Optimality Theory (OT) has a growing importance in various disciplines of linguistics. The way in which correct linguistic expressions are generated according to OT can be captured formally in an Optimality System (OS). An OS de nes a relation between an input and an output using a binary relation, called gen, on the domain, and a set of constraints. Frank and Satta ([1]) have shown that an OS ...

We call a vector x 2 IR n highly regular if it satisses < x ; m > = 0 for some short, non{zero integer vector m where < : ; : > is the inner product. We present an algorithm which given x 2 IR n and 2 IN nds a highly regular nearby point x 0 and a short integer relation m for x 0 : The nearby point x 0 is 'good' in the sense that no short relation m of length less than =2 exists for points x wi...

R is called commuting regular ring (resp. semigroup) if for each x,y $in$ R there exists a $in$ R such that xy = yxayx. In this paper, we introduce the concept of commuting $pi$-regular rings (resp. semigroups) and study various properties of them.

We investigate some basic questions about the interaction of regular and rational relations on words. The primary motivation comes from the study of logics for querying graph topology, which have recently found numerous applications. Such logics use conditions on paths expressed by regular languages and relations, but they often need to be extended by rational relations such as subword or subse...

We deal with the new class of pre-ℐ-regular pre-ℐ-open sets in which the notion of pre-ℐ-open set is involved. We characterize these sets and study some of their fundamental properties. We also present other notions called extremally pre-ℐ-disconnectedness, locally pre-ℐ-indiscreetness, and pre-ℐ-regular sets by utilizing the notion of pre-ℐ-open and pre-ℐ-closed sets by which we obtain some eq...

The Regular Post Embedding Problem is a variant of Post’s Correspondence Problem where one compares strings with the subword relation and imposes additional regular constraints on admissible solutions. It is known that this problem is decidable, albeit with very high complexity. We consider and solve variant problems where the set of solutions is compared to regular constraint sets and where on...

We examine the existential fragment of a feature logic, which is extended by regular path expressions. A regular path expression is a subterm relation, where the allowed paths for the subterms are restricted to any given regular language. In the area of computational linguistics, this notion has been introduced as \functional uncertainty". We will prove that satissability is decidable by constr...

A general relation for the total angular momentum of a regular solution of the Einstein-Yang-Mills-Higgs equations is derived. Two different physical configurations, rotating dyons and rotating magnetic dipoles are discussed as particular cases. The issue of rotating pure Einstein-Yang-Mills regular solutions is addressed as well. Based on the results, we conjecture the absence of rotating regu...

E. R. van Dam gave an example of primitive non-amorphous association schemes in which every nontrivial relation is a strongly regular graph, as a fusion scheme of the cyclotomic scheme of class 45 on GF(212). The aim of this paper is to present a new example of primitive non-amorphous association schemes in which every nontrivial relation is a strongly regular graph, as a fusion scheme of the c...