We discuss direct and inverse spectral theory for the isospectral problem of the dispersionless Camassa–Holm equation, where the weight is allowed to be a finite signed measure. In particular, we prove that this weight is uniquely determined by the spectral data and solve the inverse spectral problem for the class of measures which are sign definite. The results are applied to deduce several fa...

Categories of partial functions have become increasingly important principally because of their applications in theoretical computer science. In this note we prove that the category of partial bijections between sets as an inverse-Baer*-category with closed projections and in which the idempotent split is an exact category. Finally the Noether isomorphism theorems are given for this exact categ...

a module $m$ is called $emph{h}$-cofinitely supplemented if for every cofinite submodule $e$ (i.e. $m/e$ is finitely generated) of $m$ there exists a direct summand $d$ of $m$ such that $m = e + x$ holds if and only if $m = d + x$, for every submodule $x$ of $m$. in this paper we study factors, direct summands and direct sums of $emph{h}$-cofinitely supplemented modules. let $m$ be an $emph{h}$...

In order to alleviate the problem of local convergence of the usual EM algorithm, a split-and-merge operation is introduced into the EM algorithm for Gaussian mixtures. The split-and-merge equations are 7rst presented theoretically. These equations show that the merge operation is a well-posed problem, whereas the split operation is an ill-posed problem because it is the inverse procedure of th...

In this work we present and analyze a Kaczmarz version of the iterative regularization scheme REGINN-Landweber for nonlinear ill-posed problems in Banach spaces [Jin, Inverse Problems 28(2012), 065002]. Kaczmarz methods are designed for problems which split into smaller subproblems which are then processed cyclically during each iteration step. Under standard assumptions on the Banach space and...

1 As the clock and logic speeds increase, the energy requirements of CMOS circuits are rapidly becoming a major concern in the design of personal information systems and large computers. Earlier, we presented a new form of CMOS Charge Recovery Logic (CRL), with a power dissipation that falls with the square of the operating frequency, as opposed to the linear drop of conventional CMOS circuits ...

In this paper we defined the concept of module amenability of Banach algebras and module connes amenability of module dual Banach algebras.Also we assert the concept of module Arens regularity that is different with [1] and investigate the relation between module amenability of Banach algebras and connes module amenability of module second dual Banach algebras.In the following we studythe...

We study the notions of nuclearity and exactness for module maps on C∗-algebras which are C∗-module over another C∗-algebra with compatible actions examine finite approximation properties such C∗-modules. prove versions results Kirchberg Choi–Effros. As a concrete example, we extend dimensional reduced von Neumann algebras countable discrete groups to these operator inverse semigroups structure...

The purpose of this paper is to prove the localization theorem for torus actions in equivariant intersection theory. Using the theorem we give another proof of the Bott residue formula for Chern numbers of bundles on smooth complete varieties. In addition, our techniques allow us to obtain residue formulas for bundles on a certain class of singular schemes which admit torus actions. This class ...