Results 191 to 200 of about 568,612 (221)

q-Bernstein polynomials of the Cauchy kernel

Applied Mathematics and Computation, 2008
Let \(q>0\). For \(n=0,1,\dots\), the \(q\)-integer \([n]_q\) is defined by \([n]_q:=1+q+\dots+q^{n-1}\) if \(n\in\mathbb N\) and \([0]_q=0\). The \(q\)-factorial and \(q\)-binomials are given by \([n]_q!=[1]_q![2]_q!\dots [n]_q!\), \(n\in\mathbb N\), \([0]_q!=1\), and \(\left[\binom{n}{k}\right]_q:=\frac{[n]_q!}{[k]_q![n-k]_q!}\), \(0\leq k\leq n ...
exaly   +4 more sources

Algorithms for generalized cauchy kernels

Complex Variables, Theory and Application: An International Journal, 1983
First order, elliptic, systems in the plane are discussed. A recursive scheme is obtained for constructing their generalized Cauchy kernels. To this end, the initial problem for the kernels is posed as second order, complex, hyperbolic problems with dependent Goursat data. As an illustration of the method, the case with constant coefficients is treated
Robert P. Gilbert, Lin Wei
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Cauchy and poisson kernels for tubes

Integral Transforms and Special Functions, 1998
Let C be a regular cone in . The Cauchy and Poisson kernel functions, denoted K(z−t), and respectively, are defined and are shown to be elements in the ultradifferential spaces D(∗,Ls ) for 1 < s≤∞ and 1 ≤ s ≤ ∞, respectively, as functions of arbitrary but fixed.
R.D. Carmichael, S. Pilipović
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The derivatives of cauchy's kernel and cauchy's estimate in clifford analysis

Complex Variables, Theory and Application: An International Journal, 1989
Some refinements of estimates for the coefficients of the Taylor series are studied in Clifford analysis. An explicit estimate for the partial derivatives of Cauchy's kernel is given. With this result Cauchy's estimate for the partial derivatives of a monogenic function is obtained. These are generalizations of those in complex analysis.
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The Kernel Recursive Generalized Cauchy Kernel Loss Algorithm

2019 6th International Conference on Information, Cybernetics, and Computational Social Systems (ICCSS), 2019
As a nonlinear measure similarity developed in a kernel space, the generalized correntropic loss (GC-Loss) has been successfully used for signal processing and machine learning in non-Gaussian situations thanks to its ability of extracting high-order statistical properties of data.
Wei Shi, Kui Xiong, Shiyuan Wang
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Solving integro-differential equations with Cauchy kernel

Applied Mathematics and Computation, 2009
In the traditional reproducing kernel method for solving singular integral and integro-differential equations, the representation of the reproducing kernel function is usually complicated and the requirement for the image space of the operator is high.
Yongfang Zhou, Yingzhen Lin
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Singular Integral Operators with a Generalized Cauchy Kernel

Doklady Mathematics, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Cauchy kernel for cones

Studia Mathematica, 2004
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The cauchy and poisson kernels as ultradifferentiable functions

Complex Variables, Theory and Application: An International Journal, 1998
Let C be an open convex cone in such that does not contain any entire straight line. We previously have shown that the Cauchy and Poisson kernel functions corresponding to the tube are elements of the ultradifferentiable function spaces , where ∗ is either (Mp ) or {Mp }.
Richard D. Carmichael, S. Pilipović
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Cauchy-Stieltjes Kernel families: Some properties

Statistics & Probability Letters
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Raouf Fakhfakh, Omar Alzeley
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