In this paper, we introduce a notion of generalized states from an EQ-algebra E1 to another EQ-algebra E2, which is a generalization of internal states (or state operators) on an EQ-algebra E. Also we give a type of special generalized state from an EQ-algebra E1 to E1, called generalized internal states (or GI-state). Then we give some examples and basic properties of generalized (internal) st...

A C *-algebra A is called an ideal C * -algebra (or equally a dual algebra) if it is an ideal in its bidual A**. M.C.F. Berglund proved that subalgebras and quotients of ideal C*-algebras are also ideal C*-algebras, that a commutative C *-algebra A is an ideal C *-algebra if and only if it is isomorphicto C (Q) for some discrete space ?. We investigate ideal J*-algebras and show that the a...

let $a$ be a banach algebra and $x$ be a banach $a$-bimodule. then ${mathcal{s}}=a oplus x$, the $l^1$-direct sum of $a$ and $x$ becomes a module extension banach algebra when equipped with the algebra product $(a,x).(a',x')=(aa',ax'+xa').$ in this paper, we investigate biflatness and biprojectivity for these banach algebras. we also discuss on automatic continuity of derivations on ${mathcal{s...

Based on the Gerstenhaber Theory it is clarified how operadic dynamics may be introduced. Operadic observables satisfy the Gerstenhaber algebra identities and their time evolution is governed by the Gerstenhaber-Lax or Gerstenhaber-Heisenberg equation. In this way one can describe classical and quantum time evolution of operations. The notion of an operadic Lax pair is introduced as well.

This paper presents our proposal for the evolution of the metamodel for the Task Algebra in the Task Flow model for the Discovery Method. The original Task Algebra is based on simple and compound tasks structured using operators such as sequence, selection, and parallel composition. Recursion and encapsulation were also considered. We propose additional characteristics to improve the capabiliti...

The objective of this tutorial is to describe the evolution of the field of stochastic process algebra in the past decade, through a presentation of the main achievements in the field. In particular, the tutorial stresses the current transformation of stochastic process algebra from a simple formalism to a fully fledged architectural description language for the functional verification and perf...

In this paper we present our recent work in developing a computer-algebra tool for systems of partial differential equations (PDEs), termed ”Kranc”. Our work is motivated by the problem of finding solutions of the Einstein equations through numerical simulations. Kranc consists of Mathematica based computer-algebra packages, that facilitate the task of dealing with symbolic tensorial calculatio...

In this paper we continue development of formal theory of a special class offuzzy logics, called EQ-logics. Unlike fuzzy logics being extensions of theMTL-logic in which the basic connective is implication, the basic connective inEQ-logics is equivalence. Therefore, a new algebra of truth values calledEQ-algebra was developed. This is a lower semilattice with top element endowed with two binary...

In this paper, first we define the notion of involutive operator on bounded involutive equality algebras and by using it, we introduce a new class of equality algebras that we called it a tense like equality algebra. Then we investigate some properties of tense like equality algebra. For two involutive bounded equality algebras and an equality homomorphism between them, we prove that the tense ...

We study some properties of the $SU(1,1)$ Perelomov number coherent states. The Schr\"odinger's uncertainty relationship is evaluated for a position and momentum-like operators (constructed from Lie algebra generators) in these It shown that this minimized standard obtain time evolution states by supposing Hamiltonian proportional to third generator $K_0$ $su(1,1)$ algebra. Analogous results $S...