This paper presents a new result on absolute exponential stability (AEST) of a class of continuous-time recurrent neural networks with locally Lipschitz continuous and monotone nondecreasing activation functions. The additively diagonally stable connection weight matrices are proven to be able to guarantee AEST of the neural networks. The AEST result extends and improves the existing absolute s...

Let G be a connected graph. The eccentricity of a vertex v is defined as the distance in G between v and a vertex farthest from v. The nondecreasing sequence of the eccentricities of the vertices of G is the eccentric sequence of G. In this paper, we characterize eccentric sequences of maximal outerplanar graphs.

We consider the class of nonlinear optimal control problems with all data (differential equation, state and control constraints, cost) being polynomials. We provide a simple hierarchy of LMI-relaxations whose optimal values form a nondecreasing sequence of lower bounds on the optimal value. Preliminary results show that good approximations are obtained with few moments.

|T ] is a nondecreasing function of T , and show how it can be efficiently estimated by a simulation study that stratifies on T. Our results are applied to static and dynamic reliability systems, the pricing of derivatives related to basket default swaps, and to round robin tournaments.

Most notably we prove that for d = 1, 2 the classical Strichartz norm ‖ef‖ L 2+4/d s,x (R×Rd) associated to the free Schrödinger equation is nondecreasing as the initial datum f evolves under a certain quadratic heat-flow.

For fixed ƒ and r this mean modulus Mt(r;f) as a function of / is continuous, nonnegative, nondecreasing, and is bounded above by the maximum modulus of ƒ on C(r) [l, 2 ] . 1 Therefore the limit of Mt(r;f) exists as /—>0 and /—» oo. This limit is defined to be the mean modulus of ƒ on C(r) of order 0 and of order oo respectively. I t may be shown that the mean modulus of order 0 is the geometri...

In this paper, we study the semidiscrete approximation for the following initial-boundary value problem  ut(x, t) = uxx(x, t) + λf(x)(1− u(x, t))−p, −l < x < l, t > 0, u(−l, t) = 0, u(l, t) = 0, t > 0, u(x, 0) = u0(x) ≥ 0, −l ≤ x ≤ l, where p > 1, λ > 0 and f(x) ∈ C([−l, l]), symmetric and nondecreasing on the interval (−l, 0), 0 < f(x) ≤ 1, f(−l) = 0, f(l) = 0 and l = 1 2 . We find some cond...

In [3] we study a stochastic, continuous time model on a finite horizon for a firm that produces a single good. We model the production capacity as a suitable linear Ito diffusion controlled by a nondecreasing process representing the cumulative investment. The firm aims to maximize its expected total net profit by choosing the optimal investment process. That is a singular stochastic control p...

Consider a separable concave minimization problem with nondecreasing costs over a general ground set X ⊆ R+. We show how to efficiently approximate this problem to a factor of 1+2 in optimal cost by a single piecewise linear minimization problem over X. The number of pieces is linear in 1/2 and polynomial in the logarithm of certain ground set parameters; in particular, it is independent of the...

New sufficient conditions for the existence of a solution of the boundary value problem for an ordinary differential equation of n-th order with certain functional boundary conditions are constructed by a method of a priori estimates. Introduction In this paper we give new sufficient conditions for the existence of a solution of the ordinary differential equation (1) u(t) = f ( t, u(t), . . . ,...