In this paper we prove a new chain rule formula for the distributional derivative of the composite function v(x) = B(x, u(x)), where u :]a, b[→ Rd has bounded variation, B(x, ·) is continuously differentiable and B(·, u) has bounded variation. We propose an application of this formula in order to deal in an intrinsic way with the discontinuous flux appearing in conservation laws in one space va...

A supermartingale deflator (resp. local martingale deflator) multiplicatively transforms nonnegative wealth processes into supermartingales (resp. local martingales). A supermartingale numéraire (resp. local martingale numéraire) is a wealth process whose reciprocal is a supermartingale deflator (resp. local martingale deflator). It has been established in previous works that absence of arbitra...

The problem of determining extremal hypergraphs containing at most r isomorphic copies of some element of a given hypergraph family was first studied by Boros et al. in 2001. There are not many hypergraph families for which exact results are known concerning the size of the corresponding extremal hypergraphs, except for those equivalent to the classical Turán numbers. In this paper, we determin...

We prove the existence of a continuous BV minimizer with C boundary value for the p-area (pseudohermitian or horizontal area) in a parabolically convex bounded domain. We extend the domain of the area functional from BV functions to vector-valued measures. Our main purpose is to study the first and second variations of such a generalized area functional including the contribution of the singula...

This paper presents summary results from an analysis of the institutional subscription prices for journals in biomedical and social sciences, for a selection of 11 publishers. Overall price, price per page, and price per point of impact factor have been examined for the period 2000–2006. Considerable variation was found between publishers both in their overall levels of price and in the rates o...

According to Jordan Decomposition Theorem, every real function of bounded variation can be decomposed to a difference of two increasing functions. In this paper we will show, among others, that an effective version of this theorem does not hold for computable function of bounded variation.

This paper introduces a new method for analyzing scaling phenomena in natural images and draws some consequences as to whether natural images belong to the space of functions with bounded variation