begin{abstract} If $F,D:Rto R$ are additive mappings which satisfy $F(x^{n}y^{n})=x^nF(y^{n})+y^nD(x^{n})$ for all $x,yin R$. Then, $F$ is a generalized left derivation with associated Jordan left derivation $D$ on $R$. Similar type of result has been done for the other identity forcing to generalized derivation and at last an example has given in support of the theorems. end{abstract}

We discuss the supersymmetric contribution to ε ′ /ε in various supersymmetric flavor models. We find that in alignment models the supersymmetric contribution could be significant while in heavy squark models it is expected to be small. The situation is particularly interesting in models that solve the flavor problems by either of the above mechanisms and the remaining CP problems by means of a...

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...

In this article, we study the long time behavior of a phase-field parabolichyperbolic system arising from the phase-field theory of phase transitions. This system consists of a parabolic equation governing the (relative) temperature which is nonlinearly coupled with a weakly damped semilinear hyperbolic equation ruling the evolution of the order parameter. The latter is a singular perturbation ...

Homogenization techniques are used to derive a double porosity model for single phase flow in a reservoir with a preferred direction of fracture. The equations in the microscopic model are the usual ones derived from Darcy’s law in the fractures and matrix (rock). The permeability coefficients over the matrix domain are scaled, using a parameter ε, based on the fracture direction in the reservo...

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...