We present a descriptive definition of a multidimensional generalized Riemann integral based on a concept of generalized absolute continuity for additive functions of sets of bounded variation.

Total variation (TV) regularization, originally introduced by Rudin, Osher and Fatemi in the context of image denoising, has become widely used in the field of inverse problems. Two major directions of modifications of the original approach were proposed later on. The first concerns adaptive variants of TV regularization, the second focuses on higher-order TV models. In the present paper, we co...

We give upper bounds on the Walsh coefficients of functions for which the derivative of order at least one has bounded variation of fractional order. Further, we also consider the Walsh coefficients of functions in periodic and non-periodic reproducing kernel Hilbert spaces. A lower bound which shows that our results are best possible is also shown. Mathematical Subject Classification (2000): P...

This article examines "consistent" conjectural variations in an oligopoly model with a homogeneous product. A conjectural variation is consistent if it is equivalent to the optimal response of the otherfirms at the equilibrium defined by that conjecture. When the number of firms is fixed, we find that competitive behavior is consistent when marginal costs are constant, but that when marginal co...

In many applications it is possible to justify a reasonable bound for possible variation of subgradients of objective function rather than for their uniform magnitude. In this paper we develop a new class of efficient primal-dual subgradient schemes for such problem classes.

This paper uses a gravity model approach in order to analyse the geographical patterns of Irish exports. The gravity model in international trade has been demonstrated to be an extremely robust empirical method. The gravity model is first applied to aggregate Irish exports from 1980 to 2007. Distance is found to have a strong negative effect on exports. On the other hand, exports are positively...

This paper is devoted to the decomposition of an image f into u + v, with u a piecewise-smooth or “cartoon” component, and v an oscillatory component (texture or noise), in a variational approach. The cartoon component u is modeled by a function of bounded variation, while v, usually represented by a square integrable function, is now being modeled by a more refined and weaker texture norm, as ...

Abstract. The purpose of this paper is to provide global existence and uniqueness results for a family of fluid transport equations by establishing convergence results for the particle method applied to these equations. The considered family of PDEs is a collection of strongly nonlinear equations which yield traveling wave solutions and can be used to model a variety of flows in fluid dynamics....

We examine the performance of Total Variation (TV) smoothing for processing of noisy Electrocardiogram (ECG) recorded by an ambulatory device. The TV smoothing is compared with traditionally-used bandpass filtering using ECG with artificially added noise, as well as with real-world noise obtained during physiological monitoring. The fundamental difference between TV smoothing and traditional ba...

We characterize distributions with respect to which the members of a Tchebychev set of polynomials are orthogonal when they satisfy differential equations with polynomial coefficients. As an application, we find a real weight of bounded variation with support in [0, oo) for Bessel polynomials.