In this paper, we study some basic properties of bicomplex numbers. We introduce two different types partial order relations on numbers, discuss valued metric spaces with respect to orders, and compare them. also define a hyperbolic space, the density natural statistical convergence, Cauchy property sequence numbers investigate in space prove that is complete if only complex are complete.

We consider the Cauchy problem periodic in the spatial variable for the usual cubic nonlinear Schrödinger equation and construct an infinite sequence of invariant measures associated with higher conservation laws for dynamical systems generated by this problem on appropriate phase spaces. In addition, we obtain sufficient conditions for the boundedness of the measures constructed. 2000 Mathemat...

In this work type II Hermite-Padé approximants for a vector of Cauchy transforms of smooth Jacobi-type densities are considered. It is assumed that densities are supported on mutually disjoint intervals (an Angelesco system with complex weights). The formulae of strong asymptotics are derived for any ray sequence of multi-indices.

This paper deals with functional equations in the form of $$f(x) + g(y) = h(x,y)$$ where h is given and f g are unknown. We will show that if a Borel measurable function associated characterizations uniform or Cauchy distributions, then there no solutions equation. Our proof uses characterization Dirac measure it also applicable to arctan

‎we study dual integral equations which appear in formulation of the‎ ‎potential distribution of an electrified plate with mixed boundary‎ ‎conditions‎. ‎these equations will be converted to a system of‎ ‎singular integral equations with cauchy type kernels‎. ‎using‎ ‎chebyshev polynomials‎, ‎we propose a method to approximate the‎ ‎solution of cauchy type singular integral equation which will ...

This paper addresses some results about mild solution to time-fractional Navier–Stokes equations with bounded delay existed in the convective term and external force. Based on Schauder’s fixed point theorem, we establish sufficient conditions for existence uniqueness of global Banach spaces. Moreover, polynomial decay estimate is given. Furthermore, approximate controllability obtained by const...

Microlocal defect measures for Cauchy data of Dirichlet, resp. Neumann, eigenfunctions an ellipse $E$ are determined. We prove that, any invariant curve the billiard map on boundary phase space $B^\* E$ ellipse, there exists a sequence whose concentrates curve. use this result to give new proof that ellipses infinitesimally spectrally rigid among $C^\\infty$ domains with symmetries ellipse.

Two quadrature rules for the approximate evaluation of Cauchy principal value integrals, with nodes at the zeros of appropriate orthogonal polynomials, are discussed. An expression for the truncation error, in terms of higher order derivatives, is given for each rule. In addition, two theorems, containing sufficient conditions for the convergence of the sequence of quadrature rules to the integ...

where m is the normalized Lebesgue measure on T. By the Fatou Theorem, Kf can also be defined on T by its non-tangential boundary values. After such an extension one can view the Cauchy integral as a “transform”, i.e., an operator in L(m) which sends f into the boundary values of Kf . It is well known, and not difficult to see, that the Cauchy transform is unbounded for p = 1 or p = ∞. However,...

Let (x n) be a bounded sequence in a Banach space X. Rosenthal's l 1-theorem states that there is essentially only one exceptional situation where it is not possible to extract a subsequence which is a weak Cauchy sequence: This happpens if (x n) is the sequence of unit vectors in l 1. The aim of these lectures is twofold: On the one hand results from the last few years centering around this th...