For given positive integers a1,a2,⋯,ak with gcd(a1,a2,⋯,ak)=1, the denumerant d(n)=d(n;a1,a2,⋯,ak) is number of nonnegative solutions (x1,x2,⋯,xk) linear equation a1x1+a2x2+⋯+akxk=n for a integer n. p, let Sp=Sp(a1,a2,⋯,ak) be set all n’s such that d(n)>p. In this paper, by introducing p-numerical semigroup, where N0\Sp finite, we give explicit formulas p-Frobenius number, which maximum N0\S...

This paper is expository. It is mainly a survey of some of our work on the algebraic systems that arise in fuzzy set theory and logic. We include some of the proofs here and refer to the papers [18, 19, 20, 21, 22] for further details. Our point of view is the algebraic one: when are the various systems that arise isomorphic, and what are their symmetries (automorphisms)? The bulk of the materi...

Let us consider a 3-numerical semigroup S = 〈a, b,N 〉. Given m ∈ S, the triple (x, y, z) ∈ N3 is a factorization of m in S if xa+ yb+ zN = m. This work is focused on finding the full set of factorizations of any m ∈ S and as an application we compute the catenary degree of S. To this end, we relate a 2D tessellation to S and we use it as a main tool.

The present paper is inspired by Sylvan and Plumwood’s logicBM defined in “Non-normal relevant logics” their treatmentof negation with the ∗-operator “The semantics of first-degree en-tailment”. Given a positive logic L including Routley Meyer’sbasic included either fragment Eor that RW, we investigate essential De Morgan ex-pansions determine all deductive relations they maintainto each other....

We propose to replace Zadeh's DeMorgan-type negation in fuzzy logic by a Heyting-type negation which, unlike the former, preserves the law of the excluded contradiction and is more in line with negation in databases and logic programs. We show that the resulting system can be used for obtaining conservative extensions of relational and deductive databases (resp. normal logic programs).

An ordered semigroup is a structure S = 〈S, ·,≤〉 with a binary operation · that is associative and a partial ordering ≤ that is compatible with the binary operation. For a given congruence relation θ of the semigroup S = 〈S, ·〉 the quotient structure S/θ = 〈S/θ, , 〉 is not in general an ordered semigroup. In this paper we study quotients of ordered semigroups. We first define a special type of ...

Let $S$ be a semitopological semigroup. The $wap-$ compactification of semigroup S, is a compact semitopological semigroup with certain universal properties relative to the original semigroup, and the $Lmc-$ compactification of semigroup $S$ is a universal semigroup compactification of $S$, which are denoted by $S^{wap}$ and $S^{Lmc}$ respectively. In this paper, an internal construction of ...

in the present paper we give a partially negative answer to a conjecture of ghahramani, runde and willis. we also discuss the derivation problem for both foundation semigroup algebras and clifford semigroup algebras. in particular, we prove that if s is a topological clifford semigroup for which es is finite, then h1(m(s),m(s))={0}.