A brief introduction to the א project, a TEX extension providing most of Ω and ε-TEX features.

We study whether we can weaken the conditions given in Reny [4] and still obtain existence of pure strategy Nash equilibria in quasiconcave normal form games, or, at least, existence of pure strategy ε−equilibria for all ε > 0. We show by examples that there are: 1. quasiconcave, payoff secure games without pure strategy ε−equilibria for small enough ε > 0 (and hence, without pure strategy Nash...

In this paper we prove that there exists a random sequence θi for the Glimm scheme such that the approximate solution u (t) converges to the exact semigroup solution Stū of the strictly hyperbolic system of conservation laws ut + f(u)x = 0, u(t = 0) = ū as follows: for all T ≥ 0 it holds lim ε→0 ‖uε(T )− ST ū √ ε| log ε| = 0. This result is the extension of the analysis of [9] to the general ca...

a f(x) dx (which one would use for instance to compute the work required to move a particle from a to b). For simplicity we shall restrict attention here to functions f : R → R which are continuous on the entire real line (and similarly, when we come to differential forms, we shall only discuss forms which are continuous on the entire domain). We shall also informally use terminology such as “i...

A classical theorem of Kuratowski says that every Baire one function on a Gδ subspace of a Polish (= separable completely metrizable) space X can be extended to a Baire one function on X. Kechris and Louveau introduced a finer gradation of Baire one functions into small Baire classes. A Baire one function f is assigned into a class in this heirarchy depending on its oscillation index β(f). We p...

k-Anonymity and ε-differential privacy are two mainstream privacy models, the former introduced to anonymize data sets and the latter to limit the knowledge gain that results from the inclusion of one individual in the data set. Whereas basic k-anonymity only protects against identity disclosure, t-closeness was presented as an extension of k-anonymity that also protects against attribute discl...

We study hyperbolic maps depending on a parameter ε. Each of them has an invariant Cantor set. As ε tends to zero, the map approaches the boundary of hyperbolicity. We analyze the asymptotics of scaling function of the invariant Cantor set as ε goes to zero. We show that there is a limiting scaling function of the limiting map and this scaling function has dense jump discontinuities because the...

We construct an upper bound for the following family of functionals {Eε}ε>0, which arises in the study of micromagnetics: Eε(u) = ∫ ε|∇u|2 + 1 ε ∫ R2 |Hu |2. Here is a bounded domain in R2, u ∈ H1( , S1) (corresponding to the magnetization) and Hu , the demagnetizing field created by u, is given by { div (ũ + Hu) = 0 in R2 , curl Hu = 0 in R2 , where ũ is the extension of u by 0 in R2 \ . Our u...

Contents 1. Introduction 1 2. Preliminaries and main notations 2 2.1. Setting of the problem 2 2.2. Some facts about distances and projections 4 3. A general argument to estimate the difference between energy minimizers 5 3.1. An energy lemma 6 3.2. Extension of Lemma 3 to the case of inhomogeneous Dirichlet boundary conditions 7 4. Derivation of the 0 th order approximation of u ε 9 4.1. Asymp...

This paper concerns with the reducibility loss of (periodic) invariant curves of quasi-periodically forced one dimensional maps and its relationship with the renormalization operator. Let gα be a one-parametric family of one dimensional maps with a cascade of period doubling bifurcations. Between each of these bifurcations, there exists a parameter value αn such that gαn has a superstable perio...