Journal articles: 'Integrability condition'

1

Kevrekidis, P. G. "Integrability revisited: a necessary condition." Physics Letters A 285, no. 5-6 (July 2001): 383–89. http://dx.doi.org/10.1016/s0375-9601(01)00384-x.

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Okubo, Susumu, and Ashok Das. "The integrability condition for dynamical systems." Physics Letters B 209, no. 2-3 (August 1988): 311–14. http://dx.doi.org/10.1016/0370-2693(88)90952-5.

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Казанчян, Драстамат Хачатурович, and Виктор Макарович Круглов. "A new sufficient condition for uniform integrability of exponential local martingales." Herald of Tver State University. Series: Applied Mathematics, no. 3 (November 30, 2020): 5–13. http://dx.doi.org/10.26456/vtpmk596.

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В статье доказано новое достаточное условие для равномерной интегрируемости экспоненциальных локальных мартингалов. Условие сформулировано в терминах квадратической вариации локального мартингала. Оно обобщает ряд известных достаточных условий подобного рода. In the article it is suggested a new sufficient condition for uniform integrability of continues exponential local martingales. It is shown that the condition is much weaker then a number of known sufficient conditions for uniform integrability of exponential local martingales.

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Supriya Mukherjee et al.,, Supriya Mukherjee et al ,. "Chiellini Integrability Condition and New Integrable Systems." International Journal of Mathematics and Computer Applications Research 8, no. 2 (2018): 1–10. http://dx.doi.org/10.24247/ijmcarapr20181.

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Glushchenko, A. I., V. A. Petrov, and K. A. Lastochkin. "I-DREM: Relaxing the Square Integrability Condition." Automation and Remote Control 82, no. 7 (July 2021): 1233–47. http://dx.doi.org/10.1134/s0005117921070079.

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Kutyniok, Gitta. "The local integrability condition for wavelet frames." Journal of Geometric Analysis 16, no. 1 (March 2006): 155–66. http://dx.doi.org/10.1007/bf02930990.

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Okubo, Susumu. "Integrability condition and finite‐periodic Toda lattice." Journal of Mathematical Physics 31, no. 8 (August 1990): 1919–28. http://dx.doi.org/10.1063/1.528691.

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8

Fridli, S. "Hardy Spaces Generated by an Integrability Condition." Journal of Approximation Theory 113, no. 1 (November 2001): 91–109. http://dx.doi.org/10.1006/jath.2001.3614.

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9

Gashi, Bujar, and Jiajie Li. "Integrability of exponential process and its application to backward stochastic differential equations." IMA Journal of Management Mathematics 30, no. 4 (June 21, 2018): 335–65. http://dx.doi.org/10.1093/imaman/dpy008.

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Abstract We consider the integrability problem of an exponential process with unbounded coefficients. The integrability is established under weaker conditions of Kazamaki type, which complements the results of Yong obtained under a Novikov type condition. As applications, we consider the solvability of linear backward stochastic differential equations (BSDEs) and market completeness, the solvability of a Riccati BSDE and optimal investment, all in the setting of unbounded coefficients.

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Gumede, Sfundo C., Keshlan S. Govinder, and Sunil D. Maharaj. "First Integrals of Shear-Free Fluids and Complexity." Entropy 23, no. 11 (November 19, 2021): 1539. http://dx.doi.org/10.3390/e23111539.

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A single master equation governs the behaviour of shear-free neutral perfect fluid distributions arising in gravity theories. In this paper, we study the integrability of yxx=f(x)y2, find new solutions, and generate a new first integral. The first integral is subject to an integrability condition which is an integral equation which restricts the function f(x). We find that the integrability condition can be written as a third order differential equation whose solution can be expressed in terms of elementary functions and elliptic integrals. The solution of the integrability condition is generally given parametrically. A particular form of f(x)∼1x51−1x−15/7 which corresponds to repeated roots of a cubic equation is given explicitly, which is a new result. Our investigation demonstrates that complexity of a self-gravitating shear-free fluid is related to the existence of a first integral, and this may be extendable to general matter distributions.

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Efimova, M. P. "The sufficient condition for integrability of a generalized Q-integral and points of integrability." Moscow University Mathematics Bulletin 70, no. 4 (July 2015): 181–84. http://dx.doi.org/10.3103/s0027132215040051.

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Kwon, Kil H., and Byeong C. Song. "Local integrability of CR-hypersurfaces." Bulletin of the Australian Mathematical Society 44, no. 3 (December 1991): 375–80. http://dx.doi.org/10.1017/s0004972700029865.

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By characterising CR-hypersurfaces of dimension m having m strongly independent CR-functions, we find the necessary condition for a CR-hypersurface to be locally integrable and show that the same condition is also sufficient if the CR-hypersurface is strongly pseudoconvex and has m strongly independent CR-functions.

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13

DOIKOU, ANASTASIA. "SELECTED TOPICS IN CLASSICAL INTEGRABILITY." International Journal of Modern Physics A 27, no. 05 (February 20, 2012): 1230003. http://dx.doi.org/10.1142/s0217751x12300037.

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Basic notions regarding classical integrable systems are reviewed. An algebraic description of the classical integrable models together with the zero curvature condition description is presented. The classical r-matrix approach for discrete and continuum classical integrable models is introduced. Using this framework the associated classical integrals of motion and the corresponding Lax pair are extracted based on algebraic considerations. Our attention is restricted to classical discrete and continuum integrable systems with periodic boundary conditions. Typical examples of discrete (Toda chain, discrete NLS model) and continuum integrable models (NLS, sine–Gordon models and affine Toda field theories) are also discussed.

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14

Schwabik. "Henstock's Condition for Convergence Theorems and Equi-integrability." Real Analysis Exchange 18, no. 1 (1992): 190. http://dx.doi.org/10.2307/44133057.

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15

Lamoreaux and Armstrong. "A NECESSARY AND SUFFICIENT CONDITION FOR GAUGE INTEGRABILITY." Real Analysis Exchange 19, no. 1 (1993): 254. http://dx.doi.org/10.2307/44153835.

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16

Hanson, James D., and John R. Cary. "Magnetic field integrability and the current closure condition." Physics of Plasmas 1, no. 11 (November 1994): 3713–15. http://dx.doi.org/10.1063/1.870907.

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17

Ninomiya, Haruki. "A necessary and sufficient condition of local integrability." Journal of Mathematics of Kyoto University 39, no. 4 (1999): 685–96. http://dx.doi.org/10.1215/kjm/1250517821.

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18

Chen, Xin, and Feng-Yu Wang. "OPTIMAL INTEGRABILITY CONDITION FOR THE LOG-SOBOLEV INEQUALITY." Quarterly Journal of Mathematics 58, no. 1 (October 26, 2006): 17–22. http://dx.doi.org/10.1093/qmath/hal021.

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19

Wang, M. Z., and S. P. Zhou. "Applications of MVBV condition in L 1 integrability." Acta Mathematica Hungarica 129, no. 1-2 (March 17, 2010): 70–80. http://dx.doi.org/10.1007/s10474-010-9225-4.

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20

Zhao, Linlong. "A new integrability condition for Riccati differential equation." Chinese Science Bulletin 43, no. 5 (March 1998): 439–40. http://dx.doi.org/10.1007/bf02883728.

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21

Machida, Yoshinori, and Hajime Sato. "Twistor theory of manifolds with Grassmannian structures." Nagoya Mathematical Journal 160 (2000): 17–102. http://dx.doi.org/10.1017/s0027763000007698.

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AbstractAs a generalization of the conformal structure of type (2, 2), we study Grassmannian structures of type (n, m) forn, m≥ 2. We develop their twistor theory by considering the complete integrability of the associated null distributions. The integrability corresponds to global solutions of the geometric structures.A Grassmannian structure of type (n, m) on a manifoldMis, by definition, an isomorphism from the tangent bundleTMofMto the tensor productV ⊗ Wof two vector bundlesVandWwith ranknandmoverMrespectively. Because of the tensor product structure, we have two null plane bundles with fibresPm-1(ℝ) andPn-1(ℝ) overM. The tautological distribution is defined on each two bundles by a connection. We relate the integrability condition to the half flatness of the Grassmannian structures. Tanaka’s normal Cartan connections are fully used and the Spencer cohomology groups of graded Lie algebras play a fundamental role.Besides the integrability conditions corrsponding to the twistor theory, the lifting theorems and the reduction theorems are derived. We also study twistor diagrams under Weyl connections.

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22

Ferapontov, E. V., and K. R. Khusnutdinova. "The Haantjes tensor and double waves for multi-dimensional systems of hydrodynamic type: a necessary condition for integrability." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2068 (January 17, 2006): 1197–219. http://dx.doi.org/10.1098/rspa.2005.1627.

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An invariant differential-geometric approach to the integrability of (2+1)-dimensional systems of hydrodynamic type, is developed. We prove that the existence of special solutions known as ‘double waves’ is equivalent to the diagonalizability of an arbitrary matrix of the two-parameter family Since the diagonalizability can be effectively verified by calculating the Haantjes tensor, this provides a simple necessary condition for integrability.

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23

Tempesta, Piergiulio, and Giorgio Tondo. "Higher Haantjes Brackets and Integrability." Communications in Mathematical Physics 389, no. 3 (November 2, 2021): 1647–71. http://dx.doi.org/10.1007/s00220-021-04233-5.

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AbstractWe propose a new, infinite class of brackets generalizing the Frölicher–Nijenhuis bracket. This class can be reduced to a family of generalized Nijenhuis torsions recently introduced. In particular, the Haantjes bracket, the first example of our construction, is relevant in the characterization of Haantjes moduli of operators. We also prove that the vanishing of a higher-level Nijenhuis torsion of an operator field is a sufficient condition for the integrability of its eigen-distributions. This result (which does not require any knowledge of the spectral properties of the operator) generalizes the celebrated Haantjes theorem. The same vanishing condition also guarantees that the operator can be written, in a local chart, in a block-diagonal form.

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24

Liflyand, Elijah. "Necessary Conditions for Integrability of the Fourier Transform." gmj 16, no. 3 (September 2009): 553–59. http://dx.doi.org/10.1515/gmj.2009.553.

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Abstract We prove the necessary conditions for the integrability of the Fourier transform. The result is a generalization, on one hand, of the well known necessary condition for absolutely convergent Fourier series and, on the other hand, of an earlier multidimensional result of Trigub.

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25

Cabrera, M. Ordóñez. "Convergence in mean of weighted sums of {an,k}-compactly uniformly integrable random elements in Banach spaces." International Journal of Mathematics and Mathematical Sciences 20, no. 3 (1997): 443–50. http://dx.doi.org/10.1155/s0161171297000604.

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The convergence in mean of a weighted sum∑kank(Xk−EXk)of random elements in a separable Banach space is studied under a new hypothesis which relates the random elements with their respective weights in the sum: the{ank}-compactly uniform integrability of{Xn}. This condition, which is implied by the tightness of{Xn}and the{ank}-uniform integrability of{‖Xn‖}, is weaker than the compactly miform integrability of{Xn}and leads to a result of convergence in mean which is strictly stronger than a recent result of Wang, Rao and Deli.

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26

Mostafazadeh, Ali. "A DIFFERENTIAL INTEGRABILITY CONDITION FOR TWO-DIMENSIONAL HAMILTONIAN SYSTEMS." Acta Polytechnica 54, no. 2 (April 30, 2014): 139–41. http://dx.doi.org/10.14311/ap.2014.54.0139.

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We review, restate, and prove a result due to Kaushal and Korsch [Phys. Lett. A 276, 47 (2000)] on the complete integrability of two-dimensional Hamiltonian systems whose Hamiltonian satisfies a set of four linear second order partial differential equations. In particular, we show that a two-dimensional Hamiltonian system is completely integrable, if the Hamiltonian has the form H = T + V where V and T are respectively harmonic functions of the generalized coordinates and the associated momenta.

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27

Adell, José A., and Alberto Lekuona. "Every random variable satisfies a certain nontrivial integrability condition." Statistics & Probability Letters 76, no. 15 (September 2006): 1603–6. http://dx.doi.org/10.1016/j.spl.2006.04.002.

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28

FERREIRA, L. A. "INTEGRABILITY AND SYMMETRIC SPACES II: THE COSET SPACES." International Journal of Modern Physics A 04, no. 03 (February 1989): 675–99. http://dx.doi.org/10.1142/s0217751x89000327.

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It is shown that a sufficient condition for a model describing the motion of a particle on a coset space to possess a Fundamental Poisson bracket Relation, and consequently charges in involution, is that it must be a symmetric space. The conditions, a Hamiltonian, or any functions of the canonical variables, has to satisfy in order to commute with these charges, are studied. It is shown that, for the case of the noncompact symmetric spaces, these conditions lead to an algebraic structure which plays an important role in the construction of conserved quantities.

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Corrigan, E., and Z. M. Sheng. "Classical Integrability of the O(N) Nonlinear Sigma Model on a Half-Line." International Journal of Modern Physics A 12, no. 16 (June 30, 1997): 2825–34. http://dx.doi.org/10.1142/s0217751x97001560.

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The classical integrability of the O (N) nonlinear sigma model on a half-line is examined, and the existence of an infinity of conserved charges in involution is established for the free boundary condition. For the case N = 3 other possible boundary conditions are considered briefly.

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30

Manora, J. Joseline, and R. Deepa. "Uniform Integrability for Fuzzy Random Variables." International Journal of Fuzzy Mathematical Archive 14, no. 01 (2017): 147–54. http://dx.doi.org/10.22457/ijfma.v14n1a18.

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In this paper the uniform integrability of fuzzy random variable is introduced. An attempt is made to study the uniformly absolutely continuous fuzzy valued functions and an equivalent condition for uniform integrable and uniformly absolutely continuous is determined.

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31

LAHIRI, AMITABHA. "PARALLEL TRANSPORT ON NON-ABELIAN FLUX TUBES." Modern Physics Letters A 20, no. 22 (July 20, 2005): 1695–702. http://dx.doi.org/10.1142/s0217732305016701.

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We propose a way of unambiguously parallel transporting fields on non-Abelian flux tubes, or strings, by means of two gauge fields. One gauge field transports along the tube, while the other transports normal to the tube. Ambiguity is removed by imposing an integrability condition on the pair of fields. The construction leads to a gauge theory of mathematical objects known as Lie 2-groups, which are known to result also from the parallel transport of the flux tubes themselves. The integrability condition is also shown to be equivalent to the assumption that parallel transport along nearby string configurations are equal up to arbitrary gauge transformations. Attempts to implement this condition in a field theory leads to effective actions for two-form fields.

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32

Samet, H. Chachou, M. Benarous, M. Asad-uz-zaman, and U. Al Khawaja. "Effect of Third-Order Dispersion on the Solitonic Solutions of the Schrödinger Equations with Cubic Nonlinearity." Advances in Mathematical Physics 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/323591.

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We derive the solitonic solution of the nonlinear Schrödinger equation with cubic nonlinearity, complex potentials, and time-dependent coefficients using the Darboux transformation. We establish the integrability condition for the most general nonlinear Schrödinger equation with cubic nonlinearity and discuss the effect of the coefficients of the higher-order terms in the solitonic solution. We find that the third-order dispersion term can be used to control the soliton motion without the need for an external potential. We discuss the integrability conditions and find the solitonic solution of some of the well-known nonlinear Schrödinger equations with cubic nonlinearity and time-dependent coefficients. We also investigate the higher-order nonlinear Schrödinger equation with cubic and quintic nonlinearities.

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33

Upadhyay, S. K., and Reshma Singh. "Integrability of the continuum Bessel wavelet kernel." International Journal of Wavelets, Multiresolution and Information Processing 13, no. 05 (September 2015): 1550032. http://dx.doi.org/10.1142/s0219691315500320.

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34

Denis, Laurent, Anis Matoussi, and Jing Zhang. "The existence and uniqueness result for quasilinear stochastic PDEs with obstacle under weaker integrability conditions." Stochastics and Dynamics 15, no. 04 (October 14, 2015): 1550023. http://dx.doi.org/10.1142/s0219493715500239.

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35

STOYANOV, LUCHEZAR. "Non-integrability of open billiard flows and Dolgopyat-type estimates." Ergodic Theory and Dynamical Systems 32, no. 1 (April 5, 2011): 295–313. http://dx.doi.org/10.1017/s0143385710000933.

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AbstractWe consider open billiard flows in ℝn and show that the standard symplectic form dα in ℝn satisfies a specific non-integrability condition over their non-wandering sets Λ. This allows one to use the main result in Stoyanov [Spectra of Ruelle transfer operators for Axiom A flows. Preprint, 2010, arXiv:0810.1126v4 [math.DS]] and obtain Dolgopyat-type estimates for the spectra of Ruelle transfer operators under simpler conditions. We also describe a class of open billiard flows in ℝn(n≥3) satisfying a certain pinching condition, which in turn implies that the (un)stable laminations over the non-wandering set are C1.

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36

Chikvinidze, B. "A new sufficient condition for uniform integrability of stochastic exponentials." Stochastics 89, no. 3-4 (January 4, 2017): 619–27. http://dx.doi.org/10.1080/17442508.2016.1269769.

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37

Baker, Lynn. "Offset Dual Reflector Shaping Based On the Pfaffian Integrability Condition." IEEE Open Journal of Antennas and Propagation 1 (2020): 189–95. http://dx.doi.org/10.1109/ojap.2020.2989176.

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38

Gardiner, Stephen J. "Angular limits of holomorphic functions which satisfy an integrability condition." Monatshefte f�r Mathematik 114, no. 2 (June 1992): 97–106. http://dx.doi.org/10.1007/bf01535575.

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39

van Velthoven, Jordy Timo. "On the local integrability condition for generalised translation-invariant systems." Collectanea Mathematica 70, no. 3 (February 1, 2019): 407–29. http://dx.doi.org/10.1007/s13348-019-00238-5.

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40

Shoikhet, Boris. "The PBW property for associative algebras as an integrability condition." Mathematical Research Letters 21, no. 6 (2014): 1407–34. http://dx.doi.org/10.4310/mrl.2014.v21.n6.a11.

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41

Peng, Chia Kuei, and Zi Zhou Tang. "Integrability Condition on an Almost Complex Structure and Its Application." Acta Mathematica Sinica, English Series 21, no. 6 (October 14, 2005): 1459–64. http://dx.doi.org/10.1007/s10114-005-0605-6.

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42

Prykarpatskyy, Yarema A. "Integrability of Riemann-Type Hydrodynamical Systems and Dubrovin’s Integrability Classification of Perturbed KdV-Type Equations." Symmetry 13, no. 6 (June 16, 2021): 1077. http://dx.doi.org/10.3390/sym13061077.

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Dubrovin’s work on the classification of perturbed KdV-type equations is reanalyzed in detail via the gradient-holonomic integrability scheme, which was devised and developed jointly with Maxim Pavlov and collaborators some time ago. As a consequence of the reanalysis, one can show that Dubrovin’s criterion inherits important parts of the gradient-holonomic scheme properties, especially the necessary condition of suitably ordered reduction expansions with certain types of polynomial coefficients. In addition, we also analyze a special case of a new infinite hierarchy of Riemann-type hydrodynamical systems using a gradient-holonomic approach that was suggested jointly with M. Pavlov and collaborators. An infinite hierarchy of conservation laws, bi-Hamiltonian structure and the corresponding Lax-type representation are constructed for these systems.

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43

BELLON, M., J.-M. MAILLARD, and C. VIALLET. "ON THE SYMMETRIES OF INTEGRABILITY." International Journal of Modern Physics B 06, no. 11n12 (June 1992): 1881–903. http://dx.doi.org/10.1142/s021797929200092x.

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We show that the Yang-Baxter equations for two-dimensional models admit as a group of symmetry the infinite discrete group [Formula: see text]. The existence of this symmetry explains the presence of a spectral parameter in the solutions of the equations. We show that similarly, for three-dimensional vertex models and the associated tetrahedron equations, there also exists an infinite discrete group of symmetry. Although generalizing naturally the previous one, it is a much bigger hyperbolic Coxeter group. We indicate how this symmetry can help to resolve the Yang-Baxter equations and their higher-dimensional generalizations and initiate the study of three-dimensional vertex models. These symmetries are naturally represented as birational projective transformations. They may preserve non-trivial algebraic varieties, and lead to proper parametrizations of the models, be they integrable or not. We mention the relation existing between spin models and the Bose-Messner algebras of algebraic combinatorics. Our results also yield the generalization of the condition qn=1 so often mentioned in the theory of quantum groups, when no q parameter is available.

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BENDER, CHRISTIAN. "THE RESTRICTION OF THE FRACTIONAL ITÔ INTEGRAL TO ADAPTED INTEGRANDS IS INJECTIVE." Stochastics and Dynamics 05, no. 01 (March 2005): 37–43. http://dx.doi.org/10.1142/s0219493705001274.

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We prove that the Wick–Itô–Skorohod integral with respect to a fractional Brownian motion is injective when it is restricted to a class of adapted integrands that satisfy an appropriate integrability condition.

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45

Файнберг, Евгений Александрович, Eugene Aleksandrovich Feinberg, Павел Олегович Касьянов, Pavel Olegovich Kas'yanov, Y. Liang, and Y. Liang. "Fatou's lemma for weakly converging measures under the uniform integrability condition." Teoriya Veroyatnostei i ee Primeneniya 64, no. 4 (2019): 771–90. http://dx.doi.org/10.4213/tvp5253.

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В статье устанавливаются лемма Фату и теорема Лебега о мажорируемой сходимости для слабо сходящихся последовательностей конечных мер и равномерно интегрируемых по этим мерам функций. Заметка содержит также новые формулировки равномерной леммы Фату, равномерной теоремы Лебега о мажорируемой сходимости, теоремы Данфорда-Петтиса и фундаментальной теоремы о мерах Янга, основанные на эквивалентности условия равномерной интегрируемости и кажущегося более слабым условия асимптотической равномерной интегрируемости для последовательностей функций и конечных мер.

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46

Uwano, Yoshio. "From the Birkhoff-Gustavson normalization to the Bertrand-Darboux integrability condition." Journal of Physics A: Mathematical and General 33, no. 37 (September 6, 2000): 6635–53. http://dx.doi.org/10.1088/0305-4470/33/37/315.

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47

Feinberg, E. A., P. O. Kasyanov, and Y. Liang. "Fatou's Lemma for Weakly Converging Measures under the Uniform Integrability Condition." Theory of Probability & Its Applications 64, no. 4 (January 2020): 615–30. http://dx.doi.org/10.1137/s0040585x97t989738.

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48

Wu, Meng, and Xuhui Wang. "AH1-integrability condition of surfaces with singular parametrizations in isogeometric analysis." Computer Methods in Applied Mechanics and Engineering 332 (April 2018): 136–56. http://dx.doi.org/10.1016/j.cma.2017.12.018.

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49

Kaashoek, M. A., and S. M. V. Lunel. "An Integrability Condition on the Resolvent for Hyperbolicity of the Semigroup." Journal of Differential Equations 112, no. 2 (September 1994): 374–406. http://dx.doi.org/10.1006/jdeq.1994.1109.

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50

Di Scala, Antonio J., and Luigi Vezzoni. "Gray identities, canonical connection and integrability." Proceedings of the Edinburgh Mathematical Society 53, no. 3 (August 12, 2010): 657–74. http://dx.doi.org/10.1017/s0013091509000157.

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AbstractWe characterize quasi-Kähler manifolds whose curvature tensor associated to the canonical Hermitian connection satisfies the first Bianchi identity. This condition is related to the third Gray identity and in the almost-Kähler case implies the integrability. Our main tool is the existence of generalized holomorphic frames previously introduced by the second author. By using such frames we also give a simpler and shorter proof of a theorem of Goldberg. Furthermore, we study almost-Hermitian structures having the curvature tensor associated to the canonical Hermitian connection equal to zero. We show some explicit examples of quasi-Kähler structures on the Iwasawa manifold having the Hermitian curvature vanishing and the Riemann curvature tensor satisfying the second Gray identity.

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Journal articles on the topic 'Integrability condition'

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