This paper presents a regularization technique for the high order efficient numerical evaluation of nearly singular, principal-value, and finite-part Cauchy-type integral operators. By relying on Cauchy formula, Cauchy-Goursat theorem, on-curve Taylor interpolations input density, proposed methodology allows to recast associated operators as smooth contour integrals. As such, they can be accura...

We analytically derive a class of non-singular, static and spherically symmetric topological black hole metrics in F(R)-gravity. These have not de Sitter core at their centre, as most model standard General Relativity. study the geometric properties motion test particles around these objects. Since they two horizons, inner being Cauchy type, we focus on problem mass inflation show that it occur...

We deene a residue current of a holomorphic mapping , or more generally a holomorphic section to a holomorphic vector bundle, by means of Cauchy-Fantappie-Leray type formulas , and prove that a holomorphic function that annihilates this current belongs to the corresponding ideal locally. We also prove that the residue current coincides with the Colee-Herrera current in the case of a complete in...

We consider optimal control problems associated to generally non-well posed Cauchy in a general framework. Firstly, we approximate the ill-posed problem with family of well-posed one and show that solutions latter converge former one. Secondly, investigate minimization approximated state equation. prove existence uniqueness minimizers characterize optimality systems. Finally, subjected equation...

A function f ∈ C(Ω) is holomorphic on Ω, if it satisfies the CauchyRiemann equations: ∂̄f = ∑n k=1 ∂f ∂z̄k dz̄k = 0 in Ω. Denote the set of holomorphic functions on Ω by H(Ω). The Bergman projection, B0, is the orthogonal projection of square-integrable functions onto H(Ω)∩L2(Ω). Since the Cauchy-Riemann operator, ∂̄ above, extends naturally to act on higher order forms, we can as well define Bergm...

The inverse problem of amplitude reconstruction on an inclined line based the values or its module as recorded semi-infinite orthogonal to beam propagation direction is considered within framework 2D parabolic equation. It demonstrated that this problem, in case when complex image plane known, can be reduced a singular Cauchy type integral existence solutions requires certain conditions met but...

A Sine function approach is used to derive a new Hunter type quadrature rule for the evaluation of Cauchy principal value integrals of certain analytic functions. Integration over a general arc in the complex plane is considered. Special treatment is given to integrals over the interval (-1, 1). It is shown that the quadrature error is of order 0(e~ ), where N is the number of nodes used, and w...

Abstract One of the attractive solutions to information loss problem is that event horizon does not appear in process gravitational collapse and subsequent evaporation once spacetime singularity regularized by some mechanism, as pointed out Hayward Frolov. In this paper, we examine whether Hayward-Frolov scenario holds for a charged black hole. The modeled with Vaidya two kinds regularization c...

In this paper, aiming at solving the bidiagonal SVD problem, a classical divide-andconquer (DC) algorithm is modified, which needs to compute the SVD of broken arrow matrices by solving secular equations. The main cost of DC lies in the updating of singular vectors, which involves two matrix-matrix multiplications. We find that the singular vector matrices of a broken arrow matrix are Cauchy-li...