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 final rescattering of the two pions provides a strong enhancement of the ∆I = 1/2 amplitude, which so far has been neglected in the theoretical predictions of ε′/ε. This correction increases the Standard Model prediction of ε′/ε to v...

During the last four years several parameters relevant for the analysis of the CP-violating ratio ε/ε improved and/or changed significantly. In particular, the experimental value of ε/ε and the strange quark mass decreased, the uncertainty in the CKM factor has been reduced, and for a value of the hadronic matrix element of the dominant electroweak penguin operator Q8, some consensus has been r...

The computation of (i) ε-kernels, (ii) approximate diameter, and (iii) approximate bichromatic closest pair are fundamental problems in geometric approximation. In this paper, we describe new algorithms that offer significant improvements to their running times. In each case the input is a set of n points in R for a constant dimension d ≥ 3 and an approximation parameter ε > 0. We reduce the re...

and Applied Analysis 3 by φ(ε) := L[y+εη] and f(t, ε) := L(t, yσ(t)+εησ(t), yΔ(t)+ εη Δ (t)). If ∂f/∂ε is continuous in ε, uniformly in t, then

The Standard Model prediction for ε ′ /ε is updated, taking into account the most recent theoretical developments. The final numerical value, ε ′ /ε = (17 ± 6) × 10 −4 , is in good agreement with present measurements.

We study homogenization of a second-order elliptic differential operator Aε = −div a(x/ε) ×∇ acting in an ε-periodically perforated space, where ε is small parameter. Coefficients the are measurable ε-periodic functions. The simplest case coefficients constant also interesting for us. find approximation resolvent (Aε + 1)−1 with remainder term order ε2 as → 0 L2-norm on space. This turns to be ...

Small diameter asymptotics is obtained for scattering solutions in a network of thin fibers. The asymptotics is expressed in terms of solutions of related problems on the limiting quantum graph Γ. We calculate the Lagrangian gluing conditions at vertices v ∈ Γ for the problems on the limiting graph. If the frequency of the incident wave is above the bottom of the absolutely continuous spectrum,...

We give a polynomial time algorithm that given a graph which admits a bisection cutting a fraction (1 − ε) of edges, finds a bisection cutting a (1 − g(ε)) fraction of edges where g(ε) → 0 as ε→ 0. One can take g(ε) = O( 3 √ ε log(1/ε)). Previously known algorithms for Max Bisection could only guarantee finding a bisection that cuts a fraction of edges bounded away from 1 (in fact less than 3/4...

A symmetric subset of the reals is one that remains invariant under some reflection x 7→ c − x. We consider, for any 0 < ε ≤ 1, the largest real number ∆(ε) such that every subset of [0, 1] with measure greater than ε contains a symmetric subset with measure ∆(ε). In this paper we establish upper and lower bounds for ∆(ε) of the same order of magnitude: for example, we prove that ∆(ε) = 2ε − 1 ...