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

The Liouville–Green approximation for the differential equation z̈(t) + f (t)z(t) = 0 is exhaustively studied. New moments of f – and not only the first and second – are proposed, allowing asymptotic formulae with explicit estimates for the error functions. The recessive and Dominant character of the fundamental system of solutions is clear. Our study includes the pointwise condition limt→∞ t2f ...

Random walks in wireless sensor networks can serve as fully local, very simple strategies for sink motion that significantly reduce energy dissipation a lot but increase the latency of data collection. To achieve satisfactory energy-latency trade-offs the sink walks can be made adaptive, depending on network parameters such as density and/or history of past visits in each network region; but th...

Here we assume that the logarithmic asset price is given by a semimartingale. Jacod (2006) has derived an infeasible central limit theorem for the realised variance in such a general framework. However, here we focus on constructing a feasible limit theorem. We propose a new estimator for the asymptotic variance of the realised variance. This new estimator is based on generalised versions of th...

The distance-number of a graph G is the minimum number of distinct edgelengths over all straight-line drawings of G in the plane. This definition generalises many well-known concepts in combinatorial geometry. We consider the distancenumber of trees, graphs with no K− 4 -minor, complete bipartite graphs, complete graphs, and cartesian products. Our main results concern the distance-number of gr...