motivated by an arens regularity problem, we introduce the concepts of matrix banach space and matrix banach algebra. the notion of matrix normed space in the sense of ruan is a special case of our matrix normed system. a matrix banach algebra is a matrix banach space with a completely contractive multiplication. we study the structure of matrix banach spaces and matrix banach algebras. then we...

In this paper we present a collaborative artificial intelligence (AI) module for a turn-based, multiplayer, environmental awareness game. The game is a version of the EnerCities serious game, modified in the context of a European-Union project to support sequential plays of an emphatic robotic tutor interacting with two human players in a social and pedagogical manner. For that purpose, we crea...

In this paper we give some necessary and sufficient conditions for which each Banach lattice  is    space and we study some properties of b-weakly compact operators from a Banach lattice  into a Banach space . We show that every weakly compact operator from a Banach lattice  into a Banach space  is b-weakly compact and give a counterexample which shows that the inverse is not true but we prove ...

An original digital signature scheme based on action of infinite ring on module is presented. It is assumed that the ring contains an infinite multiplicative monoid. The ring action is defined as monoid elements's action on the module element as an operator. The signature scheme is based on particularly designed one–way functions (OWFs), using a postulated hard problem in monoid action level. T...

In this paper we introduce the notion of $varphi$-commutativity for a Banach algebra $A$, where $varphi$ is a continuous homomorphism on $A$ and study the concept of $varphi$-weak amenability for $varphi$-commutative Banach algebras. We give an example to show that the class of $varphi$-weakly amenable Banach algebras is larger than that of weakly amenable commutative Banach algebras. We charac...

The action of the symmetric group Sn on the set Parkn of parking functions of size n has received a great deal of attention in algebraic combinatorics. We prove that the action of Sn on Parkn extends to an action of Sn+1. More precisely, we construct a graded Sn+1-module Vn such that the restriction of Vn to Sn is isomorphic to Parkn. We describe the Sn-Frobenius characters of the module Vn in ...

In this work we deal with actions of vector groupoid which is a new concept in the literature‎. ‎After we give the definition of the action of a vector groupoid on a vector space‎, ‎we obtain some results related to actions of vector groupoids‎. ‎We also apply some characterizations of the category and groupoid theory to vector groupoids‎. ‎As the second part of the work‎, ‎we define the notion...

This paper deals with zero-sum average semi-Markov games with Borel state and action spaces, and unbounded payoffs and mean holding times. A solution of the Sapley equation is obtained via the Banach Fixed Point Theorem assumming that the model satisfies a Lyapunov-like condition, a growth hypothesis on the payoff function and the mean holding time, besides standard continuity and compactness r...