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Journal articles on the topic 'Multiple integrals'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Ojo-, Orobosa V.O. "Projecting Multiple Stochastic Integral unto the Wiener Functional Space Using Iterated Integrals." Continental J. Applied Sciences 13, no. 2 (2018): 44–57. https://doi.org/10.5281/zenodo.3016870.

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<em>Any square- integrable functional of the Wiener process has a canonical representation in terms of the integrals. The key of these representation is to define multiple stochastic integral of the form </em><em> where φ is (in general) a random integrand</em><em>-adapted in a suitable sense. In this paper, we construct projections with respect to stochastic integral unto the Wiener functional space and establish formulae for the transformation of multiple stochastic integrals under two operations; (a) projection formula for the projection of a multiple stochastic integrals onto </em

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2

Bandyrskii, B., L. Hoshko, I. Lazurchak, and M. Melnyk. "Optimal algorithms for computing multiple integrals." Mathematical Modeling and Computing 4, no. 1 (2017): 1–9. http://dx.doi.org/10.23939/mmc2017.01.001.

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3

Greaves, G. R. H., R. R. Hall, M. N. Huxley, and J. C. Wilson. "Multiple Franel integrals." Mathematika 40, no. 1 (1993): 51–70. http://dx.doi.org/10.1112/s0025579300013711.

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4

Dynkin, E. B. "Multiple path integrals." Advances in Applied Mathematics 7, no. 2 (1986): 205–19. http://dx.doi.org/10.1016/0196-8858(86)90032-1.

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5

Dasgupta, A., and G. Kallianpur. "Multiple fractional integrals." Probability Theory and Related Fields 115, no. 4 (1999): 505–25. http://dx.doi.org/10.1007/s004400050247.

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6

Papp, F. J. "Expressing certain multiple integrals as single integrals." International Journal of Mathematical Education in Science and Technology 21, no. 1 (1990): 137–39. http://dx.doi.org/10.1080/0020739900210120.

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7

Benabidallah, A., Y. Cherruault, and Y. Tourbier. "Approximation of multiple integrals by simple integrals." Kybernetes 30, no. 9/10 (2001): 1223–39. http://dx.doi.org/10.1108/03684920110405836.

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8

Malyutin, V. B., and B. O. Nurjanov. "The semiclassical approximation of multiple functional integrals." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 59, no. 4 (2024): 302–7. http://dx.doi.org/10.29235/1561-2430-2023-59-4-302-307.

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In this paper, we study the semiclassical approximation of multiple functional integrals. The integrals are defined through the Lagrangian and the action. Of all possible trajectories, the greatest contribution to the integral is given by the classical trajectory x̅cl for which the action S takes an extremal value. The classical trajectory is found as a solution of the multidimensional Euler – Lagrange equation. To calculate the functional integrals, the expansion of the action with respect to the classical trajectory is used, which can be interpreted as an expansion in powers of Planck’s cons

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9

Greaves, G. R. H., R. R. Hall, M. N. Huxley, and J. C. Wilson. "Multiple Franel integrals: Corrigendum." Mathematika 41, no. 2 (1994): 401. http://dx.doi.org/10.1112/s0025579300007476.

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10

Grosjean, C. C. "Two Trigonometric Multiple Integrals." SIAM Review 33, no. 1 (1991): 114. http://dx.doi.org/10.1137/1033008.

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11

Podol’skii, A. A. "Identities for multiple integrals." Mathematical Notes 98, no. 3-4 (2015): 624–30. http://dx.doi.org/10.1134/s0001434615090291.

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12

Bardina, Xavier, and Carles Rovira. "On the strong convergence of multiple ordinary integrals to multiple Stratonovich integrals." Publicacions Matemàtiques 65 (July 1, 2021): 859–76. http://dx.doi.org/10.5565/publmat6522114.

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13

Li, Haibin, Yangtian Li, and Shangjie Li. "Dual Neural Network Method for Solving Multiple Definite Integrals." Neural Computation 31, no. 1 (2019): 208–32. http://dx.doi.org/10.1162/neco_a_01145.

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This study, which examines a calculation method on the basis of a dual neural network for solving multiple definite integrals, addresses the problems of inefficiency, inaccuracy, and difficulty in finding solutions. First, the method offers a dual neural network method to construct a primitive function of the integral problem; it can approximate the primitive function of any given integrand with any precision. On this basis, a neural network calculation method that can solve multiple definite integrals whose upper and lower bounds are arbitrarily given is obtained with repeated applications of

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14

Benabidallah, A., Y. Cherruault, and Y. Tourbier. "Approximation method error of multiple integrals by simple integrals." Kybernetes 32, no. 3 (2003): 343–53. http://dx.doi.org/10.1108/03684920310458575.

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15

Wang, Zhongxiang, Cai Chang, and Jian Lu. "Direct Calculating Method for Integral of Multivariate Functions Based on Mathematica." Journal of Education and Culture Studies 9, no. 1 (2024): p16. https://doi.org/10.22158/jecs.v9n1p16.

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Mathematica is a comprehensive and efficient general mathematical software that integrates numerical and symbolic calculation, graphics and animation, programming and interactive demonstrations. This paper presents the methodology and operational procedures for the direct computation of multiple integrals, curve integrals and surface integrals utilizing Mathematica software. Through the application examples, it can be intuitively seen that this way of calculating multiple integrals with Mathematical software provides a very convenient, fast and effective way to verify the correctness of the in

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16

Haddad, Roudy El. "Repeated integration and explicit formula for the \(n\)-th integral of \(x^m(\ln x)^{m'}\)." Open Journal of Mathematical Sciences 6, no. 1 (2022): 51–75. http://dx.doi.org/10.30538/oms2022.0178.

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Repeated integration is a major topic of integral calculus. In this article, we study repeated integration. In particular, we study repeated integrals and recurrent integrals. For each of these integrals, we develop reduction formulae for both the definite as well as indefinite form. These reduction formulae express these repetitive integrals in terms of single integrals. We also derive a generalization of the fundamental theorem of calculus that expresses a definite integral in terms of an indefinite integral for repeated and recurrent integrals. From the recurrent integral formulae, we deriv

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17

Ernst, Thomas. "Further results on multiple q-Eulerian integrals for various q-hypergeometric functions." Publications de l'Institut Math?matique (Belgrade) 108, no. 122 (2020): 63–77. http://dx.doi.org/10.2298/pim2022063e.

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We continue the study of single and multiple q-Eulerian integrals in the spirit of Exton, Driver, Johnston, Pandey, Saran and Erd?lyi. The method of proof is often the q-beta integral method with the correct q-power together with the q-binomial theorem. By the Totov method we can prove summation theorems as special cases of multiple q-Eulerian integrals. The Srivastava ? notation for q-hypergeometric functions is used to enable the shortest possible form of the long formulas. The various q-Eulerian integrals are in fact meromorphic continuations of the various multiple q-functions, suitable fo

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18

Shomurodova, Dilafroz. "SURFACE INTEGRALS IN MATHEMATICAL ANALYSIS." International journal of advanced research in education, technology and management 2, no. 2 (2023): 68–71. https://doi.org/10.5281/zenodo.7677840.

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In this article, methods of working examples related to the calculation of surface integrals of the first type and some applications of surface integrals, that is, finding the mass of several bodies, are considered, and a convenient method of teaching them to students of higher education institutions is analyzed.       

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19

Shao, Zijia, Shuohao Wang, and Hetian Yu. "Application of the Residue Theorem to Euler Integral, Gaussian Integral, and Beyond." Highlights in Science, Engineering and Technology 38 (March 16, 2023): 311–16. http://dx.doi.org/10.54097/hset.v38i.5821.

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The paper is divided into three different parts, which use the residue theorem to solve several different integrals, namely, the Euler integral, the Gaussian integral, the Fresnel integral, and so forth. The process of using the resiude theorem to determine these integrals is to first turn the integrals into convenient forms of complex integrals, and then find integral perimeters so that any integral on one of the curves is the required integral, through the drawing observation of the contour to write the original integral into the form of multiple integral. By studying the resiude theorem to

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20

Bruggeman, Roelof, and Youngju Choie. "Multiple period integrals and cohomology." Algebra & Number Theory 10, no. 3 (2016): 645–64. http://dx.doi.org/10.2140/ant.2016.10.645.

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21

Yu, Chii-Huei, and Bing-Huei Chen. "Solving Multiple Integrals Using Maple." World Journal of Computer Application and Technology 2, no. 4 (2014): 83–88. http://dx.doi.org/10.13189/wjcat.2014.020401.

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22

Yu, Chii-Huei, and Bing-Huei Chen. "Evaluating Multiple Integrals Using Maple." Mathematics and Statistics 2, no. 4 (2014): 155–61. http://dx.doi.org/10.13189/ms.2014.020401.

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23

Trif, Tiberiu. "Multiple Integrals of Symmetric Functions." American Mathematical Monthly 104, no. 7 (1997): 605. http://dx.doi.org/10.2307/2975053.

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24

Blankenbecler, Richard. "Multiple scattering and functional integrals." Physical Review D 55, no. 4 (1997): 2441–48. http://dx.doi.org/10.1103/physrevd.55.2441.

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25

Tocino, A. "Multiple stochastic integrals with Mathematica." Mathematics and Computers in Simulation 79, no. 5 (2009): 1658–67. http://dx.doi.org/10.1016/j.matcom.2008.08.005.

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26

Zelikin, M. I. "Field theories for multiple integrals." Journal of Mathematical Sciences 177, no. 2 (2011): 270–98. http://dx.doi.org/10.1007/s10958-011-0457-9.

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27

Nourdin, Ivan, and Giovanni Peccati. "Noncentral convergence of multiple integrals." Annals of Probability 37, no. 4 (2009): 1412–26. http://dx.doi.org/10.1214/08-aop435.

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28

Trif, Tiberiu. "Multiple Integrals of Symmetric Functions." American Mathematical Monthly 104, no. 7 (1997): 605–8. http://dx.doi.org/10.1080/00029890.1997.11990688.

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29

Peccati, Giovanni. "Gaussian Approximations of Multiple Integrals." Electronic Communications in Probability 12 (2007): 350–64. http://dx.doi.org/10.1214/ecp.v12-1322.

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30

Mehta, M. L., and J.-M. Normand. "On some definite multiple integrals." Journal of Physics A: Mathematical and General 30, no. 24 (1997): 8671–84. http://dx.doi.org/10.1088/0305-4470/30/24/026.

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31

Bajic, Tatjana. "On relation between one multiple and a corresponding one-dimensional integral with applications." Yugoslav Journal of Operations Research 28, no. 1 (2018): 79–92. http://dx.doi.org/10.2298/yjor160916020b.

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For a given finite positive measure on an interval I ? R, a multiple stochastic integral of a Volterra kernel with respect to a product of a corresponding Gaussian orthogonal stochastic measure is introduced. The Volterra kernel is taken such that the multiple stochastic integral is a multiple iterated stochastic integral related to a parameterized Hermite polynomial, where parameter depends on Gaussian distribution of an underlying one-dimensional stochastic integral. Considering that there exists a connection between stochastic and deterministic integrals, we expose some properties of parame

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32

Benabidallah, A., Y. Cherruault, and G. Mora. "Approximation of multiple integrals by simple integrals involving periodic functions." Kybernetes 33, no. 9/10 (2004): 1472–90. http://dx.doi.org/10.1108/03684920410534470.

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33

Gupta, A. K., and D. G. Kabe. "On a zonal polynomial integral." Journal of Applied Mathematics 2003, no. 11 (2003): 569–73. http://dx.doi.org/10.1155/s1110757x03209074.

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A certain multiple integral occurring in the studies of Beherens-Fisher multivariate problem has been evaluated by Mathai et al. (1995) in terms of invariant polynomials. However, this paper explicitly evaluates the context integral in terms of zonal polynomials, thus establishing a relationship between zonal polynomial integrals and invariant polynomial integrals.

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34

Pranevich, Andrei, Alexander Grin, and Yanka Musafirov. "Multiple partial integrals of polynomial Hamiltonian systems." Acta et commentationes: Ştiinţe Exacte şi ale Naturii 12, no. 2 (2022): 33–42. http://dx.doi.org/10.36120/2587-3644.v12i2.33-42.

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We consider an autonomous real polynomial Hamiltonian ordinary differential system. Sufficient conditions for the construction of additional first integrals on polynomial partial integrals and multiple polynomial partial integrals are obtained. Classes of autonomous polynomial Hamiltonian ordinary differential systems with first integrals which analytically expressed by multiple polynomial partial integrals are identified. Also we present examples that illustrate the theoretical results.

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35

Jang, Lee-Chae. "On Multiple Generalizedw-Genocchi Polynomials and Their Applications." Mathematical Problems in Engineering 2010 (2010): 1–8. http://dx.doi.org/10.1155/2010/316870.

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We define the multiple generalizedw-Genocchi polynomials. By using fermionicp-adic invariant integrals, we derive some identities on these generalizedw-Genocchi polynomials, for example, fermionicp-adic integral representation, Witt's type formula, explicit formula, multiplication formula, and recurrence formula for thesew-Genocchi polynomials.

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36

Rybakov, Konstantin. "Features of the Expansion of Multiple Stochastic Stratonovich Integrals Using Walsh and Haar Functions." Differential Equations and Control Processes, no. 1 (2023): 137–50. http://dx.doi.org/10.21638/11701/spbu35.2023.109.

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The problem of the root-mean-square convergence for approximations of multiple stochastic Stratonovich integrals based on the generalized multiple Fourier series method using Walsh and Haar functions is considered. It is shown that when they are chosen to expand multiple stochastic integrals, the proof of the root-mean-square convergence of a subsequence of series partial sums, which is formed in a way that is quite natural for these functions, does not require the explicit fulfillment of any additional conditions, except for the condition of the existence of the multiple stochastic Stratonovi

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37

Mukha, V. S., and N. F. Kako. "Integrals and integral transformations related to the vector Gaussian distribution." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 55, no. 4 (2020): 457–66. http://dx.doi.org/10.29235/1561-2430-2019-55-4-457-466.

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This paper is dedicated to the integrals and integral transformations related to the probability density function of the vector Gaussian distribution and arising in probability applications. Herein, we present three integrals that permit to calculate the moments of the multivariate Gaussian distribution. Moreover, the total probability formula and Bayes formula for the vector Gaussian distribution are given. The obtained results are proven. The deduction of the integrals is performed on the basis of the Gauss elimination method. The total probability formula and Bayes formula are obtained on t

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38

Bazarbayeva, L., and Ye. Aitzhanov. "ALGORITHMIC APPROACH TO SOLVING MULTIPLE INTEGRALS." Scientific heritage, no. 146 (October 7, 2024): 25–33. https://doi.org/10.5281/zenodo.13896858.

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The idea of our work is showing the fastest and easiest methods for solving problems such as calculating area and volume using double and triple integrals. These are the most difficult topics of mathematical analysis and many students do not reach these paragraphs, and in order to simplify, we have made these algorithms and methods. Also, these methods of solving are given in algorithmic way, which is convenient to remember. In addition, formulas are given in table form, which shows that formulas are connected with each other and it’s as well easy to remember.

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39

Ciesielski, Mariusz, and Tomasz Blaszczyk. "The multiple composition of the left and right fractional Riemann-Liouville integrals - analytical and numerical calculations." Filomat 31, no. 19 (2017): 6087–99. http://dx.doi.org/10.2298/fil1719087c.

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New fractional integral operators of order ? ? R+ are introduced. These operators are defined as the composition of the left and right (or the right and left) Riemann-Liouville fractional order integrals. Some of their properties are studied. Analytical results of fractional integrals of several functions are presented. For a numerical calculation of fractional order integrals, two numerical procedures are given. In the final part of this paper, examples of numerical evaluations of these operators of three different functions are shown in plots and the comparison of the numerical accuracy was

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40

LAPORTA, S. "ANALYTICAL EXPRESSIONS OF THREE- AND FOUR-LOOP SUNRISE FEYNMAN INTEGRALS AND FOUR-DIMENSIONAL LATTICE INTEGRALS." International Journal of Modern Physics A 23, no. 31 (2008): 5007–20. http://dx.doi.org/10.1142/s0217751x08042869.

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In this paper we continue the work began in 2002 on the identification of the analytical expressions of Feynman integrals which require the evaluation of multiple elliptic integrals. We rewrite and simplify the analytical expression of the three-loop self-mass integral with three equal masses and on-shell external momentum. We collect and analyze a number of results on double and triple elliptic integrals. By using very high-precision numerical fits, for the first time we are able to identify a very compact analytical expression for the four-loop on-shell self-mass integral with four equal mas

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41

Lax, Peter D. "Change of Variables in Multiple Integrals." American Mathematical Monthly 106, no. 6 (1999): 497. http://dx.doi.org/10.2307/2589462.

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42

Kałamajska, Agnieszka. "On lower semicontinuity of multiple integrals." Colloquium Mathematicum 74, no. 1 (1997): 71–78. http://dx.doi.org/10.4064/cm-74-1-71-78.

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43

Kolomoitsev, Yurii, and Elijah Liflyand. "Absolute convergence of multiple Fourier integrals." Studia Mathematica 214, no. 1 (2013): 17–35. http://dx.doi.org/10.4064/sm214-1-2.

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44

Tudor, Constantin, and Maria Tudor. "Power variation of multiple fractional integrals." Central European Journal of Mathematics 5, no. 2 (2007): 358–72. http://dx.doi.org/10.2478/s11533-007-0001-9.

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45

Gunawardena, K. L. D. "On the Evaluation of Multiple Integrals." Missouri Journal of Mathematical Sciences 6, no. 1 (1994): 29–33. http://dx.doi.org/10.35834/1994/0601029.

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46

Seel, Alexander, Frank Göhmann, and Andreas Klümper. "From Multiple Integrals to Fredholm Determinants." Progress of Theoretical Physics Supplement 176 (2008): 375–83. http://dx.doi.org/10.1143/ptps.176.375.

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47

Loiseau, Jean-Francis, Jean-Pierre Codaccioni, and R{égis Caboz. "Hyperelliptic integrals and multiple hypergeometric series." Mathematics of Computation 50, no. 182 (1988): 501. http://dx.doi.org/10.1090/s0025-5718-1988-0929548-0.

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48

Koyama, Shin-ya, and Nobushige Kurokawa. "Euler's integrals and multiple sine functions." Proceedings of the American Mathematical Society 133, no. 5 (2005): 1257–65. http://dx.doi.org/10.1090/s0002-9939-04-07863-3.

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49

Tudor, Constantin, and Maria Tudor. "Approximation of Multiple Stratonovich Fractional Integrals." Stochastic Analysis and Applications 25, no. 4 (2007): 781–99. http://dx.doi.org/10.1080/07362990701419979.

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50

Kloeden, P. E., E. Platen, and I. W. Wright. "The approximation of multiple stochastic integrals." Stochastic Analysis and Applications 10, no. 4 (1992): 431–41. http://dx.doi.org/10.1080/07362999208809281.

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