We prove that the family of functionals (Iδ) defined by Iδ(g) = ∫∫ RN×RN |g(x)−g(y)|>δ δ |x− y|N+p dx dy, ∀ g ∈ L(R ), for p ≥ 1 and δ > 0, Γ-converges in L(R ), as δ goes to 0, when p ≥ 1. Hereafter | | denotes the Euclidean norm of R . We also introduce a characterization for BV functions which has some advantages in comparison with the classic one based on the notion of essential variation o...

For the nite volume method applied to scalar hyperbolic conservation law in two space dimensions, the uniform BV estimate for an approximate solution is not available on unstructured grids. Therefore the convergence proofs are based on methods which needs less regularity, e.g. on the Young measure theory. In this contribution we discuss the so-called ((t)-condition which serves as a suitable re...

When the random intersection graph G(n,m, p) proposed by Karoński, Scheinerman, and Singer-Cohen in [8] is compared with the independent-edge G(n, p), the evolutions are different under some values of m and equivalent under others. In particular, when m = nα and α > 6, the total variation distance between the graph random variables has limit 0.

The role of effective hadron masses and effective couplings in nuclear matter is studied using a generalized effective Lagrangian for σ-ω model. A simple relation among the effective masses, the effective couplings and the incompressibility K is derived. Using the relation, it is found that the effective repulsive and the effective attractive forces are almost canceled to each other at the norm...

Given an increasing process (At)t≥0, we characterize the non-decreasing right-continuous functions f : R+ → R+ that map A to a pure-jump process. As an example of application, we show for instance that functions with bounded variation belong to the domain of the extended generator of any subordinator with no drift and infinite Lévy measure.

We consider the class of integer rectifiable currents without boundary in Rn × R satisfying a positivity condition. We establish that these currents can be written as a linear superposition of graphs of finitely many functions with bounded variation.

Let L be a linear space of real bounded random variables on the probability space (Ω,A, P0). A finitely additive probability P on A such that P ∼ P0 and EP (X) = 0 for each X ∈ L is called EMFA (equivalent martingale finitely additive probability). In this note, EMFA’s are investigated in case P0 is atomic. Existence of EMFA’s is characterized and various examples are given. Given y ∈ R and a b...

We introduce a new class of control problems in which the gain depends on the solution of a stochastic differential equation reflected at the boundary of a bounded domain, along directions which are controlled by a bounded variation process. We provide a PDE characterization of the associated value function. This study is motivated by applications in mathematical finance where such equations ar...

We analyze the variation of prices in a model of an exchange market introduced by Kakade et al. [11], in which buyers and sellers are represented by vertices of a bipartite graph and trade is allowed only between neighbors. In this model the graph is generated probabilistically, and each buyer is connected via preferential attachment to v sellers. We show that even though the tail of the degree...

We provide a short proof of that case of the Gilbert-Pearson theorem that is most often used: That all eigenfunctions bounded implies purely a.c. spectrum. Two appendices illuminate Weidmann's result that potentials of bounded variation have strictly a.c. spectrum on a half-axis. 5