In this paper, the notions of tense operators and filters in \(BL\)-algebras are introduced several characterizations them obtained. Also, relation among \(BL\)-algebras, \(MV\)-algebras Boolean algebras investigated. Moreover, it is shown that set all a \(BL\)-algebra complete sublattice \(F(L)\) \(L\). maximal simple between studied. Finally, congruence relations strict an one-to-one correspo...

m ƒ qn‚ r , and 0 r < jnj. Not surprisingly, q is the quotient and r is the remainder when m is divided by n.1 We say that n divides m, or n is a divisor of m, when the remainder is zero. The notation n jm is used to signify that n divides m. An integer p is a prime number if 1 < jpj and the only divisors of p are 1 and p. We write a b „mod n… if b a is divisible by n.2 This notion, called cong...

Prior research on the impact of Afrocentric features on health has focused primarily on a single feature, skin color. We explored the effects of two other Afrocentric features (lip thickness, nose width) on Blacks' health status and whether unfair treatment mediates any relationship between these features and health. A secondary analysis of a prior study of Black patients' health was conducted....

The modular degree and congruence number are two fundamental invariants of an elliptic curve over the rational field. Frey and Müller have asked whether these invariants coincide. We find that the question has a negative answer, and show that in the counterexamples, multiplicity one (defined below) does not hold. At the same time, we prove a theorem about the relation between the two invariants...

Data ow analysis expresses the solution of an information gathering problem as the xed point of a system of monotone equations. This paper presents a technique to improve the performance of data ow analysis by systematically reducing the size of the equation system in any monotone data ow problem. Reductions result from partitioning the equations in the system according to congruence relations....

An important optimization tool in the design of synchronous systems is retiming, which in many cases allows a significant reduction in the length of the systems’ clock period. Even though the internal structure of systems changes upon retiming, their input-output behavior remains essentially the same. The original system and the one after the retiming can simulate each other in a suitable way. ...

The combined trace (i.e., comtrace) notion was introduced by Janicki and Koutny in 1995 as a generalization of the Mazurkiewicz trace notion. Comtraces are congruence classes of step sequences, where the congruence relation is defined from two relations simultaneity and serializability on events. They also showed that comtraces correspond to some class of labeled stratified order structures, bu...

This paper is an attempt to clear some philosophical questions about the nature of logic by setting up a mathematical framework. The notion of congruence in logic is defined. A logical structure in which there is no non-trivial congruence relation, like some paraconsistent logics, is called simple. The relations between simplicity, the replacement theorem and algebraization of logic are studied...

Birget, J.-C., SW. Margolis and J.C. Meakin, The word problem for inverse monoids presented by one idempotent relator, Theoretical Computer Science 123 (1994) 2733289. We study inverse monoids presented by a finite set of generators and one relation e= I, where e is a word representing an idempotent in the free inverse monoid, and 1 is the empty word. We show that (1) the word problem is solvab...