This is likely": 17, "Therefore it should": 10, "The production cross": 14, "Taylor series kernel": 12, "The result will": 16, "TLs END END": 10, "The most straightforward": 21, "To obtain these": 11, "Thus we only": 29, "The third step": 10, "The reason lies": 11, "This is exactly": 48, "The same approach": 16, "Therefore the existence": 11, "To solve the": 90, "The literature on": 30, "This process was": 10, "The coincidence of": 10, "The maximum likelihood": 24, "Thus _MATH_ implies": 12, "To interpret the": 10, "This construction is": 15, "There is however": 52, "The result in": 34, "Thus for any": 63, "The data in": 19, "Therefore it makes": 10, "The higher order": 23, "Thus with the": 13, "To produce a": 13, "Then letting _MATH_": 13, "Then the unique": 17, "The meaning of": 36, "The representation _REF_": 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": 14, "The density _MATH_": 10, "The separation between": 10, "The exact solution": 25, "To construct the": 29, "The third row": 11, "To apply this": 19, "The boundaries of": 13, "The rationale behind": 15, "Therefore for a": 23, "This value can": 12, "Therefore we define": 14, "Tree END END": 18, "The beam is": 11, "This configuration is": 10, "The plan of": 38, "That is each": 26, "The origin is": 10, "To give an": 26, "Then the random": 13, "Toward this end": 15, "To remedy this": 17, "This is known": 47, "The transfer function": 30, "The sum over": 13, "To overcome the": 49, "This indicates the": 24, "This is most": 21, "The sign of": 50, "The rates of": 11, "Then we prove": 15, "Therefore _MATH_ as": 21, "The slope of": 35, "The top quark": 33, "The basis for": 12, "Theorem 6 2": 16, "Theorem 6 1": 28, "This defines the": 21, "These oscillations are": 16, "Type 1 and": 10, "The black hole": 15, "The second result": 15, "The paper concludes": 13, "This approach will": 10, "The second row": 20, "The scheme is": 21, "Type II radio": 19, "The bound _REF_": 11, "The main technical": 15, "Thus we see": 36, "This applies to": 12, "The concentration of": 21, "The analytic solution": 12, "Therefore the only": 19, "This mechanism is": 28, "Take an arbitrary": 12, "Tan et al": 17, "The realization of": 14, "This is usually": 46, "Thus one has": 17, "The difficulty with": 10, "They have also": 19, "Theorem _REF_ above": 28, "The form factors": 26, "The numerical solution": 26, "Then for a": 30, "This equation can": 51, "To fix ideas": 12, "Theorem A END": 13, "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, "Table 3 3": 16, "The following examples": 18, "Taylor expansion END": 17, "Theorem 5 END": 16, "Thus if one": 10, "The two step": 10, "The trajectories of": 23, "This section shows": 19, "They also found": 22, "The leading term": 12, "To the authors": 14, "Theorem 4 7": 10, "This is expressed": 11, "Thomson scattering sphere": 12, "Table 3 shows": 14, "The precision of": 21, "This book is": 14, "Therefore Lemma _REF_": 10, "The critical manifold": 11, "This hypothesis is": 12, "Type II censoring": 12, "These effects are": 24, "The other terms": 11, "The case when": 21, "The following notation": 22, "This bound is": 20, "This class is": 13, "This discrepancy is": 10, "The stability condition": 14, "This contrasts with": 19, "These plots show": 10, "The fixed point": 31, "Therefore we expect": 35, "The main issue": 17, "Theorem _REF_ iii": 20, "The principle is": 10, "The Jacobian of": 16, "Thus significant modeling": 13, "The random vector": 10, "These regions are": 18, "Therefore _MATHDISP_ for": 11, "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 coupling constants": 10, "The model in": 17, "The more general": 13, "Then by applying": 16, "This quantity is": 36, "Taylor expansion we": 10, "The similarity between": 21, "The second integral": 16, "The architecture of": 21, "The coordinates _MATH_": 13, "Then we show": 33, "This assumption implies": 10, "They are shown": 16, "Then following the": 13, "TeV _MATH_ TeV": 12, "Then _MATH_ must": 16, "This algorithm can": 10, "The trade off": 15, "This would also": 10, "The approach described": 12, "To understand this": 21, "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, "Theorem 1 that": 14, "The idea that": 12, "The detailed description": 11, "To create a": 16, "That is all": 11, "Taking account of": 15, "The latter condition": 20, "The small scale": 10, "The distance _MATH_": 20, "The result was": 12, "The radiative corrections": 10, "Thus the above": 16, "To express the": 11, "Therefore the model": 16, "Telescope EIT _CITE_": 19, "The generating functional": 18, "This result confirms": 14, "Turing machine that": 10, "The vast majority": 12, "The matrix element": 16, "This inequality is": 20, "This yields _MATH_": 28, "These findings are": 19, "The converse of": 15, "Take _MATH_ then": 15, "The physics of": 20, "Taking _MATH_ in": 49, "The rationale for": 16, "This paper analyzes": 10, "That is that": 10, "The quantities _MATH_": 50, "This is very": 46, "This region is": 20, "The frequency drift": 13, "This is somewhat": 19, "Theorem 1 of": 38, "The problem we": 15, "The estimated values": 17, "This is evident": 10, "Taylor s formula": 22, "This estimator is": 11, "Tang et al": 18, "Thus in general": 22, "The other three": 18, "Thus the resulting": 19, "Therefore the mean": 10, "Theorem 1 are": 13, "Toolbox END END": 15, "These results will": 11, "The framework is": 12, "Therefore Eq _REF_": 18, "The mass _MATH_": 11, "The steps of": 12, "The onset of": 17, "There are very": 12, "The image of": 35, "The rank of": 22, "The absorption of": 14, "This process continues": 14, "Theorem _REF_ of": 38, "The activation energy": 10, "The third one": 21, "Then _MATH_ i": 12, "The condition on": 12, "Theorem _REF_ applies": 37, "The applications of": 13, "To check whether": 12, "The physical properties": 14, "The _MATH_ parameters": 12, "The drawback of": 28, "Thus we write": 15, "The cross sections": 31, "The notation used": 14, "These problems are": 21, "Then the desired": 12, "Theorem 2 and": 20, "Thompson et al": 27, "The second inequality": 28, "There is the": 21, "Theorem 4 6": 13, "The simulation was": 10, "This is discussed": 18, "Theorem 1 5": 16, "This approach provides": 11, "T F unit": 23, "This clearly shows": 26, "The error in": 22, "To see the": 55, "The points _MATH_": 20, "The running of": 10, "To maintain the": 12, "To prove our": 14, "Then _MATH_ the": 12, "Then the transition": 13, "Then we introduce": 20, "This process of": 17, "The Hamilton Jacobi": 12, "The algorithm takes": 12, "That is one": 15, "These are also": 14, "The first integral": 17, "The likelihood function": 25, "To introduce the": 12, "The standard error": 11, "The spread of": 10, "Theorem _REF_ _REF_": 24, "T is the": 11, "This asymmetry is": 10, "This method of": 19, "This must be": 10, "The root mean": 13, "The work _CITE_": 13, "The computational complexity": 25, "The Hamiltonian is": 11, "The Lagrangian density": 11, "They argue that": 13, "The methods of": 18, "Taylor s theorem": 10, "The _MATH_ meson": 11, "The correlation coefficients": 20, "This calls for": 10, "The probability distribution": 21, "Tevatron and the": 20, "Thus Theorem _REF_": 19, "The reasons for": 19, "The derivatives of": 20, "The expectation is": 13, "To address these": 13, "This analysis is": 19, "The color of": 11, "The nonlinear functions": 13, "The scale of": 13, "These properties are": 34, "The main components": 14, "The characteristic time": 10, "This means END": 14, "Theorem 1 _MATH_": 13, "The second class": 20, "The main obstacle": 13, "Therefore based on": 15, "The average value": 15, "The self energy": 10, "Theorem _REF_ has": 31, "Thus although the": 12, "Theorem 5 in": 11, "The contribution to": 16, "The limit _MATH_": 14, "The expression in": 13, "The estimation error": 12, "Then the operator": 33, "The _MATH_ term": 35, "The total _MATH_": 12, "This creates a": 14, "Thus the system": 26, "To explore the": 15, "Then up to": 11, "The case in": 17, "Thus it appears": 10, "This then means": 10, "The paper _CITE_": 27, "The model consists": 15, "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 _MATH_ matrices": 11, "The frequencies of": 16, "The probability density": 23, "The production of": 40, "Therefore we focus": 15, "Thus as _MATH_": 22, "These models have": 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"The third section": 11, "Then the matrix": 18, "To bound the": 13, "The inequality in": 12, "Then in section": 18, "Table 5 END": 27, "Thus the only": 18, "Then the inequality": 15, "Thus this is": 11, "They should be": 11, "The situation becomes": 10, "The model includes": 12, "This topic has": 10, "The ground state": 15, "They are called": 10, "The algorithm proceeds": 14, "They are all": 17, "The presentation of": 10, "The splitting of": 11, "The implication of": 12, "The bifurcation diagram": 15, "The potential field": 15, "The metric is": 11, "The algorithm was": 22, "The problems of": 14, "The input to": 26, "Table 2 the": 12, "The new method": 10, "The refractive index": 15, "The first law": 10, "The curves of": 17, "The functional _MATH_": 33, "This cannot be": 12, "This combined with": 14, "This subsection is": 12, "The action _MATH_": 15, "The transition from": 38, "The second section": 12, "To study this": 11, "The pseudo code": 19, "The signal _MATH_": 20, "This is even": 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"That is given": 19, "The estimator is": 11, "The key point": 65, "Therefore from Lemma": 10, "The well posedness": 17, "The algorithm uses": 13, "There exist positive": 23, "These structures are": 10, "Then the complex": 12, "This analysis shows": 10, "The _MATH_ component": 24, "The bottom right": 10, "The times of": 10, "The usage of": 18, "Theorem 1 6": 12, "The convex hull": 26, "The adversary _MATH_": 21, "The first time": 13, "This phenomenon can": 12, "Ta END END": 17, "Therefore the stability": 16, "The numerical values": 20, "The Hamiltonian for": 12, "The method to": 12, "Turning to the": 25, "Thus the optimal": 16, "The initial states": 10, "There exist constants": 38, "The main part": 18, "The linear stability": 16, "The optimal value": 21, "The feasibility of": 15, "The improvement of": 17, "Thus we define": 18, "To achieve a": 20, "The extraction of": 17, "To define a": 14, "This change of": 15, "The following table": 15, "There exist functions": 15, "This analysis has": 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"The Lie algebra": 21, "This operation is": 19, "Then by virtue": 14, "The cause of": 14, "The measurements of": 19, "Theorem 6 5": 11, "Theorem can be": 10, "Theorem 5 3": 14, "The main interest": 14, "The integral _MATH_": 14, "Two of the": 24, "The non zero": 18, "The fourth order": 10, "The height of": 41, "The explicit forms": 11, "Tu et al": 18, "This rule is": 10, "Theorem _REF_ Theorem": 16, "This generalizes the": 11, "This change is": 12, "The covariance matrix": 20, "Table 2 we": 17, "This problem arises": 10, "The third component": 10, "The phase space": 21, "The PID controller": 10, "The model presented": 19, "The second issue": 24, "The two terms": 14, "The response of": 30, "This constraint is": 11, "The inclusive cross": 10, "There is evidence": 10, "Then either _MATH_": 21, "To understand how": 10, "To represent the": 17, "This gives END": 13, "That is when": 18, "This result also": 10, "The temporal variation": 10, "The histogram of": 14, "The condition of": 36, "Then 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"Theorem _REF_ imply": 17, "The block diagram": 33, "Therefore we find": 13, "Theorem 3 6": 21, "The potential for": 10, "Therefore it suffices": 16, "The amplitude for": 10, "The Kullback Leibler": 11, "To determine whether": 14, "The diffusion coefficient": 13, "The infinitesimal generator": 13, "Table 4 shows": 13, "The relations _REF_": 11, "The net effect": 10, "The nonlinear system": 20, "This work presents": 17, "Then the map": 13, "The proof consists": 11, "The disease free": 17, "The light cone": 13, "Then _MATH_ becomes": 10, "Therefore the function": 26, "The validation of": 10, "The second way": 15, "This situation can": 10, "The following property": 12, "The corresponding equations": 12, "This algorithm was": 11, "The works of": 10, "The same method": 18, "Throughout the remainder": 12, "The one dimensional": 32, "The basic model": 14, "The on line": 11, "The event was": 12, "The enhancement of": 11, "The horizontal axis": 17, "Tables 1 and": 20, "The result that": 11, "Theorem _REF_ guarantees": 21, "Therefore the above": 15, "The off diagonal": 19, "The boundedness of": 12, "The code is": 12, "This relation can": 15, "This follows immediately": 16, "Then we derive": 13, "Then we choose": 12, "This yields for": 11, "The other possibility": 12, "The question whether": 14, "Thus for our": 10, "This has motivated": 13, "The directions of": 15, "The rows of": 17, "Thus in our": 22, "The reason of": 17, "The resulting system": 15, "Type II seesaw": 21, "Therefore the same": 13, "Thus a single": 10, "The dashed line": 27, "The images in": 18, "The velocity of": 28, "Therefore in our": 25, "The simplest approach": 14, "This section introduces": 14, "Though it is": 15, "The action is": 15, "This model allows": 15, "To find _MATH_": 18, "Type I error": 24, "They are of": 11, "The most promising": 11, "The calculated values": 12, "These will be": 23, "This work was": 23, "The mass difference": 12, "The method involves": 12, "The signature of": 16, "Then the 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"the line through": 30, "through the origin": 97, "to the unit": 79, "the unit vector": 120, "that both _MATH_": 201, "that the normalized": 25, "the vector _MATH_": 696, "the same order": 343, "the private sector": 16, "the extent of": 147, "to those of": 334, "the correlation is": 39, "the variables and": 19, "their sources END": 11, "that allow us": 26, "the continuum and": 17, "transitions of the": 44, "to the difficulty": 39, "the difficulty in": 61, "the single mode": 17, "the Lamb Dicke": 21, "the previous sections": 232, "to a lower": 103, "temperature _CITE_ END": 53, "the quantum state": 15, "the clock transition": 16, "three methods END": 15, "the center of": 1204, "transition END END": 292, "the second method": 31, "the beam waist": 12, "the _MATH_P_MATH_ state": 13, "the previous studies": 42, "to assure the": 17, "the clock laser": 13, "the optical lattice": 19, "to establish the": 249, "these three methods": 14, "type _MATH_ END": 276, "the extension of": 223, "to a 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assumptions in": 40, "the following properties": 275, "the ray is": 10, "to connect the": 49, "the top of": 343, "to the bottom": 65, "the bottom of": 290, "the spectral analysis": 26, "that the plasma": 54, "than the surrounding": 22, "the surrounding plasma": 25, "the idea that": 171, "the plasma is": 54, "the post CME": 21, "the relations _REF_": 59, "the following way": 357, "the following notations": 45, "that we shall": 51, "the tiling problem": 10, "the tiles in": 12, "this approach END": 99, "this work we": 769, "tiling of the": 13, "the plane by": 10, "the low solar": 17, "to probe the": 82, "the plasma parameters": 14, "the solar atmosphere": 358, "taken using the": 12, "the Atmospheric Imaging": 31, "the Extreme ultraviolet": 31, "the Hinode spacecraft": 15, "to examine the": 218, "the variability of": 86, "that the magnetic": 244, "the quiet corona": 15, "the height of": 277, "the Helioseismic and": 31, "the agreement between": 52, "the PFSS model": 40, "that EIT waves": 12, "the variable _MATH_": 392, "the remaining variables": 14, "table of _MATH_": 14, "to obtain a": 954, "the operators in": 11, "the same form": 179, "the following corollary": 167, "to _REF_ END": 487, "to a power": 26, "to interpret the": 102, "the loop length": 39, "the detection of": 331, "that it depends": 17, "the pre and": 20, "the literature e": 29, "the one proposed": 49, "to _MATH_ vertices": 11, "the service of": 19, "the objective is": 85, "this problem END": 278, "that for fixed": 38, "those _MATH_ such": 16, "that _MATH_ holds": 172, "those for which": 33, "true END END": 568, "to compute a": 175, "the input is": 63, "to the cavity": 30, "time _CITE_ END": 134, "the central limit": 69, "two degrees of": 75, "the noise END": 45, "the sum over": 125, "the occasion of": 10, "to give an": 121, "the three classes": 12, "three classes of": 23, "the buffer END": 19, "therefore _MATH_ END": 196, "that this definition": 21, "this definition of": 31, "take _MATH_ where": 23, "the holding cost": 16, "take _MATH_ the": 13, "takes the following": 84, "the parts _MATH_": 16, "that _MATH_ implies": 189, "the details and": 15, "the shape information": 15, "two in the": 24, "the simplest case": 149, "the event selection": 13, "to begin with": 23, "that as _MATH_": 206, "the rate _MATH_": 88, "the Kullback Leibler": 61, "the above equality": 61, "to _MATHDISP_ END": 1356, "that _MATH_ has": 1064, "the recent paper": 22, "the authors present": 27, "that has a": 127, "that the gap": 18, "the gap is": 20, "two parts END": 84, "the splitting of": 52, "the flux rope": 478, "the filament is": 79, "that the functions": 135, "to the present": 114, "that the diffusion": 43, "the diffusion layer": 10, "the linear functions": 10, "the necessary conditions": 75, "the linear function": 27, "the invertibility of": 28, "the initial guess": 53, "the formulation and": 12, "the sky brightness": 13, "the second and": 235, "the observation and": 19, "to find that": 80, "the times of": 78, "than the second": 29, "the second third": 17, "to _REF_ _MATHDISP_": 70, "the change of": 623, "that depends only": 46, "the right end": 22, "to see the": 154, "the above expression": 141, "to infinity as": 40, "time Markov chain": 76, "to the computation": 55, "the computation of": 749, "the average of": 337, "the free energy": 298, "this direction END": 65, "the transition metal": 12, "the magnetic properties": 33, "than the ones": 88, "to do this": 150, "this by using": 18, "the other to": 28, "two ways to": 39, "the _MATH_ parameter": 176, "this does not": 221, "to access a": 10, "the event END": 83, "to derive the": 514, "transport of angular": 23, "those for the": 118, "the time evolution": 257, "the combined action": 15, "the first mode": 58, "the meridional circulation": 73, "torque of the": 25, "the Lorentz force": 191, "thus obtain _MATHDISP_": 13, "that leads to": 131, "to a net": 10, "to eliminate the": 182, "term of the": 296, "the second equation": 201, "the new system": 37, "the original system": 183, "the sequel we": 183, "the input END": 81, "the LST of": 64, "to _REF_ we": 240, "to be _MATHDISP_": 346, "the Young modulus": 12, "the shear modulus": 16, "the moment of": 109, "the example the": 17, "the recent progress": 10, "this context END": 78, "to figure out": 38, "the Type IIB": 10, "this set up": 23, "the Calabi Yau": 20, "the distributions _MATH_": 34, "the formulae of": 13, "the relation _MATHDISP_": 288, "to run the": 52, "the engine torque": 50, "that the second": 221, "than the first": 60, "than END END": 58, "to find their": 16, "talk about the": 21, "the non rotating": 15, "the solutions _REF_": 11, "the three dimensional": 517, "to what extent": 105, "the forces acting": 14, "the gravitational force": 37, "to the ambient": 31, "the ambient solar": 76, "the other two": 383, "the neighborhood of": 234, "the discrimination of": 10, "the observed signal": 25, "the received signal": 67, "the instrument is": 18, "the following stability": 22, "the objective of": 110, "the automaton is": 12, "to the length": 74, "the source string": 12, "the hypotheses on": 10, "the corresponding expressions": 18, "turns out that": 519, "the high energy": 241, "the Monte Carlo": 200, "the first time": 633, "to describe the": 873, "that the argument": 11, "the corresponding solution": 69, "the norms of": 29, "that in the": 1815, "the quark sector": 24, "the Higgs potential": 33, "the phase in": 15, "the evolutionary process": 34, "the fitness function": 61, "the search END": 31, "to show how": 112, "to find good": 16, "the exploration of": 38, "the behaviour space": 10, "that we assume": 43, "the time period": 100, "the ML estimator": 14, "this paper was": 48, "the threshold of": 71, "the vanishing of": 59, "the cumulative distribution": 58, "the top panel": 68, "top panel of": 63, "two to three": 37, "three orders of": 48, "to a couple": 10, "than 10 END": 23, "the middle panel": 25, "that the curves": 23, "the curves of": 53, "two regimes END": 13, "to understand this": 17, "to look at": 124, "the PDF of": 37, "the bottom panel": 92, "the peak at": 36, "this subsection we": 290, "the _MATH_ control": 48, "the same _MATH_": 239, "to the left": 508, "the left by": 44, "to the right": 575, "the right by": 24, "the same reasoning": 48, "that _REF_ and": 106, "that _REF_ holds": 350, "the above choice": 10, "the age of": 129, "tax rate for": 16, "the two instruments": 20, "tax END END": 69, "the previous literature": 17, "take into account": 890, "the negative impact": 10, "the second derivative": 118, "the ratios _MATH_": 45, "to _MATH_ at": 280, "the entire region": 18, "that the same": 233, "the same situation": 15, "the zero initial": 59, "the purpose of": 464, "this article we": 378, "the gauge theory": 42, "theory of the": 164, "to start from": 26, "the Einstein Hilbert": 50, "the same result": 145, "the most general": 203, "the need for": 356, "the test vectors": 21, "the prediction for": 18, "this analysis END": 55, 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"the decision rule": 16, "the top mass": 30, "the beam s": 45, "the curvature of": 141, "the beam END": 73, "the model with": 215, "the dynamic stability": 12, "the structure END": 87, "to the harmonic": 24, "the numerical and": 19, "that quantifies the": 10, "to occur at": 47, "that this model": 71, "the same basic": 21, "the exponential growth": 24, "the _MATH_ s": 511, "to zero for": 79, "then there exists": 447, "to some _MATH_": 61, "the compact embedding": 15, "to _MATH_ in": 945, "that by the": 117, "the following inequality": 349, "true _MATHDISP_ END": 38, "the first type": 44, "type of END": 18, "to a family": 25, "the origin and": 191, "the _MATH_ axis": 898, "to develop new": 25, "time for a": 90, "to this problem": 177, "this problem is": 252, "the destination address": 11, "the routing table": 18, "to which the": 230, "there is some": 197, "the time to": 196, "this is because": 50, "the universe is": 128, "the future END": 219, "the external world": 11, "the contrary 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"the Semantic Web": 52, "transforms END END": 76, "there exists an": 792, "the _MATH_ dimensional": 573, "to _MATH_ satisfying": 21, "theory of self": 10, "to be designed": 60, "to run on": 22, "this corresponds to": 111, "to solving the": 44, "the results are": 348, "the following sections": 214, "the challenges in": 12, "to generate the": 293, "the Mandelbrot set": 11, "the complex numbers": 17, "the norms _MATH_": 43, "the _MATH_ case": 244, "the effect of": 2481, "the standard deviation": 347, "the window _MATH_": 17, "that was introduced": 15, "to extend this": 56, "this result to": 86, "the boundary _MATH_": 171, "the main interest": 10, "to carry out": 207, "the proof in": 79, "the same for": 498, "the proofs of": 188, "tree level contributions": 12, "to the Higgs": 73, "the constraints of": 65, "the model which": 56, "three of the": 73, "the low energy": 357, "to calculate END": 27, "to the Kahler": 13, "the Kahler potential": 28, "the upper and": 208, "the top boundary": 35, 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"that condition _REF_": 84, "that the characteristic": 75, "the characteristic equation": 211, "the vertical axis": 75, "that we can": 754, "the boundary condition": 275, "the price of": 225, "to a spatially": 11, "the slow variable": 10, "the timescale of": 30, "the concentration at": 11, "that make it": 20, "the analysis results": 17, "to the particular": 58, "takes advantage of": 73, "that arise in": 55, "the past two": 53, "the coexistence of": 68, "the processes that": 16, "that occur in": 49, "that the scalar": 60, "the interface is": 16, "the two dimensional": 456, "two dimensional domain": 12, "that is proportional": 32, "that solves the": 36, "the late 1990s": 11, "to implement it": 10, "transformation is a": 16, "that preserves the": 32, "two dimensions the": 24, "the solutions of": 608, "terms of two": 32, "the complex plane": 183, "this transformation is": 20, "the following section": 194, "the aggregation of": 30, "to the growing": 18, "these two processes": 19, "two 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"that with this": 33, "the interval _MATH_": 995, "times continuously differentiable": 40, "that in contrast": 66, "the restriction of": 271, "the same characteristic": 13, "the interval END": 41, "the fundamental interactions": 11, "the model _CITE_": 30, "the term _MATH_": 581, "term _MATH_ has": 18, "the regularity of": 123, "to the infinite": 49, "the computations of": 40, "time and in": 30, "the response to": 44, "this framework we": 22, "the query language": 18, "the object _MATH_": 21, "the crystal is": 18, "temporal delay between": 11, "to the previous": 315, "the light induced": 16, "the quasi steady": 33, "the density of": 648, "that the mean": 160, "the mean intensity": 22, "total cross section": 227, "the optical theorem": 15, "the contributions from": 151, "the two contributions": 16, "the energy range": 60, "that is for": 154, "to determine whether": 162, "the same period": 67, "the creation of": 233, "the method using": 13, "to all three": 17, "time series as": 15, "time 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13, "the labels of": 21, "the input and": 179, "temperature gradient is": 15, "this reduces to": 24, "the mixing length": 18, "the three point": 41, "the two models": 114, "the reliability of": 151, "the diversity of": 43, "techniques used for": 12, "techniques from the": 12, "to the hard": 23, "the hard X": 99, "techniques and the": 28, "techniques such as": 177, "techniques for the": 48, "the high resolution": 91, "thanks to the": 186, "to the unique": 66, "the source and": 137, "tunability of the": 16, "the X ray": 171, "the laboratory END": 13, "then each _MATH_": 12, "the MLE and": 15, "to have better": 12, "the MLE is": 12, "the Whittle estimator": 21, "the location parameter": 14, "theoretical results on": 16, "to be due": 62, "the most probable": 83, "the emission measure": 61, "travel END END": 18, "to 4 END": 23, "the peak in": 39, "the total weight": 40, "total weight of": 36, "the current cycle": 30, "the northern and": 68, "to rotation END": 10, "the video sequence": 14, "the synoptic maps": 27, "to be of": 349, "to the charged": 26, "that we call": 53, "the highest energy": 27, "the _MATH_ evolution": 13, "the area within": 10, "the hysteresis loop": 20, "the stress _MATH_": 13, "the chiral quark": 15, "the flow equation": 64, "the scale dependent": 23, "temperature and density": 50, "to formulate and": 15, "their influence on": 26, "the quark meson": 14, "this scheme the": 19, "the order parameter": 106, "transverse and longitudinal": 52, "the chiral phase": 39, "the scaling properties": 14, "the critical point": 173, "the broken phase": 10, "the scaling function": 31, "the variational iteration": 18, "there are a": 216, "that a significant": 35, "the observations END": 160, "the reason for": 111, "the photometric mass": 11, "that in Ref": 10, "to different results": 17, "the image END": 255, "the stellar mass": 10, "the procedure of": 93, "the Finslerian MOND": 16, "the solar maximum": 48, "the newly developed": 17, "the Sun during": 36, "the low and": 46, "the simulation are": 29, "the high density": 40, "the solar wind": 956, "the simulations END": 63, "trends of the": 17, "their upper bounds": 12, "to their own": 14, "the processing times": 89, "the other one": 183, "then compare the": 16, "the new vertex": 13, "the _MATH_ associated": 19, "they will not": 25, "the graph structure": 10, "that we cannot": 75, "the entries of": 181, "the cells in": 35, "this is also": 90, "the conditions to": 18, "the solution depends": 13, "the mapping _MATHDISP_": 39, "two steps END": 150, "the following proposition": 221, "to the symbol": 16, "the symbols are": 17, "to be found": 144, "the user wants": 12, "the zones of": 10, "the queried symbol": 12, "the one to": 39, "to be computed": 106, "the entire collection": 14, "the most used": 24, "the decay rates": 27, "the response curves": 10, "the Anchor Model": 10, "to the cell": 44, "the cell boundary": 17, "time varying delay": 155, "the measurement vector": 17, "the signal to": 172, "time 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result is": 319, "the medial axis": 45, "the ratio between": 257, "the largest and": 27, "that the latter": 89, "the boundary surface": 18, "the _MATH_ algorithm": 66, "the graph of": 186, "the new variable": 29, "to _MATH_ implies": 14, "the property _MATH_": 118, "this implies that": 336, "that _MATH_ or": 192, "the same limit": 39, "the _MATH_ gauge": 83, "the gaugino masses": 30, "that make up": 25, "to the U": 10, "the U 1": 37, "the connectivity of": 52, "the weights for": 20, "the cycle 23": 24, "the MHD equations": 26, "the coronal streamer": 10, "the study by": 29, "the source surface": 112, "that are closer": 16, "to the solar": 300, "the field lines": 191, "the energy balance": 50, "that the coronal": 56, "the photospheric field": 47, "the largest scale": 15, "the source regions": 27, "the utility of": 134, "temperature _MATH_ and": 99, "the superconducting transition": 12, "transition temperature _MATH_": 27, "temperature _MATH_ END": 113, "the temperature is": 94, "temperature is lowered": 14, "the positive sign": 12, "that the dominant": 52, "the Hausdorff measure": 18, "the interface between": 78, "the paper the": 36, "the last condition": 22, "that any two": 42, "that the sampling": 25, "the sampling of": 47, "the large number": 109, "to the deterministic": 32, "the characteristic functions": 29, "the volume fraction": 24, "the mean _MATH_": 67, "the conditional mean": 43, "to the mean": 156, "the region occupied": 11, "the material from": 10, "to _MATH_ can": 118, "to the scattering": 38, "the scattering amplitude": 58, "to one loop": 32, "the Bose Einstein": 23, "the labour supply": 17, "to the degree": 34, "the social planner": 38, "to the poor": 14, "the publicly provided": 15, "they would have": 19, "this approach is": 295, "the potential END": 50, "the Cornell potential": 12, "the AdS QCD": 14, "the same behavior": 60, "typical of the": 26, "the different models": 38, "to see if": 85, "the parameters of": 692, "the model using": 27, "the available experimental": 21, "the model are": 121, "that we use": 165, "together with some": 38, "the diagonal _MATH_": 39, "the diagonal END": 45, "the two solutions": 41, "two solutions END": 23, "that even in": 69, "time consuming process": 13, "to accelerate the": 84, "that has been": 248, "terrain END END": 23, "the universal _MATH_": 10, "the field of": 630, "two vertices in": 19, "that the induced": 29, "the incidence graph": 11, "the main features": 81, "the concentration of": 318, "the germ of": 13, "the general _MATH_": 48, "that is of": 50, "the covariant derivative": 80, "theorem in _CITE_": 30, "the assignment of": 63, "the flexible operation": 14, "the _MATH_ st": 26, "that the rate": 105, "the rate of": 833, "to a logarithmic": 11, "the zero knowledge": 30, "the following claim": 32, "theory of differential": 30, "two linearly independent": 47, "turn out to": 228, "to 0 or": 19, "the second solution": 22, "the investigation of": 212, "these solutions are": 28, "the 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41, "this is not": 661, "the pair _MATH_": 412, "the pairs _MATH_": 87, "translation END END": 84, "to access the": 93, "the same configuration": 23, "this expression into": 21, "the sense that": 930, "that the amount": 67, "the one hand": 440, "that _MATH_ it": 97, "then compute the": 38, "the following representation": 49, "the Green tensor": 11, "tensor _MATHDISP_ where": 16, "this representation the": 19, "the spectral component": 12, "the expressions _MATHDISP_": 24, "that the term": 78, "taken with the": 46, "those in _REF_": 15, "the evaluation of": 347, "to that for": 85, "them END END": 1454, "to be less": 135, "the basic reproduction": 73, "times faster than": 67, "the throughput of": 43, "to search the": 30, "the application s": 16, "the computation END": 67, "the last decades": 72, "the network with": 36, "that formula _REF_": 10, "to the coalition": 12, "the coalition that": 13, "that will form": 12, "that they do": 88, "that in general": 163, "the above formula": 71, "the common information": 19, "the optimization problem": 255, "the mass _MATH_": 90, "that is to": 193, "to be minimized": 74, "the subset _MATH_": 96, "to point out": 209, "the theoretical framework": 29, "the describing function": 39, "the local stability": 77, "the proposed criterion": 11, "the second one": 368, "that the selection": 20, "the selection of": 297, "to the proposed": 52, "to ensure the": 228, "to extend the": 343, "to the lepton": 20, "the situation is": 163, "the neutrino sector": 19, "the eigenvalues and": 63, "to circumvent this": 16, "to the one": 578, "the charged lepton": 62, "the sensitivity of": 321, "the human body": 67, "to train a": 13, "the task of": 166, "the same methodology": 14, "the first chapter": 12, "this part of": 89, "the book END": 53, "the predictions from": 21, "to a normal": 35, "the near IR": 13, "thickness _MATH_ END": 18, "to the film": 12, "to the external": 80, "the external magnetic": 47, "to the propagation": 28, "the spontaneous 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"therefore does not": 24, "to be well": 100, "the hard process": 10, "the Cauchy problem": 266, "the following type": 26, "type _MATHDISP_ where": 45, "the contraction mapping": 20, "the line _MATH_": 258, "the distance from": 278, "the angle between": 316, "the problem can": 68, "the filtering problem": 22, "the optimal control": 294, "the optimal cost": 46, "the terms in": 148, "terms in _REF_": 137, "the membership of": 10, "the nodes with": 14, "the aid of": 189, "to the equation": 149, "the equation is": 72, "theorem _CITE_ END": 67, "the negative of": 43, "the advantages of": 222, "their ability to": 67, "to the norm": 77, "the condition number": 85, "the diagonal matrix": 101, "to level _MATH_": 30, "the multi scale": 27, "terms of three": 24, "this case if": 55, "the permutation _MATH_": 47, "the next period": 12, "to a limit": 31, "the two wheels": 11, "the robot END": 41, "to set the": 97, "the desired angular": 16, "that the mass": 93, "the mass differences": 10, "the squarks and": 14, "to the mass": 129, "to show the": 477, "the dark matter": 168, "the neutralino LSP": 10, "the _MATH_ _MATH_": 746, "the control problem": 64, "that produces the": 23, "that the control": 137, "the full dynamics": 16, "then the same": 24, "the same control": 20, "to the full": 136, "the indistinguishability of": 11, "the proposed one": 16, "to the least": 24, "the plane at": 24, "to the underlying": 90, "tuning END END": 57, "the time domain": 183, "the frequency domain": 264, "the next chapter": 71, "the honest _MATH_": 12, "that computes _MATH_": 19, "the independent variables": 50, "the approximate solution": 92, "to find END": 66, "that is when": 101, "that our method": 97, "to compensate the": 43, "the initial period": 13, "the robustness and": 22, "the accuracy END": 17, "that _MATH_ occurs": 13, "that for _MATHDISP_": 11, "three mass system": 25, "the normal to": 43, "the first one": 285, "this system can": 26, "to rank END": 12, "the query is": 23, "the query 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"the real values": 16, "to play the": 28, "the position _MATH_": 111, "that a number": 31, "time delays has": 11, "time delays which": 13, "the research community": 38, "these can be": 51, "than on the": 69, "the phase portrait": 55, "that the orbit": 20, "that even if": 109, "to decode the": 21, "that _MATHDISP_ we": 88, "the equivalence relation": 31, "the most suitable": 66, "the one that": 157, "two Higgs doublets": 36, "the vacuum expectation": 70, "the Higgs fields": 36, "the linear terms": 28, "terms are the": 23, "the mass matrices": 17, "to the physical": 90, "the physical fields": 10, "the Higgs sector": 78, "tree level END": 48, "that the occurrence": 31, "the oscillations are": 27, "the most remarkable": 14, "this must be": 15, "take _MATH_ for": 40, "this approach a": 16, "the largest of": 26, "the result follows": 155, "to an exponential": 27, "the following formula": 152, "to _MATH_ s": 42, "the only way": 85, "to the randomness": 10, "time is not": 41, "the coverage 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"that the derived": 21, "the Rasch tree": 22, "the task END": 42, "to the ideal": 64, "that the adversary": 75, "the trusted party": 66, "then the adversary": 10, "the previous definition": 13, "this section and": 46, "the main advantage": 22, "transpose of _MATH_": 34, "to a constrained": 11, "the output estimate": 11, "the filter gain": 30, "the general form": 150, "the eigenvalue spread": 10, "to Step 1": 26, "to operate on": 16, "the transport properties": 25, "transport properties in": 13, "this section a": 89, "to be given": 69, "the sequences END": 10, "this way of": 22, "the membership problem": 20, "this case one": 116, "the Christoffel symbols": 15, "the Ricci tensor": 31, "time is _MATHDISP_": 22, "the scalar curvature": 45, "the explicit expression": 63, "term _MATHDISP_ END": 65, "the cooling system": 10, "to a set": 224, "to Table _REF_": 57, "the Lie group": 88, "this case a": 173, "to perform better": 21, "to find _MATHDISP_": 39, "the monotone convergence": 31, "turn 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"the Sun we": 18, "the results suggest": 13, "the dynamic equations": 49, "the symmetric positive": 12, "two dimensional cubic": 13, "the MLE of": 26, "to conduct a": 10, "that the marginal": 52, "the phenomena of": 19, "this chapter _MATH_": 10, "through a combination": 11, "the displacements of": 21, "the adjacency matrix": 99, "the same graph": 14, "the same network": 11, "the occurrence probability": 22, "time _MATH_ can": 40, "the conventional matrix": 25, "to the necessity": 13, "time is more": 10, "the correspondence between": 90, "the lower left": 38, "the same algorithm": 28, "to be distinct": 11, "this direction is": 34, "time distribution is": 23, "that this was": 27, "this was not": 30, "the more the": 48, "to verify END": 25, "the infinitesimal transformation": 12, "the approach to": 52, "to the classical": 183, "the previous argument": 16, "to prove END": 55, "that appear as": 15, "the projectile and": 25, "to the projectile": 13, "that now the": 28, "that the amplitude": 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"we were unable": 18, "were unable to": 43, "were found to": 152, "was recorded END": 11, "with Eq _REF_": 178, "with up to": 70, "with constant coefficients": 67, "with initial condition": 122, "with a lot": 15, "which must be": 140, "which led to": 44, "was also used": 52, "which the coefficient": 11, "we determine _MATH_": 14, "we first note": 28, "which because of": 10, "we may choose": 71, "with the boundary": 151, "weight matrix and": 12, "we recall that": 132, "with high precision": 31, "we would have": 170, "would have a": 64, "with the norm": 192, "will be used": 634, "with step size": 26, "which the system": 74, "with this interpretation": 11, "we fixed the": 16, "when compared to": 200, "which is what": 36, "we emphasize that": 38, "we have used": 743, "which have to": 35, "written in terms": 209, "we construct a": 193, "with the geometric": 25, "with the projected": 10, "was found to": 261, "whereas the results": 10, "which agrees well": 13, "with the simulation": 23, "wind 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"where _MATH_ _MATH_": 2938, "with the second": 116, "was fitted to": 22, "with the increasing": 71, "were shown in": 17, "which is able": 52, "wide range of": 609, "we consider is": 49, "we also have": 261, "we assume END": 22, "we adopt the": 183, "where the initial": 57, "where the constant": 103, "will be removed": 15, "where _MATH_ represents": 453, "with the following": 665, "we get a": 302, "with the same": 1343, "which has the": 260, "with _MATH_ 2": 13, "we now proceed": 10, "we take a": 130, "we know the": 151, "with a certain": 110, "words we assume": 13, "we show that": 1360, "we have also": 176, "way as for": 40, "we have taken": 100, "where the first": 221, "which have a": 91, "was taken as": 29, "whole period of": 11, "will be considered": 190, "we add the": 76, "with the left": 35, "which we denote": 139, "with _MATH_ _MATH_": 1405, "we have that": 1266, "we can derive": 178, "which is usually": 97, "with an image": 13, "with the object": 13, "we have assumed": 159, "we 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d f": 10, "with the expectation": 24, "with both the": 59, "we use our": 31, "with the current": 138, "which we could": 12, "which gives a": 106, "we shall discuss": 59, "with _MATH_ we": 559, "will be in": 76, "weak projective synchronization": 10, "with an error": 36, "will find the": 32, "will choose the": 16, "which have been": 261, "was chosen for": 21, "with a few": 87, "with _CITE_ the": 10, "with at least": 152, "we establish the": 96, "wireless networks END": 28, "we propose to": 139, "we obtain that": 614, "we are ready": 81, "we restrict our": 82, "we focus on": 624, "we describe the": 380, "weights _MATH_ END": 72, "when using the": 137, "with larger _MATH_": 20, "with the strongest": 21, "we try to": 182, "which solves the": 25, "well known see": 93, "where _MATHDISP_ with": 148, "with _MATH_ being": 514, "way in the": 29, "with a simple": 152, "we let _MATH_": 406, "we can analyze": 21, "we find that": 1502, "we follow the": 162, "we call the": 167, "which we now": 32, "would consist of": 15, "will be explained": 66, "we note the": 40, "we introduce an": 72, "whether a given": 53, "we deduce that": 449, "will be proportional": 10, "written as _MATH_": 375, "we can choose": 327, "where the second": 123, "will be derived": 39, "which was later": 16, "when the ratio": 18, "were proposed END": 31, "when _MATH_ to": 10, "written in an": 10, "which could be": 203, "with a low": 112, "was observed for": 30, "was to find": 16, "when _MATH_ a": 25, "will be the": 395, "with those from": 33, "we have analyzed": 69, "wave END END": 362, "with the solutions": 23, "which case the": 139, "wavelength range is": 11, "we mention that": 41, "with _MATH_ that": 110, "we revisit the": 21, "with other approaches": 16, "wide field of": 15, "wide END END": 38, "within the time": 43, "we denote by": 575, "were accompanied by": 24, "weight functions _MATH_": 21, "widely used for": 66, "with a linear": 119, "which is fully": 10, "weak END END": 87, "we employ the": 142, "we 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59, "with the different": 33, "with the magnetic": 123, "we thus obtain": 17, "we first introduce": 48, "we use _MATH_": 328, "would be interesting": 158, "well understood in": 14, "which represent the": 65, "we can classify": 10, "we can talk": 10, "wind END END": 249, "we choose to": 78, "well posed END": 29, "we have already": 177, "with a time": 121, "working in the": 55, "with a proper": 31, "which is important": 39, "waves END END": 593, "we find END": 55, "with the phase": 43, "was able to": 112, "we assume a": 141, "we want to": 868, "which appears in": 54, "with a slight": 49, "we present a": 606, "with partial observations": 16, "written as the": 120, "what follows the": 23, "we get after": 11, "with the above": 159, "whether the two": 11, "when it exists": 26, "which implies _MATH_": 242, "we also consider": 65, "with results obtained": 21, "weak mixing angle": 14, "which is used": 214, "we use Eq": 16, "which includes the": 119, "where all the": 112, "with Monte Carlo": 14, "we can see": 966, "work in the": 205, "whereas END END": 33, "which was then": 12, "written _MATH_ if": 16, "we can set": 64, "words _MATH_ END": 42, "where the coefficients": 99, "will have the": 113, "with _MATH_ vertices": 115, "with time varying": 184, "with the generic": 11, "with a significant": 32, "with the key": 11, "we will also": 112, "which affect the": 16, "weights of evidence": 14, "weakly converges to": 32, "we infer that": 99, "weakly in _MATH_": 86, "we find _MATHDISP_": 399, "which we shall": 63, "we shall call": 18, "we cannot use": 41, "will in the": 11, "would be different": 18, "world END END": 287, "was observed in": 123, "which are not": 357, "which is very": 139, "with the QCD": 32, "word of the": 14, "word _MATH_ of": 26, "we obtain the": 2088, "we can assume": 437, "was discovered by": 24, "which follows from": 81, "with the properties": 78, "which has two": 23, "were first observed": 15, "with the strong": 32, "which is also": 338, "which is 1": 24, "which 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"with the number": 304, "we illustrate how": 28, "with the local": 64, "with a hierarchical": 10, "we discuss this": 18, "wavelength END END": 187, "with a target": 11, "we do a": 12, "we will explain": 42, "were recorded by": 19, "we see the": 102, "with the Higgs": 21, "were concerned with": 11, "with the Cauchy": 16, "within the cell": 16, "with the optimal": 69, "we will show": 395, "which defines a": 34, "well known END": 78, "with entries _MATH_": 40, "with order _MATH_": 26, "which _MATH_ in": 12, "we call such": 12, "we focus only": 13, "where we can": 66, "we can replace": 82, "we can achieve": 41, "we provide a": 220, "we shall apply": 14, "will see in": 127, "worse than the": 57, "which causes a": 14, "with the normal": 31, "we take the": 402, "we approximate the": 61, "with _MATHDISP_ where": 236, "works on the": 63, "were obtained END": 52, "which is obtained": 126, "will be calculated": 23, "we may assume": 458, "which indicates that": 132, "we define _MATHDISP_": 273, 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"Hence by Lemma": 43, "However we found": 20, "However as in": 17, "However we believe": 19, "Hence for every": 30, "Huang et al": 70, "Here _MATH_ _MATH_": 189, "Hence for _MATH_": 104, "Here we employ": 19, "Hence we get": 64, "However we can": 109, "However we shall": 20, "Hopf bifurcation is": 44, "Hopf bifurcation of": 41, "Hamiltonian _MATH_ and": 16, "Hessian of _MATH_": 18, "HMM based systems": 10, "HXR emission END": 19, "However we should": 17, "Here _MATH_ if": 10, "Hence _REF_ is": 45, "However it should": 61, "However the same": 13, "However we must": 16, "Here we present": 85, "Hz END END": 166, "However we note": 51, "Here are some": 12, "Here the _MATH_": 43, "Here we give": 52, "However most of": 63, "However in our": 77, "However note that": 50, "Holder inequality we": 31, "However one may": 14, "Here we should": 18, "However for a": 64, "Hence we only": 25, "However if _MATH_": 92, "Hence using the": 38, "Here _MATH_ are": 102, "Here the function": 28, "He ii line": 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"However we did": 15, "However it would": 16, "However in many": 44, "However in a": 48, "Hint END END": 48, "Hausdorff distance END": 14, "However _MATH_ can": 15, "Hence we see": 27, "Hence the two": 15, "Here we make": 12, "However according to": 30, "Here we follow": 20, "Hopfield neural networks": 22, "Hence we arrive": 10, "Here we briefly": 31, "Hinode SOT SP": 19, "Hopf bifurcation curve": 18, "Hopf bifurcation points": 17, "However since there": 10, "However when the": 111, "However it seems": 30, "Hence it suffices": 26, "Higgs bosons are": 24, "Hawking temperature of": 24, "Hawking temperature END": 15, "Here we show": 77, "Hilbert space of": 60, "However depending on": 11, "Here we note": 26, "Hamiltonian of a": 11, "However despite the": 23, "Here we focus": 65, "However the system": 10, "Higgs doublet model": 25, "However we need": 19, "However as is": 18, "Here and below": 21, "However they did": 10, "However these are": 10, "Hamilton END END": 11, "Hence we find": 20, "Hence _MATH_ which": 35, "However the solution": 16, "Hooke s law": 11, "However _MATH_ END": 11, "Hence the sequence": 16, "H_MATH_ H_MATH_ H_MATH_": 13, "H_MATH_ H_MATH_ and": 22, "Hamiltonian system _REF_": 39, "Henkin END END": 21, "However in both": 14, "Horn Theorem I": 11, "Here we only": 47, "However for small": 11, "However since this": 11, "Here _MATHDISP_ END": 57, "However for some": 17, "However since we": 32, "However when a": 13, "Hilbert Schmidt norm": 11, "Here _MATH_ for": 22, "However because of": 52, "However due to": 138, "However this method": 41, "Heaviside step function": 19, "Here we set": 20, "However in contrast": 34, "Higgs END END": 31, "Here the first": 27, "Hurwitz zeta function": 10, "He showed that": 22, "HMM END END": 24, "Hausdorff distance is": 11, "However in some": 37, "Here we prove": 19, "Here we must": 10, "Here it should": 15, "How can we": 23, "Hence they are": 17, "Here is the": 24, "Hamiltonian _MATH_ in": 14, "Here we summarize": 13, "Higgs sector END": 20, "Here we discuss": 46, "However for our": 11, "H_MATH_ images END": 11, "Here we extend": 21, "Hawking temperature and": 20, "Hamilton Jacobi Bellman": 41, "Hessian matrix of": 20, "Hyers Ulam Rassias": 20, "Hamiltonian _REF_ is": 13, "However this kind": 10, "Hence since _MATH_": 16, "Here we study": 44, "Hopf bifurcation which": 13, "However if one": 32, "Hopf bifurcation point": 13, "However a more": 13, "Here _MATH_ with": 14, "Here we describe": 40, "However END END": 40, "Hence the _MATH_": 34, "However in general": 38, "Halevi and Krawczyk": 16, "Here we concentrate": 19, "Hamiltonian and the": 16, "Hence to prove": 11, "However the analysis": 21, "Hence the number": 23, "However in practical": 17, "Here we just": 13, "Hence _MATH_ if": 18, "However because the": 29, "However notice that": 11, "Hopf bifurcation in": 26, "However for large": 10, "H END END": 35, "Hamiltonian path END": 15, "Hence there exist": 21, "Hard X ray": 17, "However after the": 14, "Haar measure on": 15, "Holder inequality and": 36, "Hausdorff dimension of": 41, "However these methods": 25, "However all these": 28, "Higgs bosons _MATH_": 23, "HMMs END END": 28, "However on the": 22, "However we see": 18, "Hence by Corollary": 11, "However the above": 23, "Hence _MATH_ by": 10, "Hessian matrix is": 10, "Hence _MATH_ _MATH_": 26, "However the performance": 20, "However such a": 43, "Hamiltonian for the": 33, "Higgs mass is": 21, "However this condition": 10, "Hence _MATHDISP_ for": 14, "Here _MATHDISP_ _MATHDISP_": 14, "Hurwitz END END": 30, "Hermite rank of": 12, "Hamiltonian of the": 73, "Here is a": 28, "However it must": 11, "Hence the first": 30, "However it remains": 10, "Hence we will": 18, "H2 and H3": 26, "Hamiltonian system _MATHDISP_": 19, "Hilbert spaces END": 22, "Harra et al": 20, "Hilbert space _MATHDISP_": 13, "Hence for all": 20, "Here as in": 10, "Hence it follows": 68, "Hamiltonian function _MATHDISP_": 15, "HCS END END": 25, "Hence _MATHDISP_ _MATHDISP_": 18, "Hamiltonian system END": 16, "High Energy Solar": 42, "Hamiltonian _MATH_ END": 22, "Hence as _MATH_": 14, "Harvey et al": 15, "However in most": 25, "Here is an": 15, "He ii 30": 26, "Here we introduce": 33, "However there may": 13, "Hence we need": 26, "Hopf algebra _MATH_": 20, "Hinode Solar Optical": 10, "Helly s theorem": 20, "Here we propose": 38, "Hence from the": 21, "Hessian of the": 16, "However the model": 28, "However we show": 11, "Hence we must": 14, "However the effects": 11, "Hubble parameter as": 11, "Hill and Marty": 11, "However the _MATH_": 38, "He proved that": 14, "Hence the function": 19, "Here _MATH_ refers": 10, "Here _MATH_ stands": 22, "Hence _MATH_ satisfies": 21, "Hence we assume": 16, "However we would": 19, "He burning phase": 23, "HZ of the": 20, "HB phase END": 11, "However as it": 16, "Hopf bifurcating periodic": 16, "Hence if the": 51, "How does the": 20, "Higgs mass _MATH_": 17, "Hooft Feynman gauge": 13, "Hence by virtue": 12, "Here we define": 26, "Hence the proof": 20, "However the total": 17, "Higgs masses END": 10, "Here and throughout": 16, "Hence the following": 26, "Hamiltonian system with": 33, "Hamilton Jacobi equation": 36, "Hamiltonian _MATHDISP_ where": 26, "However it may": 23, "Here we also": 23, "However the fact": 24, "Heavy Ion Collider": 15, "Horava Lifshitz gravity": 19, "Here we derive": 11, "However the proposed": 25, "However all the": 20, "However such an": 17, "Hermite Rosenblatt process": 20, "However the authors": 18, "Hu et al": 37, "However the first": 27, "However one must": 10, "Heusler compounds END": 16, "Hopf bifurcations in": 13, "Hopf bifurcations are": 13, "Hence we conclude": 42, "Higgs field and": 11, "Here we denote": 21, "Hinode SP data": 21, "Hasse diagram for": 10, "Hence we do": 14, "Here we can": 25, "Hence the optimal": 10, "Hence the problem": 18, "However one has": 12, "H1 H2 and": 14, "However here we": 20, "Here we suppose": 13, "However if there": 28, "However the best": 10, "However let us": 14, "Higgs boson are": 10, "However this would": 21, "However all of": 12, "Hence the model": 11, "Hence the probability": 11, "He is currently": 13, "His main research": 11, "Here _MATH_ where": 11, "Here we want": 24, "Here we apply": 17, "He i 10": 14, "However we find": 20, "HER2 over expression": 20, "HER2 over expressing": 18, "However the difference": 22, "Here _MATHDISP_ and": 13, "Higgs mechanism END": 12, "However it has": 83, "H_MATH_ line center": 15, "Here we report": 23, "He was a": 13, "However the standard": 12, "However they are": 49, "High Performance Computing": 12, "Henkin s proof": 18, "However even with": 14, "Higgs sector of": 27, "Higgs bosons with": 10, "Hopf algebroid structure": 18, "He i and": 15, "Hubble parameter _MATH_": 52, "Helmholtz free energy": 17, "However one should": 13, "Hamiltonian _MATH_ is": 48, "Higgs boson production": 29, "Hawking radiation of": 25, "Hawking radiation as": 17, "However to our": 19, "Higgs boson coupling": 10, "Higgs boson self": 20, "Hamiltonian path _MATH_": 36, "Hamiltonian path in": 16, "HXR loop top": 16, "Hence the result": 20, "However as END": 11, "However the latter": 18, "How do we": 13, "Hence according to": 24, "Haar measure _MATH_": 12, "However we will": 56, "Higgs bosons and": 16, "HL black hole": 13, "However the assumption": 10, "Hamiltonian can be": 20, "However Fig _REF_": 11, "Hopf bifurcations END": 22, "Hamiltonian is _MATHDISP_": 18, "However at the": 32, "Hopf bifurcation can": 14, "Hence _MATH_ has": 46, "Holder continuous with": 15, "Ha Noi and": 16, "Here we observe": 14, "Hence when the": 11, "However the following": 18, "HIV END END": 10, "Hopf bifurcation occurs": 42, "However one can": 39, "However this model": 16, "However given the": 21, "Hence as in": 10, "However considering the": 10, "Hence _MATH_ a": 11, "Hamiltonian _MATHDISP_ and": 10, "However we were": 10, "He II 304": 23, "Higgs field _MATH_": 21, "Higgs doublets _MATH_": 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"Hamilton s equations": 11, "Hz and _MATH_": 14, "Hernandez Lerma 2003": 12, "Here we would": 26, "Har Peled _CITE_": 10, "Hermitian END END": 12, "Hardy END END": 16, "Higgs doublet END": 10, "Heliospheric Investigation SECCHI": 22, "Here only the": 10, "H2 END END": 21, "Higgs self energies": 16, "However for simplicity": 11, "Haigh et al": 25, "Hence _MATH_ as": 28, "He ii 304": 31, "H 264 AVC": 42, "However for an": 12, "Hamiltonian path problem": 14, "Ho and Hsing": 11, "Hubble constant _MATH_": 13, "However the proof": 11, "H1 END END": 12, "Hamming distance between": 13, "Hence _MATH_ must": 16, "Harish Chandra modules": 15, "Here we recall": 14, "Higgs bosons can": 12, "However if it": 11, "Hence in view": 14, "However we stress": 13, "Hamiltonian vector field": 17, "Hai Murphy model": 17, "Hilbert type integral": 33, "Hernandez Lerma and": 11, "Higgs boson with": 36, "However we now": 10, "However the problem": 37, "Here we first": 17, "Here we mention": 10, "Hamiltonian 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"Here we review": 14, "Hardy s inequality": 12, "HMI END END": 24, "Hence our claim": 13, "However using the": 28, "Hawking temperature _MATH_": 11, "Hence one can": 28, "Howard et al": 16, "Hopf algebra END": 12, "Hardy and Ramanujan": 17, "Here are the": 15, "Hamiltonian has the": 11, "Higgs vacuum expectation": 15, "Hall effect _CITE_": 11, "However even when": 10, "H_MATH_ line END": 15, "However the experimental": 10, "He I 1083": 12, "HM fitting method": 10, "Hence _REF_ yields": 10, "HI 1 and": 15, "Hardy type integral": 12, "Hence all the": 12, "However so far": 12, "However in view": 12, "Henkin s question": 12, "Hodge theory END": 12, "However these results": 12, "Higgs mechanism is": 11, "Horava Lifshitz cosmology": 11, "Here we provide": 16, "Hamiltonian function _REF_": 12, "Hence _REF_ and": 12, "Hilbert series of": 10, "Hurvich Moulines and": 12, "Herbig Ae Be": 19, "Hernandez et al": 10, "Holder inequality _MATHDISP_": 10, "Hence under the": 10, "Heuvel Panhuizen et": 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"_MATH_ in a": 979, "_MATH_ uniformly for": 34, "_MATH_ and independent": 26, "_MATH_ need not": 68, "_MATH_ vectors in": 16, "_REF_ where the": 424, "_MATH_ is based": 56, "_MATH_ between the": 318, "_MATH_ is taken": 253, "_REF_ a shows": 194, "_REF_b END END": 287, "_MATH_ _MATH_ which": 310, "_REF_ becomes _MATHDISP_": 454, "_MATHDISP_ Using the": 93, "_MATH_ gravity END": 48, "_REF_ _MATHDISP_ which": 80, "_MATHDISP_ which implies": 499, "_MATH_ when the": 379, "_MATH_ into four": 14, "_MATH_ satisfies the": 1225, "_MATH_ AdS black": 19, "_MATH_ there will": 44, "_MATHDISP_ if _MATH_": 138, "_MATH_ are disjoint": 92, "_MATH_ we deduce": 195, "_MATHDISP_ holds for": 155, "_REF_ there exist": 78, "_REF_ and _MATHDISP_": 154, "_MATH_ _MATH_ we": 551, "_MATH_ satisfies _REF_": 278, "_REF_ implies _MATH_": 121, "_MATH_ be given": 267, "_MATHDISP_ that is": 343, "_MATH_ also in": 13, "_MATH_ is surjective": 70, "_MATH_ possesses a": 62, "_MATH_ and charge": 19, "_MATHDISP_ is 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"Caputo derivative of": 15, "Chapter _REF_ and": 51, "CDF and D0": 14, "CCA secure encryption": 10, "Chapter _REF_ are": 11, "Consider _MATH_ as": 17, "Clark et al": 10, "CPU time of": 13, "Consequently the following": 11, "Consider _MATHDISP_ END": 43, "Cloud END END": 32, "Combining Eq _REF_": 15, "Consequently _MATHDISP_ and": 21, "CMEs observed by": 16, "Chapter _REF_ we": 85, "Cygnus X 3": 14, "Corollary _REF_ are": 16, "Clearly _MATH_ for": 23, "Ca II K": 40, "Cycle 22 END": 12, "CPU time and": 10, "Coriolis and centrifugal": 14, "Conversely assume that": 22, "Collaboration END END": 16, "Consider the class": 10, "Corollary _REF_ yields": 17, "Ca ii lines": 10, "Ca ii line": 14, "COR1 A and": 29, "Case 1 END": 88, "Christensen Dalsgaard et": 10, "Consider the closed": 15, "Conversely when the": 11, "Corollaries _REF_ _REF_": 11, "Consequently _MATH_ is": 80, "Cauchy stress tensor": 11, "CPUs and GPUs": 10, "Complex Event Processing": 11, "Corollary _REF_ in": 12, "Corollary 4 3": 12, "Chernov et al": 22, "Clearly we have": 25, "China END END": 45, "Consider _MATH_ and": 33, "Consider the operator": 17, "Case 2 2": 20, "Consider the differential": 15, "Construction of the": 19, "Consistent with the": 23, "CX A method": 11, "Clearly _MATH_ as": 13, "Chapter _REF_ that": 20, "Chapter 1 END": 17, "CME with a": 17, "Chain Monte Carlo": 39, "Clearly there is": 18, "CME source region": 21, "Cartesian coordinate system": 30, "Consequently for all": 10, "Corollary 1 END": 50, "Consider _MATH_ END": 56, "Consequently for _MATH_": 11, "Coxeter group _MATH_": 14, "Consider a finite": 18, "Consider first the": 62, "CEP cross section": 14, "Corresponding to the": 24, "Concluding remarks are": 16, "Cremer and Pestieau": 13, "Conf END END": 12, "Consequently we can": 37, "Consider the two": 24, "Cressie 1993 END": 12, "Conversely let _MATH_": 48, "Computer Science and": 30, "Casimir invariant _MATH_": 12, "Clifford Algebra for": 10, "Combined with the": 31, "Comparing with 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"Consequently there exists": 21, "CMEs are the": 13, "Cabibbo Kobayashi Maskawa": 16, "Cartesian coordinates of": 19, "Connection Coronal and": 24, "Coronal and Heliospheric": 24, "Consider a nonlinear": 14, "Clearly there exists": 15, "Corollary _REF_ can": 18, "Consider a given": 10, "Chapman Kolmogorov equation": 11, "Cycles 22 and": 12, "Cartier divisor _MATH_": 12, "CP violation END": 15, "Corollary _REF_ the": 51, "Consider the second": 20, "Choose _MATH_ _MATH_": 11, "Case I END": 16, "Corollary _REF_ to": 39, "Consequently if we": 10, "Consider now _MATH_": 14, "Convergence of the": 11, "C_MATH_ END END": 12, "CPU time is": 15, "Collaboration _CITE_ END": 15, "Consider an _MATH_": 24, "Cauchy Riemann equations": 25, "Consequently by virtue": 12, "Crump et al": 21, "Choose _MATH_ and": 26, "Chao s estimator": 13, "Consider a group": 12, "Coleff Herrera current": 15, "CMEs which are": 13, "CPU utilization of": 15, "Computer Science from": 17, "CME occurrence rate": 11, "Comparing 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and": 13, "Cycles 21 and": 16, "Consider the process": 11, "Corollary _REF_ for": 20, "Chapter 3 of": 12, "Comparing _REF_ with": 32, "CML END END": 10, "Coulomb interaction END": 10, "Coulomb interaction _MATH_": 11, "Choose _MATH_ END": 28, "Cartesian coordinates END": 12, "Chapter 3 we": 10, "Case 2 _MATH_": 50, "Consequently we get": 13, "Cai et al": 10, "Case 3 _MATH_": 20, "C L END": 26, "Chapter _REF_ for": 36, "Constraints _REF_ _REF_": 12, "CSI END END": 16, "Corollary _REF_ which": 12, "Conditions _REF_ _REF_": 11, "CDS END END": 22, "Cheriton and Skeen": 13, "Continuing in this": 21, "CMS and ATLAS": 12, "Choosing _MATH_ _MATH_": 12, "C poly filter": 10, "Control END END": 18, "Combining the two": 22, "Constraints END END": 11, "Consider the linear": 33, "CLP MILP model": 14, "CA END END": 35, "Consider the matrix": 11, "Case II _MATH_": 10, "Consequently _MATH_ and": 41, "Conversely if the": 23, "Chang et al": 15, "Consider a point": 14, "Chapter _REF_ is": 27, "Corollary 3 5": 12, "CKM matrix element": 10, "Center END END": 10, "Cauchy problem _REF_": 52, "C1 and C2": 17, "CMSSM END END": 16, "CA based S": 23, "Construction of _MATH_": 10, "Consequently from _REF_": 12, "Cu_MATH_S thin films": 12, "Changes in the": 21, "Clearly if _MATH_": 42, "Consider the stochastic": 22, "Cartan subalgebra of": 17, "Conjecture END END": 14, "Chapter 7 END": 16, "Consider a linear": 14, "Coronal Mass Ejections": 20, "Consequently by _REF_": 11, "Comparing _REF_ and": 24, "Case END END": 10, "Core 2 Duo": 19, "Case 2 and": 12, "Combining the results": 10, "Combining all the": 10, "Claim END END": 12, "CL END END": 14, "Consider a _MATH_": 15, "Consequently there is": 23, "C2 END END": 26, "Corollary _REF_ _MATHDISP_": 25, "Consider a network": 13, "Carlo Euler method": 18, "Case 1 and": 18, "CMEs and the": 16, "Corollary _REF_ _MATH_": 34, "CME energy at": 35, "Casimir operator _MATH_": 14, "Coulomb interaction between": 14, "Case 1 the": 17, "Chapter 9 END": 12, "CPU and memory": 10, "Chen system and": 14, "CME _CITE_ END": 14, "Case I _MATH_": 13, "Consider the initial": 13, "Chaps END END": 11, "Cambridge END END": 13, "CS END END": 18, "Corollary 1 1": 16, "Consider _MATHDISP_ where": 15, "CME speed END": 10, "Choi et al": 14, "Clearly it is": 15, "Consequently _MATH_ for": 15, "Consider for instance": 19, "Compared to previous": 11, "Comparing Eq _REF_": 16, "CPU and the": 41, "Commander END END": 13, "Coronagraph LASCO _CITE_": 13, "COR1 and COR2": 33, "Crooker et al": 11, "Contradiction END END": 12, "CFT correspondence END": 11, "Considering the above": 11, "Comparison with the": 16, "Castelnuovo Mumford regularity": 10, "Cycle 23 and": 20, "Consider _MATH_ with": 13, "Consequently we obtain": 21, "Consider the sequence": 16, "CP violating MSSM": 11, "Consider any _MATH_": 23, "Consequently by the": 15, "Corollary 3 1": 22, "Consequently in the": 21, "Clifford Fourier transform": 25, "Co_MATH_ based Heusler": 17, "Corollary 4 2": 12, "Chapter 6 of": 10, "Chapter 6 END": 13, "CMOS technology END": 10, "Central Committee END": 13, "Committee END END": 20, "Claim 2 END": 11, "Consider a set": 14, "Chapter 8 of": 10, "CME is a": 10, "Case 2 the": 10, "CM energy of": 17, "C3 END END": 19, "Cartesian stiffness matrix": 15, "Cribari Neto 2004": 11, "CME observed by": 10, "Chapter _REF_ by": 11, "CAs END END": 10, "Conclusions are drawn": 13, "CMS END END": 14, "Consider the family": 18, "Consider that the": 10, "Conditions _MATH_ and": 24, "C1 3 flare": 10, "Combining the estimates": 16, "Consequently we will": 10, "Chae et al": 16, "Constructing a Lyapunov": 10, "Color Glass Condensate": 10, "CLP MILP approach": 15, "CME speed and": 15, "Consider the general": 11, "Chapter 8 END": 12, "Canny edge detector": 13, "Cases I and": 11, "Combining the last": 12, "Consider the time": 11, "CME travel times": 12, "CERN Large Hadron": 10, "Consider the optimal": 11, "Christmas cactus graph": 13, "Chapt END END": 14, "CMB END END": 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"For the general": 35, "For the non": 31, "For a fixed": 115, "Fig _REF_ and": 756, "Fig 2 d": 10, "Fermi surface END": 11, "Fig 1 END": 282, "Finally we get": 27, "Figure 8 shows": 28, "For simplicity we": 385, "For the sake": 331, "For this we": 237, "Fisher information matrix": 46, "Following _CITE_ the": 29, "From this point": 68, "Figure _REF_ illustrates": 454, "From the definition": 175, "From the point": 58, "For technical reasons": 19, "Fig _REF_ for": 441, "Figs _REF_ and": 562, "For the given": 60, "For any _MATH_": 905, "Fabry Perot cavity": 18, "From the proof": 73, "FIG END END": 20, "For comparison the": 53, "For a single": 30, "For a given": 434, "Fig _REF_ the": 983, "First of all": 376, "From Theorem 3": 26, "Finally we use": 28, "For this reason": 486, "For a symmetric": 16, "Figure _REF_ reveals": 21, "Fig 2 END": 201, "Fix _MATH_ and": 124, "Fermi surface is": 10, "For example there": 42, "For convenience we": 196, "For _MATH_ define": 114, "First there is": 27, "Figure _REF_ b": 461, "Fig 4 we": 25, "Fig _REF_b END": 130, "Furthermore it is": 165, "From this and": 62, "From _REF_ and": 309, "Finally we are": 10, "Finally we propose": 15, "Finally we show": 67, "For example using": 17, "Fig 1 a": 61, "Figure 2 shows": 96, "From this perspective": 20, "For the first": 230, "Finally we apply": 18, "Fourier series expansion": 24, "From the fact": 25, "From Lemma _REF_": 164, "Figure 6 END": 70, "Figure 5 in": 10, "For this case": 87, "Finally we conclude": 45, "Fig _REF_ is": 424, "For the numerical": 33, "For example we": 247, "Fig 8 END": 50, "Fig _REF_ one": 64, "First consider the": 57, "Fig _REF_ shows": 562, "For the purpose": 118, "Fig _REF_ some": 11, "Fig _REF_ that": 177, "For given positive": 13, "Furthermore the number": 13, "FD LMS algorithm": 11, "Figure 2 END": 130, "Figure _REF_ presents": 154, "Figure 5 b": 13, "Figure 6 a": 11, "From this figure": 42, "Fig _REF_ are": 188, "Finally an example": 14, "Fourier series of": 21, "For 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"Figure _REF_ that": 92, "Fig _REF_ Fig": 38, "Fig _REF_ after": 12, "Fig _REF_ f": 36, "Figure END END": 22, "Fig _REF_ h": 11, "For example this": 35, "For _MATH_ and": 498, "For a vector": 22, "Fig _REF_ there": 45, "From now on": 178, "For _MATH_ set": 30, "For later use": 18, "From this we": 146, "Fermat s Last": 13, "Figure _REF_a the": 18, "For a long": 20, "Figure 1 shows": 118, "First we will": 57, "For the set": 12, "For further details": 25, "For the _MATH_": 236, "Furthermore _MATHDISP_ END": 55, "For this the": 31, "Figure 7 END": 48, "Figure 4 and": 14, "Figure 5 the": 18, "Fourier transform FFT": 29, "For example an": 58, "For each parameter": 12, "First note that": 118, "Fig 5 END": 86, "From _MATH_ and": 64, "From Lemma 2": 55, "From the above": 289, "For _MATH_ since": 12, "For instance when": 37, "Fig _REF_ _CITE_": 63, "Figs _REF_a and": 19, "Figure _REF_ right": 119, "Fig _REF_ right": 124, "Fig _REF_ show": 75, "Fig _REF_ on": 25, "Finally we draw": 11, "Furthermore the _MATH_": 31, "For _MATH_ both": 10, "For given scalars": 28, "Furthermore there is": 29, "For a proof": 27, "Figures 1 and": 42, "For the same": 109, "Fig 3 END": 138, "Figure _REF_b is": 11, "From END END": 48, "Figures _REF_ a": 116, "Figure _REF_ as": 95, "Figure _REF_ was": 30, "Figures _REF_ c": 34, "Figures _REF_ d": 12, "For example a": 286, "For the magnetic": 11, "Fe xii 195": 40, "For the cases": 31, "For the other": 80, "Finally the conclusions": 19, "Figure 3 shows": 85, "Figure 3 and": 12, "Figure 3 of": 16, "For ease of": 66, "For example _MATH_": 218, "For any such": 12, "From _MATH_ one": 11, "For example suppose": 75, "For example if": 440, "Figure 3 a": 26, "Figure 4 b": 11, "Figure 2 b": 18, "Figure 4 a": 14, "Figure 3 b": 17, "First we need": 36, "For each of": 142, "Figure _REF_ because": 13, "Fourier transforms of": 53, "From _MATH_ we": 114, "First we are": 14, "For _MATH_ i": 19, "Fig 3 a": 56, "Feynman Kac formula": 22, "For the continuous": 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instance it": 62, "Figure _REF_ plots": 61, "Fig _REF_ have": 20, "Figure _REF_ displays": 182, "Fig _REF_ top": 43, "Finally the _MATH_": 19, "Finally two numerical": 11, "For example considering": 11, "For the Gaussian": 14, "Fig 4 a": 39, "Figure _REF_ gives": 120, "February 2011 END": 16, "For each image": 21, "For each point": 18, "From these two": 22, "Fig 5 the": 13, "For purposes of": 20, "First in Section": 13, "Finally for _MATH_": 32, "Following the procedure": 22, "Furthermore we can": 38, "Furthermore we note": 16, "Fig 6 END": 71, "Finally we note": 63, "For _MATH_ or": 24, "For _MATH_ they": 13, "Frechet differentiable at": 21, "For the scalar": 13, "For _MATH_ to": 26, "Fig _REF_ i": 28, "For the lower": 25, "For the following": 37, "Fig 7 a": 23, "Finally we construct": 10, "For a certain": 11, "Fig 1 and": 40, "From this END": 21, "Figure 9 END": 27, "For example even": 12, "For notational simplicity": 23, "Fourier transform which": 11, "Finally in Section": 163, "Fisher et al": 37, "For the linear": 21, "Fourier transform _MATHDISP_": 28, "Finally based on": 12, "For the parameters": 17, "For the third": 33, "For the present": 57, "For instance an": 28, "For the details": 12, "From Definition _REF_": 17, "Fig _REF_ will": 18, "Fourier transform DFT": 16, "Fig 2 and": 31, "Figure _REF_ there": 32, "Furthermore if we": 33, "Furthermore we show": 26, "For _MATH_ this": 103, "For this example": 41, "For details on": 21, "Furthermore END END": 19, "Finally it is": 103, "Finally we would": 20, "First we present": 26, "Figure _REF_ depicts": 169, "Finally assume that": 11, "F and H": 14, "For the high": 10, "Furthermore for each": 21, "Finally we need": 20, "From _REF_ for": 18, "FSR of the": 11, "From the model": 14, "Fig 3 and": 22, "Fig 4 is": 12, "Fig _REF_ contains": 12, "Fig 7 END": 63, "From the physical": 10, "For any finite": 13, "Figure _REF_f END": 10, "For other values": 13, "For arbitrary _MATH_": 30, "For instance a": 108, "Furthermore there are": 23, "Figure _REF_ represents": 39, "Furthermore in the": 48, "For fixed _MATH_": 71, "Finally we present": 58, "F END END": 21, "Furthermore since the": 38, "Fig _REF_ as": 101, "Fig 3 in": 11, "Fig 1 shows": 32, "Figure _REF_ describes": 15, "First one can": 10, "From the perspective": 27, "Furthermore _MATH_ is": 101, "For a set": 33, "For a matrix": 16, "Frobenius norm of": 16, "Figure _REF_ both": 10, "Figure _REF_ but": 45, "From Figs _REF_": 16, "Figure 1 and": 24, "Figure 3 END": 96, "Furthermore we also": 20, "Firstly it is": 19, "Fano 3 fold": 18, "For even _MATH_": 10, "For instance there": 14, "Focusing on the": 21, "Fe i _MATH_": 23, "For simplicity the": 48, "Figure _REF_ from": 15, "Finally we obtain": 34, "Fig _REF_ _REF_": 40, "Figure _REF_ f": 30, "FARIMA _MATH_ process": 24, "Figure 2 the": 22, "From the results": 58, "Following the standard": 17, "For these cases": 13, "Fig _REF_ or": 29, "From this equation": 25, "Figure 2 we": 12, "Figures 3 and": 34, "Figs 7 and": 10, "Finally if _MATH_": 51, "Fresnel transmission ratio": 14, "Figure _REF_ or": 16, "Figure _REF_ compares": 74, "Further details on": 20, "Fig _REF_a END": 153, "Firstly we will": 13, "For _MATH_ _MATHDISP_": 131, "First we prove": 63, "For comparison we": 68, "Figure _REF_ clearly": 22, "Furthermore we assume": 52, "From the second": 26, "FEM END END": 11, "For _MATH_ using": 18, "For the initial": 41, "For the nonlinear": 15, "Finally we can": 48, "Fig 3 c": 17, "Following _CITE_ and": 16, "For the single": 12, "For _MATH_ is": 15, "From the experimental": 24, "For each pixel": 29, "Furthermore due to": 25, "For the proof": 75, "Fourier series with": 16, "For all other": 20, "FC END END": 23, "FFT END END": 33, "For simplicity let": 32, "From the simulation": 18, "For the moment": 32, "For clarity the": 16, "Figure 2 which": 10, "For instance by": 13, "Fourier transform limited": 13, "Fig _REF_ _MATHDISP_": 77, "Finally we remark": 10, "For the data": 20, "For the evaluation": 13, "From Theorem _REF_": 139, "Finally Section 5": 15, "For an overview": 22, "Fama and French": 20, "Figure _REF_a END": 114, "Figure _REF_b END": 121, "Figure _REF_c END": 46, "For the particular": 38, "Fe i line": 37, "For the description": 15, "For example two": 11, "Fig _REF_ since": 14, "For a detailed": 61, "Figure 1 we": 28, "For example as": 39, "Finally we prove": 44, "Furthermore for a": 16, "For details see": 50, "For _MATH_ there": 89, "For convenience let": 17, "For an _MATH_": 28, "Finally _MATHDISP_ END": 25, "For the next": 21, "Finally by the": 17, "Fourier coefficients _MATH_": 24, "First we look": 11, "Friedmann Robertson Walker": 48, "Figure _REF_ an": 14, "First let _MATH_": 33, "Fourier transform can": 10, "For each such": 15, "For the last": 51, "For example END": 19, "For notational convenience": 35, "Figure _REF_ suggests": 14, "Fig _REF_ respectively": 47, "For any vector": 10, "Figure _REF_ by": 47, "Fermi level is": 10, "Figure 2 where": 11, "From the properties": 16, "Figure _REF_ see": 12, "Finally we also": 32, "Fig 2 we": 30, "Figure 1 illustrates": 12, "For both the": 22, "Fig 2 in": 13, "Fig _REF_ each": 16, "Fig _REF_ were": 25, "From the assumption": 12, "Fig _REF_e END": 12, "From Fig 1": 20, "Furthermore when the": 15, "Finally we give": 46, "For the three": 37, "For the decay": 12, "For more detailed": 15, "From _MATH_ the": 11, "Furthermore the results": 11, "Figures _REF_a and": 58, "Functions END END": 12, "For the experiments": 19, "For a full": 13, "Finally we point": 16, "Fourier component of": 11, "Finally there are": 16, "Formally _MATH_ is": 10, "Figure 10 END": 15, "Fig _REF_ while": 28, "Fig _REF_ correspond": 14, "Following a similar": 18, "For any bounded": 10, "For instance we": 83, "Figure 5 we": 11, "Fubini s Theorem": 18, "Finally using the": 26, "First in order": 13, "Feng et al": 19, "Furthermore we obtain": 13, "Fig _REF_ has": 44, "Fig 6 a": 21, "For this system": 21, "For the complete": 18, "Figure 5 a": 27, "Fig _REF_b the": 18, "Finally we consider": 54, "For that purpose": 56, "Fig _REF_ was": 32, "Fubini s theorem": 87, "For the current": 16, "For each node": 12, "For example from": 18, "Feynman diagrams for": 12, "Finally in Sect": 38, "For _MATH_ an": 16, "For the term": 16, "For completeness we": 70, "Finally we calculate": 16, "Fu ci kspectrum": 30, "Following the proof": 10, "Furthermore in _CITE_": 11, "Figure 1 of": 22, "For each event": 14, "Faddeev Popov operator": 29, "From Lemma 3": 20, "Fig _REF_ indicate": 14, "From _REF_ one": 30, "Fe 6302 5": 13, "For a survey": 16, "Figure _REF_ i": 17, "Fourier coefficient of": 14, "Figure _REF_ to": 46, "Figure 6 shows": 38, "Further _MATH_ is": 30, "From the viewpoint": 30, "Furthermore we see": 10, "Figs _REF_ c": 22, "Fig _REF_ of": 30, "Fourier transform the": 13, "For the large": 11, "For example some": 28, "Further in the": 19, "For the reader": 24, "Fourier transform on": 12, "Finally since _MATH_": 39, "Figure _REF_ middle": 13, "From 3 2": 11, "Finally conclusions are": 21, "For _MATH_ consider": 26, "Finally we have": 101, "First we study": 12, "Friedmann equation _REF_": 20, "Fig 7 b": 14, "For a node": 12, "For the definition": 11, "Finally the following": 11, "For the matrix": 11, "From the hypothesis": 14, "For values of": 21, "Furthermore the following": 19, "Finally the results": 16, "For _MATH_ if": 30, "Fig _REF_ by": 60, "Figure 3 the": 10, "Fig 2 c": 18, "For each fixed": 46, "Follows from Item": 44, "Figure _REF_ confirms": 11, "Figs 2 and": 24, "FWHM of the": 53, "For such _MATH_": 13, "For example at": 32, "For a finite": 28, "For _MATH_ GeV": 12, "Figs _REF_ END": 22, "Figure 4 shows": 59, "For illustration purposes": 10, "For such an": 10, "Further suppose that": 23, "From left to": 10, "Fig _REF_ gives": 22, "Fig 1 where": 17, "Fig _REF_ then": 15, "Fig _REF_ can": 72, "For this problem": 21, "For an example": 23, "From this theorem": 10, "Furthermore for _MATH_": 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"From this observation": 13, "Figs _REF_ to": 24, "FOV of the": 20, "Finally we define": 23, "Friedmann universe with": 22, "Fig 5 b": 22, "Furthermore _MATH_ _MATH_": 16, "Figures _REF_d and": 11, "Figure _REF_ does": 13, "Fix an arbitrary": 15, "From equations _REF_": 13, "From this definition": 20, "Figure 1 b": 21, "Finally the third": 26, "Furthermore we find": 12, "Fig 1 is": 10, "Finally numerical simulations": 10, "Further it is": 28, "FRW universe END": 19, "Figures 1 3": 10, "From the figures": 22, "Fig 4 shows": 17, "Fast Fourier Transform": 27, "Fourier Transform FFT": 15, "For practical purposes": 17, "From Fig 2": 17, "F2 END END": 18, "F1 and F2": 13, "Figures 5 and": 19, "Fig 2 shows": 28, "Fig 2 the": 19, "For the model": 30, "First we define": 31, "For example many": 16, "For instance let": 25, "For the point": 10, "For example see": 10, "Further we can": 12, "Finally we introduce": 14, "For this study": 23, "Fix _MATH_ _MATH_": 15, "Friedmann equation in": 14, "Figure 4 presents": 12, "Fourier coefficients of": 56, "Further if we": 10, "Fe END END": 17, "From these figures": 18, "February END END": 15, "For any two": 53, "From the last": 33, "For the theory": 10, "Figures _REF_ e": 16, "Finally we END": 12, "Finally from the": 16, "Finally we compare": 22, "Figs 5 and": 13, "Figure _REF_ exhibits": 14, "For any constant": 24, "France END END": 21, "For large _MATH_": 54, "Fig _REF_ so": 10, "Fig _REF_ reveals": 14, "For the simulation": 19, "Fig _REF_ this": 39, "Firstly we prove": 12, "Fig 3 is": 11, "For larger values": 16, "Following the notation": 18, "Figure 3 in": 11, "Figures _REF_b and": 16, "From _REF_ the": 35, "Fig 6 and": 15, "From _CITE_ we": 28, "For definiteness we": 11, "Fig _REF_ panels": 11, "For the calculation": 18, "Fermi level END": 27, "For instance to": 13, "From _REF_ _MATH_": 26, "Feynman gauge END": 11, "For the final": 12, "Fourier Bargmann transform": 10, "For an arbitrary": 68, "Fig _REF_ when": 32, "For the 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diff --git a/data/corpus_n=4.json b/data/corpus_n=4.json
new file mode 100644
index 0000000000000000000000000000000000000000..03287e758152fe12478cce9dff939d313bb8b75e
Binary files /dev/null and b/data/corpus_n=4.json differ
diff --git a/src/create_corpus.py b/src/create_corpus.py
index 75cf5d5b1c42b166abf16e581164cf8c0dee640a..67d34bbf30e524a3c7026595176d538ad3950276 100644
--- a/src/create_corpus.py
+++ b/src/create_corpus.py
@@ -61,6 +61,9 @@ def create_corpus(n, verbose=False):
# print sentence
print(f"{sid}: {sentence}")
+ # remove case
+ sentence = sentence.lower()
+
# add padding
sentence = "START "*(n-1) + sentence + " END"*(n-1)
@@ -114,8 +117,10 @@ def trim_corpus(n, threshold):
if __name__ == "__main__":
- n = 3
- threshold = 10
- create_corpus(n)
- trim_corpus(n, threshold)
+ for n in range(1, 6):
+ print(f"n={n}")
+ create_corpus(n)
+ # threshold = 10
+ # print(f"threshold={threshold}")
+ # trim_corpus(n, threshold)