A characterization of Riesz-dual sequences which are near-Markushevich bases

The concept of Riesz-duals of a frame is a recently introduced concept with broad implications to frame theory in general, as well as to the special cases of Gabor and wavelet analysis. In this paper, we introduce various alternative Riesz-duals, with a focus on what we call Riesz-duals of type I and II. Next, we provide some characterizations of Riesz-dual sequences in Banach spaces. A basic problem of interest in connection with the study of Riesz-duals in Banach spaces is that of characterizing those Riesz-duals which can essentially be regarded as M-basis. We give some conditions under which an Riesz-dual sequence to be an M-basis for [Formula: see text].

An inexact proximal decomposition method for variational inequalities with separable structure

This paper presents an inexact proximal method for solving monotone variational inequality problems with a given separable structure. The proposed algorithm is a natural extension of the Proximal Multiplier Algorithm with Proximal Distances (PMAPD) proposed by Sarmiento et al. [Optimization, 65(2), (2016), pp. 501-537], which unified the works of Chen and Teboulle (PCPM method) and Kyono and Fukushima (NPCPMM) developed for solving convex programs with a particular separable structure. The resulting method combines the recent proximal distances theory introduced by Auslender and Teboulle [SIAM J. Optim., 16 (2006), pp. 697-725] with a decomposition method given by Chen and Teboulle for convex problems and extends the results of the Entropic Proximal Decomposition Method proposed by Auslender and Teboulle, which used to Logarithmic Quadratic proximal distances. Under some mild assumptions on the problem we prove a global convergence of the primal-dual sequences produced by the algorithm.

Ideals of Numerical Semigroups and Error-Correcting Codes

Several results relating additive ideals of numerical semigroups and algebraic-geometrycodes are presented. In particular, we deal with the set of non-redundant parity-checks, the codelength, the generalized Hamming weights, and the isometry-dual sequences of algebraic-geometrycodes from the perspective of the related Weierstrass semigroups. These results are related tocryptographic problems such as the wire-tap channel, t-resilient functions, list-decoding, networkcoding, and ramp secret sharing schemes.

A Proof of Donsker’s Invariance Principle Based on Support Functions of Fuzzy Random Vectors

In this note — starting from d-dimensional (with d > 1) fuzzy vectors — we prove Donsker’s classical invariance principle. We consider a fuzzy random walk [Formula: see text], where [Formula: see text] is a sequence of mutually independent and identically distributed d-dimensional fuzzy random variables whose α-cuts are assumed to be compact and convex. Our reasoning and technique are based on the well known conjugacy correspondence between convex sets and support functions, which allows for the association of an appropriately normalized and interpolated time-continuous fuzzy random process with a real valued random process in the space of support functions. We show that each member of the associated family of dual sequences tends in distribution to a standard Brownian motion.