The paper discusses regularisation of dualities. A given duality between (concrete) categories, e.g. a variety of algebras and a category of representation spaces, is lifted to a duality between the respective categories of semilattice representations in the category of algebras and the category of spaces. In particular, this gives duality for the regularisation of an irregular variety that has a duality. If the type of the variety includes constants, then the regularisation depends critically on the location or absence of constants (...) within the defining identities. The role of schizophrenic objects is discussed, and a number of applications are given. Among these applications are different forms of regularisation of Priestley, Stone and Pontryagin dualities. (shrink)

A Priestley duality is developed for the variety j of all modal lattices. This is achieved by restricting to j a known Priestley duality for the variety of all bounded distributive lattices with a meet-homomorphism. The variety j was first studied by R. Beazer in 1986.The dual spaces of free modal lattices are constructed, paralleling P.R. Halmos'' construction of the dual spaces of free monadic Boolean algebras and its generalization, by R. Cignoli, to distributive lattices with a quantifier.

A Priestley duality is developed for the variety jω of all modal lattices. This is achieved by restricting to jω a known Priestley duality for the variety of all bounded distributive lattices with a meet-homomorphism. The variety jω was first studied by R. Beazer in 1986.The dual spaces of free modal lattices are constructed, paralleling P.R. Halmos' construction of the dual spaces of free monadic Boolean algebras and its generalization, by R. Cignoli, to distributive lattices with a quantifier.

This study investigates specific behavioral perceptual differences of ethics between practitioners and students enrolled in sales classes. Respondents were asked to indicate their beliefs to issues related to ethics in sales. A highly significant difference was found between mean responses of students and sales personnel. Managers indicated a greater concern for ethical behavior and less attention to sales than did the students. Students indicated a strong desire for success regardless of ethical constraints violated.

Practitioners in the vanguard of new economic thinking will also find plenty of useful information in this path-breaking book.

Biologists have as yet taken but little cognizance of the revolution in human thought which has been inaugurated by physicists in the last five years, and philosophers have stressed its negative rather than its positive side.

Woodger's substitution of the "allegedly more precise term 'an environmentally insensitive set of lives'" for the term 'an inborn character' is discussed by haldane. He proposes that "woodger's definitions do not appear to have reached precision." (staff).

Although the existence of tachyons is not ruled out by special relativity, it appears that causal paradoxes will arise if there are tachyons. The usual solutions to these paradoxes employ some form of the reinterpretation principle. In this paper it is argued first that the principle is incoherent, second that even if it is not, some causal paradoxes remain, and third, the most plausible “solution,” which appeals to boundary conditions of the universe, will conflict with special relativity.

Virgil, in his description of the establishment of a new city by Aeneas for those Trojans who wished to remain in Sicily, is thinking of the Roman practice of colonial foundation: ‘Meanwhile Aeneas marked out the city with the plough and allocated the houses ’. We may note the personal role of the founder, the ploughing of the ritual first furrow, the organized grants to the settlers and the equality of treatment implied in the use of lot . Virgil was (...) writing at the end of the first century B.C. at a time of great activity in land distribution, but the Romans had been founding colonies from the mid fourth century. Each colony involved the creation of an urban area and the settlement of people on the surrounding agricultural land, and so perpetuated the city state, which was central to ancient life and culture. Indeed a colony was a smaller image of Rome itself. In the early Republic, colonies, either of Latins or of Roman citizens, were established on the periphery of Roman territory, largely for military and strategic reasons. Between 200 and 173 B.C. more than 40,000 may have received plots of land, amounting to about 1,000 square miles of territory. Later, the motives for colonial foundations became more complex, being closely connected with increasing economic and political problems. There can have been few more important aspects in the development of colonies than the need to find land for discharged troops. These in the main were rank and file soldiers who would expect equal shares in land allocations. (shrink)