Associated primes of graded components of local cohomology modules

The -th local cohomology module of a finitely generated graded module over a standard positively graded commutative Noetherian ring , with respect to the irrelevant ideal , is itself graded; all its graded components are finitely generated modules over , the component of of degree . It is known that the -th component of this local cohomology module is zero for all > 0$">. This paper is concerned with the asymptotic behaviour of as .

The smallest for which such study is interesting is the finiteness dimension of relative to , defined as the least integer for which is not finitely generated. Brodmann and Hellus have shown that is constant for all (that is, in their terminology, is asymptotically stable for ). The first main aim of this paper is to identify the ultimate constant value (under the mild assumption that is a homomorphic image of a regular ring): our answer is precisely the set of contractions to of certain relevant primes of whose existence is confirmed by Grothendieck's Finiteness Theorem for local cohomology.

Brodmann and Hellus raised various questions about such asymptotic behaviour when f$">. They noted that Singh's study of a particular example (in which ) shows that need not be asymptotically stable for . The second main aim of this paper is to determine, for Singh's example, quite precisely for every integer , and, thereby, answer one of the questions raised by Brodmann and Hellus.

     

A multiple regression model for urban traffic noise in Hong Kong

This article describes the roadside traffic noise surveys conducted in heavily built-up urban areas in Hong Kong. Noise measurements were carried out along 18 major roads in 1999. The measurement data included L10, L50, L90, Leq, Lmax, the number of light vehicles, the number of heavy vehicles, the total traffic flow, and the average speed of vehicles. Statistical analysis using the analysis of variance (ANOVA) and Tukey test (p<0.05) reveals that the total traffic flow and the number of heavy vehicles are the most significant factors of urban traffic noise. Multiple regression was used to derive a set of empirical formulas for predicting L10 noise level due to road traffic. The accuracy of these empirical formulas is quantified and compared to that of another widely used prediction model in Hong Kong--the Calculation of Road Traffic Noise. The applicability of the selected multiple regression model is validated by the noise measurements performed in the winter of 2000.     

Collector Probe Measurements of Impurity Fluxes Injected into the Plasma of the T-10 Tokamak

It is shown that the efflux of impurities injected into the core plasma can be detected by collector probes in the scrape-off plasma. The time evolution, orientation and radial dependences of these effluxes allow to conclude on the impurity confinement in the core plasma and the scrape-off plasma. Moreover, recycling effects can also be measured.     

The influence of a γ-oxygen in the spacer of liquid crystal side group polysiloxanes on their ferroelectric properties

Two types of side group polysiloxanes which differ in their spacer between backbone and mesogenic part were synthesized via polymer analogous reaction. The impact of an oxygen atom localized in the γ position to the siloxane main chain on the ferroelectric properties was investigated. In addition, the link between the terminal chiral moiety and the mesogenic part in each series was varied. The phase transition behaviour, spontaneous polarization and the electro-optical response time for the two series of polymers are compared. The mesophase structures were determined by X-ray measurements on magnetically oriented samples at different temperatures. The additional oxygen atom in the spacer near to the main chain leads to broader range smectic C* phases and shorter electro-optical response times, which suggests that the ether linkage promotes a better decoupling between main chain and mesogenic side group.     

2-(2-pyridyl-)ethyl esters A new carboxyl protecting group in peptide synthesis

2-(2-pyridyl-)ethyl esters are used as chemically inert, highly selective protecting groups that are removable under mild conditions via a two step procedure.     

Liquid crystalline side group polymers with azo-chromophores and fluorinated tails of varying length

A series of side group liquid crystalline polymethacrylates with 4'-(1H,1H-perfluoroalkoxy)-azobenzene mesogenic units was synthesized and characterized by differential scanning calorimetry, polarizing optical microscopy and X-ray diffraction methods depending on the tail length. The phase behaviour is discussed as a function of the length of the tail groups. Very high clearing temperatures up to 290°C were observed for the polymers with long tail groups.