K e y w o r d s N o n l i n e a r programming, Exact penalty function, Objective penalty function. 1. I N T R O D U C T I O N The problem we consider in this paper is as follows: f0(x), s.t. k ( a ) < 0, i E I = { 1 , 2 , . . . , m } , (P) The authors would like to thank anonymous referees' comments and remarks that help us to improve the presentation of this paper considerably. This research w...

It is a well-known fact that for every k-safe Petri net, i.e. a Petri net in which no place contains more than k 2 N tokens under any reachable marking, there is a 1-safe Petri net with the same interleaving behaviour. Indeed these types of Petri nets generate regular languages. In this paper, we show that this equivalence of k-safe and 1-safe Petri nets holds also for their pomset languages, a...

In this paper we prove that each element of any regular Baer ring is a sum of two units if no factor ring of R is isomorphic to Z_2 and we characterize regular Baer rings with unit sum numbers $omega$ and $infty$. Then as an application, we discuss the unit sum number of some classes of group rings.

The aim of this paper is to study semigroups possessing $E$-regular elements, where an element $a$ of a semigroup $S$ is {em $E$-regular} if $a$ has an inverse $a^circ$ such that $aa^circ,a^circ a$ lie in $ Esubseteq E(S)$. Where $S$ possesses `enough' (in a precisely defined way) $E$-regular elements, analogues of Green's lemmas and even of Green's theorem hold, where Green's relations ${mathc...

The tight upper bound on the state complexity of the reverse of R-trivial and J -trivial regular languages of the state complexity n is 2n−1. The witness is ternary for R-trivial regular languages and (n− 1)ary for J -trivial regular languages. In this paper, we prove that the bound can be met neither by a binary R-trivial regular language nor by a J -trivial regular language over an (n − 2)-el...

The tight upper bound on the state complexity of the reverse of R-trivial and J -trivial regular languages of the state complexity n is 2n−1. The witness is ternary for R-trivial regular languages and (n− 1)ary for J -trivial regular languages. In this paper, we prove that the bound can be met neither by a binary R-trivial regular language nor by a J -trivial regular language over an (n − 2)-el...

We propose an algebraic model called concurrent regular expressions for modeling and analysis of distributed systems. These expressions extend regular expressions with four operators-interleaving, interleaving closure, synchronous composition and renaming. Their expressive power is equivalent to those of Petri nets, and therefore they are more general than Path expressions and COSY expressions.

Let R be a commutative ring and Max (R) be the set of maximal ideals of R. The regular digraph of ideals of R, denoted by −−→ Γreg(R), is a digraph whose vertex set is the set of all non-trivial ideals of R and for every two distinct vertices I and J , there is an arc from I to J whenever I contains a J-regular element. The undirected regular (simple) graph of ideals of R, denoted by Γreg(R), h...

This paper establishes two new connections between the familiar function ring functor ${mathfrak R}$ on the category ${bf CRFrm}$ of completely regular frames and the category {bf CR}${mathbf sigma}${bf Frm} of completely regular $sigma$-frames as well as their counterparts for the analogous functor ${mathfrak Z}$ on the category {bf ODFrm} of 0-dimensional frames, given by the integer-valued f...

A ring R is defined to be semiabelian if every idempotent of R is either right semicentral or left semicentral. It is proved that the set N(R) of nilpotent elements in a π-regular ring R is an ideal of R if and only if R/J(R) is abelian, where J(R) is the Jacobson radical of R. It follows that a semiabelian ring R is π-regular if and only if N(R) is an ideal of R and R/N(R) is regular, which ex...