Given a set P of n points in R ̄ , an ε-kernel K ⊆ P approximates the directional width of P in every direction within a relative (1 − ε) factor. In this paper we study the stability of ε-kernels under dynamic insertion and deletion of points to P and by changing the approximation factor ε. In the first case, we say an algorithm for dynamically maintaining a ε-kernel is stable if at most O(1) po...

The material properties of greatest importance in microwave processing of a dielectric are the complex relative permittivity ε = ε′ jε′′, and the loss tangent, tan δ = ε′′/ ε′. The real part of the permittivity, ε′, sometimes called the dielectric constant, mostly determines how much of the incident energy is reflected at the air-sample interface, and how much enters the sample. This paper show...

The geometric-arithmetic index is another topological index was defined as 2 deg ( )deg ( ) ( ) deg ( ) deg ( ) G G uv E G G u v GA G u v     , in which degree of vertex u denoted by degG (u). We now define a new version of GA index as 4 ( ) 2 ε ( )ε ( ) ( ) ε ( ) ε ( ) G G e uv E G G G u v GA G   u v    , where εG(u) is the eccentricity of vertex u. In this paper we compute this new t...

Consider the equation −ε 2 ∆u ε + q(x)u ε = f (u ε) in R 3 , |u(∞)| < ∞, ε = const > 0. Under what assumptions on q(x) and f (u) can one prove that the solution u ε exists and lim ε→0 u ε = u(x), where u(x) solves the limiting problem q(x)u = f (u)? These are the questions discussed in the paper.

We consider a second order damped-vibration equation Mẍ + D(ε)ẋ + Kx = 0, where M, D(ε), K are real, symmetric matrices of order n. The damping matrix D(ε) is defined by D(ε) = Cu + C(ε), where Cu presents internal damping and rank(C(ε)) = r, where ε is dampers’ viscosity. We present an algorithm which derives a formula for the trace of the solution X of the Lyapunov equation AX + XA = −B, as a...

It is known that Nash equilibria and approximate Nash equilibria not necessarily optimize social optima of bimatrix games. In this paper, we show that for every fixed ε > 0, every bimatrix game (with values in [0, 1]) has an ε-approximate Nash equilibrium with the total payoff of the players at least a constant factor, (1 − √ 1− ε), of the optimum. Furthermore, our result can be made algorithmi...

UNLABELLED Clostridium perfringens epsilon toxin (ε-toxin) is responsible for a devastating multifocal central nervous system (CNS) white matter disease in ruminant animals. The mechanism by which ε-toxin causes white matter damage is poorly understood. In this study, we sought to determine the molecular and cellular mechanisms by which ε-toxin causes pathological changes to white matter. In pr...

A new lattice estimate of K → 2π transitions claims, contrary to all other computations, that the hadronic matrix element for the gluon penguin operator Q6 has opposite sign and, in addition, is much larger than the vacuum saturation approximation. We comment under what conditions (if any) it is possible to reconcile this lattice result with the experimental value of ε/ε . The dramatic impact o...

We analyze the rare kaon decays KL → π0νν̄, K+ → π+νν̄, KL → π0e+e− and KL → μ+μ− in conjunction with the CP violating ratio ε/ε in a general class of supersymmetric models in which Zand magnetic-penguin contributions can be substantially larger than in the Standard Model. We point out that radiative effects relate the double left-right mass insertion to the single left-left one, and that the phe...

We present a recent analysis of ε′/ε in the 1/Nc expansion. We show that the 1/Nc corrections to the matrix element of Q6 are large and positive, indicating a ∆I = 1/2 enhancement similar to the one of Q1 and Q2 which dominate the CP conserving amplitude. This enhances the CP ratio and can bring the standard model prediction close to the measured value for central values of the parameters. Talk...