Related papers: Potential theory and a characterization of polynom…
We survey over some recent applications of motivic homotopy theory in the definition and the study of $p$-adic cohomology theories. In particular, we revisit the proof of the $p$-adic weight-monodromy conjecture for smooth projective…
There are important problems in physics related to the concept of probability. One of these problems is related to negative probabilities used in physics from 1930s. In spite of many demonstrations of usefulness of negative probabilities,…
We derive a general large deviation principle for a canonical sequence of probability measures, having its origins in random matrix theory, on unbounded sets $K$ of ${\bf C}$ with weakly admissible external fields $Q$ and very general…
In this paper we give a factorization theorem for the ring of exponential polynomials in many variables over an algebraically closed field of characteristic 0 with an exponentiation. This is a generalization of the factorization theorem due…
Floquet theory is a powerful tool in the analysis of many physical phenomena, and extended to spatial coordinates provides the basis for Bloch's theorem. However, in its original formulation it is limited to linear systems with periodic…
We provide a characterization of the set of real-valued functions that can be the value function of some polynomial game. Specifically, we prove that a function $u : \dR \to \dR$ is the value function of some polynomial game if and only if…
In this paper, a randomized algorithm for deciding the irreducibility of an irreducible polynomial and factoring a reducible polynomial over the field of rational numbers is presented. The main idea underlying the algorithm is based on…
Weighted cone-volume functionals are introduced for the convex polytopes in $\mathbb{R}^n$. For these functionals, geometric inequalities are proved and the equality conditions are characterized. A variety of corollaries are derived,…
In the current debate referring to the construction of a tenable background independent theory of Quantum Gravity we introduce the notion of topos-theoretic relativization of physical representability and demonstrate its relevance…
It is shown that a wide range of probabilities and limiting probabilities in finite classical groups have integral coefficients when expanded as a power series in 1/q. Moreover it is proved that the coefficients of the limiting…
We focus on rational solutions or nearly-feasible rational solutions that serve as certificates of feasibility for polynomial optimization problems. We show that, under some separability conditions, certain cubic polynomially constrained…
This paper extends earlier work on the distribution in the complex plane of the roots of random polynomials. In this paper, the random polynomials are generalized to random finite sums of given "basis" functions. The basis functions are…
We study the pullback of the apolarity invariant of complex polynomials in one variable under a polynomial map on the complex plane. As a consequence, we obtain variations of the classical results of Grace and Walsh in which the unit disk,…
We introduce a novel resource analysis for typed term rewrite systems based on a potential-based type system. This type system gives rise to polynomial bounds on the innermost runtime complexity. We relate the thus obtained amortised…
We study the relation between weighted pluripotential on a compact set E in C^N and the pluripotential theory of an associated circed set Z in C^(N+1)
A classical inequality, which is known for families of monotone functions, is generalized to a larger class of families of measurable functions. Moreover we characterize all the families of functions for which the equality holds. We apply…
We present a method to compute high-order derivatives of the total energy which can be used in the framework of density functional theory. We provide a proof of the $2n+1$ theorem for a general class of energy functionals in which the…
The concept of polynomials in the sense of algebraic analysis, for a single right invertible linear operator, was introduced and studied originally by D. Przeworska-Rolewicz \cite{DPR}. One of the elegant results corresponding with that…
In this paper we give an alternative exposition of a recent paper regarding the classification of growth rates of real functions. We take a different point of view, focussing on understanding possible growth rates between polynomial and…
We first prove some weighted inequalities for compositions of functions on time scales which are in turn applied to establish some new dynamic Opial-type inequalities in several variables. Some generalizations and applications to partial…