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pro vyhledávání: '"Hypersingular integrals"'
Akademický článek
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Publikováno v:
Mathematics, Vol 11, Iss 23, p 4752 (2023)
The paper is devoted to the approximate calculation of Riemann definite integrals, singular and hypersingular integrals over closed and open non-rectifiable curves and fractals. The conditions of existence for the Riemann definite integrals over non-
Externí odkaz:
https://doaj.org/article/c906a8336a79491d8fedcc795d2235d2
Autor:
Andrei P. Shilin
Publikováno v:
Журнал Белорусского государственного университета: Математика, информатика, Iss 2, Pp 17-28 (2021)
The paper provides an exact analytical solution to a hypersingular inregro-differential equation of arbitrary order. The equation is defined on a closed curve in the complex plane. A characteristic feature of the equation is that if is written using
Externí odkaz:
https://doaj.org/article/bedc1cb23ced43baaecd5e33e3537468
Publikováno v:
Researches in Mathematics, Vol 28, Iss 1, Pp 29-42 (2020)
We introduce a family of Balakrishnan-Rubin type hypersingular integrals depending on a parameter $\varepsilon $ and generated by the Generalized Poisson semigroup. Then the rate of convergence of these families of truncated hypersingular integrals,
Externí odkaz:
https://doaj.org/article/e210c5520a4f4ff89e8f1235c89feba0
Publikováno v:
Journal of Inequalities and Applications, Vol 2020, Iss 1, Pp 1-12 (2020)
Abstract Hypersingular integrals have appeared as effective tools for inversion of multidimensional potential-type operators such as Riesz, Bessel, Flett, parabolic potentials, etc. They represent (at least formally) fractional powers of suitable dif
Externí odkaz:
https://doaj.org/article/e19973f0b479405ba606768d62104c5e
Autor:
Andrei P. Shilin
Publikováno v:
Журнал Белорусского государственного университета: Математика, информатика, Iss 3, Pp 48-56 (2019)
The linear hypersingular integro-differential equation of arbitrary order on a closed curve located on the complex plane is considered. A scheme is proposed to study this equation in the case when its coefficients have some particular structure. This
Externí odkaz:
https://doaj.org/article/02d06d8170ee4665b12bee2f648e7137
Autor:
I.V. Boykov, P.V. Aykashev
Publikováno v:
Известия высших учебных заведений. Поволжский регион: Физико-математические науки, Iss 1 (2021)
Background. Hypersingular integrals are now finding more and more fields of application – aerodynamics, elasticity theory, electrodynamics and geophysics. Moreover, their calculation in an analytical form is possible only in very special cases. Th
Externí odkaz:
https://doaj.org/article/e8461b1aab984cd1a27fb498fc4046a9
Akademický článek
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Publikováno v:
Axioms, Vol 11, Iss 4, p 150 (2022)
The article is devoted to the issue of construction of an optimal with respect to order passive algorithms for evaluating Cauchy and Hilbert singular and hypersingular integrals with oscillating kernels. We propose a method for estimating lower bound
Externí odkaz:
https://doaj.org/article/ba2931f82ac341fbb391415cab4d0417
Publikováno v:
IEEE Access, Vol 5, Pp 26852-26866 (2017)
This paper presents the modified quadrature rules for 1-D hypersingular integrals, and then constructs the quadrature formulas to numerically evaluate multi-dimensional hypersingular integrals in the form of f .p. f.Ω g(x)/(Πi=1s |xi-ti|1+γi) Πi=
Externí odkaz:
https://doaj.org/article/6b9cb9ab26174edf9b7086fc50406a90