We present a new methodology for computing approximate Nash equilibria for two-person non-cooperative games based upon certain extensions and specializations of an existing optimization approach previously used for the derivation of fixed approximations for this problem. In particular, the general two-person problem is reduced to an indefinite quadratic programming problem of special structure ...

This study is about outlier detection in time series data. The main objective is to derive and to test statistics for detecting additive outlier (AO) and innovative outlier (IO) in GARCH(1,1) processes and subsequently to develop a procedure for testing the presence of outliers using the statistics. A test statistic has been derived for each type of outlier. In the derivation of the statistics,...

A unital $C^*$ -- algebra $mathcal A,$ endowed withthe Lie product $[x,y]=xy- yx$ on $mathcal A,$ is called a Lie$C^*$ -- algebra. Let $mathcal A$ be a Lie $C^*$ -- algebra and$g,h:mathcal A to mathcal A$ be $Bbb C$ -- linear mappings. A$Bbb C$ -- linear mapping $f:mathcal A to mathcal A$ is calleda Lie $(g,h)$ -- double derivation if$f([a,b])=[f(a),b]+[a,f(b)]+[g(a),h(b)]+[h(a),g(b)]$ for all ...

Let M be a type I von Neumann algebra with the center Z, a faithful normal semi-finite trace τ. Let L(M, τ) be the algebra of all τ -measurable operators affiliated with M and let S0(M, τ) be the subalgebra in L(M, τ) consisting of all operators x such that given any ε > 0 there is a projection p ∈ P(M) with τ(p) < ∞, xp ∈ M and ‖xp‖ < ε. We prove that any Z-linear derivation of S0(M, τ) is spa...

We study the limit of high activation energy of a special Fokker–Planck equation known as the Kramers–Smoluchowski equation (KS). This equation governs the time evolution of the probability density of a particle performing a Brownian motion under the influence of a chemical potential H/ε. We choose H having two wells corresponding to two chemical states A and B. We prove that after a suitable r...

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 ))

A simple derivation of the effective spin-wave Hamiltonian for a double-exchange system with infinitely large Hund’s-rule coupling is demonstrated. The formalism can be applied to models with arbitrary range of hopping as well as those with randomness. The result shows that, within the leading order of the 1/S expansion, one magnon excitation spectrum can be described by the Heisenberg model.