In this paper, we first introduce the notion of self-regular functions. Various appealing properties of self-regular functions are explored and we also discuss the relation between selfregular functions and the well-known self-concordant functions. Then we use such functions to define self-regular proximity measure for path-following interior point methods for solving linear optimization (LO) p...

We analyse the CP problem in the context of a supersymmetric extension of the standard model with universal strength of Yukawa couplings. A salient feature of these models is that the CP phases are constrained to be very small by the hierarchy of the quark masses, and the pattern of CKM mixing angles. This leads to a small amount of CP violation from the usual KM mechanism and a significant con...

An analytical framework is developed for passing to the homogenisation limit in (not necessarily convex) variational problems for composites whose material properties oscillate with a small period ε and that exhibit high contrast of order ε−1 between the constitutive, “stress-strain”, response on different parts of the period cell. The approach of this article is based on the concept of “two-sc...

Let L be an n-dimensional lattice and let x be a point chosen uniformly from a large ball in R. In this note we consider the distribution of the distance from x to L, normalized by the largest possible such distance (i.e., the covering radius of L). By definition, the support of this distribution is [0, 1]. We show that there exists a universal constant α2 that provides a natural ‘threshold’ fo...

We study the continuity of the correspondence of interim ε-rationalizable actions in incomplete information games. We introduce a topology on types, called uniformweak topology, under which two types of a player are close if they have similar firstorder beliefs, attach similar probabilities to other players having similar first-order beliefs, and so on, where the degree of similarity is uniform...

Let X ⊂ R d be a set of n points in general position (i.e. no d + 1 points of X lie on the same hyperplane.) For a positive 0 < ε < 1, we define A finite set S ⊂ R d is called a (weak) ε-net of X if S ∩ F = ∅ for any F ∈ F ε. We note that S is called a strong ε-net if, in addition, it also satisfies S ⊂ X. Since we are only going to discuss weak ε-nets, we will simply call these ε-nets. Our goa...

A finite element implementation of the standard k − ε turbulence model including Chien’s Low-Reynolds number modification is presented. The incompressible Navier-Stokes equations are solved using an extension of the in-house software package FeatFlow (http://www.featflow.de). Algebraic flux correction based on a multidimensional flux limiter of TVD type (Kuzmin and Turek, 2004) is invoked to su...

We extend some aspects of the theory of fractal strings and their complex dimensions from the real line to general Euclidean spaces. This is accomplished by using the explicit formulas and techniques of [La-vF4]. We use the self-similar tilings constructed in [Pe1] to define a zeta function which encodes the scaling properties of the tiling. This allows us to define a generating function for th...