Results 21 to 30 of about 341 (205)
Integral Representation and Explicit Formula at Rational Arguments for Apostol–Tangent Polynomials
, 2021 The Fourier series expansion of Apostol–tangent polynomials is derived using the Cauchy residue theorem and a complex integral over a contour. This Fourier series and the Hurwitz–Lerch zeta function are utilized to obtain the explicit formula
Cristina B. Corcino +3 more
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Application of Cauchy’s Residue Theorem in Several Improper Integrals
Highlights in Science, Engineering and Technology, 2023 Calculating definite integrals in complex functions requires the Cauchy's residue theorem, which is a key concept in the complex variables. It is based on several ideas, including the isolated singular points theory, the Laurent theorem, and the Cauchy integral theorem.
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Analytical Solution for the Problem of Point Location in Arbitrary Planar Domains
AlgorithmsThis paper presents a general analytical solution for the problem of locating points in planar regions with an arbitrary geometry at the boundary. The proposed methodology overcomes the traditional solutions used for polygonal regions.
Vitor Santos
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Highlights in Science, Engineering and Technology, 2023 Integration is a useful mathematical tool which is applied in a wide range of studies and assists people to solve many problems. Despite methods of real analysis, complex integrations in complex analysis are more beneficial and more convenient than real integrations under certain circumstances.
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Revisiting stress propagation in a three-dimensional elastic sphere under diametric loading
Nihon Kikai Gakkai ronbunshuThe stress propagation for a three-dimensional elastic sphere under a diametric loading condition in the framework of the linear elastodynamics is revisited. By describing displacements in terms of scalar and vector potentials using the Helmholtz theorem,
Yosuke SATO, Satoshi TAKADA
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JOURNAL OF RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES, 2022 Cauchy's residue theorem gives a relatively general form for a complex integral along a simple closed contour. With the help of Cauchy's residue theorem, an appropriate closed contour can be chosen to calculate some abnormal definite integrals that might be very complicated and difficult to solve by conventional methods.
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Asymptotic properties of cross‐classified sampling designs
Canadian Journal of Statistics, EarlyView.Abstract We investigate the family of cross‐classified sampling designs across an arbitrary number of dimensions. We introduce a variance decomposition that enables the derivation of general asymptotic properties for these designs and the development of straightforward and asymptotically unbiased variance estimators.
Jean Rubin, Guillaume Chauvet
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Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT The leading‐order asymptotic behavior of the solution of the Cauchy initial‐value problem for the Benjamin–Ono equation in L2(R)$L^2(\mathbb {R})$ is obtained explicitly for generic rational initial data u0$u_0$. An explicit asymptotic wave profile uZD(t,x;ε)$u^\mathrm{ZD}(t,x;\epsilon)$ is given, in terms of the branches of the multivalued ...
Elliot Blackstone +3 more
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Front Propagation Through a Perforated Wall
Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT We consider a bistable reaction– diffusion equation ut=Δu+f(u)$u_t=\Delta u +f(u)$ on RN${\mathbb {R}}^N$ in the presence of an obstacle K$K$, which is a wall of infinite span with many holes. More precisely, K$K$ is a closed subset of RN${\mathbb {R}}^N$ with smooth boundary such that its projection onto the x1$x_1$‐axis is bounded and that ...
Henri Berestycki +2 more
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, 2019 Complex integrals associated with homogeneous independently scattered random measures on the line are discussed. Theorems corresponding to Cauchy’s theorem and the residue theorem are given. Furthermore, the converse of Cauchy’s theorem is
Yamamuro, Kouji
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