On the regularization of the first kind integral equation with analytical kernel of logarithmic type [PDF]
, 1999 We study regularization methods for the integral equation of the first kind with analytical kernel of logarithmic type. The problem is severely ill-posed. In [1] a logarithmic type convergence rate for the Tikhonov regularized solution was proved.
Bruckner, Gottfried
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A Law of the Logarithm for Kernel Density Estimators
The Annals of Probability, 1982 In this paper we derive a law of the logarithm for the maximal deviation between a kernel density estimator and the true underlying density function. Extensions to higher derivatives are included. The results are applied to get optimal window-widths with respect to almost sure uniform convergence.
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Construction of Boundary Invariants and the Logarithmic Singularity of the Bergman Kernel [PDF]
The Annals of Mathematics, 2000 This paper studies Fefferman's program \cite{F3} of expressing the singularity of the Bergman kernel, for smoothly bounded strictly pseudoconvex domains $Ω\subset\C^n$, in terms of local biholomorphic invariants of the boundary. By \cite{F1}, the Bergman kernel on the diagonal $K(z,cz)$ is written in the form $$ K=ϕr^{-n-1}+ψ\log r \qtext{with} ϕ,ψ\in ...
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Spectral relationships of the integral equation with logarithmic kernel in some different domains [PDF]
, 2014 In this work, the Fredholm integral equation (FIE) with logarithmic kernel is investigated from the contact problem in the plane theory of elasticity. Then, using potential theory method (PTM), the spectral relationships (SRs) of this integral equation ...
Abdou, M. A., Youssef, M. I.
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On logarithmic Sobolev inequalities for the heat kernel on the Heisenberg group [PDF]
, 2020 International audienceIn this note, we derive a new logarithmic Sobolev inequality for the heat kernel on the Heisenberg group. The proof is inspired from the historical method of Leonard Gross with the Central Limit Theorem for a random walk.
Chafaï, Djalil +5 more
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Multimodal Data‐Driven Microstructure Characterization
Advanced Engineering Materials, EarlyView.A self‐consistent autonomous workflow for EBSP‐based microstructure segmentation by integrating PCA, GMM clustering, and cNMF with information‐theoretic parameter selection, requiring no user input. An optimal ROI size related to characteristic grain size is identified.
Qi Zhang +4 more
wiley +1 more source
A Novel Hybrid Kernel Adaptive Filtering Algorithm for Nonlinear Channel Equalization
IEEE Access, 2019 In this paper, a novel kernel mixed error criterion (KMEC) algorithm is proposed for nonlinear system identification, which uses a combination of two different error schemes to implement a newly constructed cost function, which is realized by using a ...
Qishuai Wu +3 more
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Optimal heat kernel bounds under logarithmic Sobolev inequalities
, 2002 We establish optimal uniform upper estimates on heat kernels whose generators satisfy a logarithmic Sobolev inequality (or entropy-energy inequality) with the optimal constant of the Euclidean space.
Daniel Concordet +2 more
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Complexity of primal-dual interior-point algorithm for linear programming based on a new class of kernel functions [PDF]
, 2023 summary:In this paper, we first present a polynomial-time primal-dual interior-point method (IPM) for solving linear programming (LP) problems, based on a new kernel function (KF) with a hyperbolic-logarithmic barrier term. To improve the iteration bound,
Chikouche, Wided +3 more
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A Law of the Logarithm for Kernel Quantile Density Estimators
The Annals of Probability, 1994 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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