A finite metric tree is a finite connected graph that has no cycles, endowed with an edge weighted path metric. Finite metric trees are known to have strict 1-negative type. In this paper we introduce a new family of inequalities (1) that encode the best possible quantification of the strictness of the non trivial 1-negative type inequalities for finite metric trees. These inequalities are suff...

in this paper, two pairs of new inequalities are given, which decompose two hilbert-type inequalities.

In the quadratic traveling salesman problem a cost is associated with any three nodes traversed in succession. This structure arises, e. g., if the succession of two edges represents energetic conformations, a change of direction or a possible change of transportation means. In the symmetric case, costs do not depend on the direction of traversal. We study the polyhedral structure of a lineariz...

Let G1 be the acyclic tournament with the topological sort 0 < 1 < 2 < · · · < n < n + 1 defined on node set N ∪ {0, n + 1}, where N = {1, 2, . . . , n}. For integer k ≥ 2, let Gk be the graph obtained by taking k copies of every arc in G1 and colouring every copy with one of k different colours. A k-colour partition of N is a set of k paths from 0 to n + 1 such that all arcs of each path have ...

This paper is concerned with sample path properties of anisotropic Gaussian random fields. We establish Fernique-type inequalities and utilize them to study the global and local moduli of continuity for anisotropic Gaussian random fields. Applications to fractional Brownian sheets and to the solutions of stochastic partial differential equations are investigated.

In this paper, we study some functional inequalities (such as Poincaré inequality, logarithmic Sobolev inequality, generalized Cheeger isoperimetric inequality, transportation-information inequality and transportation-entropy inequality) for reversible nearest-neighbor Markov processes on connected finite graphs by means of (random) path method. We provide estimates of the involved constants.

Moreau-Yosida based approximation techniques for optimal control of variational inequalities are investigated. Properties of the path generated by solutions to the regularized equations are analyzed. Combined with a semi-smooth Newton method for the regularized problems these lead to an efficient numerical technique.

We study a generalization of the classical Marcinkiewicz-Zygmund inequalities. We relate this problem to the sampling sequences in the Paley-Wiener space and by using this analogy we give sharp necessary and sufficient computable conditions for a family of points to satisfy the Marcinkiewicz-Zygmund inequalities.

Using isoperimetry and symmetrization we provide a unified framework to study the classical and logarithmic Sobolev inequalities. In particular, we obtain new Gaussian symmetrization inequalities and connect them with logarithmic Sobolev inequalities. Our methods are very general and can be easily adapted to more general contexts.

We consider the reduction of problems on general noncommutative Lp-spaces to the corresponding ones on those associated with finite von Neumann algebras. The main tool is an unpublished result of the first-named author which approximates any noncommutative Lpspace by tracial ones. We show that under some natural conditions a map between two von Neumann algebras extends to their crossed products...