Related papers: Moments from their very truncations
In recent years, the so-called polynomial moment problem, motivated by the classical Poincare center-focus problem, was thoroughly studied, and the answers to the main questions have been found. The study of a similar problem for rational…
In this paper we study the complexity of solving a problem when a solution of a similar instance is known. This problem is relevant whenever instances may change from time to time, and known solutions may not remain valid after the change.…
We consider various curious features of general relativity, and relativistic field theory, in two spacetime dimensions. In particular, we discuss: the vanishing of the Einstein tensor; the failure of an initial-value formulation for vacuum…
A boundary value problem on an unbounded domain, associated to difference equations with the Euclidean mean curvature operator is considered. The existence of solutions which are positive on the whole domain and decaying at infinity is…
For a 4th order 3-dimensional symmetric tensor with its some entries $1$ or $-1$, we show the analytic sufficient and necessary conditions of its positive definiteness. By applying these conclusions, several strict inequalities is bulit for…
In this paper we give solutions to Hamburger moment problems with missing entries. The problem of completing partial positive sequences is considered. The main result is a characterization of positive definite completable patterns, namely…
The topic of diversity is an interesting subject, both as a purely mathematical concept and also for its applications to important real-life situations. Unfortunately, although the meaning of diversity seems intuitively clear, no precise…
The concepts of symmetry and its breakdown are investigated in two different terms according to whether the resulting asymmetry is universal or only obtained for a special configuration: we shall illustrate this by considering in the first…
We obtain some rigidity results for overdetermined boundary value problems for singular solutions in bounded domains.
In this work, we investigate the existence of positive solutions for a multi-point boundary value problem for a second order delay differential equation. Under certain growth conditions on the nonlinearity, and by the mean of Leray-Schauder…
We submit the viewpoint that, perhaps, some of the controversies in gravitation occurred during this century are not due to insufficiencies of Einstein's field equations, but rather to insufficiencies in the mathematics used for their…
We summarize significant classical results on (in)determinacy of measures in terms of their finite positive integer order moments. Well-known is the role of the smallest eigenvalues of Hankel matrices, starting from Hamburger's results a…
In the literature two notions of the word problem for a variety occur. A variety has a decidable word problem if every finitely presented algebra in the variety has a decidable word problem. It has a uniformly decidable word problem if…
After a brief review of current scenarios for the resolution and/or avoidance of the Big Bang, an alternative hypothesis is put forward implying an infinite increase in complexity towards the initial singularity. This may result in an…
The possibility that spacetime is extended beyond the familiar 3+1-dimensions has intrigued physicists for a century. Indeed, the consequences of a dimensionally richer spacetime would be profound. Recently, new theories with higher…
Many widely different problems have a common mathematical structure wherein limited knowledge lead to ambiguity that can be captured conveniently using a concept of invisibility that requires the introduction of negative values for…
It is shown that Newton's inequalities and the related Maclaurin's inequalities provide several refinements of the fundamental Arithmetic mean - Geometric mean - Harmonic mean inequality in terms of the means and variance of positive real…
In a series of papers, a many-minds interpretation of quantum theory has been developed. The aim in these papers is to present an explicit mathematical formalism which constitutes a complete theory compatible with relativistic quantum field…
A brief overview of dimensional reductions for diffeomorphism invariant theories is given. The distinction between the physical idea of compactification and the mathematical problem of a consistent truncation is discussed, and the typical…
We study a truncated two-dimensional moment problem in terms of the Stieltjes transform. The set of the solutions is described by the Schur step-by-step algorithm, which is based on the continued fraction expansion of the solution. In…