A classical result of Higman [H], [S, Exer. 6.3], asserts that the roots of unity in the group ring Z[Γ] of a finite commutative group Γ are the elements ±γ for γ ∈ Γ. One application of this result is the determination of the group of finite-order automorphisms of a torus T = ResS′/S(Gm) for a finite étale Galois covering f : S′ → S with S and S′ connected schemes and abelian Galois group Γ = ...

We propose a framework of consistent finite-order priors to facilitate the incorporation of higher-order uncertainties into Bayesian game analysis, without invoking the concept of a universal type space. Several recent models, which give rise to stunning results with higher-order uncertainties, turn out to operate with certain consistent order-2 priors. We introduce canonical representations of...

Many familiar models of the untyped lambda calculus are constructed by order theoretic methods. This paper provides some basic new facts about ordered models of the lambda calculus. We show that in any partially ordered model that is complete for the theory of βor βη-conversion, the partial order is trivial on term denotations. Equivalently, the open and closed term algebras of the untyped lamb...

I characterize the implications of the common prior assumption for finite orders of beliefs about beliefs at a state and show that in finite models, the only such implications are those stemming from the weaker assumption of a common support. More precisely, given any finite N and any finite partitions model where priors have the same support, there is another finite partitions model with commo...

‎‎in this paper we determine all finite $2$-groups of‎ ‎class $2$ in which every automorphism of order $2$ leaving the frattini subgroup elementwise fixed is inner‎.

in this paper, under the existence of system uncertainties, external disturbances, and input nonlinearity, global finite time synchronization between two identical attractors which belong to a class of second-order chaotic nonlinear gyros are achieved by considering a method of continuous smooth second-order sliding mode control (hoamsc). it is proved that the proposed controller is robust to m...

now a days, structures with planar geometry such as sheet metals, have attracted special consideration among advanced techno logia, and hence investing vibration behavior of sheet metal is of prim important . in particular regarding dynamical investigations, if the natural frequencies get ignored, the resonance phenomena can exert noun computing damages to the structure and systems. in this res...