Based on work related to the R-matrix theory, we first abstract Lax pairs proposed by Blaszak and Sergyeyev into a unified form. Then, generalized zero-curvature equation expressed Poisson bracket is exhibited. As an application of this (2+1)-dimensional integrable system obtained, from which resulting Davey–Stewartson (DS) Pavlov (gPe) are further obtained. Via use nonisospectral zero-curvatur...

The purpose of this paper is to introduce and study a new class operators that we call pseudogeneralized invertible operators. This includes both the generalized Drazin Some results connected with ascent essential are also obtained for class. relationship between pseudo-generalized operators, semi-Fredholm explored.

We show that if T is an isometry (as metric spaces) between the invertible groups of unital Banach algebras, then T is extended to a surjective real-linear isometry up to translation between the two Banach algebras. Furthermore if the underling algebras are closed unital standard operator algebras, (T (eA)) −1 T is extended to a surjective real algebra isomorphism; if T is a surjective isometry...

Given two two-dimensional conformal field theories, a domain wall – or defect line – between them is called invertible if there is another defect with which it fuses to the identity defect. A defect is called topological if it is transparent to the stress tensor. A conformal isomorphism between the two CFTs is a linear isomorphism between their state spaces which preserves the stress tensor and...

Generalized frames are an extension of frames in Hilbert  spaces and  Hilbert $C^*$-modules. In this paper, the concept ''Similar" for modular $g$-frames is introduced and all of operator duals (ordinary duals) of similar $g$-frames with respect to each other are characterized. Also, an operator dual of a given $g$-frame is studied where $g$-frame is constructed by a primary $g$-frame and an or...

Let M(R) denote the measure algebra on the additive group of the reals. R. G. Douglas recently pointed out to us the importance of the following question in the study of Wiener-Hopf integral equations: if fxÇ:M(R) is invertible, then under what conditions does jit = exp(j>) for some vGM(R)? The relevance of the above question in integral equations stems from the fact that if JJLÇÏM(R) is invert...

Sliding-window aggregation is a widely-used approach for extracting insights from the most recent portion of a data stream. Most aggregation operations of interest can be cast as binary operators that are associative, but not necessarily commutative nor invertible. However, non-invertible operators are nontrivial to support efficiently. The best existing algorithms for this setting require Oplo...

The invertible, compact and Fredholm multiplication operators on generalized Lorentz-Zygmund (GLZ) spaces Lp,q;α, 1 < p ≤ ∞, 1 ≤ q ≤ ∞, α in the Euclidean space R, are characterized in this paper.

The Drazin inverse has important applications in matrix theory and fields such as statistics, probability, linear systems theory, differential and difference equations, Markov chains, and control theory ([1, 2, 11]). In [9], Koliha extended the Drazin invertibility in the setting of Banach algebras with applications to bounded linear operators on a Banach space. In this paper, Koliha was able t...

‎The present paper is devoted to the existence and uniqueness result of the fractional evolution equation $D^{q}_c u(t)=g(t,u(t))=Au(t)+f(t)$‎ ‎for the real $qin (0,1)$ with the initial value $u(0)=u_{0}intilde{R}$‎, ‎where $tilde{R}$ is the set of all generalized real numbers and $A$ is an operator defined from $mathcal G$ into itself‎. Here the Caputo fractional derivative $D^{q}_c$ is used i...