Related papers: On a convexity problem
In a previous paper the second author developed a new approach to the abelian p-adic Stark Conjecture at s=1 and stated some related conjectures. This paper develops and applies techniques using p-adic measures and continued fractions to…
We present a direct proof of the second conjecture made by M. Atiyah and P. Sutcliffe for the case of convex quadrilaterals. Unlike previous work on this conjecture, our proof does not require any computer aided computations. The new proof…
Ways to access transversity through asymmetry measurements are reviewed. The recent first extraction and possible near future extractions are discussed.
The article provides a counterexample to a conjecture by Blocki-Zwonek.
We hereby reply concisely and hopefully clearly to the ongoing claims of incorrectness made by Chen et al. about our work on two-dimensional flocks.
We introduce and study a new kind of congruent number problem on the right trapezoid.
In this note, we give a slight improvement of a result of A. K\"uronya and V. Lozovanu about higher syzygies on abelian surfaces.
We collect and present in a unified way several results in recent years about the elastic flow of curves and networks, trying to draw the state of the art of the subject. In particular, we give a complete proof of global existence and…
The aim of the present work is to show that the results obtained earlier on the approximation of distributions of sums of independent summands by infinitely divisible laws may be transferred to the estimation of the closeness of…
Covering numbers of convex bodies based on homothetical copies and related illumination numbers are well-known in combinatorial geometry and, for example, related to Hadwiger's famous covering problem. Similar numbers can be defined by…
New cases of the multiplicity conjecture are considered.
This update to my article on Congruent numbers, elliptic curves, and the passage from the local to the global, which appeared in Resonance, December 2009, pp. 1183--1205 (https://www.ias.ac.in/describe/article/reso/014/12/1183-1205) and was…
We prove bounds for the covering numbers of classes of convex functions and convex sets in Euclidean space. Previous results require the underlying convex functions or sets to be uniformly bounded. We relax this assumption and replace it…
In this survey article we give an overview of the developments on the congruence subgroup and the metaplectic problems after the work of Bass, Milnor and Serre.
A selection of basic results on Borel reducibility of ideals and equivalence relations, especially those with comparably short proofs. This is an unfinished text as yet. Some proofs have missing parts and loose ends. [email protected] and…
Reply to the Comment by S.V. Kravchenko, A.A. Shashkin, and V.T. Dolgopolov [cond-mat/0106056]
This is a reply to the recent comment from Ikeda, Berthier, and Sollich (arXiv:1602.04796) on "Constant stress and pressure rheology of colloidal suspensions", Phys. Rev. Lett. 115, 158301 (2015).
A conjecture regarding the structure of expander graphs is discussed.
Gives a short proof of Dehornoy's latest result. The same simple argument (and more) was discovered by Laver's student Larue.
We provide proof that the optimal value function of a convex parametrized optimization problem in Euclidean spaces is itself a convex function onto the extended real line.