Salimov, R. B.
Published in
Russian Mathematics

We derive an asymptotical representation for singular integral with the Hilbert kernel near a fixed point where its density vanishes as a negative power of module of logarithm of distance from this point.

Anikonov, D. S. Konovalova, D. S.
Published in
Siberian Mathematical Journal

In a general integral geometry problem, there are given the integrals of an unknown function over certain manifolds. The traditional statement of the problem consists in determining the integrand. We consider the case of an underdetermined problem when the unknown functions depend on a greater number of variables than the given integrals. These sit...

Zhongxiang, Zhang
Published in
Advances in Applied Clifford Algebras

In this paper, Cauchy type integral and singular integral over hyper-complex plane ∏\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\prod}$$\end{document} are consider...

Chen, Yanping Ding, Yong
Published in
Journal of Inequalities and Applications

Vector-valued inequalities are considered for the commutator of the singular integral with rough kernel. The results obtained in this paper are substantial improvement and extension of some known results. MSC: 42B20, 42B25.

Zhu, Maochun Niu, Pengcheng
Published in
Milan Journal of Mathematics

We consider a class of Kolmogorov equation Lu=∑i,j=1p0∂xi(aij(z)∂xju)+∑i,j=1Nbijxi∂xju-∂tu=∑j=1p0∂xjFj(z)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Lu={\sum^{p_0}_...

Salimov, R. B.
Published in
Russian Mathematics

We study properties of a singular integral with the Hilbert kernel at a fixed point, where the modulus of continuity of its density has logarithmic order, and the integral is not necessarily convergent.

Saakyan, A. V.
Published in
Mechanics of Solids

The present paper presents a Gauss type quadrature formula for a Cauchy type integral whose density is the product of a Hölder function by the weight function (1 − x)α(1 + x)β (Re α, Reβ > −1) of orthogonal Jacobi polynomials. It is shown that at the roots of the function of the second kind corresponding to the Jacobi polynomial Pn(α,β) (x), the qu...

Gasimova, N. F.
Published in
Mathematical Notes

We obtain solutions for a class of two-dimensional nonlinear singular integral equations with Hilbert kernel using the contraction mapping method and find the rate of convergence of successive approximations to the exact solution.

Salimov, R. B.
Published in
Russian Mathematics

We study the behavior of a singular integral with the Hilbert kernel near a point where the continuous density of the integral does not satisfy the Hölder condition and, as a result, the integral, possibly, diverges.

Zakharov, E. V. Kalinin, A. V.
Published in
Computational Mathematics and Modeling

Methods of assessing the electrophysiological state of the heart by solving the inverse problem of electrocardiography in potential form are actively used in clinical practice. Some results suggest, however, that on its own the electric potential of the heart may not be sufficient for diagnosing complex cases of cardiac arrhythmia. Studies have sho...