相关论文: Some Questions around The Hilbert 16th Problem

In this paper we consider the remaining cases of Hebey-Vaugon conjecture.

After discussing two senses in which the notion of undecidability is used, we present a survey of undecidable decision problems arising in various branches of mathematics.

We study Hilbert's epsilon calculus and Hilbert's partial epsilon calculus in toposes.

In this paper, by using the theory of elliptic curves, we discuss several Diophantine equations related with the so-called figurate primes. Meanwhile, we raise several conjectures related with figurate primes and Hilbert's 8th problem,…

Beyond normal surfaces there are several open questions concerning 2- dimensional spaces. We present some results and conjectures along this line.

We provide a brief topical outline of the persisting problem of the hyperon polarization and consider some future experimental prospects. The predictions which deserve experimental verification are proposed.

New cases of the multiplicity conjecture are considered.

We present a reduction of the Hilbert-Smith conjecture in the case of the finite dimensional orbit space to some algebraic topology problems.

This survey article on Hilbert's first and second problems is adapted from a one-hour colloquium lecture given at the University of Auckland in May, 2000, just three months before the 100th anniversary of Hilbert's lecture. It includes an…

We study the analogue of the infinitesimal 16th Hilbert problem in dimension zero. Lower and upper bounds for the number of the zeros of the corresponding Abelian integrals (which are algebraic functions) are found. We study the relation…

We discuss some aspects of the theory of subelliptic estimates.

We consider the two weight problem for the Hilbert transform, namely the question of finding real-variable characterization of those pair of weights for which the Hilbert transform acts boundedly on $ L ^2 $ of the weights. Such a…

In this article we give a survey on open problems and conjectures concerning L^2-invariants. We cover the whole portfolio and not only certain aspects as they are considered in the previous more specialized (and within their scope more…

In this small paper we bring together various open problems on geometric multidimensional continued fractions.

We attempt to survey recent results and open problems connected to Lieb-Thirring inequalities.

The aim of this work is to present the first problems that appear in the study of nilpotent Leibniz superalgebras. These superalgebras and so the problems, will be considered as a natural generalization of nilpotent Leibniz algebras and Lie…

These highly informal lecture notes aim at introducing and explaining several closely related problems on zeros of analytic functions defined by ordinary differential equations and systems of such equations. The main incentive for this…

I survey problems concerning Lindelof spaces which have partial set- theoretic solutions.

We present and discuss a number of known results and open problems abelian squares in words on small alphabets.

We collect a number of open questions concerning Diophantine equations, Diophantine Approximation and transcendental numbers. Revised version: corrected typos and added references.