We quantify the important effect of strong final state interactions in the weak K → 2π amplitudes, using the measured π-π phase shifts with J = 0 and I = 0, 2. The main results of this analysis, with their implications for ε/ε and the ∆I = 1/2 rule, have been already presented in a previous paper [1]. Here we provide a detailed formal derivation of those results and further discuss the Standard...

An analytical expression for the maximal Lyapunov exponent λ1 in generalized Fermi-PastaUlam oscillator chains is obtained. The derivation is based on the calculation of modulational instability growth rates for some unstable periodic orbits. The result is compared with numerical simulations and the agreement is good over a wide range of energy densities ε. At very high energy density the power...

We give a nonstandard variant of Jordan’s proof of the Jordan curve theorem which is free of the defects his contemporaries criticized and avoids the epsilontic burden of the classical proof. The proof is selfcontained, except for the Jordan theorem for polygons taken for granted.

The main purpose of this article is to offer some characterizations of $delta$-double derivations on rings and algebras. To reach this goal, we prove the following theorem:Let $n > 1$ be an integer and let $mathcal{R}$ be an $n!$-torsion free ring with the identity element $1$. Suppose that there exist two additive mappings $d,delta:Rto R$ such that $$d(x^n) =Sigma^n_{j=1} x^{n-j}d(x)x^{j-1}+Si...

We give a new derivation, based on the complementary energy formulation, of a simplified model for a multi-structure made up of two anisotropic hyper-elastic bodies connected by a thin strong material layer. The model is obtained by identifying the Mosco-limit of the stored complementary energy functional when the thickness is of order ε and the stiffness of order 1/ε where ε is a positive real...

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...

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...

A severe case of stenosis in coronary arteries results in turbulence in the blood flow which may lead to the formation or progression of atherosclerosis. This study investigated the turbulent blood flow in a coronary artery with rigid walls, as well as 80% single and double stenoses on blood flow. A finite element-based software package, ADINA 8.8, was employed to model the blood flow. The hemo...

This work presents exact tracking analysis of the ε-normalized least mean square (ε-NLMS) algorithm for circular complex correlated Gaussian input. The analysis is based on the derivation of a closed form expression for the cumulative distribution function (CDF) of random variables of the form [||ui||2D1 ][ε+ ||ui|| 2 D2 ] −1. The CDF is then used to derive the first and second moments of these...

In this paper we present a rigorous derivation of the effective model for enhanced diffusion through a narrow and long 2D pore. The analysis uses the anisotropic singular perturbation technique. Starting point is a local pore scale model describing the transport by convection and diffusion of a reactive solute. The solute particles undergo an adsorption process at the lateral tube boundary, wit...