Balázs Imreh

Process network synthesis: Problem definition

Analyses of network problems have yielded mathematically and practically significant results. Naturally, it should be of substantial interest to extend such results to a general class of network problems where the structure of any system can be represented by a directed bipartite graph containing two types of vertices; the model for one of them is nonlinear. This class of problems is frequently encountered in the design of process systems for carrying out transformation of chemical or material species through physical, chemical, or biological means. General-purpose mathematical programming methods have failed so far to solve large-scale network problems involved in the design of such systems. This paper is intended to define this class of network problems, i.e., the problems of process network synthesis, and to elucidate the unique features of these problems.

Traps, Cores, Extensions and Subdirect Decompositions of Unary Algebras

Subdirect decompositions of unary algebras are studied in connection with one-element subalgebras, cores, Rees extensions of congruences of subalgebras, dense extensions and disjunctive elements. In particular, subdirectly irreducible unary algebras are described in terms of these notions.

On Some Special Classes of Regular Languages

In [5], the directable non deterministic automata are studied. For non-deterministic automata, the directability can be defined in several ways. In each case considered, the directing words constitute a regular language and one can study the families of such regular languages. In this paper, six classes of regular languages are defined in accordance with the different definitions of directability given in [5], and we investigate the properties of the classes considered.

Finite isomorphically complete systems

Abstract In the theory of finite automata it is an important problem to characterize such systems of automata from which any automaton can be built under a given composition and representation. Such systems are called complete with respect to the fixed composition and representation. From practical point of view, it is useful to determine those compositions and representations for which there are finite complete systems. In this paper we show that the existence of finite complete systems implies the unboundedness of the feedback dependency of the composition.

On Product Hierarchies of Automata

We have seen that, with respect to homomorphic realization, the ν i —products behave in a way similar to the α i —products on classes satisfying the Leticevskii criterion or not satisfying the Leticevskii criteria. In particular, a class K is homomorphically ν3—complete if and only if it satisfies the Leticevskii criterion. As opposed to the α i —products, the ν i —hierarchy is proper on classes with the semi-Leticevskii criterion. This holds also for homomorphic realization.