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Journal articles on the topic 'Poisson integral'

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Published: 4 June 2021
Last updated: 9 February 2022

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1

Mehrazin, Hashem. "Laplace equation and Poisson integral." Applied Mathematics and Computation 145, no. 2-3 (2003): 451–63. http://dx.doi.org/10.1016/s0096-3003(02)00499-x.

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2

Valtancoli, P. "Path integral and noncommutative Poisson brackets." Journal of Mathematical Physics 56, no. 6 (2015): 063501. http://dx.doi.org/10.1063/1.4922107.

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3

Goli, M., and M. Najafi-Alamdari. "Planar, spherical and ellipsoidal approximations of Poisson's integral in near zone." Journal of Geodetic Science 1, no. 1 (2011): 17–24. http://dx.doi.org/10.2478/v10156-010-0003-6.

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Planar, spherical and ellipsoidal approximations of Poisson's integral in near zonePlanar, spherical, and ellipsoidal approximations of Poisson's integral for downward continuation (DWC) of gravity anomalies are discussed in this study. The planar approximation of Poisson integral is assessed versus the spherical and ellipsoidal approximations by examining the outcomes of DWC and finally the geoidal heights. We present the analytical solution of Poisson's kernel in the point-mean discretization model that speed up computation time 500 times faster than spherical Poisson kernel while preserving a good numerical accuracy. The new formulas are very simple and stable even for regions with very low height. It is shown that the maximum differences between spherical and planar DWC as well as planar and ellipsoidal DWC are about 6 mm and 18 mm respectively in the geoidal heights for a rough mountainous area such as Iran.
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4

Su, Baiyun. "Dirichlet Problem for the Schrödinger Operator in a Half Space." Abstract and Applied Analysis 2012 (2012): 1–14. http://dx.doi.org/10.1155/2012/578197.

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For continuous boundary data, the modified Poisson integral is used to write solutions to the half space Dirichlet problem for the Schrödinger operator. Meanwhile, a solution of the Poisson integral for any continuous boundary function is also given explicitly by the Poisson integral with the generalized Poisson kernel depending on this boundary function.
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5

Pavlovic, M. "Integral Means of the Poisson Integral of a Discrete Measure." Journal of Mathematical Analysis and Applications 184, no. 2 (1994): 229–42. http://dx.doi.org/10.1006/jmaa.1994.1196.

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6

Chen, Hongwei. "Four Ways to Evaluate a Poisson Integral." Mathematics Magazine 75, no. 4 (2002): 290. http://dx.doi.org/10.2307/3219167.

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7

Orsingher, Enzo, and Federico Polito. "On the integral of fractional Poisson processes." Statistics & Probability Letters 83, no. 4 (2013): 1006–17. http://dx.doi.org/10.1016/j.spl.2012.12.016.

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8

Zhu, Tonglin, and Wei Lin. "Fast wavelet algorithm of the Poisson integral." Applied Mathematics and Computation 96, no. 2-3 (1998): 127–44. http://dx.doi.org/10.1016/s0096-3003(97)10111-4.

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9

Chen, Hongwei. "Four Ways to Evaluate a Poisson Integral." Mathematics Magazine 75, no. 4 (2002): 290–94. http://dx.doi.org/10.1080/0025570x.2002.11953148.

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10

Steutel, F. W. "Poisson Processes and a Bessel Function Integral." SIAM Review 27, no. 1 (1985): 73–77. http://dx.doi.org/10.1137/1027004.

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11

Chen, J. T., and C. S. Wu. "Alternative derivations for the Poisson integral formula." International Journal of Mathematical Education in Science and Technology 37, no. 2 (2006): 165–85. http://dx.doi.org/10.1080/00207390500226028.

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12

Fan, Hong-Yi, and Nian-Quan Jiang. "Quantum Mechanical Correspondence of Poisson Integral Formula." Communications in Theoretical Physics 55, no. 2 (2011): 217–20. http://dx.doi.org/10.1088/0253-6102/55/2/06.

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13

Victor, J. M. "Poisson–Boltzmann integral equation for polyelectrolyte solutions." Journal of Chemical Physics 95, no. 1 (1991): 600–605. http://dx.doi.org/10.1063/1.461461.

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14

Potseiko, P. G., and E. A. Rovba. "Approximations on Classes of Poisson Integrals by Fourier–Chebyshev Rational Integral Operators." Siberian Mathematical Journal 62, no. 2 (2021): 292–312. http://dx.doi.org/10.1134/s0037446621020099.

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15

O'Brien, Frank, Sherry E. Hammel, and Chung T. Nguyen. "A General Exponential Integral Formula." Perceptual and Motor Skills 79, no. 3_suppl (1994): 1645–46. http://dx.doi.org/10.2466/pms.1994.79.3f.1645.

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16

Li, Zhen, Zuoqiang Shi, and Jian Sun. "Point Integral Method for Solving Poisson-Type Equations on Manifolds from Point Clouds with Convergence Guarantees." Communications in Computational Physics 22, no. 1 (2017): 228–58. http://dx.doi.org/10.4208/cicp.111015.250716a.

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AbstractPartial differential equations (PDE) on manifolds arise in many areas, including mathematics and many applied fields. Due to the complicated geometrical structure of the manifold, it is difficult to get efficient numerical method to solve PDE on manifold. In the paper, we propose a method called point integral method (PIM) to solve the Poisson-type equations from point clouds. Among different kinds of PDEs, the Poisson-type equations including the standard Poisson equation and the related eigenproblem of the Laplace-Beltrami operator are one of the most important. In PIM, the key idea is to derive the integral equations which approximates the Poisson-type equations and contains no derivatives but only the values of the unknown function. This feature makes the integral equation easy to be discretized from point cloud. In the paper, we explain the derivation of the integral equations, describe the point integral method and its implementation, and present the numerical experiments to demonstrate the convergence of PIM.
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17

Nakhman, A. D., and B. P. Osilenker. "NON-TANGENTIAL CONVERGENCE OF THE GENERALIZED POISSON INTEGRAL." Vestnik Tambovskogo gosudarstvennogo tehnicheskogo universiteta 21, no. 4 (2015): 660–68. http://dx.doi.org/10.17277/vestnik.2015.04.pp.660-668.

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18

Pogány, Tibor K. "Integral form of the COM–Poisson renormalization constant." Statistics & Probability Letters 119 (December 2016): 144–45. http://dx.doi.org/10.1016/j.spl.2016.07.008.

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19

Siaulys, J. "Integral additive arithmetic functions and the Poisson distribution." Lithuanian Mathematical Journal 28, no. 2 (1989): 191–200. http://dx.doi.org/10.1007/bf01027195.

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20

Hirshfeld, Allen C., and Thomas Schwarzweller. "Path integral quantization of the Poisson-Sigma model." Annalen der Physik 9, no. 2 (2000): 83–101. http://dx.doi.org/10.1002/(sici)1521-3889(200002)9:2<83::aid-andp83>3.0.co;2-s.

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21

Levy, Jason. "A Truncated Integral of the Poisson Summation Formula." Canadian Journal of Mathematics 53, no. 1 (2001): 122–60. http://dx.doi.org/10.4153/cjm-2001-006-1.

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AbstractLet G be a reductive algebraic group defined over , with anisotropic centre. Given a rational action of G on a finite-dimensional vector space V, we analyze the truncated integral of the theta series corresponding to a Schwartz-Bruhat function on V(). The Poisson summation formula then yields an identity of distributions on V(). The truncation used is due to Arthur.
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22

Symeonidis, Eleutherius. "THE POISSON INTEGRAL AS AN APPROPRIATE MEAN VALUE." Analysis 19, no. 1 (1999): 13–18. http://dx.doi.org/10.1524/anly.1999.19.1.13.

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23

Kuliev, E. A. "Boundary limits of derivatives of Poisson-Szegö integral." Mathematical Notes 57, no. 4 (1995): 375–80. http://dx.doi.org/10.1007/bf02304166.

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24

Frolov, S. I. "Elements of Poisson Integral Calculus and Quantum Mechanics." Journal of Mathematical Sciences 220, no. 6 (2016): 691–700. http://dx.doi.org/10.1007/s10958-016-3212-4.

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25

Tyurin, Eugene, and Rikard von Unge. "Poisson-Lie T-duality: the path-integral derivation." Physics Letters B 382, no. 3 (1996): 233–40. http://dx.doi.org/10.1016/0370-2693(96)00680-6.

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26

Koshanova, M., М. Muratbekova, and B. Turmetov. "SOME BOUNDARY VALUE PROBLEMS WITH INVOLUTION FOR THE NONLOCAL POISSON EQUATION." BULLETIN Series of Physics & Mathematical Sciences 71, no. 3 (2020): 74–83. http://dx.doi.org/10.51889/2020-3.1728-7901.10.

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In this paper, we study new classes of boundary value problems for a nonlocal analogue of the Poisson equation. The boundary conditions, as well as the nonlocal Poisson operator, are specified using transformation operators with orthogonal matrices. The paper investigates the questions of solvability of analogues of boundary value problems of the Dirichlet and Neumann type. It is proved that, as in the classical case, the analogue of the Dirichlet problem is unconditionally solvable. For it, theorems on the existence and uniqueness of the solution to the problem are proved. An explicit form of the Green's function, a generalized Poisson kernel, and an integral representation of the solution are found. For an analogue of the Neumann problem, an exact solvability condition is found in the form of a connection between integrals of given functions. The Green's function and an integral representation of the solution of the problem under study are also constructed.
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27

Talvila, Erik. "Estimates of Henstock-Kurzweil Poisson Integrals." Canadian Mathematical Bulletin 48, no. 1 (2005): 133–46. http://dx.doi.org/10.4153/cmb-2005-012-8.

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AbstractIf f is a real-valued function on [−π, π] that is Henstock-Kurzweil integrable, let ur(θ) be its Poisson integral. It is shown that ∥ur∥p = o(1/(1 − r)) as r → 1 and this estimate is sharp for 1 ≤ p ≤ ∞. If μ is a finite Borel measure and ur(θ) is its Poisson integral then for each 1 ≤ p ≤ ∞ the estimate ∥ur∥p = O((1−r)1/p−1) as r → 1 is sharp. The Alexiewicz norm estimates ∥ur∥ ≤ ∥f ∥ (0 ≤ r &lt; 1) and ∥ur − f∥ → 0 (r → 1) hold. These estimates lead to two uniqueness theorems for the Dirichlet problem in the unit disc with Henstock-Kurzweil integrable boundary data. There are similar growth estimates when u is in the harmonic Hardy space associated with the Alexiewicz norm and when f is of bounded variation.
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28

Sohn, Byung Keun. "Cauchy and Poisson Integral of the Convolutor in Beurling Ultradistributions ofLp-Growth." International Journal of Mathematics and Mathematical Sciences 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/926790.

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LetCbe a regular cone inℝand letTC=ℝ+iC⊂ℂbe a tubular radial domain. LetUbe the convolutor in Beurling ultradistributions ofLp-growth corresponding toTC. We define the Cauchy and Poisson integral ofUand show that the Cauchy integral of Uis analytic inTCand satisfies a growth property. We represent Uas the boundary value of a finite sum of suitable analytic functions in tubes by means of the Cauchy integral representation ofU. Also we show that the Poisson integral ofUcorresponding toTCattainsUas boundary value in the distributional sense.
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29

Grafarend, E. W., and F. Krumm. "The Abel-Poisson kernel and the Abel-Poisson integral in a moving tangent space." Journal of Geodesy 72, no. 7-8 (1998): 404–10. http://dx.doi.org/10.1007/s001900050179.

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30

Ortenzi, G., V. Rubtsov, and S. R. Tagne Pelap. "Integer Solutions of Integral Inequalities and -Invariant Jacobian Poisson Structures." Advances in Mathematical Physics 2011 (2011): 1–18. http://dx.doi.org/10.1155/2011/252186.

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We study the Jacobian Poisson structures in any dimension invariant with respect to the discrete Heisenberg group. The classification problem is related to the discrete volume of suitable solids. Particular attention is given to dimension 3 whose simplest example is the Artin-Schelter-Tate Poisson tensors.
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31

Aliev, Ilham A., Sinem Sezer, and Melih Eryigit. "An integral transform associated to the Poisson integral and inversion of Flett potentials." Journal of Mathematical Analysis and Applications 321, no. 2 (2006): 691–704. http://dx.doi.org/10.1016/j.jmaa.2005.08.086.

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32

Prestin, J., V. V. Savchuk та A. L. Shidlich. "Approximation of 2π-periodic functions by Taylor—Abel—Poisson operators in the integral metric". Reports of the National Academy of Sciences of Ukraine, № 1 (16 лютого 2017): 17–20. http://dx.doi.org/10.15407/dopovidi2017.01.017.

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33

Haruki, Hiroshi, and Themistocles M. Rassias. "New generalizations of the Poisson Kernel." Journal of Applied Mathematics and Stochastic Analysis 10, no. 2 (1997): 191–96. http://dx.doi.org/10.1155/s1048953397000233.

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34

Serdyuk, A. S. "Approximation of Poisson integrals by one linear approximation method in uniform and integral metrics." Ukrainian Mathematical Journal 60, no. 7 (2008): 1144–52. http://dx.doi.org/10.1007/s11253-008-0115-7.

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35

Vlasic, Andrew, and Troy Day. "Poisson integral type quarantine in a stochastic SIR system." Mathematical Biosciences and Engineering 17, no. 5 (2020): 5534–44. http://dx.doi.org/10.3934/mbe.2020297.

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36

Kalugin, German A., David J. Jeffrey, and Robert M. Corless. "Bernstein, Pick, Poisson and related integral expressions for LambertW." Integral Transforms and Special Functions 23, no. 11 (2011): 817–29. http://dx.doi.org/10.1080/10652469.2011.640327.

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37

LI, Ta-Hsin. "Time Series Characterization, Poisson Integral, and Robust Divergence Measures." Technometrics 39, no. 4 (1997): 357–71. http://dx.doi.org/10.1080/00401706.1997.10485155.

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38

Haan, Laurens de, and Sidney Resnick. "Random transformations for poisson processes and sup—integral processes." Communications in Statistics. Stochastic Models 10, no. 1 (1994): 205–21. http://dx.doi.org/10.1080/15326349408807293.

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39

Hjelmeland, Svend E., and Ulf Lindström. "Script N = 1 supersymmetric path-integral Poisson-Lie duality." Journal of High Energy Physics 2001, no. 04 (2001): 027. http://dx.doi.org/10.1088/1126-6708/2001/04/027.

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40

Xiong, Jin Gang. "On a Conformally Invariant Integral Equation Involving Poisson Kernel." Acta Mathematica Sinica, English Series 34, no. 4 (2018): 681–90. http://dx.doi.org/10.1007/s10114-018-7309-1.

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41

Kalaj, David. "On Some Integral Operators Related to the Poisson Equation." Integral Equations and Operator Theory 72, no. 4 (2012): 563–75. http://dx.doi.org/10.1007/s00020-012-1952-1.

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42

Fabbiano, Ruggero, Carlos Canudas de Wit, and Federica Garin. "Source localization by gradient estimation based on Poisson integral." Automatica 50, no. 6 (2014): 1715–24. http://dx.doi.org/10.1016/j.automatica.2014.04.029.

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43

Duman, Oktay, and Merve Kester. "Statistical Approximation by Double Poisson–Cauchy Singular Integral Operators." Results in Mathematics 62, no. 1-2 (2011): 53–65. http://dx.doi.org/10.1007/s00025-011-0129-6.

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44

Chen, Jie-Cheng. "Weights andL Φ-boundedness of the Poisson integral operator". Israel Journal of Mathematics 81, № 1-2 (1993): 193–202. http://dx.doi.org/10.1007/bf02761305.

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45

Zhang, Shibin, and Xinsheng Zhang. "On the Transition Law of Tempered Stable Ornstein–Uhlenbeck Processes." Journal of Applied Probability 46, no. 03 (2009): 721–31. http://dx.doi.org/10.1017/s0021900200005842.

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In this paper, a stochastic integral of Ornstein–Uhlenbeck type is represented to be the sum of two independent random variables: one has a tempered stable distribution and the other has a compound Poisson distribution. In distribution, the compound Poisson random variable is equal to the sum of a Poisson-distributed number of positive random variables, which are independent and identically distributed and have a common specified density function. Based on the representation of the stochastic integral, we prove that the transition distribution of the tempered stable Ornstein–Uhlenbeck process is self-decomposable and that the transition density is aC∞-function.
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46

Zhang, Shibin, and Xinsheng Zhang. "On the Transition Law of Tempered Stable Ornstein–Uhlenbeck Processes." Journal of Applied Probability 46, no. 3 (2009): 721–31. http://dx.doi.org/10.1239/jap/1253279848.

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In this paper, a stochastic integral of Ornstein–Uhlenbeck type is represented to be the sum of two independent random variables: one has a tempered stable distribution and the other has a compound Poisson distribution. In distribution, the compound Poisson random variable is equal to the sum of a Poisson-distributed number of positive random variables, which are independent and identically distributed and have a common specified density function. Based on the representation of the stochastic integral, we prove that the transition distribution of the tempered stable Ornstein–Uhlenbeck process is self-decomposable and that the transition density is a C∞-function.
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47

Gorringe, V. M., and P. G. L. Leach. "The first integrals and their Lie algebra of the most general autonomous Hamiltonian of the form H = T + V possessing a Laplace-Runge-Lenz vector." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 34, no. 4 (1993): 511–22. http://dx.doi.org/10.1017/s033427000000905x.

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AbstractIn two dimensions it is found that the most general autonomous Hamiltonian possessing a Laplace-Runge-Lenz vector is The Poisson bracket of the two components of this vector leads to a third first-integral, cubic in the momenta. The Lie algebra of the three integrals under the operation of the Poisson bracket closes, and is shown to be so(3) for negative energy and so(2, 1) for positive energy. In the case of zero energy, the algebra is W(3, 1). The result does not have a three-dimensional analogue, apart from the usual Kepler problem.
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48

Grabowski, Janusz. "Z-Graded Extensions of Poisson Brackets." Reviews in Mathematical Physics 09, no. 01 (1997): 1–27. http://dx.doi.org/10.1142/s0129055x97000026.

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A Z-graded Lie bracket { , }P on the exterior algebra Ω(M) of differential forms, which is an extension of the Poisson bracket of functions on a Poisson manifold (M,P), is found. This bracket is simultaneously graded skew-symmetric and satisfies the graded Jacobi identity. It is a kind of an 'integral' of the Koszul–Schouten bracket [ , ]P of differential forms in the sense that the exterior derivative is a bracket homomorphism: [dμ, dν]P=d{μ, ν}P. A naturally defined generalized Hamiltonian map is proved to be a homomorphism between { , }P and the Frölicher–Nijenhuis bracket of vector valued forms. Also relations of this graded Poisson bracket to the Schouten–Nijenhuis bracket and an extension of { , }P to a graded bracket on certain multivector fields, being an 'integral' of the Schouten–Nijenhuis bracket, are studied. All these constructions are generalized to tensor fields associated with an arbitrary Lie algebroid.
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49

Štikonienė, Olga, and Mifodijus Sapagovas. "Numerical investigation of alternating-direction method for Poisson equation with weighted integral conditions." Lietuvos matematikos rinkinys 51 (October 22, 2019): 385–90. http://dx.doi.org/10.15388/lmr.2010.14665.

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The present paper deals with a generalization of the alternating-direction implicit(ADI) method for a two dimensional Poisson equation in a rectangle domain with aweighted integral boundary condition in one coordinate direction. We consider the alternatingdirection method for a system of difference equations that approximates Poisson equationwith weighed integral boundary conditions with the fourth-order accuracy. Sufficient conditionsof stability for ADI method are investigated numerically. An analysis of results ofcomputational experiments is presented. &#x0D;
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50

Bulut, Serap. "Integral Averages of Two Generalizations of the Poisson Kernel by Haruki and Rassias." Journal of Applied Mathematics and Stochastic Analysis 2008 (March 16, 2008): 1–6. http://dx.doi.org/10.1155/2008/760214.

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In 1997, Haruki and Rassias introduced two generalizations of the Poisson kernel in two dimensions and discussed integral formulas for them. Furthermore, they presented an open problem. In 1999, Kim gave a solution to that problem. Here, we give a solution to this open problem by means of a different method. The purpose of this paper is to give integral averages of two generalizations of the Poisson kernel, that is, we generalize the open problem.
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