Character (mathematics)

About: Character (mathematics) is a research topic. Over the lifetime, 46723 publications have been published within this topic receiving 411412 citations.

Bora-aromatic systems. Part 8. The physical and chemical consequences of cyclic conjugation in boracyclopolyenes. The antiaromatic character of pentaarylboroles.

Abstract: Pentasubstituted boroles or boracyclopentadienes have been prepared by two routes: (1) the interaction of an (E&)-( 1,2,3,4-tetraaryl-1,3-butadien-l,4-ylidene)dilithium in ether solution with an aryl(diha1o)borane to form the borole etherate; and (2) the exchange reaction between a 1,1-dialky1-2,3,4,5-tetraarylstannole in nondonor media to produce the unsolvated borole. The boroles are unexpectedly strong Lewis acids, complexing with amines and even ethers and nitriles, and very prone to oxidation, solvolytic cleavage, and Diels-Alder reactions. The foregoing chemical behavior, taken together with their unusual nuclear magnetic and electronic spectral properties, can be straightforwardly interpreted in terms of the Hiickel antiaromatic character of the 4-*-electron boracyclopentadiene nucleus. By treating such nuclei as perturbed cyclopentadienyl 7r-systems, a qualitative understanding of both the spectral and chemical properties can be attained. From such considerations, it is evident that the conjugation between the tricoordinate boron's 2p,-orbital and the four-carbon butadienylidene array is destabilizing and is the source of the high reactivity of boroles. An $-hybridized boron atom might be expected to form cyclic conjugated systems with arrays of sp2-hybridized carbons, because both the covalent radius (0.80 A) and the Allred-Rochow electronegativity (2.01) of boron are similar to those of carbon (0.77 A and 2.51).4 In such conjugated rings the boron center might exert a stabilizing influence if the total number of x electrons would conform to the Hiickel 4n + 2 criterion for a r o m a t i ~ i t y . ~ ~ In fact, heterocyclic organoboranes bearing the isoelectronic J3=N unit in place of one or more C=C linkages of a benzenoid ring have been shown to possess chemical and physical properties similar to classic aromatic compounds.5b Boracyclopolyenes not possessing the appropriate number of ?r electrons might be destabilized by conjugation and accordingly display unusual reactivity or antiaromaticityS6 An example of the destabilization of a carbocyclic ring by such antiaromaticity is the instability of the pentaphenylcyclopentadienyl cation (1). This deep-blue ion is highly reactive and has a thermally populated triplet (compound 2). This behavior indicates that the gain in conjugated stabilization attained by placing the four A electrons as pairs in bonding molecular orbitals is not large.

Bullying and social identity: The effects of group norms and distinctiveness threat on attitudes towards bullying

Abstract: Drawing from social identity theory (Tajfel & Turner, 1979), an experiment was carried out to determine the extent to which children's attitudes towards bullying could be moderated by in-group norms and perceived threat to group distinctiveness. The study investigated the responses of 120 male primary school students aged 10-13 years from five schools. The children read a story about a popular in-group and an unpopular out-group which involved the manipulation of three variables: the norms of the in-group (bullying vs. fairness); distinctiveness threat (out-group similarity vs. out-group difference); and the behaviour of the in-group character towards the out-group character (bullying vs. helpful). It was predicted that a perceived threat to group distinctiveness, represented by similarity between the in-group and the out-group, and salient group norms that prescribed either bullying or fairness, would moderate the acceptability of bullying behaviours. Two story response measures were analysed: in-group character liking and whether the in-group character would be retained as a group member following his behaviour. The strongest support for social identity theory was revealed in the retention of in-group character variable. The in-group character was much more likely to have been retained as a group member when he behaved in accordance with group norms. Evidence was also found that bullying was more acceptable when directed at an out-group member who was similar and therefore possibly represented a threat to the in-group.

Character formulas for tilting modules over Kac-Moody algebras

Abstract: We show how to express the characters of tilting modules in a (possibly parabolic) category O over a Kac-Moody algebra in terms of the characters of simple highest weight modules. This settles, in lots of cases, Conjecture 7.2 of Kazhdan-Lusztig-Polynome and eine Kombinatorik für Kipp-Moduln, Representation Theory (An electronic Journal of the AMS) (1997), by the author, describing the character of tilting modules for quantum groups at roots

Character and Academics: What Good Schools Do:

Abstract: Despite the clear national interest in character education, many schools are leery of engaging in supplementary initiatives that, although worthy, might detract from what they see as their primary focus: increasing academic achievement. Moreover, many schools lack the resources to create new curricular initiatives. Yet the enhancement of student character is a bipartisan mandate that derives from the very Character and Academics: What Good Schools Do

The Character of Physical Law

Abstract: The Messenger Lectures at Cornell University were instituted in 1924 by Hiram J. Messenger ‘to provide a course or courses of lectures on the evolution of civilization for the special purpose of raising the moral standard of our political, business and social life’. In November 1964, Feynman gave seven lectures, extempore with the help of brief notes, on ‘The Character of Physical Law’. The transcripts were prepared and published by BBC in 1965.