In (5), GF is the Fermi coupling, the functions zi(μ) and yi(μ) are the Wilson coefficients and τ = −VtdV ∗ ts/VudV ∗ us. According to the standard parameterization of the CKM matrix, in order to determine ε/ε , we only need to consider the yi(μ) components, which control the CP -violating part of the lagrangian. The coefficients yi(μ), and zi(μ) contain all the dependence of short-distance phy...

We provide a complete characterization for the computational complexity of finding approximate equilibria in two-action graphical games. consider two most well-studied approximation notions: ε-Nash (ε-NE) and ε-well-supported Nash (ε-WSNE), where ε is [0,1]. prove that computing an ε-NE PPAD-complete any constant smaller than 1/2, while very simple algorithm (namely, letting all players mix uni...

We determine explicitly the formal moduli space of certain complete topological modules over a topologically finitely generated local k-algebra R, not necessarily commutative, where k is a field. The class of topological modules we consider include all those of finite rank over k and some of infinite rank as well, namely those with a Schauder basis in the sense of §1. This generalizes the resul...

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and Applied Analysis 3 radius δ ∈ 0, 1/2 . For φ, ε∗, ε 0 < ε∗ < ε, φ1 < φ − ε < φ − ε∗ < φ ε∗ < φ ε < φ2 , and R > R∗ > 2, we have ( q − 2)S(Ω(φ − ε∗, φ ε∗), R∗,W) n ( Ω ( φ − ε, φ ε), R, ̃ Rz ) q ∑ j 1 n ( Ω ( φ − ε, φ ε), R,W aj ) 256vπ24 lnR δ38 ε − ε∗ lnR − lnR∗ ( q − 2)S ( Ω ( φ − ε∗, φ ε∗, 1 R∗ ,W ))