Cores and Compactness of Infinite Directed Graphs

AbstractIn this paper we define the property of homomorphic compactness for digraphs. We prove that if a digraphHis homomorphically compact thenHhas a core, although the converse does not hold. We also examine a weakened compactness condition and show that when this condition is assumed, compactness is equivalent to containing a core. We use this result to prove that if a digraphHof sizeκis not compact, then there is a digraphGof size at mostκ+such thatHis not compact with respect toG. We then give examples of some sufficient conditions for compactness

The development of cognitive skills in the preschool child

The study attempted to evaluate the levels of cognitive skills of kindergarten children attending day care, and the apparent growth of cognitive skills over a period of time, using published tests as instruments of measurement. An informal evaluation of the tests was made. The review of literature presented three points of view regarding approaches to the development of cognitive skills. An analysis of the data, using t-tests, was carried out and conclusions were stated. Implications of the study were made, and questions concerning the growth of cognitive skills of kindergarten children attending day care centres were raised.Education, Faculty ofGraduat

The photochemistry of cholesta -3, 5- diene and related systems. The chemical constituents of Trichophyton Schoenleinii and T. Violaceum.

Photochemistry is rapidly becoming one of the important fields of organic chemical research. Several recent reviews and books on the subject attest to this fact. Part of the reason for this interest is the potential value of photochemistry as a synthetic tool. For example, on a laboratory scale, many cis-trans isomerisations, valence isomerisations, skeletal rearrangements, and dimerisations have been accomplished. Many of the products of these reactions would be very difficult to obtain by nonphotochemical means. The most obvious examples of the success of photochemistry on a large scale are the irradiation of ergosterol to give vitamin D, and photosynthesis. [...

The concept of neutrality in classical Greece

Looking at Classical warfare from the perspective of the non-belligerents, Robert A. Bauslaugh brings together the scattered evidence testifying to neutral behavior among the Greek city-states and their non-Greek neighbors. Were the Argives of 480/479 B.C. really "Medizers," as many have accused, or were they pursuing a justifiable policy of neutrality as they claimed? On what basis in international law or custom did the Corcyraeans claim non-alignment? Why were the leading belligerent states willing to accept the inclusion of a "neutrality clause" in the Common Peace of 371? These questions have not been asked by historians of international law, and the answers provide a far more complex and sophisticated picture of interstate relations than has so far been available.Despite the absence of exclusively diplomatic language, the concept of respect for neutrals appears early in Greek history and remains a nearly constant feature of Classical wars. The problems confronting uncommitted states, which have clear parallels in modern history, were balanced by widespread acceptance of the need for limitations on the chaos of warfare

Generating Alternating Permutations Lexicographically

Abstract A permutation ss1ss2 \Delta \Delta \Delta ssn is alternating if ss1! ss2? ss3! ss4 \Delta \Delta \Delta. We present a constant average-time algorithm for generating all alternating permutations in lexicographic order. Ranking and unranking algorithms are also derived

Silver coinage with the types of Aesillas the Quaestor /

Includes bibliographical references and indexes.Mode of access: Internet