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Journal articles on the topic 'Singular integral'

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Published: 4 June 2021
Last updated: 7 September 2023

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1

Jefferies, Brian, and Susumu Okada. "Pettis integrals and singular integral operators." Illinois Journal of Mathematics 38, no. 2 (June 1994): 250–72. http://dx.doi.org/10.1215/ijm/1255986799.

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2

Du, Jinyuan. "SINGULAR INTEGRAL OPERATORS AND SINGULAR QUADRATURE OPERATORS ASSOCIATED WITH SINGULAR INTEGRAL EQUATIONS." Acta Mathematica Scientia 18, no. 2 (April 1998): 227–40. http://dx.doi.org/10.1016/s0252-9602(17)30757-9.

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3

Estrada, Ricardo, and Ram P. Kanwal. "Singular Integral Equations." Mathematical Gazette 84, no. 500 (July 2000): 379. http://dx.doi.org/10.2307/3621739.

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4

Carbery, A. "SINGULAR INTEGRAL OPERATORS." Bulletin of the London Mathematical Society 20, no. 4 (July 1988): 373–75. http://dx.doi.org/10.1112/blms/20.4.373.

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5

Namazi, Javad. "A singular integral." Proceedings of the American Mathematical Society 96, no. 3 (March 1, 1986): 421. http://dx.doi.org/10.1090/s0002-9939-1986-0822432-2.

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6

Shi, Yanlong, Li Li, and Zhonghua Shen. "Boundedness of p -Adic Singular Integrals and Multilinear Commutator on Morrey-Herz Spaces." Journal of Function Spaces 2023 (April 18, 2023): 1–11. http://dx.doi.org/10.1155/2023/9965919.

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In this paper, we establish the boundedness of classical p -adic singular integrals on Morrey-Herz spaces, as well as the boundedness of multilinear commutator generated by p -adic singular integral operators and Lipschitz functions or by p -adic singular integral operators and λ -central BMO functions.
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7

Banerjea, Sudeshna, Barnali Dutta, and A. Chakrabarti. "Solution of Singular Integral Equations Involving Logarithmically Singular Kernel with an Application in a Water Wave Problem." ISRN Applied Mathematics 2011 (May 12, 2011): 1–16. http://dx.doi.org/10.5402/2011/341564.

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A direct function theoretic method is employed to solve certain weakly singular integral equations arising in the study of scattering of surface water waves by vertical barriers with gaps. Such integral equations possess logarithmically singular kernel, and a direct function theoretic method is shown to produce their solutions involving singular integrals of similar types instead of the stronger Cauchy-type singular integrals used by previous workers. Two specific ranges of integration are examined in detail, which involve the following: Case(i) two disjoint finite intervals (0,a)∪(b,c) and (a,b,c being finite ) and Case(ii) a finite union of n disjoint intervals. The connection of such integral equations for Case(i), with a particular water wave scattering problem, is explained clearly, and the important quantities of practical interest (the reflection and transmission coefficients) are determined numerically by using the solution of the associated weakly singular integral equation.
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8

Xu, Yong Jia. "On Weighted Hadamard-Type Singular Integrals and Their Applications." Abstract and Applied Analysis 2007 (2007): 1–17. http://dx.doi.org/10.1155/2007/62852.

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By means of an expression with a kind of integral operators, some properties of the weighted Hadamard-type singular integrals are revealed. As applications, the solution for certain strongly singular integral equations is discussed and illustrated.
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9

Zozulya, V. V. "Divergent Integrals in Elastostatics: General Considerations." ISRN Applied Mathematics 2011 (August 2, 2011): 1–25. http://dx.doi.org/10.5402/2011/726402.

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This article considers weakly singular, singular, and hypersingular integrals, which arise when the boundary integral equation methods are used to solve problems in elastostatics. The main equations related to formulation of the boundary integral equation and the boundary element methods in 2D and 3D elastostatics are discussed in details. For their regularization, an approach based on the theory of distribution and the application of the Green theorem has been used. The expressions, which allow an easy calculation of the weakly singular, singular, and hypersingular integrals, have been constructed.
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10

SATO, SHUICHI. "ESTIMATES FOR SINGULAR INTEGRALS ALONG SURFACES OF REVOLUTION." Journal of the Australian Mathematical Society 86, no. 3 (June 2009): 413–30. http://dx.doi.org/10.1017/s1446788708000773.

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AbstractWe prove certain Lp estimates (1<p<∞) for nonisotropic singular integrals along surfaces of revolution. The singular integrals are defined by rough kernels. As an application we obtain Lp boundedness of the singular integrals under a sharp size condition on their kernels. We also prove a certain estimate for a trigonometric integral, which is useful in studying nonisotropic singular integrals.
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11

Lorist, Emiel, and Mark Veraar. "Singular stochastic integral operators." Analysis & PDE 14, no. 5 (August 22, 2021): 1443–507. http://dx.doi.org/10.2140/apde.2021.14.1443.

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12

Chen, Lung-Kee. "On a singular integral." Studia Mathematica 85, no. 1 (1987): 61–72. http://dx.doi.org/10.4064/sm-85-1-61-72.

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13

Agarwal, R. P., and D. O'Regan. "Singular Volterra integral equations." Applied Mathematics Letters 13, no. 1 (January 2000): 115–20. http://dx.doi.org/10.1016/s0893-9659(99)00154-8.

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14

Flanders, Harley. "92.36 A singular integral." Mathematical Gazette 92, no. 524 (July 2008): 276–78. http://dx.doi.org/10.1017/s0025557200183159.

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15

Prenov, B. B., and N. N. Tarkhanov. "Martinelli-Bochner singular integral." Siberian Mathematical Journal 33, no. 2 (March 1992): 355–59. http://dx.doi.org/10.1007/bf00971114.

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16

Karaiev, Artem, and Elena Strelnikova. "Singular integrals in axisymmetric problems of elastostatics." International Journal of Modeling, Simulation, and Scientific Computing 11, no. 01 (February 2020): 2050003. http://dx.doi.org/10.1142/s1793962320500038.

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Singular integral equations arisen in axisymmetric problems of elastostatics are under consideration in this paper. These equations are received after applying the integral transformation and Gauss–Ostrogradsky’s theorem to the Green tensor for equilibrium equations of the infinite isotropic medium. Initially, three-dimensional problems expressed in Cartesian coordinates are transformed to cylindrical ones and integrated with respect to the circumference coordinate. So, the three-dimensional axisymmetric problems are reduced to systems of one-dimensional singular integral equations requiring the evaluation of linear integrals only. The thorough analysis of both displacement and traction kernels is accomplished, and similarity in behavior of both kernels is established. The kernels are expressed in terms of complete elliptic integrals of first and second kinds. The second kind elliptic integrals are nonsingular, and standard Gaussian quadratures are applied for their numerical evaluation. Analysis of external integrals proved the existence of logarithmic and Cauchy’s singularities. The numerical treatment of these integrals takes into account the presence of this integrable singularity. The numerical examples are provided to testify accuracy and efficiency of the proposed method including integrals with logarithmic singularity, Catalan’s constant, the Gaussian surface integral. The comparison between analytical and numerical data has proved high precision and availability of the proposed method.
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17

Medved’, M. "Singular integral inequalities with several nonlinearities and integral equations with singular kernels." Nonlinear Oscillations 11, no. 1 (January 2008): 70–79. http://dx.doi.org/10.1007/s11072-008-0015-7.

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18

Zhou, H. L., B. X. Bian, Y. Tian, B. Yu, and Z. R. Niu. "The Calculation of Potential Derivatives by Using NBIE for Anisotropic Potential Problems." Journal of Mechanics 33, no. 2 (July 15, 2016): 183–91. http://dx.doi.org/10.1017/jmech.2016.66.

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AbstractThe natural boundary integral equation (NBIE) is developed to calculate potential derivatives for potential problems with anisotropic media. Firstly, the governing equation of the two-dimensional anisotropic potential problem is transformed into standard Laplace equation by a coordinate transformation method. Then a potential derivative boundary integral equation named as NBIE is extended to solve the anisotropic potential problem. The most important virtue of the NBIE is that the singularity of the integral kernel function is reduced by one order in comparison with the conventional potential derivative boundary integral equation(CDBIE). Therefore the new potential derivative boundary integral equation only contains strongly singular integrals rather than hyper-singular integrals. Thus the NBIE can calculate more accurate potential derivative results for both boundary nodes and interior points. Moreover, in combination with the analytical integral regularization algorithm of nearly singular integrals, the NBIE can obtain more accurate potential derivatives of interior points very close to the boundary than the CDBIE. Numerical examples on heat conduction in anisotropic media demonstrate the accuracy and efficiency of the NBIE.
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19

Aghili, Arman. "Non-homogeneous impulsive time fractional heat conduction equation." Journal of Numerical Analysis and Approximation Theory 52, no. 1 (July 10, 2023): 22–33. http://dx.doi.org/10.33993/jnaat521-1316.

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This article provides a concise exposition of the integral transforms and its application to singular integral equation and fractional partial differential equations. The author implemented an analytical technique, the transform method, for solving the boundary value problems of impulsive time fractional heat conduction equation. Integral transforms method is a powerful tool for solving singular integral equations, evaluation of certain integrals involving special functions and solution of partial fractional differential equations. The proposed method is extremely concise, attractive as a mathematical tool. The obtained result reveals that the transform method is very convenient and effective.Certain new integrals involving the Airy functions are given.
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20

Amini, S., and N. D. Maines. "Regularization of strongly singular integrals in boundary integral equations." Communications in Numerical Methods in Engineering 12, no. 11 (November 1996): 787–93. http://dx.doi.org/10.1002/(sici)1099-0887(199611)12:11<787::aid-cnm19>3.0.co;2-5.

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21

Abdulkawi, M. "Bounded solution of Cauchy type singular integral equation of the first kind using differential transform method." JOURNAL OF ADVANCES IN MATHEMATICS 14, no. 1 (April 30, 2018): 7580–95. http://dx.doi.org/10.24297/jam.v14i1.7049.

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In this paper, an efficient approximate solution for solving the Cauchy type singular integral equation of the first kind is presented. Bounded solution of the Cauchy type singular Integral equation is discussed. Two type of kernel, separable and convolution, are considered. The differential transform method is used in the solution. New theorems for transformation of Cauchy singular integrals are given with proofs. Approximate results areshown to illustrate the efficiency and accuracy of the approximate solution.
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22

Hu, Jin-Xiu, Hai-Feng Peng, and Xiao-Wei Gao. "Numerical Evaluation of Arbitrary Singular Domain Integrals Using Third-Degree B-Spline Basis Functions." Mathematical Problems in Engineering 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/284106.

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A new approach is presented for the numerical evaluation of arbitrary singular domain integrals. In this method, singular domain integrals are transformed into a boundary integral and a radial integral which contains singularities by using the radial integration method. The analytical elimination of singularities condensed in the radial integral formulas can be accomplished by expressing the nonsingular part of the integration kernels as a series of cubic B-spline basis functions of the distancerand using the intrinsic features of the radial integral. In the proposed method, singularities involved in the domain integrals are explicitly transformed to the boundary integrals, so no singularities exist at internal points. A few numerical examples are provided to verify the correctness and robustness of the presented method.
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23

Yee, Tat-Leung, Ka-Luen Cheung, and Kwok-Pun Ho. "Integral operators on local Orlicz-Morrey spaces." Filomat 36, no. 4 (2022): 1231–43. http://dx.doi.org/10.2298/fil2204231y.

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We establish a general principle on the boundedness of operators on local Orlicz-Morrey spaces. As applications of this principle, we obtain the boundedness of the Calder?n-Zygmund operators, the nonlinear commutators of the Calder?n-Zygmund operators, the oscillatory singular integral operators, the singular integral operators with rough kernels and the Marcinkiewicz integrals on the local Orlicz-Morrey spaces.
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24

Al-Qassem, H. M. "Weighted norm inequalities for a class of rough singular integrals." International Journal of Mathematics and Mathematical Sciences 2005, no. 5 (2005): 657–69. http://dx.doi.org/10.1155/ijmms.2005.657.

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Weighted norm inequalities are proved for a rough homogeneous singular integral operator and its corresponding maximal truncated singular operator. Our results are essential improvements as well as extensions of some known results on the weighted boundedness of singular integrals.
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25

Bijura, Angelina. "Singularly perturbed Volterra integral equations with weakly singular kernels." International Journal of Mathematics and Mathematical Sciences 30, no. 3 (2002): 129–43. http://dx.doi.org/10.1155/s016117120201325x.

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We consider finding asymptotic solutions of the singularly perturbed linear Volterra integral equations with weakly singular kernels. An interesting aspect of these problems is that the discontinuity of the kernel causes layer solutions to decay algebraically rather than exponentially within the initial (boundary) layer. To analyse this phenomenon, the paper demonstrates the similarity that these solutions have to a special function called the Mittag-Leffler function.
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26

Ashour, Samir A. "Numerical solution of integral equations with finite part integrals." International Journal of Mathematics and Mathematical Sciences 22, no. 1 (1999): 155–60. http://dx.doi.org/10.1155/s0161171299221552.

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27

Meskhi, A. "Asymptotic Behavior of Singular and Entropy Numbers for Some Riemann–Liouville Type Operators." gmj 8, no. 2 (June 2001): 323–32. http://dx.doi.org/10.1515/gmj.2001.323.

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Abstract The asymptotic behavior of the singular and entropy numbers is established for the Erdelyi–Köber and Hadamard integral operators (see, e.g., [Samko, Kilbas and Marichev, Integrals and derivatives. Theoryand Applications, Gordon and Breach Science Publishers, 1993]) acting in weighted L 2 spaces. In some cases singular value decompositions are obtained as well for these integral transforms.
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28

Gopinath, D. V., and A. R. Nayak. "Chebyshev-hilbert transform method for the solution of singular integrals and singular integral equations." Transport Theory and Statistical Physics 25, no. 6 (October 1996): 635–57. http://dx.doi.org/10.1080/00411459608222916.

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29

Szufla, Stanisław. "On the Volterra integral equation with weakly singular kernel." Mathematica Bohemica 131, no. 3 (2006): 225–31. http://dx.doi.org/10.21136/mb.2006.134139.

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30

Rovba, Yevgeniy A., and Pavel G. Potsejko. "Jackson’s rational singular integral on the cut." Doklady of the National Academy of Sciences of Belarus 63, no. 4 (September 13, 2019): 398–407. http://dx.doi.org/10.29235/1561-8323-2019-63-4-398-407.

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The introduction presents the main results of previously known papers on Jackson’s singular integral in polynomial and rational cases. Next, we introduce Jackson’s singular integral on the interval [–1, 1] with the kernel obtained by one system of rational Chebyshev–Markov fractions and establish its basic approximative properties: a theorem on uniform convergence of a sequence of Jackson’s singular integrals for an even function is obtained, and conditions are specified that the parameter must satisfy in order for uniform convergence to take place; the approximative properties of sequences of Jackson’s singular integrals on classes of functions satisfying on the interval [–1, 1] the condition of Lipschitz class with constant M. are investigated. The obtained estimates are asymptotically exact as n → ∞; an estimate of deviation of Jackson’s rational singular integral from the function |x|s, 0 < s < 2 depending on the position of the point on the segment, a uniform estimate of the deviation on the segment [–1, 1] and its asymptotics are found. The optimal value of the parameter is obtained, for which the deviation error of the studied approximation apparatus from the function |x|s, 0 < s < 2 on the interval [–1, 1] has the highest rate of zero; the order of approximation of the function |x| on the interval [–1, 1] byJackson’s considered singular integral is found. It is shown that with a special choice of the parameter, the velocity of the approximation error tending to zero is higher in comparison with the polynomial case. All results of this article are new. The work is both theoretical and applied. It is possible to apply the results to solve specific problems of computational mathematics and to read special courses at mathematical faculties.
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31

Alphonse, A., and Shobha Madan. "On ergodic singular integral operators." Colloquium Mathematicum 66, no. 2 (1993): 299–307. http://dx.doi.org/10.4064/cm-66-2-299-307.

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32

Reyes, Juan Bory, and Ricardo Abreu Blaya. "One-dimensional Singular Integral Equations." Complex Variables, Theory and Application: An International Journal 48, no. 6 (June 2003): 483–93. http://dx.doi.org/10.1080/0278107032000077033.

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33

Juberg, R. K. "Certain singular integral operators revisited." Applicable Analysis 27, no. 1-3 (January 1988): 125–32. http://dx.doi.org/10.1080/00036818808839727.

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34

Boimatov, K. Kh, and G. Dzhangibekov. "On a singular integral operator." Russian Mathematical Surveys 43, no. 3 (June 30, 1988): 199–200. http://dx.doi.org/10.1070/rm1988v043n03abeh001746.

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35

Shayya, Bassam. "Nonisotropic strongly singular integral operators." Transactions of the American Mathematical Society 354, no. 12 (August 1, 2002): 4893–907. http://dx.doi.org/10.1090/s0002-9947-02-03097-0.

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36

Filippychev, D. S. "Solving a Singular Integral Equation." Computational Mathematics and Modeling 25, no. 3 (June 15, 2014): 356–64. http://dx.doi.org/10.1007/s10598-014-9232-3.

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37

Fenton, Peter C., and John Rossi. "Estimates for Singular Integral Operators." Computational Methods and Function Theory 8, no. 1 (March 27, 2007): 35–46. http://dx.doi.org/10.1007/bf03321668.

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38

Dashan, Fan, Lu Shanzhen, and Pan Yibiao. "A discrete singular integral operator." Acta Mathematica Sinica 14, no. 2 (April 1998): 235–44. http://dx.doi.org/10.1007/bf02560210.

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39

Pavlov, E. A. "Class of singular integral operators." Ukrainian Mathematical Journal 43, no. 1 (January 1991): 86–90. http://dx.doi.org/10.1007/bf01066909.

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40

Bosch-Camós, Anna, Joan Mateu, and Joan Orobitg. "L P estimates for the maximal singular integral in terms of the singular integral." Journal d'Analyse Mathématique 126, no. 1 (April 2015): 287–306. http://dx.doi.org/10.1007/s11854-015-0018-0.

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41

Saleh, M. H., and D. Sh Mohammed. "NUMERICAL SOLUTION OF SINGULAR AND NON SINGULAR INTEGRAL EQUATIONS." Cubo (Temuco) 15, no. 2 (2013): 89–104. http://dx.doi.org/10.4067/s0719-06462013000200009.

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42

Lifanov, I. K. "SINGULAR SOLUTIONS OF SINGULAR INTEGRAL EQUATIONS AND THEIR APPLICATIONS." Proceedings of the Estonian Academy of Sciences. Physics. Mathematics 48, no. 2 (1999): 101. http://dx.doi.org/10.3176/phys.math.1999.2.04.

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43

Alqudah, Manar A., Pshtiwan Othman Mohammed, and Thabet Abdeljawad. "Solution of Singular Integral Equations via Riemann–Liouville Fractional Integrals." Mathematical Problems in Engineering 2020 (September 30, 2020): 1–8. http://dx.doi.org/10.1155/2020/1250970.

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In this attempt, we introduce a new technique to solve main generalized Abel’s integral equations and generalized weakly singular Volterra integral equations analytically. This technique is based on the Adomian decomposition method, Laplace transform method, and Ψ-Riemann–Liouville fractional integrals. Finally, some examples are proposed and they illustrate the rapidness of our new technical method.
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44

Pan, Yali, Changwen Li, and Xinsong Wang. "Boundedness of Oscillatory Integrals with Variable Calderón-Zygmund Kernel on Weighted Morrey Spaces." Journal of Function Spaces and Applications 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/946435.

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Oscillatory integral operators play a key role in harmonic analysis. In this paper, the authors investigate the boundedness of the oscillatory singular integrals with variable Calderón-Zygmund kernel on the weighted Morrey spacesLp,k(ω). Meanwhile, the corresponding results for the oscillatory singular integrals with standard Calderón-Zygmund kernel are established.
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45

Seeger, Andreas, and Stephen Wainger. "Bounds for singular fractional integrals and related Fourier integral operators." Journal of Functional Analysis 199, no. 1 (April 2003): 48–91. http://dx.doi.org/10.1016/s0022-1236(02)00114-3.

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46

Butris, Raad Noori. "SOME RESULTS IN THE EXISTENCE, UNIQUENESS AND STABILITY PERIODIC SOLUTION OF NEW VOLTERRA INTEGRAL EQUATIONS WITH SINGULAR KERNEL." IJISCS (International Journal of Information System and Computer Science) 4, no. 3 (November 15, 2020): 143. http://dx.doi.org/10.56327/ijiscs.v4i3.938.

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The aim of this work is to study the existence, uniqueness and stability of periodic solutions of some classes for non-linear systems of new Volterra integral equations with singular kernel in two variables by using Riemann integrals. Furthermore, we investigation the existence, uniqueness and stability of the fundamental tools employed in the analysis are based on applications by depending on the numerical-analytic method for studying the periodic solutions of ordinary differential equations which were introduced by Samoilenko.The study of such nonlinear Volterra integral equations with singular kernel leads us to improve and extend Samoilenko method. Thus the non-linear integral equations with singular kernel that we have introduced in the study become more general and detailed than those introduced by Butris .
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47

Tsalamengas, John L. "Quadrature rules for weakly singular, strongly singular, and hypersingular integrals in boundary integral equation methods." Journal of Computational Physics 303 (December 2015): 498–513. http://dx.doi.org/10.1016/j.jcp.2015.09.053.

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48

Ioakimidis, N. I. "A new interpretation of Cauchy type singular integrals with an application to singular integral equations." Journal of Computational and Applied Mathematics 14, no. 3 (March 1986): 271–78. http://dx.doi.org/10.1016/0377-0427(86)90065-8.

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49

Du, Jinyuan. "SINGULAR INTEGRAL OPERATORS AND SINGULAR QUADRATURE OPERATORS ASSOCIATED WITH SINGULAR INTEGRAL EQUATIONS OF THE FIRST KIND AND THEIR APPLICATIONS." Acta Mathematica Scientia 15, no. 2 (1995): 219–34. http://dx.doi.org/10.1016/s0252-9602(18)30043-2.

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50

Al-Qassem, H., and M. Ali. "Singular integrals related to homogeneous mapping with rough kernels on product spaces." Tamkang Journal of Mathematics 39, no. 2 (June 30, 2008): 165–76. http://dx.doi.org/10.5556/j.tkjm.39.2008.27.

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In this paper, we study the $ L^{p} $ mapping properties of singular integral operators related to homogeneous mappings on product spaces with kernels which belong to block spaces. Our results extend as well as improve some known results on singular integrals.
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