Let E be a B-complete (B -complete) locally convex algebra and $ the topological direct sum of countably many copies of the scalar field with a jointly continuous algebra multiplication. It has been shown that E is also B-complete (B -complete) for componentwise multiplication on E . B-and Br-completeness of E , the unitization of E, and also of E x for other multiplications on E ...

In this paper, we present explicit expressions for the mixed and componentwise condition numbers of truncated total least squares (TTLS) solution A x ? b under genericity condition, where is a m × n real data matrix m-vector. Moreover, reveal that normwise, componentwise, TTLS problem can recover previous corresponding counterparts (TLS) when level n. When structured matrix, perturbations TLS (...

We investigate the structure of nodal solutions for coupled nonlinear Schrödinger equations in repulsive coupling regime. Among other results, following system N equations, we prove existence infinitely many which share same componentwise-prescribed numbers (0.1) { ? ? u j + ? = ? 3 ? i ? ? 2 ? , ? H 0 r 1 ( ) … where is a radial domain R n and bounded interval > < . More precisely, let p be pr...

Classical techniques for analysing multivariate extremes can often be framed in terms of the point process representation of de Haan (1985). Amongst other things, this representation provides a characterisation of the limiting distribution of the normalised componentwise maxima of independent and identically distributed unit Fréchet variables, i.e. the class of multivariate extreme value distri...

In the equivalent transformation (ET) computation model, a program is a set of procedural rewriting rules for answer-preserving transformation of problems with respect to given background knowledge. In this paper, we discuss an approach to program construction by creating and accumulating individually correct and efficient program components one by one, referred to as componentwise program cons...

let a be a banach algebra and e be a banach a-bimodule then s = a  e, the l1-direct sum of a and e becomes a module extension banach algebra when equipped with the algebras product (a; x):(a′; x′) = (aa′; a:x′ + x:a′). in this paper, we investigate △-amenability for these banach algebras and we show that for discrete inverse semigroup s with the set of idempotents es, the module extension bana...

let $r$ be a commutative ring with identity and $m$ be a finitely generated unital $r$-module. in this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. moreover, we investigate some conditions which imply that the module $m$ is the direct sum of some cyclic modules and free modules. then some properties of fitting ideals of...

1. Let G be an algebraic linear group over a field F. If G acts by linear automorphisms on some vector space M over F we say that M is a rational G-module if it is the sum of finite-dimensional G-stable subspaces V such that the representation of G on each F is a rational representation of G. The rational G-module M is said to be rationally injective if, whenever U is a rational G-module and 0 ...

This paper discusses the task of learning a classifier from observed data containing missing values amongst the inputs which are missing completely at random. A non-parametric perspective is adopted by defining a modified risk taking into account the uncertainty of the predicted outputs when missing values are involved. It is shown that this approach generalizes the approach of mean imputation ...