• Title/Summary/Keyword: $C^*$-integral

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Numerical solution of singular integral equation for multiple curved branch-cracks

  • Chen, Y.Z.;Lin, X.Y.
    • Structural Engineering and Mechanics
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    • v.34 no.1
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    • pp.85-95
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    • 2010
  • In this paper, numerical solution of the singular integral equation for the multiple curved branch-cracks is investigated. If some quadrature rule is used, one difficult point in the problem is to balance the number of unknowns and equations in the solution. This difficult point was overcome by taking the following steps: (a) to place a point dislocation at the intersecting point of branches, (b) to use the curve length method to covert the integral on the curve to an integral on the real axis, (c) to use the semi-open quadrature rule in the integration. After taking these steps, the number of the unknowns is equal to the number of the resulting algebraic equations. This is a particular advantage of the suggested method. In addition, accurate results for the stress intensity factors (SIFs) at crack tips have been found in a numerical example. Finally, several numerical examples are given to illustrate the efficiency of the method presented.

SINGULAR AND MARCINKIEWICZ INTEGRAL OPERATORS ON PRODUCT DOMAINS

  • Badriya Al-Azri;Ahmad Al-Salman
    • Communications of the Korean Mathematical Society
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    • v.38 no.2
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    • pp.401-430
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    • 2023
  • In this paper, we prove Lp estimates of a class of singular integral operators on product domains along surfaces defined by mappings that are more general than polynomials and convex functions. We assume that the kernels are in L(log L)2 (𝕊n-1 × 𝕊m-1). Furthermore, we prove Lp estimates of the related class of Marcinkiewicz integral operators. Our results extend as well as improve previously known results.

AN AUTOMATIC AUGMENTED GALERKIN METHOD FOR SINGULAR INTEGRAL EQUATIONS WITH HILBERT KERNEL

  • Abbasbandy, S.;Babolian, E.
    • Journal of applied mathematics & informatics
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    • v.8 no.2
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    • pp.429-437
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    • 2001
  • In [1, 2], described a Chebyshev series method for the numerical solution of integral equations with three automatic algorithms for computing tow regularization parameters, C/sub f/ and r. Here we describe a Fourier series expansion method for a class singular integral equations with Hilbert kernel and constant coefficients with using a new automatic algorithm.

DEGENERATE BERNOULLI NUMBERS AND POLYNOMIALS ASSOCIATED WITH DEGENERATE HERMITE POLYNOMIALS

  • Haroon, Hiba;Khan, Waseem Ahmad
    • Communications of the Korean Mathematical Society
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    • v.33 no.2
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    • pp.651-669
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    • 2018
  • The article is themed to classify new (fully) degenerate Hermite-Bernoulli polynomials with formulation in terms of p-adic fermionic integrals on $\mathbb{Z}_p$. The entire paper is designed to illustrate new properties in association with Daehee polynomials in a consolidated and generalized form.

AN ANALOGUE OF WIENER MEASURE AND ITS APPLICATIONS

  • Im, Man-Kyu;Ryu, Kun-Sik
    • Journal of the Korean Mathematical Society
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    • v.39 no.5
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    • pp.801-819
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    • 2002
  • In this note, we establish a translation theorem in an analogue of Wiener space (C[0,t],$\omega$$\phi$) and find formulas for the conditional $\omega$$\phi$-integral given by the condition X(x) = (x(to), x(t$_1$),…, x(t$_{n}$)) which is the generalization of Chang and Chang's results in 1984. Moreover, we prove a translation theorem for the conditional $\omega$$\phi$-integral.l.

WEIGHTED ESTIMATES FOR CERTAIN ROUGH SINGULAR INTEGRALS

  • Zhang, Chunjie
    • Journal of the Korean Mathematical Society
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    • v.45 no.6
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    • pp.1561-1576
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    • 2008
  • In this paper we shall prove some weighted norm inequalities of the form $${\int}_{R^n}\;|Tf(x)|^pu(x)dx\;{\leq}\;C_p\;{\int}_{R^n}\;|f(x)|^pNu(x)dx$$ for certain rough singular integral T and maximal singular integral $T^*$. Here u is a nonnegative measurable function on $R^n$ and N denotes some maximal operator. As a consequence, some vector valued inequalities for both T and $T^*$ are obtained. We shall also get a boundedness result of T on the Triebel-Lizorkin spaces.

HYPONORMAL SINGULAR INTEGRAL OPERATORS WITH CAUCHY KERNEL ON L2

  • Nakazi, Takahiko
    • Communications of the Korean Mathematical Society
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    • v.33 no.3
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    • pp.787-798
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    • 2018
  • For $1{\leq}p{\leq}{\infty}$, let $H^p$ be the usual Hardy space on the unit circle. When ${\alpha}$ and ${\beta}$ are bounded functions, a singular integral operator $S_{{\alpha},{\beta}}$ is defined as the following: $S_{{\alpha},{\beta}}(f+{\bar{g}})={\alpha}f+{\beta}{\bar{g}}(f{\in}H^p,\;g{\in}zH^p)$. When p = 2, we study the hyponormality of $S_{{\alpha},{\beta}}$ when ${\alpha}$ and ${\beta}$ are some special functions.

FRACTIONAL CALCULUS AND INTEGRAL TRANSFORMS OF INCOMPLETE τ-HYPERGEOMETRIC FUNCTION

  • Pandey, Neelam;Patel, Jai Prakash
    • Communications of the Korean Mathematical Society
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    • v.33 no.1
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    • pp.127-142
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    • 2018
  • In the present article, authors obtained certain fractional derivative and integral formulas involving incomplete ${\tau}$-hypergeometric function introduced by Parmar and Saxena [14]. Some interesting special cases and consequences of our main results are also considered.

NUMERICAL METHOD FOR A SYSTEM OF SINGULARLY PERTURBED CONVECTION DIFFUSION EQUATIONS WITH INTEGRAL BOUNDARY CONDITIONS

  • Raja, Velusamy;Tamilselvan, Ayyadurai
    • Communications of the Korean Mathematical Society
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    • v.34 no.3
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    • pp.1015-1027
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    • 2019
  • A class of systems of singularly perturbed convection diffusion type equations with integral boundary conditions is considered. A numerical method based on a finite difference scheme on a Shishkin mesh is presented. The suggested method is of almost first order convergence. An error estimate is derived in the discrete maximum norm. Numerical examples are presented to validate the theoretical estimates.

CONVEXITY OF INTEGRAL OPERATORS GENERATED BY SOME NEW INEQUALITIES OF HYPER-BESSEL FUNCTIONS

  • Din, Muhey U.
    • Communications of the Korean Mathematical Society
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    • v.34 no.4
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    • pp.1163-1173
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    • 2019
  • In this article, we deduced some new inequalities related to hyper-Bessel function. By using these inequalities we will find some sufficient conditions under which certain families of integral operators are convex in the open unit disc. Some applications related to these results are also the part of our investigation.