The dimension of orthomodular posets constructed by pasting Boolean algebras

The main aim of this paper is the calculation of the dimension of certain atomic amalgams. These consist of finite Boolean algebras (blocks) pasted together in such a way that a pair of blocks intersects either trivially in the bounds, or the intersection consists of the bounds, an atom, and its complement.     

Hybrid genetic algorithms with selective crossover for the capacitated p-median problem

Central European Journal of Operations Research - The paper suggests two ways of combining a genetic algorithm with integer programming to improve the quality of the problem solution. The...     

Piggyback dualities revisited

In natural duality theory, the piggybacking technique is a valuable tool for constructing dualities. As originally devised by Davey and Werner, and extended by Davey and Priestley, it can be applied to finitely generated quasivarieties of algebras having term-reducts in a quasivariety for which a well-behaved natural duality is already available. This paper presents a comprehensive study of the method in a much wider setting: piggyback duality theorems are obtained for suitable prevarieties of structures. For the first time, and within this extended framework, piggybacking is used to derive theorems giving criteria for establishing strong dualities and two-forone dualities. The general theorems specialise in particular to the familiar situation in which we piggyback on Priestley duality for distributive lattices or Hofmann–Mislove– Stralka duality for semilattices, and many well-known dualities are thereby subsumed. A selection of new dualities is also presented.     

Full dualisability is independent of the generating algebra

Given a full duality based on a finite algebra M, we show how to create a full duality based on any other finite algebra N for which \mathbbISP(M) = \mathbbISP(N){\mathbb{ISP}({\bf M}) = \mathbb{ISP}({\bf N})}. So the full dualisability of a quasivariety is independent of the algebra chosen as the generator. We obtain this result by proving the corresponding result for multisorted full dualities.     

Multisorted dualisability: change of base

We prove that if a quasivariety A{mathcal{A}} generated by a finite family M{mathcal{M}} of finite algebras has a multisorted duality based on M{mathcal{M}}, then A{mathcal{A}} has a multisorted duality based on any finite family of finite algebras that generates it.     

A criterion for a finite endoprimal algebra to be endodualisable

In this note the strategy for finding endoprimal algebras due to B. A. Davey and J. G. Pitkethly is further explored in the finite case. The Retraction Test Algebra Lemma is used as a tool to show that, in many quasivarieties, endoprimality is equivalent to endodualisability for finite algebras which are suitably related to finitely generated free algebras. Received September 2, 1998; accepted in final form June 3, 1999.     

9,9′-Thiobis-(1,2,3,4,7,8-hexahydro-7-methyl-6H-pyrimido[1,6-a]pyrimidine-6,8-dione)

The 6-(3-hydroxypropylamino)-3-methylpyrimidine-2,4-dione (1) did not afford the expected 6-(3-chloro-propylamino)- derivative on reaction with thionyl chloride, but, instead, the pyrimidine rings were joined via a sulfur bridge to give 9,9′-thiobis(1,2,3,4,7,8-hexahydro-7-melnyl-6H-pyrimido[1,6-a]pyrirnidine-6,8-dione) ( 3 ). An identical 9,9′-thiobis- derivative 3 was obtained when reacting thionyl chloride with 1,2,3,4,7,8-hexahydro-7-methyl-6H-pyrimido[1,6-a]pyrimidine-6,8-dione ( 4 ). We suppose the sulfoxide- derivative 2 to be the intermediate of both routes: it underwent reduction to the final sulfide 3 in excess thionyl chloride.