Abstract. A characteriation of continuity of the p-Λ-variation function is given and the Helly’s selection principle for ΛBV (p) functions is established. A characterization of the inclusion of Waterman-Shiba classes into classes of functions with given inte-gral modulus of continuity is given. A

This paper presents an abstract analysis of bounded variation (BV) methods for ill-posed operator equations Au = z. Let T (u) def = kAu \Gamma zk 2 + ffJ(u); where the penalty, or "regularization", parameter ff ? 0 and the functional J(u) is the BV norm or seminorm of u, also known

A variational problem for three fluids in which gravitational and surface tension forces are in equilibrium is studied using sets of finite perimeter and functions of bounded variation. Existence theorems are proven which imply the existence of an axisymmetric floating drop. This problem has been

Abstract. The class of functions of ΛBV (p) shares many properties of functions of bounded variation. Here we have shown that ΛBV (p) is a Banach space with a suitable norm, the intersec-tion of ΛBV (p), over all sequences Λ, is the class of functions of BV(p) and the union of ΛBV (p), over all

Abstract. The goal of this paper is to extend Poincaré-Wirtinger inequalities from Sobolev spaces to spaces of functions of bounded variation of second order.

Abstract. The classical Sobolev embedding theorem of the space of functions of bounded variation BV (Rn) into Ln ′ (Rn) is proved in a sharp quantitative form. 1.

, their close relationship with the variational distance and the probability of misclassification error are established in terms of bounds. These bounds are crucial in many applications of divergence measures. The new measures are also well characterized by the properties of nonnegativity, finiteness

was the exploration of variations around a point, within the bounds imposed by the constraints, in order to help characterize solutions and portray them in terms of ‘variational principles’. Notions of perturbation, approximation and even generalized differentiability were extensively investigated. Variational theory

a unified variational Bayesian (VB) framework which approximates these computations in models with latent variables using a lower bound on the marginal likelihood. Chapter 1 presents background material on Bayesian inference, graphical models, and propaga-tion algorithms. Chapter 2 forms

the variation in the perturbed quantity. Up to the higher-order terms that are ignored in the expansion, these statistics tend to be more realistic than perturbation bounds obtained in terms of norms. The technique is applied to a number of problems in matrix perturbation theory, including least squares