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...

We update our 1993 analysis of the CP violating ratio ε/ε in view of the changes in several input parameters, in particular the improved value of the top quark mass. We also investigate the strange quark mass ms dependence of ε/ε in view of rather low values found in the most recent lattice calculations. A simple scanning of the input parameters within one standard deviation gives the ranges: −...

The total cross section for baryon number violating processes at high energies is usually parametrized as σtotal ∝ exp( α F (ε)), where ε = √ s/E0, E0 = √ 6πmw/α. In the present paper the third nontrivial term of the expansion F (ε) = −1 + 9 8 ε − 9 16 ε − 9 32 ( mh mw )2 ε log (