Related papers: On a convexity problem

The term "tropical convexity" was coined by Develin and Sturmfels who published a landmark paper with that title in 2004. However, the topic has much older roots and is deeply connected to linear and combinatorial optimization and other…

Corrigendum : An inverse problem in corrosion detection:stability estimates, J. Inv. Ill-posed Problems 12 (4) (2004), 349-367.

Methods for measuring convexity defects of compacts in R^n abound. However, none of the those measures seems to take into account continuity. Continuity in convexity measure is essential for optimization, stability analysis, global…

Rely to the comment by Doering et al. in Phys. Rev. Lett. 123, 259401 (2019)

This is a summary of the proof of BAB conjecture. All material are taken from the two BAB paper in the reference. The aim of this summary is to help reader to understand the more technical side of the proof of BAB.

In this paper we describe some recent works on quantitative unique continuation for elliptic, parabolic and dispersive equations. The elliptic results are joint work with J.Bourgain, while the remainder of the works discussed are joint…

This is an overview of merging the techniques of Riesz space theory and convex geometry.

In the paper based on the question of Zhang and L\"{u}[15], we present one theorem which will improve and extend the results of Banerjee-Majumder [2] and a recent result of Li-Huang [9].

A problem from Democritus is used to illustrate the building, and use, of infinitesimal covectors from its regularized, finite, counterpart.

This is the reply to a Comment by Alava and Zapperi (cond-mat/0401568) on Schmittbuhl, Hansen and Batrouni, PRL, 90, 045505 (2003).

We relate the graph isomorphism problem to the solvability of certain systems of linear equations with nonnegative variables. This version replaces the two previous versions of this paper.

We define new natural variants of the notions of weighted covering and separation numbers and discuss them in detail. We prove a strong duality relation between weighted covering and separation numbers and prove a few relations between the…

The invariant subspace problem is solved correcting my earlier attempts [6]-[12].

This is a comment on "Universal Fluctuations in Correlated Systems", by Bramwell et al, Phys. Rev. Lett., 84, 3744 (2000.

The purpose of this note is to highlight and address inaccuracies in the convergence guarantees of SCvx, a nonconvex trajectory optimization algorithm proposed by Mao et al. (arXiv:1804.06539), and make connections to relevant prior work.…

We comment on the latest paper [K.-H. Ding, Z.-G. Zhu, and J. Berakdar, J. Phys.: Condens. Matter 24, 266003 (2012)].

Recently, W. M. Schmidt and L. Summerer developed a new theory called Parametric Geometry of Numbers which approximates the behaviour of the successive minima of a family of convex bodies in $\mathbb{R}^{n}$ related to the problem of…

In the first part of this investigation, [Ha], we generalized a weighted distance function of [Li] and found necessary and sufficient conditions for it being a metric. In this paper some properties of this so-called M-relative metric are…

In this paper, we give two new generalizations of Clarkson-McCarthy with several operators, which depends on the unitary orbit technique developed by Bourin, Hadamard Three-lines Theorem and the duality argument developed by Ball, Carlen…

This is a write up on some sections of convex geometry, functional analysis, optimization, and nonstandard models that attract the author.