In this paper, a construction of a congruence having a given filter is presented. Also as a generalization of an BE-algebra homomorphism, the notion of a relation on BE-algebra, called an BE-relation is introduced and some fundamental properties to BE-algebras are discussed. Mathematics Subject Classification: 06F35, 03G25, 08A30

The paper investigates the non-symbolic algebraic semantics of the weak bisimulation congruenceson finite pi processes. The weak bisimulation congruences are studied both in the absence and inthe presence of the mismatch operator. Some interesting phenomena about the open congruences arerevealed. Several new tau laws are discovered and their relationship is discussed. The contributi...

In this paper we develop the method of diagrams for fuzzy predicate logics and give a characterization of different kinds of preserving mappings in terms of diagrams. Our work is a contribution to the modeltheoretic study of equality-free fuzzy predicate logics. We present a reduced semantics and we prove a completeness theorem of the logics with respect to this semantics. The main concepts bei...

Myhill-Nerode Theorem is regarded as a basic theorem in the theories of languages and automata and is used to prove the equivalence between automata and their languages. The significance of this theorem has stimulated researchers to develop that on different automata thus leading to optimizing computational models. In this article, we aim at developing the concept of congruence in general fuzzy...

1. Preview 2 Complex multiplication on elliptic curves over C 2 Traces of singular moduli 3 Class field theory 3 The Kronecker limit formula and Kronecker’s solution of Pell’s equation 4 Application to Diophantine equations (Villegas) 4 L-series and CM modular forms 5 Other topics 6 2. Complex Multiplication on Elliptic Curves over C 6 Elliptic Curves over C 6 Elliptic functions 7 Complex multi...

By using a special t-level relation U(μ, t) = {(x, y) ∈ S × S|(μ(x) ∧ μ(y)) ∨ IdS(x, y) ≥ t} based on a fuzzy ideal μ of a semigroup S, which is a congruence relation, we study the roughness of soft semigroups under this special ideal of S, such as rough soft subsemigroups, rough soft ideals and rough soft prime ideals.

A description and an example are given of numerical experiments which look for a relation between modular forms for certain congruence subgroups of SL(3, ZZ) and Galois representations.

We consider two linear algebraic groups G and G over the field of complex numbers, both of which are reductive. Take a finite dimensional rational representation W of G × G. Let Y = W//G := SpecC[W ] and X = W//G := SpecC[W ] ′ be the affine quotients. Since the action of G and G commutes on W , the quotient space X (respectively Y ) naturally inherits the action of G (respectively G). In this ...

A generalization of the Apéry-like numbers, which is used to describe the special values ζQ(2) and ζQ(3) of the spectral zeta function for the non-commutative harmonic oscillator, are introduced and studied. In fact, we give a recurrence relation for them, which shows a ladder structure among them. Further, we consider the ‘rational part’ of the higher Apéry-like numbers. We discuss several kin...

In this paper we find closed forms of the generating function ∞ ∑ k=0 U r nx , for powers of any non-degenerate second-order recurrence sequence, Un+1 = aUn+bUn−1, a +4b 6= 0, completing a study began by Carlitz [1] and Riordan [4] in 1962. Moreover, we generalize a theorem of Horadam [3] on partial sums involving such sequences. Also, we find closed forms for weighted (by binomial coefficients...