In general Banach space setting, we study the perturbed distance function d J S (·) determined by a closed subset S and a lower semicontinuous function J (·). In particular, we show that the Fréchet subdifferential and the proximal subdifferential of a perturbed distance function are representable by virtue of corresponding normal cones of S and subdifferentials of J (·).

Article history: Received 8 December 2011 Received in revised form 24 May 2012 Accepted 26 September 2012 Available online 6 October 2012

In this work we continue the nonsmooth analysis of absolutely symmetric functions of the singular values of a real rectangular matrix. Absolutely symmetric functions are invariant under permutations and sign changes of its arguments. We extend previous work on subgradients to analogous formulae for the proximal subdifferential and Clarke subdifferential when the function is either locally Lipsc...

The purpose of this paper is to introduce the concepts of semi*-connected spaces, semi*-compact spaces and semi*-Lindelof spaces. We investigate their basic properties. We also discuss their relationship with already existing concepts. Mathematics Subject Classification: 54D05, 54D30.

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Fault-tolerant quantum computation is a basic problem in quantum computation, and teleportation is one of the main techniques in this theory. Using teleportation on stabilizer codes, the most well-known quantum codes, Pauli gates and Clifford operators can be applied fault-tolerantly. Indeed, this technique can be generalized for an extended set of gates, the so called Ck hierarchy gates, intro...

This document proposes an algebra for XML Query. The algebra has been submitted to the W3C XML Query Working Group. A novel feature of the algebra is the use of regular-expression types, similar in power to DTDs or XML Schemas, and closely related to Hasoya and Pierce’s work on Xduce. The iteration construct is based on the notion of a monad, and involves novel typing rules not encountered else...

let $r$ be a ring and $m$ a right $r$-module with $s=end_r(m)$. a module $m$ is called semi-projective if for any epimorphism $f:mrightarrow n$, where $n$ is a submodule of $m$, and for any homomorphism $g: mrightarrow n$, there exists $h:mrightarrow m$ such that $fh=g$. in this paper, we study sgq-projective and$pi$-semi-projective modules as two generalizations of semi-projective modules. a m...

background: nematodes are among the most common and important parasites of man and animal. dna of a single worm can be used for several purposes, such as identification to the species, subspecies, strain and antihelmenthic resistance. dna extraction from a single small worm using traditional methods such as phenol extraction technique faces serious prob lems. methods: dna from 20 single haemonc...