In this note first we define a BCK‐algebra on the states of a deterministic finite automaton. Then we show that it is a BCK‐algebra with condition (S) and also it is a positive implicative BCK‐algebra. Then we find some quotient BCK‐algebras of it. After that we introduce a hyper BCK‐algebra on the set of all equivalence classes of an equivalence relation on the states of a deterministic finite...

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...

Other names: CCN1, GIG1, IGFBP10 HGNC (Hugo): CYR61 Location: 1p22.3 Note CYR61 (cysteine-rich angiogenic inducer 61; also named CCN1), first identified as a serum-inducible immediate-early gene, encodes a secreted, extracellular matrix-associated protein that regulates diverse cellular functions (Lau, 2011). CYR61 and five later identified homologs comprise the six-member CCN family, named aft...

Résumé. Soit H(x) = ∑ n≤x φ(n) n − 6 π2x. Motivé par une conjecture de Erdös, Lau a développé une nouvelle méthode et il a démontré que #{n ≤ T : H(n)H(n + 1) < 0} T. Nous considérons des fonctions arithmétiques f(n) = ∑ d|n bd d dont l’addition peut être exprimée comme ∑ n≤x f(n) = αx+ P (log(x)) + E(x). Ici P (x) est un polynôme, E(x) = − ∑ n≤y(x) bn n ψ ( x n ) + o(1) avec ψ(x) = x − bxc − 1...

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 ...