scholarly journals Geometric Realization of Some Triangle-Free Combinatorial Configurations

ISRN Geometry ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Branko Grünbaum

The main purpose of this paper is to illustrate the mutual benefit to combinatorics and geometry by considering a topic from both sides. Al-Azemi and Betten enumerate the distinct combinatorial (223) configurations that are triangle free. They find a very large number of such configurations, but when taking into account the automorphism group of each, they find two cases in which there is only a single configuration. On the heuristic assumption that an object that is unique in some sense may well have other interesting properties, the geometric counterparts of these configurations were studied. Several unexpected results and problems were encountered. One is that the combinatorially unique (223) configuration with automorphisms group of order 22 has three distinct geometric realizations by astral configurations.

2020 ◽  
Vol 76 (3) ◽  
pp. 358-368
Author(s):  
Jonn Angel L. Aranas ◽  
Mark L. Loyola

A geometric realization of an abstract polyhedron {\cal P} is a mapping that sends an i-face to an open set of dimension i. This work adapts a method based on Wythoff construction to generate a full rank realization of an abstract regular polyhedron from its automorphism group Γ. The method entails finding a real orthogonal representation of Γ of degree 3 and applying its image to suitably chosen (not necessarily connected) open sets in space. To demonstrate the use of the method, it is applied to the abstract polyhedra whose automorphism groups are isomorphic to the non-crystallographic Coxeter group H 3.


1990 ◽  
Vol 78 (1) ◽  
pp. 1-1
Author(s):  
M. J. Brown

From this issue, Clinical Science will increase its page numbers from an average of 112 to 128 per monthly issue. This welcome change — equivalent to at least two manuscripts — has been ‘forced’ on us by the increasing pressure on space; this has led to an undesirable increase in the delay between acceptance and publication, and to a fall in the proportion of submitted manuscripts we have been able to accept. The change in page numbers will instead permit us now to return to our exceptionally short interval between acceptance and publication of 3–4 months; and at the same time we shall be able not only to accept (as now) those papers requiring little or no revision, but also to offer hope to some of those papers which have raised our interest but come to grief in review because of a major but remediable problem. Our view, doubtless unoriginal, has been that the review process, which is unusually thorough for Clinical Science, involving a specialist editor and two external referees, is most constructive when it helps the evolution of a good paper from an interesting piece of research. Traditionally, the papers in Clinical Science have represented some areas of research more than others. However, this has reflected entirely the pattern of papers submitted to us, rather than any selective interest of the Editorial Board, which numbers up to 35 scientists covering most areas of medical research. Arguably, after the explosion during the last decade of specialist journals, the general journal can look forward to a renaissance in the 1990s, as scientists in apparently different specialities discover that they are interested in the same substances, asking similar questions and developing techniques of mutual benefit to answer these questions. This situation arises from the trend, even among clinical scientists, to recognize the power of research based at the cellular and molecular level to achieve real progress, and at this level the concept of organ-based specialism breaks down. It is perhaps ironic that this journal, for a short while at the end of the 1970s, adopted — and then discarded — the name of Clinical Science and Molecular Medicine, since this title perfectly represents the direction in which clinical science, and therefore Clinical Science, is now progressing.


1986 ◽  
Vol 31 (5) ◽  
pp. 339-340
Author(s):  
Brenda Major

2018 ◽  
Vol 12 (2) ◽  
pp. 313-328
Author(s):  
Fathul Aminudin Aziz

Fines are sanctions or punishments that are applied in the form of the obligation to pay a sum of money imposed on the denial of a number of agreements previously agreed upon. There is debate over the status of fines in Islamic law. Some argue that fines may not be used, and some argue that they may be used. In the context of fines for delays in payment of taxes, in fiqh law it can be analogous to ta'zir bi al-tamlīk (punishment for ownership). This can be justified if the tax obligations have met the requirements. Whereas according to Islamic teachings, fines can be categorized as acts in order to obey government orders as taught in the hadith, and in order to contribute to the realization of mutual benefit in the life of the state. As for the amount of the fine, the government cannot arbitrarily determine fines that are too large to burden the people. Penalties are applied as a message of reprimand and as a means to cover the lack of the state budget.


Author(s):  
Robert Sugden

Chapter 8 asks what properties a market economy must have if it is to be psychologically stable—that is, if it is to reproduce a general belief that its governing principles are fair. I argue that, because of the division of knowledge and because the opportunities open to each person depend on how other people choose to use their opportunities, full equality of opportunity is not compatible with a market economy. Psychological stability has to rest on continuing expectations of mutual benefit, defined relative to a baseline that evolves over time and that cannot be justified in terms of abstract principles of fairness. However, if the market is to be recommended to each individual separately, each individual must be able to expect to share in the benefits that markets create. Maintaining such expectations typically requires redistributive mechanisms.


1998 ◽  
Vol 43 (2) ◽  
pp. 57-58 ◽  
Author(s):  
A.J. Trevett ◽  
J.R. Martin ◽  
W.A. Ross ◽  
E. Macfarlane

Improving access to medical advice by telephone may reduce unnecessary consultations, limit interruptions through the day and provide a more flexible service to meet patient needs. We advertised and introduced a daily advice line for patients and found that it was used appropriately and to mutual benefit.


2019 ◽  
Vol 31 (1) ◽  
pp. 265-273
Author(s):  
Fabio Podestà ◽  
Alberto Raffero

Abstract We prove that the automorphism group of a compact 6-manifold M endowed with a symplectic half-flat {\mathrm{SU}(3)} -structure has Abelian Lie algebra with dimension bounded by {\min\{5,b_{1}(M)\}} . Moreover, we study the properties of the automorphism group action and we discuss relevant examples. In particular, we provide new complete examples on {T\mathbb{S}^{3}} which are invariant under a cohomogeneity one action of {\mathrm{SO}(4)} .


Author(s):  
HUA HAN ◽  
HONG CI LIAO ◽  
ZAI PING LU
Keyword(s):  

Abstract A graph is edge-primitive if its automorphism group acts primitively on the edge set, and $2$ -arc-transitive if its automorphism group acts transitively on the set of $2$ -arcs. In this paper, we present a classification for those edge-primitive graphs that are $2$ -arc-transitive and have soluble edge-stabilizers.


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