and Applied Analysis 3 for all x, y ∈ E. The least positive number K satisfying the above condition is called the normal constant of P . It is clear that K ≥ 1. Definition 2.1 see 9 . Let X be a nonempty set and E a real Banach space equipped with the partial ordering with respect to the cone P . Suppose that the mapping d : X × X → E satisfies the following conditions: 1 θ d x, y for all x, y ...

In this paper the notion of Rees short exact sequence for S-posets is introduced, and we investigate the conditions for which these sequences are left or right split. Unlike the case for S-acts, being right split does not imply left split. Furthermore, we present equivalent conditions of a right S-poset P for the functor Hom(P;-) to be exact.

In this work, a refinement of the Cauchy–Schwarz inequality in inner product space is proved. A more general Kato’s or so called mixed Schwarz established. Refinements some famous numerical radius inequalities are also pointed out. As shown these refinements generalize and refine recent old results obtained literature. Among others, it proved that if $$T\in \mathscr {B}\left( {H}\right) $$ , th...

This paper presents a new construction of matrices with no singular square submatrix. This construction allows designing erasure codes over finite fied with fast encoding and decoding algorithms. 1 Systematic MDS Erasure Codes It is well known that a [n, k, d]-error correcting code is Maximum Distance Separable (MDS) if and only if its k × n-generator matrix does not contain any singular k×k-sq...

We give elementary proofs of the theorems mentioned in the title. Our methods rely on a simple version of Ramsey theory and a martingale difference lemma. They also provide quantitative results: if a Banach space contains l only with a bad constant then every bounded sequence admits a subsequence which is “nearly” a weak Cauchy sequence.

The asymptotic behaviour of vacuum Bianchi models of class A near the initial singularity is studied, in an effort to confirm the standard picture arising from heuristic and numerical approaches by mathematical proofs. It is shown that for solutions of types other than VIII and IX the singularity is velocity dominated and that the Kretschmann scalar is unbounded there, except in the explicitly ...

In the framework of metric spaces, we introduce concept Geraghty-Ciric type contractions and show existence uniqueness fixed point such mappings. This result improves unifies those obtained by Geraghty (Proc. Amer. Math. Soc. 40, 604-608 (1973)) Ciric 45, 267-273, (1974)). Several technical lemmas are employed to ensure that a Picard sequence is Cauchy sequence. addition, two illustrative examp...

Abstract The orbit space for a scalar field in complex square matrix representation obtains Minkowski structure from the Cauchy–Schwarz inequality. It can be used to find vacuum stability conditions and minima of potential. method is suitable fields such as bidoublet, an SU (2) triplet or (3) octet. We use formalism left-right symmetric potential bidoublet left right Higgs doublets.

The Cauchy problem for 1-dimensional nonlinear sto-chastic partial diierential equations is studied. The uniqueness and existence of solutions in H 2 p (T)-space are proved. 1. Introduction The aim of this paper is to prove the unique solvability of the following one-dimensional nonlinear stochastic partial diierential equa-tions(SPDEs): du = a(t; x; u)u 00 + f(t; x)] dt + k (t)u 0 + g k (t; x)...