BACKGROUND Impaired left ventricular (LV) function has been shown by strain rate (SR) imaging in patients with coronary artery disease (CAD). Our aim was to investigate global and regional, systolic and diastolic left atrial (LA) and right atrial (RA) longitudinal deformation in CAD using velocity vector imaging. METHODS Echocardiographic and velocity vector imaging studies were performed in ...

We study the general packing problem with M constraints. In [Jansen and Zhang, TCS 2002] a c(1 + ε)-approximation algorithm for the general packing problem was proposed. A block solver ABS(p, ε/6, c) with price vector p, given accuracy ε and ratio c is required. In addition, in [Villavicencio and Grigoriadis, Network Optimization (1997)] a (1 + ε)approximation algorithm for standard packing pro...

We prove an useful upper bound for the measure of spherical caps. Consider the uniformly distributed measure σn−1 on the Euclidean unit sphere Sn−1 ⊂ R. On the sphere, as among only a handful other spaces, the isoperimetric problem is completely solved. This goes back to Lévy [Lé] and Schmidt [Sch] and states that caps have the minimal measure of a boundary among all sets with a fixed mass. For...

The ∆I = 1/2 rule and direct CP violation ε ′ /ε in kaon decays are studied within the framework of the effective Hamiltonian approach in conjunction with generalized factorization for hadronic matrix elements. Conventionally the K → ππ matrix elements are evaluated under the factorization assumption so that O(µ) is factorized into the product of two matrix elements of single currents, governed...

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 ...