Lattice congruences of the weak order

We study the congruence lattice of the poset of regions of a hyperplane arrangement, with particular emphasis on the weak order on a finite Coxeter group. Our starting point is a theorem from a previous paper which gives a geometric description of the poset of join-irreducibles of the congruence lattice of the poset of regions in terms of certain polyhedral decompositions of the hyperplanes. For a finite Coxeter system (W,S) and a subset K of S, let \eta_K:w \mapsto w_K be the projection onto the parabolic subgroup W_K. We show that the fibers of \eta_K constitute the smallest lattice congruence with 1\equiv s for every s\in(S-K). We give an algorithm for determining the congruence lattice of the weak order for any finite Coxeter group and for a finite Coxeter group of type A or B we define a directed graph on subsets or signed subsets such that the transitive closure of the directed graph is the poset of join-irreducibles of the congruence lattice of the weak order.Comment: 26 pages, 4 figure

Properties and Analysis of Thermally Aged Poly(ethylene oxide)

Recent studies have been performed into the use of polyethylene oxide (PEO) as a model system for observing the fundamental effects of adding micro and nano sized fillers to create polymeric composite systems. Many factors contribute to the successful creation of such a composite system, including dispersion of the filler and treatment of the material during creation. For example, while producing thin films of the materials for testing, high temperatures were used for short periods of time in open air to press the samples into small discs. It is well known that prolonged high temperature exposure can alter the chemistry and structure of polymeric materials and that small variations in the original chemistry, such as longer molecular weights or introduction of fillers, can reduce or possibly accelerate this 'ageing' effect. From these previous investigations many property changes were observed during addition of filler or variation of molecular weight, therefore to accurately attribute these changes to a cause the thermal ageing of the material should be observed. This investigation looks at the same 3 molecular weight PEO systems as those used in the previous investigations and analyses them for their vulnerability to thermal ageing. One thermally aged sample is then taken and tested alongside an unaged sample to observe the effects that the process has on the properties. This includes rheology in solution, differential scanning calorimetry (DSC), AC electrical breakdown, dielectric spectroscopy and Fourier transform infra-red (FTIR). By observing the property changes of aged samples it is possible to better understand the thermal ageing process occurring and possibly a way to reduce the effect, along with considering the effect with regard to the behaviour of the previously tested composite samples

Hip Versus Square: 1960s Advertising and Clothing Industries and the Counterculture

This research paper explores the use of Countercultural themes and images by the advertising and menswear industries in the 1960s. Historians have traditionally held that the Counterculture and American business during this era were fierce opponents of one another. More recent scholarship, however, suggest that the advertising industry of the 1960s co-opted and marketed Countercultural themes, such as ‘youth’ and ‘rebellion,’ and images like natural looking make-up and free-flowing clothing. The co-optation of these themes and images, historians have charged, commercialized the Countercultural revolution and ultimately led to its demise. This paper examines the ways in which the Counterculture influenced the advertising and menswear industries in the 1960s and questions whether the use of Countercultural themes and images was co-optation or emulation of the youth movement

Enumeration of bigrassmannian permutations below a permutation in Bruhat order

In theory of Coxeter groups, bigrassmannian elements are well known as elements which have precisely one left descent and precisely one right descent. In this article, we prove formulas on enumeration of bigrassmannian permutations weakly below a permutation in Bruhat order in the symmetric groups. For the proof, we use equivalent characterizations of bigrassmannian permutations by Lascoux-Schutzenberger and Reading.Comment: 7 pages

Socially inherited memory, gender and the public sphere in Poland

More recent theories of the 'revolutions' of 1989 in the societies of Eastern and Central Europe now suggest that the underlying dynamic was continuity rather than disjuncture in terms of social and political relations. Yet such theories fail to explain the nature of and the reasons for this continuity in terms of gender relations in the public sphere. The thesis suggests that the clue to understanding the nature of the gendered transformation in Poland's public sphere in its mediated aspects between the years 1980 and 1994 lies in the role of 'socially inherited memory'. Socially inherited memory is the dialectical and gendered process by which a given society both remembers and forgets past events, feelings, thoughts and knowledge through representations. The key to Poland's social memory concerns the repressed stories of political right developed during the nation's period of identity formation in the nineteenth century and interwar years. Certain aspects of this social inheritance were recalled by the Polish United Workers' Party and then by Solidarity to legitimize their power: Because Poland's social memory was formed around the public exclusion of women and Poland's ethnic minorities this resulted in the continuation of exclusionary mechanisms and public ghettoization after World War Two, and, in the 1980s and 1990s. However, the evidence of the thesis also suggests that there were sub-plots of women's resistance and inclusion within the public sphere from at least the nineteenth century onwards. Thus the exclusionary impact of socially inherited memory is not an inevitable historical process: At particular historical moments inclusive representations of women and ethnic minorities are recalled or reenacted in the form of Public organisations or alternative cultural productions. Socially inherited memory it is suggested may provide a useful concept for examining the (en)gendering of the public sphere in other societies