Related papers: On Schurs exponent conjecture and its relation to …
Nonuniform ellipticity is a classical topic in the theory of partial differential equations. While several results in regularity theory have been adding up over decades, many basic issues, as for instance the validity of Schauder theory and…
Information-theoretic arguments are used to obtain a link between the accurate linearity of Schrodinger's equation and Lorentz invariance: A possible violation of the latter at short distances would imply the appearance of nonlinear…
In this paper, we proved the normal scalar curvature conjecture and the Bottcher-Wenzel conjecture.
We study Noether's problem from the perspective of torsors under linear algebraic groups and descent.
We survey classical and recent results on exponents of Diophantine approximation. We give only a few proofs and highlight several open problems.
The paper is mostly a survey on recent results in Diophantine approximation, with emphasis on properties of exponents measuring various notions of Diophantine <approximation.
We obtain some inequalities which are stronger than the Schur majorization inequalities.
Dorpalen-Barry et al. proved Elser's conjecture about sign of Elser's number by interpreting them as certain sums of reduced Euler characteristics of an abstract simplicial complex known as $U$-nucleus complex. We prove a conjecture posed…
We introduce and discuss a variant of Schanuel conjecture in the framework of the Carlitz exponential function over Tate algebras and allied functions. Another purpose of the present paper is to widen the horizons of possible investigations…
In this note we will review the most important results and questions related to Chern conjecture and isoparametric hypersurfaces, as well as their interactions and applications to various aspects in mathematics.
The theory of Schur functors provides a powerful and elegant approach to the representation theory of GL_n - at least to the so-called polynomial representations - especially to questions about how the theory varies with n. We develop…
In this small note we ask several questions which are relevant to the construction of the self-consistent neutrino theory of light. The previous confusions in such attempts are explained in the more detailed publication.
We survey recent developments towards a proof of the Penrose conjecture and results on Penrose-type and other geometric inequalities for quasi-local masses in general relativity.
In this paper we are concerned with a long-standing conjecture of Huneke and Wiegand. We introduce a new class of ideals and prove thateach ideal from such class satisfies the conclusion of the conjecture in question. We also study the…
This paper is a preliminary expository paper that outlines the relationship between solutions to the Erd\H{o}s-Straus conjecture for a given prime $p$ and their corresponding Pythagorean triples. This paper also uses B\'{e}zout Coefficients…
In a recent work, Andrews gave analytic proofs of two conjectures concerning some variations of two combinatorial identities between partitions of a positive integer into odd parts and partitions into distinct parts discovered by Beck.…
In this paper we introduce the notion of $e$-computability as a method of finding the Waring rank of forms. We use this notion to find infinitely many new examples which satisfy Strassen's Conjecture.
We survey the proof of the Nash conjecture for surfaces and show how geometric and topological ideas developed in previous articles by the authors influenced it. Later we summarize the main ideas in the higher dimensional statement and…
Inspired by recent works on rings satisfying Auslander's conjecture, we study invariants, which we call Auslander bounds, and prove that they have strong relations to some homological conjectures.
We study the Rellich inequalities in the framework of equalities. We present equalities which imply the Rellich inequalities by dropping remainders. This provides a simple and direct understanding of the Rellich inequalities as well as the…