scholarly journals Gorenstein rings through face rings of manifolds

2009 ◽  
Vol 145 (4) ◽  
pp. 993-1000 ◽  
Author(s):  
Isabella Novik ◽  
Ed Swartz

AbstractThe face ring of a homology manifold (without boundary) modulo a generic system of parameters is studied. Its socle is computed and it is verified that a particular quotient of this ring is Gorenstein. This fact is used to prove that the algebraic g-conjecture for spheres implies all enumerative consequences of its far-reaching generalization (due to Kalai) to manifolds. A special case of Kalai’s conjecture is established for homology manifolds that have a codimension-two face whose link contains many vertices.

2020 ◽  
Author(s):  
Peter Schulz ◽  
Elin Andersson ◽  
Nicole Bizzotto ◽  
Margareta Norberg

BACKGROUND The foray of Covid-19 around the globe is sure to have instigated worries in many humans, and lockdown measures may well have created their own worries. Sweden, in contrast to most other countries, had first relied on voluntary measures, but had to change its policy in the face of an increasing number of infections. OBJECTIVE The aim was to better understand the worried reactions to the virus and the lockdown measures. To grasp the reactions, their development over time was studied. METHODS Results were based on an unbalanced panel sample of 261 Swedish participants filling in 3218 interview questionnaires by smartphone in a 7-week period in 2020. Causal factors considered in this study include the perceived severity of an infection, the susceptibility of a person to the threat posed by the virus, the perceived efficacy of safeguarding measures and the assessment of government action against the spread of Covid-19. The effect of these factors on worries was traced in two analytical steps: the effects at the beginning of the study, and the effect on the trend during the study. RESULTS Findings confirmed that the hypothesized causal factors (severity of infection, susceptibility to the threat of the virus, efficacy of safeguarding and the assessment of government preventive action did indeed affect worries. CONCLUSIONS The results confirmed earlier research in a very special case and demonstrated the usefulness of a different study design, which takes a longitudinal perspective, and a new type of data analysis borrowed from multi-level study design.


2009 ◽  
Vol 16 (04) ◽  
pp. 653-660
Author(s):  
Kazem Khashyarmanesh

Given a commutative Noetherian local ring (R, 𝔪), it is shown that R is Gorenstein if and only if there exists a system of parameters x1,…,xd of R which generates an irreducible ideal and [Formula: see text] for all t > 0. Let n be an arbitrary non-negative integer. It is also shown that for an arbitrary ideal 𝔞 of a commutative Noetherian (not necessarily local) ring R and a finitely generated R-module M, [Formula: see text] is finitely generated if and only if there exists an 𝔞-filter regular sequence x1,…,xn∈ 𝔞 such that [Formula: see text] for all t > 0.


Author(s):  
Uwe Backes

This chapter analyzes and compares political developments in Germany, Austria, and Switzerland. It highlights the common ground between groups on the right-wing fringe of each country’s party system. To an extent the differences between the way right-wing groups developed in each of these countries is due to the different histories of the respective states. Recently however, they have moved closer to each other in the face of very similar problems. To a degree Switzerland is a special case because of its multilingual cantons and the early development of a pluralist civic culture that sustains an extraordinarily dynamic democratic constitutional state. This is particularly true given the autocratic relapses toward right-wing politics in neighboring German-speaking countries.


Author(s):  
N. Martin

Recall that in (2) we showed that it was possible to make transverse a homology manifold and PL-manifold inside a large dimensional homology manifold, subject to being able to do some general position inside the large manifold. In (1) we were able to relax the condition that one of the submanifolds be a PL-manifold to it being a homotopy manifold. The way in which the making transverse was achieved was via a system of h-cobordisms from the original situation to the transverse one. The problem we tackle here is that of making a map between homology manifolds transverse regular. Thus we ask: given a map f: M → N of homology manifolds with P a proper submanifold of N, is it possible to homotop f to a map g: M → N such that g−1(P) is a proper submanifold of M and g induces a map from the normal bundle of g−1(P) in M to the normal bundle of P in N?


2002 ◽  
Vol 12 (10) ◽  
pp. 2123-2135 ◽  
Author(s):  
IRENE M. MOROZ

In this paper we seek to bridge the gap between the study of a self-exciting Faraday disk homopolar dynamo with a linear series motor [Hide et al., 1996] and the case when the torque acting on the armature of the motor is proportional to the square of the current flowing through the dynamo [Hide, 1998]. We also focus on the issue of when the nonlinear quenching of oscillatory solutions can occur. The present study is a special case of the more general problem when azimuthal eddy currents are permitted to flow [Moroz & Hide, 2000] and shares with that problem the existence of multiple steady states and Hopf bifurcations. This results in distinct double-zero bifurcations for the trivial and the nontrivial equilibrium states as well as other codimension-two bifurcations, which leads to the suppression of oscillatory solutions.


2004 ◽  
Vol 12 ◽  
pp. 131-139
Author(s):  
S. Robert Ramsey

Abstract. At the beginning of the 21st century, South Koreans have embraced foreign languages with almost unbridled enthusiasm. Most of the enthusiasm is directed toward English of course but, for both economic and cultural reasons, Japanese also looms large. Moreover, the decision by the Ministry of Culture and Tourism in October 1998 to open up the country to Japanese popular culture has increased the appetite for the Japanese language, especially among the young. Koreans now study Japanese again; they access Japanese Web sites; they travel to Japan. Yet Koreans' enthusiasm for Japanese is qualitatively different from their appetite for English. Japanese may be learned, but it is to be kept out of the Korean language itself. English loans may be adopted "out of necessity," but not Japanese. The South Korean policy of linguistic purism is aimed explicitly at Japanese, and numerous books, manuals, and pamphlets instruct the public on how to recognize and purge Japanese influences from their speech and writing. Newspapers and other media wage periodic campaigns to do the same. The Korean public generally supports and cooperates with these policies and campaigns, which, for the most part, are surprisingly effective. There are numerous problems with Korean linguistic purism, however, and prescriptive intervention in the Korean language by government and media requires a continued investment of research, resources, and public support. How successful these efforts will be in the face of ever-closer ties with Japan remains to be seen.


2018 ◽  
Vol 16 (1) ◽  
pp. 250-259
Author(s):  
Zahid Raza ◽  
Agha Kashif ◽  
Imran Anwar

AbstractIn this paper, some algebraic and combinatorial characterizations of the spanning simplicial complex Δs(𝓙n,m) of the Jahangir’s graph 𝓙n,m are explored. We show that Δs(𝓙n,m) is pure, present the formula for f-vectors associated to it and hence deduce a recipe for computing the Hilbert series of the Face ring k[Δs(𝓙n,m)]. Finally, we show that the face ring of Δs(𝓙n,m) is Cohen-Macaulay and give some open scopes of the current work.


2005 ◽  
Vol 12 (04) ◽  
pp. 541-552
Author(s):  
Kelly Jeanne Pearson ◽  
Tan Zhang

The Orlik–Solomon algebra is a graded algebra defined by the partially ordered set of subspace intersections of the hyperplanes in an arrangement. Define the cohomology of an Orlik–Solomon algebra as that of the complex formed by its homogeneous components with the differential defined via multiplication by an element of degree one. The dimension of the cohomology of the Orlik–Solomon algebra in dimension one has been determined by Libgöber and Yuzvinsky. Using similar techniques, we study the dimension of the cohomology groups of the Orlik–Solomon algebra in higher dimensions under the special case where the element of degree one which defines the multiplication is concentrated under an element of the intersection lattice of codimension two. We provide computational methods for the dimension of the second cohomology group.


1970 ◽  
Vol 13 (2) ◽  
Author(s):  
A. Williams

This paper attempts to extend the debate over labour market flexibility by incorporating some of the larger exogenous issues that are currently shaping New Zealand's future as a trading nation. It argues that structural shifts in the face of global price competition have important consequences for labour demand and in turn for both the institutional agencies of industial relations and for operational practices. The increasing importance of the formative role of mu;lti-national corporate practices are also discussed, particularly their tendency to treat labour supply requirements as a special case of factor markets in which the human factor is melded into an integrated socio-economic system. The paper concludes that current changes in labour law have still not addressed the question of the degree of flexibility that a deregulated labour market might require and that the potential for considerable conflict exists between employer and trade union perceptions as to the roles of current institutions.


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