We describe our present understanding of the relations between the behaviour of asymptotically flat Cauchy data for Einstein’s vacuum field equations near space-like infinity and the asymptotic behaviour of their evolution in time at null infinity.

The problem of self-gravitating, isolated systems is undoubtedly an important and intriguing area of research in General Relativity. However, due to the involved nature of Einstein's equations physicists found themselves unable to fully explore such systems. From Einstein's theory we know that besides the electromagnetic spectrum , objects like quasars, active galactic nuclei, pulsars and black...

We study the stability in the Cauchy Problem for the Helmholtz equation in dependence of the wave number k. For simple geometries, we show analytically that this problem is getting more stable with increasing k. In more detail, there is a subspace of the data space on which the Cauchy Problem is well posed, and this subspace grows with larger k. We call this a subspace of stability. For more ge...

It is well-known that on quasi-pseudometric space $(X,q)$, every $q^s$-Cauchy sequence left (or right) $K$-Cauchy but the converse does not hold in general. In this article, we study a class of maps preserve (right) sequences call sequentially-regular maps. Moreover, characterize totally bounded sets terms and right uniformly locally semi-Lipschitz

In this paper, the Schwarz boundary value problem (BVP) for the inhomogeneous Cauchy-Riemann equation in a triangle is investigated explicitly. Firstly, by the technique of parquetingreflection and the Cauchy-Pompeiu representation formula a modified Cauchy-Schwarz representation formula is obtained. Then, the solution of the Schwarz BVP is explicitly solved. In particular, the boundary behavio...

The symmetric shape of some inequalities between two sequences real numbers generates the same in operator theory. In this paper, we study a new refinement Cauchy–Bunyakovsky–Schwarz inequality for Euclidean spaces and several bounded linear operators on Hilbert space, where mention Bohr’s Bergström’s operators. We present an type operators, by technique monotony sequence. also prove Aczél spac...