We introduce the notion of bilinear moment functional and study their general properties. The analogue of Favard’s theorem for moment functionals is proven. The notion of semiclassical bilinear functionals is introduced as a generalization of the corresponding notion for moment functionals and motivated by the applications to multi-matrix random models. Integral representations of such function...

We define notions of resource-bounded continuity and sequentiality for type-two functionals with total inputs, and prove that there are continuous functionals which cannot be efficiently simulated by sequential functionals. We also show that for some naturally-defined classes of continuous functionals, an efficient simulation is possible.

We study a one-dimensional reaction-diffusion system which describes an isothermal autocatalytic chemical reaction involving both a quadratic (A + B → 2B) and a cubic (A+ 2B → 3B) autocatalysis. The parameters of this system are the ratio D = DB/DA of the diffusion constants of the reactant A and the autocatalyst B, and the relative activity k of the cubic reaction. First, for all values of D >...

The distributional k-dimensional Jacobian of a map u in the Sobolev space W 1,k−1 which takes values in the the sphere S can be viewed as the boundary of a rectifiable current of codimension k carried by (part of) the singularity of u which is topologically relevant. The main purpose of this paper is to investigate the range of the Jacobian operator; in particular, we show that any boundary M o...

Distorted measures have been used in pricing of insurance contracts for a long time. This paper reviews properties of related acceptability functionals in risk management, called distortion functionals. These functionals may be characterized by being mixtures of average values-at-risk. We give a dual representation of these functionals and show how they functionals may be used in portfolio opti...

We characterize the convergence in distribution to a standard normal law for a sequence of multiple stochastic integrals of a fixed order with variance converging to 1. Some applications are given, in particular to study the limiting behavior of quadratic functionals of Gaussian processes. 1. Introduction. In this paper, we characterize the convergence in distribution to a normal N (0, 1) law f...

This paper concerns the problem of estimating linear functionals of the mixing distribution from Poisson mixture observations. In particular, linear functionals for which parametric rate of convergence cannot be achieved are studied. It appears that Gaussian functionals are rather easy to estimate. Estimation of the distibution functions is then considered by approximating this functional by Ga...

The energy minimization involved in density functional calculations of electronic systems can be carried out using an exponential transformation that preserves the orthonormality orbitals. system is then represented as a function elements skew-Hermitian matrix optimized directly unconstrained methods. An implementation based on limited memory Broyden-Fletcher-Goldfarb-Shanno approach with inexa...

Aggelos K. Katsaggelos Northwestern University McCormick School of Engineering and Applied Science Department of Electrical and Computer Engineering Evanston, Illinois 60208 E-mail: [email protected] Abstract. We develop a regularized mixed-norm image restoration algorithm to deal with various types of noise. A mixed-norm functional is introduced, which combines the least mean square (LMS) and t...