The main goal of this paper is to introduce a new class in the category modules. It called quasi-invertibility monoform (briefly QI-monoform) This modules generalization Various properties and another characterization QI-monoform are investigated. So, we prove that an R-module M if only for each non-zero homomorphism f:M E(M), kernel not quasi-invertible submodule M. Moreover, cases under which...

The paper describes various approaches to the invertibility of Toeplitz plus Hankel operators in Hardy and lp-spaces, integral difference Wiener-Hopf generalized operators. Special attention is paid a newly developed method, which allows establish necessary, sufficient also necessary conditions invertibility, one-sided for wide classes derive efficient formulas corresponding inverses. work cont...

This article addresses the invertibility problem for switched nonlinear systems affine in controls. The problem is concerned with reconstructing the input and switching signal uniquely from given output and initial state. We extend the concept of switch-singular pairs, introduced recently, to nonlinear systems and develop a formula for checking if the given state and output form a switch-singul...

This paper presents a new wavelet family for lossless image compression by re-factoring the channel representation of the update-then-predict lifting wavelet, introduced by Claypoole, Davis, Sweldens and Baraniuk, into lifting steps. We name the new wavelet family as invertible update-then-predict integer lifting wavelets (IUPILWs for short). To build IUPILWs, we investigate some central issues...

We construct discrete analogs of multidimensional singular integral operators and study their invertibility. Moreover, we give a comparison between continual case. the theory periodic Riemann problem also, because it is needed for studying invertibility so-called paired equations. For more general case pseudo-differential operators, solvability equations in Sobolev–Slobodetskii spaces. Some res...