Atomic Latin squares of order eleven

A Latin square is pan-Hamiltonian if the permutation which defines row i relative to row j consists of a single cycle for every i j. A Latin square is atomic if all of its conjugates are pan-Hamiltonian. We give a complete enumeration of atomic squares for order 11, the smallest order for which there are examples distinct from the cyclic group. We find that there are seven main classes, including the three that were previously known. A perfect 1-factorization of a graph is a decomposition of that graph into matchings such that the union of any two matchings is a Hamiltonian cycle. Each pan-Hamiltonian Latin square of order n describes a perfect 1-factorization of Kn,n, and vice versa. Perfect 1-factorizations of Kn,n can be constructed from a perfect 1-factorization of Kn+1. Six of the seven main classes of atomic squares of order 11 can be obtained in this way. For each atomic square of order 11, we find the largest set of Mutually Orthogonal Latin Squares (MOLS) involving that square. We discuss algorithms for counting orthogonal mates, and discover the number of orthogonal mates possessed by the cyclic squares of orders up to 11 and by Parker's famous turn-square. We find that the number of atomic orthogonal mates possessed by a Latin square is not a main class invariant. We also define a new sort of Latin square, called a pairing square, which is mapped to its transpose by an involution acting on the symbols. We show that pairing squares are often orthogonal mates for symmetric Latin squares. Finally, we discover connections between our atomic squares and Franklin's diagonally cyclic self-orthogonal squares, and we correct a theorem of Longyear which uses tactical representations to identify self-orthogonal Latin squares in the same main class as a given Latin square.

James Parkinson (1755-1824): A pioneer of child care

James Parkinson (1755-1824) of Parkinson's disease, is well recognized as a pioneer of clinical neurology; and is even more famous as a founder of modem palaeontology. We have reviewed from primary sources his extensive contributions to clinical child care and his pioneering advocacy for child welfare, protection and safety. His writings, outreach and advocacy for children's health characterizes him as one whose influence was an important springboard from which evolved the modern specialty of paediatrics. Parkinson was one of the first to write on child-rearing practices and in this context antedated Benjamin Spock by 150 years. Parkinson was a pioneer of child safety and the prevention of childhood trauma. He wrote of the resuscitation of near-drowned children and of first aid for injured children. This critical analysis reviews his pioneering description of child abuse and the development of post-abuse hydrocephalus. He wrote the datum description (in English) of the pathophysiology and pathology of appendicitis in children, of fatal rabies in children and highlighted the risk of death even when the biting dog was not clinically rabid. His advocacy for social reform for children's welfare was courageous and pioneering. James Parkinson, hitherto unacknowledged, was a significant founder of the evolving discipline of paediatrics and child health.

A. W. Campbells Australian career: 1905-1937

The Australian Alfred Walter Campbell (1868-1937) is remembered as one of the two chief pioneers of the study of the cytoarchitectonics of the primate cerebral cortex. He had worked in Britain carrying out neuroanatomical and neuropathological research for almost two decades before his famous monograph on Histological Studies on the Localisation of Cerebral Function appeared in 1905. In that year he returned to his native Australia and practiced for over 30 years in Sydney as a neurologist rather than a neuropathologist, publishing mainly clinical material though he was involved in the investigation of the epidemic of Australian X disease, a viral encephalitis. His abrupt change in both the nature and the location of his career at a time when he was well established in Britain appears to have been a consequence of his marriage and the need to provide for a family. His simultaneous apparent abandonment of research seems not to have really been the case. As judged from the contents of a paper presented to a local medical congress in Sydney in 1911, it appears that, in Australia, Campbell did carry out a major comparative anatomical and histological investigation of the possibility of localization of function in the cerebellar cortex. He never published this work in detail. His investigation let him to conclude that no such localization of function existed, a view contrary to the then topical interpretation of Bolk (1906), but one in accordance with Gordon Holmes' views a decade later. Campbell's circumstances in Sydney, his extremely reticent nature and the essentially negative outcome of his investigation probably explain his failure to make his study more widely known.

Existence of a semicontinuous or continuous utility function: a unified approach and an elementary proof

In this paper, we present a new unified approach and an elementary proof of a very general theorem on the existence of a semicontinuous or continuous utility function representing a preference relation. A simple and interesting new proof of the famous Debreu Gap Lemma is given. In addition, we prove a new Gap Lemma for the rational numbers and derive some consequences. We also prove a theorem which characterizes the existence of upper semicontinuous utility functions on a preordered topological space which need not be second countable. This is a generalization of the classical theorem of Rader which only gives sufficient conditions for the existence of an upper semicontinuous utility function for second countable topological spaces. (C) 2002 Elsevier Science B.V. All rights reserved.

The influence of role models on strudents' entrepreneurial intentions

The Smart State initiative requires both improved education and training, panicularly in technical fields, plus entrepreneurship to commercialise new ideas. In this study, we propose an entrepreneurial intentions model as a guide to examine the educational choices and entrepreneurial intentions of first-year University students, focusing on the effect of role models. A survey of over 1000 first-year University students revealed that the most enterprising students were choosing to study in the disciplines of information technology and business, economics and law, or selecting dual degree programs that include business. The role models most often identified for their choice of field of study were parents, followed by teachers and peers, with females identifying more role models than males. For entrepreneurship, students' role models were parents and peers, followed by famous persons and teachers. Males andfemales identified similar numbers of role models, but malesfound starting a business more desirable and more feasible, and reponed higher entrepreneurial intention. The implications of these findings for Sman State policy are discussed.

A reduced load approximation accounting for link interactions in a loss network

This paper is concerned with evaluating the performance of loss networks. Accurate determination of loss network performance can assist in the design and dimen- sioning of telecommunications networks. However, exact determination can be difficult and generally cannot be done in reasonable time. For these reasons there is much interest in developing fast and accurate approximations. We develop a reduced load approximation that improves on the famous Erlang fixed point approximation (EFPA) in a variety of circumstances. We illustrate our results with reference to a range of networks for which the EFPA may be expected to perform badly.

Application of ICP-MS trace element analysis in study of ancient Chinese ceramics

Thirty-nine trace elements of the Song-Yuan period (960-1368 AD) porcelain bodies from Cizhou, Jizhou and Longquanwu kilns were analyzed with ICP-MS, a technique rarely used in Chinese archaeometry, to investigate its potential application in such studies. Trace element compositions clearly reflect the distinctive raw materials and their mineralogy at the three kilns and allow their products to be distinguished. Significant chemical variations are also observed between Yuan and Song-Jing dynasties samples from Cizhou as well as fine and coarse porcelain bodies from Longquanwu. In Cizhou, porcelains of better quality which imitate the famous Ding kiln have trace element features distinctive from ordinary Cizhou products, that indicates geochemically distinctive raw materials were used and which possibly also underwent extra refining prior to use. The distinct trace element features of different kilns and the various types of porcelains from an individual kiln can be interpreted from a geochemical perspective. ICP-MS can provide a large amount of valuable information about ancient Chinese ceramics as it is capable of analyzing >40 elements with a typical of precision < 2%.

The natural jurisprudence of Jean Barbeyrac: translation as an art of political adjustment

The article makes the case for redescribing Jean Barbeyrac [1674-1744], the great French translator and influential glossator of seventeenth-century Latin natural-law texts, as something quite other than a neutral mediator of Samuel Pufendorf. To consider the specific religious and political charge of his strategies as translator is to recognize the independence of Barbeyrac's Huguenot stance on natura; jurisprudence. This stance is provoked by the profound challenge that Pufendorf's radical post-Wespthalian secularizing of civil authority posed for a Huguenot: how to grant that the state had legitimate authority to regulate all external conduct, but at the same time preserve an inviolable moral space for the exercise of individual conscience. The argument--pointing to Barbeyrac's construction of a 'Lockeanized' Pufendorf--rests both on his famous presentation of Leibniz's critique of Pufendorf's De officio hominis et civis and on more neglected elements of Barbeyrac's corpus.

Uniqueness criteria for continuous-time Markov chains with general transition structures

We derive necessary and sufficient conditions for the existence of bounded or summable solutions to systems of linear equations associated with Markov chains. This substantially extends a famous result of G. E. H. Reuter, which provides a convenient means of checking various uniqueness criteria for birth-death processes. Our result allows chains with much more general transition structures to be accommodated. One application is to give a new proof of an important result of M. F. Chen concerning upwardly skip-free processes. We then use our generalization of Reuter's lemma to prove new results for downwardly skip-free chains, such as the Markov branching process and several of its many generalizations. This permits us to establish uniqueness criteria for several models, including the general birth, death, and catastrophe process, extended branching processes, and asymptotic birth-death processes, the latter being neither upwardly skip-free nor downwardly skip-free.

Delivering demons punishing wives: False imprisonment, exoricism and other matrimonial duties in a late 20th-century manslaughter case

This article provides an analysis of R v Vollmer and Others, Australia’s most famous ‘exorcism-manslaughter’ case, in which a woman, Joan Vollmer, underwent an ‘exorcism’ performed by four people, resulting in her death. We examine how taken-for-granted distinctions were collapsed during the resulting trial - distinctions between crime and punishment, exorcism and punishment, church and state, the past and the present, law and religion, reason and unreason and between a demon and a woman. We show how the defence argument for the reality of demonic possession normalized the bizarre, while simultaneously exoticizing the mundane or ‘traditional’ criminal case involving a husband defendant and a dead wife. The apparent assumption on the part of the police and the media that this case was bizarre serves to veil the fact of its relative ordinariness. A wife is killed, and the lethal punishing violence inflicted on her body downplayed, to be reinterpreted in the legal context as somehow a consequence of something she herself precipitated. Our analysis of the Vollmer case provides a novel perspective on that always intriguing conundrum of crime and punishment.

Yield functions for porous materials with cubic symmetry using different definitions of yield

Plastic yield criteria for porous ductile materials are explored numerically using the finite-element technique. The cases of spherical voids arranged in simple cubic, body-centred cubic and face-centred cubic arrays are investigated with void volume fractions ranging from 2 % through to the percolation limit (over 90 %). Arbitrary triaxial macroscopic stress states and two definitions of yield are explored. The numerical data demonstrates that the yield criteria depend linearly on the determinant of the macroscopic stress tensor for the case of simple-cubic and body-centred cubic arrays - in contrast to the famous Gurson-Tvergaard-Needleman (GTN) formula - while there is no such dependence for face-centred cubic arrays within the accuracy of the finite-element discretisation. The data are well fit by a simple extension of the GTN formula which is valid for all void volume fractions, with yield-function convexity constraining the form of the extension in terms of parameters in the original formula. Simple cubic structures are more resistant to shear, while body-centred and face-centred structures are more resistant to hydrostatic pressure. The two yield surfaces corresponding to the two definitions of yield are not related by a simple scaling.

A reduced load approximation accounting for link interactions in a loss network

This paper is concerned with evaluating the performance of loss networks. Accurate determination of loss network performance can assist in the design and dimensioning of telecommunications networks. However, exact determination can be difficult and generally cannot be done in reasonable time. For these reasons there is much interest in developing fast and accurate approximations. We develop a reduced load approximation which improves on the famous Erlang fixed point approximation (EFPA) in a variety of circumstances. We illustrate our results with reference to a range of networks for which the EFPA may be expected to perform badly.