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We study vectors chosen at random from a compact convex polytope in $\mathbb{R}^n$ given by a finite number of linear constraints. We determine which projections of these random vectors are asymptotically normal as $n\to\infty$. Marginal…

Compared with constraint satisfaction problems, counting problems have received less attention. In this paper, we survey research works on the problems of counting the number of solutions to constraints. The constraints may take various…

We present a class of inequality constraints on the set of distributions induced by local interventions on variables governed by a causal Bayesian network, in which some of the variables remain unmeasured. We derive bounds on causal effects…

In this paper we introduce a notion of Poincar\'e exponent for isometric representations of discrete groups on Hilbert spaces. Similarly as growth exponents control the geometry this exponent is shown to control the size of spectral gaps.…

This article describes the various experimental bounds on the variation of the fundamental constants of nature. After a discussion on the role of fundamental constants, of their definition and link with metrology, the various constraints on…

The minimal set of Shannon-type inequalities (referred to as elemental inequalities), plays a central role in determining whether a given inequality is Shannon-type. Often, there arises a situation where one needs to check whether a given…

We prove an optimal lower bound for the best constant in a class of weighted anisotropic Poincar\'e inequalities

We show how to use Lyapunov functions to obtain functional inequalities which are stronger than Poincar\'e inequality (for instance logarithmic Sobolev or $F$-Sobolev). The case of Poincar\'e and weak Poincar\'e inequalities was studied in…

In the setting of a metric space equipped with a doubling measure and supporting a Poincar\'e inequality, and based on results by Bj\"orn and Shanmugalingam (2007), we show that functions of bounded variation can be extended from any…

In the paper, we investigate Poincare type inequalities for the functions having zero mean value on the whole boundary of a Lipschitz domain or on a measurable part of the boundary. We derive exact and easily computable constants for some…

We show that fractional (p,p)-Poincar\'e inequalities and even fractional Sobolev-Poincar\'e inequalities hold for bounded John domains, and especially for bounded Lipschitz domains. We also prove sharp fractional (1,p)-Poincar\'e…

In this paper we will establish different weighted Poincar\'{e} inequalities with variable exponents on Carnot-Carath\'{e}odory spaces or Carnot groups. We will use different techniques to obtain these inequalities. For vector fields…

In this article, we study new methods for constructing uninorms on bounded lattices. First, we present new methods for constructing uninorms on bounded lattices under the additional constraints and prove that some of these constraints are…

We establish a family of parametric isoperimetric-type inequalities with multiple geometric quantities for closed convex curves. These inequalities hold under certain parameter conditions. We also prove the equality conditions. Some new…

In metric measure spaces, we study boundary traces of BV functions in domains equipped with a doubling measure and supporting a Poincar\'e inequality, but possibly having a very large and irregular boundary. We show that the trace exists in…

We discuss the constraints induced by the algebra of the Poincare' generators on non-relativistic effective field theories. In the first part we derive some relations among the matching coefficients of the HQET (and NRQCD), which have been…

Using a method of Korobenko, Maldonado and Rios we show a new characterization of doubling metric-measure spaces supporting Poincar\'e inequalities without assuming a priori that the measure is doubling.

In this paper, we consider a problem in calculus of variations motivated by a quantitative isoperimetric inequality in the plane. More precisely, the aim of this article is the computation of the minimum of the variational problem…

We prove a new vectorial functional inequality of Poincar\'{e}-Beckner type. The inequality may be interpreted as an entropy-entropy production one for a gradient flow in the metric space of Radon measures. The proof uses subtle analysis of…

We deal with nonlinear systems of parabolic type satisfying component-wise structural conditions. The nonlinear terms are Carath\'eodory maps having controlled growth with respect to the solution and the gradient and the data are in…