There is a constant c > 0 such that for every ε ∈ (0, 1) and n > 1/ε, the following holds. Any mapping from the n-point star metric into l1 with bi-Lipschitz distortion 1 + ε requires dimension d > c log n ε log(1/ε) .

Dynamic recrystallization, DRX, behaviour of a precipitation hardened, PH, stainless steel was studied in connection with microstructural developments in a compression test. The experimental results showed that the dominant mechanism of softening is DRX, but at high strain rates and low temperatures, ie, high Zener-Holman parameter, Z, work hardening and dynamic recovery, DRV, produced a pancke...

The introduction of high-speed circuits to realize an arithmetic function f as a piecewise linear approximation has created a need to understand how the number of segments depends on the interval a ≤ x < b and the desired approximation error ε. For the case of optimum non-uniform segments, we show that the number of segments is given as s(ε) ∼ c √ ε , (ε → 0), where c = 1 4 ∫ b a √ |f ′′(x)|dx....

Claim 1 Let q and q′ be any two points in Σ so that d(q, q′) ≤ εmin{f(q), f(q′)} for ε ≤ 1 3 . Then, ∠nq, nq′ ≤ ε 1−3ε . Unfortunately, the proof of this claim as given in Amenta and Bern [1] is wrong; it also appears in the book by Dey [2]. In this short note, we provide a correct proof with an improved bound of ε 1−ε . Theorem 2 Let q and q′ be two points in Σ with d(q, q′) ≤ εf(q) where ε ≤ ...

We show that for every ε > 0 there exists an r0 = r0(ε) such that for all integers r ≥ r0 every graph of average degree at least r + ε and girth at least 1000 contains a subdivision of Kr+2. Combined with a result of Mader this implies that for every ε > 0 there exists an f(ε) such that for all r ≥ 2 every graph of average degree at least r + ε and girth at least f(ε) contains a subdivision of ...

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...