We present a simple approach to study the one–dimensional pressureless Euler system via adhesion dynamics in the Wasserstein space P 2 (R) of probability measures with finite quadratic moments. Starting from a discrete system of a finite number of " sticky " particles, we obtain new explicit estimates of the solution in terms of the initial mass and momentum and we are able to construct an evol...

This paper investigates the absolute exponential stability of a general class of delayed neural networks, which require the activation functions to be partially Lipschitz continuous and monotone nondecreasing only, but not necessarily differentiable or bounded. Three new sufficient conditions are derived to ascertain whether or not the equilibrium points of the delayed neural networks with addi...

This paper introduces two concepts of exceptional families for a class of nonlinear projection equations which provide a uniied formulation of nite-dimensional variational inequalities and complementarity problems. Based on these concepts, two alternative theorems are established for this class of nonlinear projection equations. We utilize one of the alternative theorems to establish several ne...

We give a precise description of spectral types the Mosaic Maryland model with any irrational frequency, which provides quasi-periodic unbounded non-monotone potential has arithmetic phase transition.

In this paper, the existence and uniqueness of the equilibrium point and its global asymptotic stability are discussed for a general class of recurrent neural networks with time-varying delays and Lipschitz continuous activation functions. The neural network model considered includes the delayed Hopfield neural networks, bidirectional associative memory networks, and delayed cellular neural net...

We identify best monotone degree bounds for the chromatic number and independence number of a graph. These bounds are best in the same sense as Chvátal’s hamiltonian degree condition. 1 Terminology and Notation We consider only undirected graphs without loops or multiple edges. Our terminology and notation will be standard except as indicated, and a good reference for any undefined terms is [14...

Where N is a nite set of the cardinality n and P the family of all its subsets, we study real functions on P having nonnegative diierences of orders n?2, n?1 and n. Nonnegative diierences of zeroth order, rst order, and second order may be interpreted as nonnegativity, nonincreasingness and convexity, respectively. If all diierences up to order n of a function are nonnegative, the set function ...

For any integer s ≥ 0, we derive a combinatorial interpretation for the family of sequences generated by the recursion (parameterized by s) hs(n) = hs(n − s − hs(n − 1)) + hs(n − 2− s − hs(n − 3)), n > s + 3, with the initial conditions hs(1) = hs(2) = · · · = hs(s+2) = 1 and hs(s+3) = 2. We show how these sequences count the number of leaves of a certain infinite tree structure. Using this int...

Given a finite set E of r andom variables, the entropy function h on E is a mapp ing f rom the set of all subsets of E into the set of all nonnegative real number s such that for each A C_ E h(A) is the entropy of A. T h e present paper points out that the entropy function h is a fi-function, i.e., a monotone nondecreasing and submodular function with h (~) = 0 and that the pair (E, h) is a pol...

We present a simple approach to study the one–dimensional pressureless Euler system via adhesion dynamics in the Wasserstein space P2(R) of probability measures with finite quadratic moments. Starting from a discrete system of a finite number of “sticky” particles, we obtain new explicit estimates of the solution in terms of the initial mass and momentum and we are able to construct an evolutio...