Results 1 to 10 of about 568,612 (221)

Non-symmetric Cauchy kernels [PDF]

Discrete Mathematics & Theoretical Computer Science, 2013
Using an analogue of the Robinson-Schensted-Knuth (RSK) algorithm for semi-skyline augmented fillings, due to Sarah Mason, we exhibit expansions of non-symmetric Cauchy kernels $∏_(i,j)∈\eta (1-x_iy_j)^-1$, where the product is over all cell-coordinates $(i,j)$ of the stair-type partition shape $\eta$ , consisting of the cells in a NW-SE diagonal of a ...
Olga Azenhas, Aram Emami
openaire   +3 more sources

Multikernel Adaptive Filters Under the Minimum Cauchy Kernel Loss Criterion

IEEE Access, 2019
The Cauchy loss has been successfully applied in robust learning algorithms in the presence of large outliers, but it may suffer from performance degradation in complex nonlinear tasks.
Shiyuan Wang, Kui Xiong
exaly   +3 more sources

A rank-conditioned α-stable perturbation for differential evolution: Separating perturbation frequency and tail heaviness. [PDF]

PLoS One
Heavy-tailed perturbations are commonly used in differential evolution (DE) to restore diversity and mitigate premature convergence. Adaptive Cauchy perturbation refines this strategy by varying perturbation probabilities according to dimension-wise ...
Choi TJ, An Y.
europepmc   +2 more sources

The kernel theorem for Cauchy ultradistribution

Journal of Mathematical Analysis and Applications, 2003
Because of the popularity currently gained by ultradistribution theory (after the heydays of Schwartz distribution theory) the authors have tried to extend the results concerning kernel theorems to ultradistributions. Some elementary results are proved under the heading ``The kernel theorem''.
Banerji, P.K., Debnath, Lokenath, Bhandari, Deshna   +2 more
exaly   +2 more sources

Notes on Cauchy–Stieltjes Kernel Families

Axioms
The free Meixner family (FMF) is the family of measures that produces quadratic Cauchy–Stieltjes Kernel (CSK) families (i.e., meaning that the associated variance function (VF) is a polynomial with degree ≤2 in the mean). Furthermore, a cubic class is introduced in the context of CSK families and is connected to the quadratic class via a reciprocity ...
Shokrya Saleh Alshqaq, Raouf Fakhfakh, Fatimah Alshahrani   +2 more
openaire   +4 more sources

On some properties of Cauchy-Stieltjes Kernel families

Indian Journal of Pure and Applied Mathematics, 2021
The author studies and proves theorems about properties of the Cauchy-Stieltjes kernel families which have counterparts in natural exponential families. The author concentrates on properties of the variance function of finite mixtures of distributions of these families.
Raouf Fakhfakh
exaly   +2 more sources

A Cauchy kernel for slice regular functions [PDF]

Annals of Global Analysis and Geometry, 2009
In this paper we show how to construct a regular, non commutative Cauchy kernel for slice regular quaternionic functions. We prove an (algebraic) representation formula for such functions, which leads to a new Cauchy formula. We find the expression of the derivatives of a regular function in terms of the powers of the Cauchy kernel, and we present ...
Graziano Gentili, Fabrizio Colombo, Irène Sabadini   +2 more
exaly   +5 more sources

Studies on Cauchy–Stieltjes Kernel Families

Mathematics
In the setting of Cauchy–Stieltjes kernel (CSK) families, this study provides some features of free Poisson, free Gamma, and free Binomial laws, as well as some innovative limit theorems linked to Fermi convolution. These findings highlight the fundamental links between noncommutative probability and analytic function theory, demonstrating the ...
Abdulmajeed Albarrak, Raouf Fakhfakh, Ghadah Alomani   +2 more
openaire   +3 more sources

A note on solving integro-differential equation with Cauchy kernel

Mathematical and Computer Modelling, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Abdelaziz Mennouni
exaly   +3 more sources

On Cauchy–Stieltjes kernel families [PDF]

Journal of Multivariate Analysis, 2014
We explore properties of Cauchy-Stieltjes families that have no counterpart in exponential families. We relate the variance function of the iterated Cauchy-Stieltjes family to the pseudo-variance function of the initial Cauchy-Stieltjes family. We also investigate when the domain of means can be extended beyond the "natural domain".
Wlodek Bryc, Raouf Fakhfakh, Abdelhamid Hassairi   +2 more
  +11 more sources