In this short note, we construct a right adjoint to the functor which associates ring R equipped with group action its twisted ring. This admits an interpretation as semilinearization, in that it sends R-module of semilinear automorphisms module. As immediate corollary, provide novel proof classical observation modules over are base together action.

This article introduces our research efforts to build the Essex Rovers’01 robot soccer team participated in the RoboCup-2001 competition. A modular design for implementing a behavior-based hierarchy is introduced, which consists of three modules such as Perception module, Cognition module and Action module. This architecture is used for the team to achieve intelligent actions in real time. The ...

This paper studies the existence of pure-strategy Nash equilibria for nonatomic games where players take actions in an infinite-dimensional Banach space. For any infinitedimensional Banach space, we construct a nonatomic game with actions in this space which has no pure-strategy Nash equilibria, provided that the player space is modeled by the usual Lebesgue unit interval. We also show that if ...

‎In this paper‎, ‎we prove some theorems related to properties of‎ ‎generalized symmetric hybrid mappings in Banach spaces‎. ‎Using Banach‎ ‎limits‎, ‎we prove a fixed point theorem for symmetric generalized‎ ‎hybrid mappings in Banach spaces‎. ‎Moreover‎, ‎we prove some weak‎ ‎convergence theorems for such mappings by using Ishikawa iteration‎ ‎method in a uniformly convex Banach space.

A finite module M over a noetherian local ring R is said to be Gorenstein if Ext(k, M) = 0 for all i 6= dimR. A endomorphism φ : R → R of rings is called contracting if φ(m) ⊆ m for some i ≥ 1. Letting R denote the R-module R with action induced by φ, we prove: A finite R-module M is Gorenstein if and only if HomR( R,M) ∼= M and ExtiR( R,M) = 0 for 1 ≤ i ≤ depthR.

In this paper we investigate some hereditary properties of amenability modulo an ideal of Banach algebras. We show that if $(e_alpha)_alpha$ is a bounded approximate identity modulo I of a Banach algebra A and X is a neo-unital modulo I, then $(e_alpha)_alpha$ is a bounded approximate identity for X. Moreover we show that amenability modulo an ideal of a Banach algebra A can be only considered ...

This talk presents a general framework for refined spectral analysis of a group of isometries acting on a Banach space, which extends the spectral theory of Arveson. The concept of continuous Arveson spectrum is introduced and the corresponding spectral subspace is defined. The absolutely continuous and singular-continuous parts of this spectrum are specified. Conditions are given, in terms of ...