Related papers: Correlation Inequality for Formal Series

In this paper, by using hardy inequality, we establish some new integral inequalities of Hardy-Hilbert type with general kernel. As applications, equivalent forms and some particular results are built; the corresponding to the double series…

We show the existence of formal equivalences between reversible and Hamiltonian vector fields. The main tool we employ is the normal form theory.

In the first part of the paper we prove a necessary and sufficient condition for the existence of the composition of formal power series in the case when the outer series is a series of one variable while the inner one is a series of…

Preliminary results from Nathanson [5] are used to prove the Muirhead and Rado inequalities.

We introduce two types of ordinal pattern dependence between time series. Positive (resp. negative) ordinal pattern dependence can be seen as a non-paramatric and in particular non-linear counterpart to positive (resp. negative)…

We prove that small deformations of canonical singularities are canonical.

Given two couplings between "primal" and "dual" sets, we prove a general implication that relates an inequality involving "primal" sets to a reverse inequality involving the "dual" sets.% More precisely, let be given two "primal" sets…

We derive symmetries and adjunction inequalities of the knot Floer homology groups which appear to be especially interesting for homologically essential knots. Furthermore, we obtain an adjunction inequality for cobordism maps in knot Floer…

We prove a Green--Tao theorem for multiplicative functions.

We show that it is possible to have arbitrarily long sequences of Alices and Bobs so every (Alice, Bob) pair violates a Bell inequality. We propose an experiment to observe this effect with two Alices and two Bobs.

We give a proof of the uniform convergence of Fourier series, using the methods of nonstandard analysis.

We prove two congruences for the coefficients of power series expansions in t of modular forms where t is a modular function. As a result, we settle two recent conjectures of Chan, Cooper and Sica. Additionally, we provide a table of…

We prove a recent conjecture on the duality relation for correlation functions of the Potts model for boundary spins of a planar lattice. Specifically, we deduce the explicit expression for the duality of the n-site correlation functions,…

Robin's Conjecture is strengthened, deformed, and proved. Nicolas conjecture follows.

We conjecture new uncertainty relations which restrict correlations between results of measurements performed by two separated parties on a shared quantum state. The first uncertainty relation bounds the sum of two mutual informations when…

We discuss a general method to prove quantitative improvements on correlation inequalities and apply it to arm estimates for Bernoulli bond percolation on the square lattice. Our first result is that the two-arm exponent is strictly larger…

We consider the isomorphism problem for formal matrix rings over a given ring. Principal factor matrices of such rings play an important role in this case. The work is supported by Russian Scientific Foundation, project 23-21-00375 (P.A.…

We prove some Hardy-type inequalities via an approach that involves constructing auxiliary sequences.

We provide the detailed proof of a strengthened version of the M. Artin Approximation Theorem.

We prove explicit doubling inequalities and obtain uniform upper bounds (under $(d-1)$-dimensional Hausdorff measure) of nodal sets of weak solutions for a family of linear elliptic equations with rapidly oscillating periodic coefficients.…