Related papers: On a convexity problem

We close a gap appearing at the same time in the author's thesis "Iterated rings of bounded elements and generalizations of Schm\"udgen's theorem" [1] and in the author's article "Iterated rings of bounded elements and generalizations of…

In this paper, we bring a complete solution to the Ovals problem, as formulated in [3] and [24].

This note is the follow up to a paper by M. Waldschmidt.

The convergence of the algorithm for solving convex feasibility problem is studied by the method of sequential averaged and relaxed projections. Some results of H. H. Bauschke and J. M. Borwein are generalized by introducing new methods.…

In these notes, uniform convergence on compacta is studied on the space of functions taking values in the set of finite Borel measures. Related limit theorems, including L\'evy's continuity theorem and functional limit theorems for…

We prove a number of conjectures [arXiv:2005.04066] recently stated by P. Barry, related to the paperfolding sequence and the Rueppel sequence.

We give a new characterization of pseudoconvex point, and of finite type point, using analytic discs.

We consider convex trace functions $\Phi_{p,q,s} = Trace[ (A^{q/2}B^p A^{q/2})^s]$ where $A$ and $B$ are positive $n\times n$ matrices and ask when these functions are convex or concave. We also consider operator convexity/concavity of…

We reply to the comment by Ying Zhang and S. Das Sarma on our PRL 94, 226405 (2005).

See http://www.math.msu.edu/~abbas or Wiley preprint server.

Generalizing work of Marin [12], we construct in a unified way all the "braids and ties'' algebras available in literature and new ones.

This article is concerned with the approximation of unbounded convex sets by polyhedra. While there is an abundance of literature investigating this task for compact sets, results on the unbounded case are scarce. We first point out the…

This text is a somewhat reformatted (e.g., some statements that were not as such in the original paper, are given the names "Corollary" or "Theorem.") translation of the old and practically inaccessible paper: P. Kuchment, On the question…

We address a deep study of the convexity notions that arise in the study of weak* lower semicontinuity of supremal functionals as well as those raised by the power-law approximation of such functionals. Our quest is motivated by the…

The following is a compilation of some techniques in Alexandrov's geometry which are directly connected to convexity.

These notes are connected to a "potpourri" topics class and deal with some basic issues involving norms and convexity.

This paper replies the comment by E. Kapuscik [Am. J. Phys. 77, 754 (2009)]

The purpose of this paper is to study the reflections of a convex body. In particular, we are interested in orthogonal reflections of its sections that can be extended to reflections of the whole body. For this reason, we need to study the…

We present a new, very short proof of a conjecture by I. Ra\c{s}a, which is an inequality involving basic Bernstein polynomials and convex functions. It was affirmed positively very recently by J. Mrowiec, T. Rajba and S. W\k{a}sowicz…

We present a review of recent work on the mathematical aspects of the BCS gap equation, covering our results of [arXiv:0801.4159] as well our recent joint work with Hamza and Solovej [arXiv:math-ph/0703086] and with Frank and Naboko…