Related papers: Multivariate Gauss-Lucas Theorems

In this note we prove a more general (and topological) version of Gr\"unbaum's conjecture about affine invariant points. As an application of our result we show that, if we consider the action of the group of similarities, Gr\"unbaum's…

We prove a new sum uncertainty relation in quantum theory which states that the uncertainty in the sum of two or more observables is always less than or equal to the sum of the uncertainties in corresponding observables. This shows that the…

Galois theory is developed using elementary polynomial and group algebra. The method follows closely the original prescription of Galois, and has the benefit of making the theory accessible to a wide audience. The theory is illustrated by a…

In this paper we develop tools for studying limit theorems by means of convexity. We establish bounds for the discrepancy in total variation between probability measures $\mu$ and $\nu$ such that $\nu$ is log-concave with respect to $\mu$.…

We prove a version of the Bernstein-Walsh theorem on uniform polynomial approximation of holomorphic functions on compact sets in several complex variables. Here we consider subclasses of the full polynomial space associated to a convex…

A rigorous connection between large deviations theory and Gamma-convergence is established. Applications include representations formulas for rate functions, a contraction principle for measurable maps, a large deviations principle for…

A combinatorial proof of the unimodality of the generalized q-Gaussian coefficients based on the explicit formula for Kostka-Foulkes polynomials is given.

In this paper, authors study the convexity and concavity properties of real-valued function with respect to the classical means, and prove a conjecture posed by Bruce Ebanks in \cite{e}.

Using the recently proposed covariant framework of general relativistic stochastic mechanics and stochastic thermodynamics, we proved the detailed and integral fluctuation theorems in curved spacetime. The time-reversal transformation is…

We consider the problem of predicting the covariance of a zero mean Gaussian vector, based on another feature vector. We describe a covariance predictor that has the form of a generalized linear model, i.e., an affine function of the…

We provide yet another proof of the classical Lagrange-Good multivariable inversion formula using techniques of quantum field theory.

The object of this paper is to generalize a theorem on the binomial coefficient [4] to the case in an arithmetic progression. We will also give a slightly stronger result than Langevin's [2].

The assumptions needed to prove Cox's Theorem are discussed and examined. Various sets of assumptions under which a Cox-style theorem can be proved are provided, although all are rather strong and, arguably, not natural.

This paper revisits the well-studied fixed point problem from a unified viewpoint of mathematical modeling and canonical duality theory, i.e. the original problem is first reformulated as a nonconvex optimization problem, its well-posedness…

The purpose of this paper is to generalize the classical Mazur's lemma from the classical convex analysis to the framework of locally $L^0$-convex modules. In this version an extra condition of countable concatenation is included. We…

We prove invariance theorems for general inequalities of different metrics and apply them to limit relations between the sharp constants in the multivariate Markov-Bernstein-Nikolskii type inequalities with the polyharmonic operator for…

In this paper we study the genralized q-Euler numbers and polynomials. From our results, we derive some interesting congruences related tothe generalized q-Euler numbers.

We give a combinatorial upper bound for the gonality of a curve that is defined by a bivariate Laurent polynomial with given Newton polygon. We conjecture that this bound is generically attained, and provide proofs in a considerable number…

The purpose of this article is to formulate a number of probabilistic hidden-variable theorems, to provide proofs in some cases, and counterexamples to some conjectured relationships. The first theorem is the fundamental one. It asserts the…

The Gauss--Lucas and B\^{o}cher--Grace--Marden theorems are classical results in the geometry of polynomials. Proofs of the these results are available in the literature, but the approaches are seemingly different. In this work, we show…