Mixed multiplicities and the minimal number of generator of modules

Let (R, m) be a d-dimensional Noetherian local ring. In this work we prove that the mixed Buchsbaum-Rim multiplicity for a finite family of R-submodules of R(p) of finite colength coincides with the Buchsbaum-Rim multiplicity of the module generated by a suitable superficial sequence, that is, we generalize for modules the well-known Risler-Teissier theorem. As a consequence, we give a new proof of a generalization for modules of the fundamental Rees` mixed Multiplicity theorem, which was first proved by Kirby and Rees in (1994, [8]). We use the above result to give an upper bound for the minimal number of generators of a finite colength R-submodule of R(p) in terms of mixed multiplicities for modules, which generalize a similar bound obtained by Cruz and Verma in (2000, [5]) for m-primary ideals. (C) 2009 Elsevier B.V. All rights reserved.

Acetylation of cellulose in LiCl-N,N-dimethylacetamide: first report on the correlation between the reaction efficiency and the aggregation number of dissolved cellulose

The acylation of three cellulose samples by acetic anhydride, Ac(2)O, in the solvent system LiCl/N,N-dimethylacetamide, DMAc (4 h, 110 A degrees C), has been revisited in order to investigate the dependence of the reaction efficiency on the structural characteristics of cellulose, and its aggregation in solution. The cellulose samples employed included microcrystalline, MCC; mercerized cotton linters, M-cotton, and mercerized sisal, M-sisal. The reaction efficiency expresses the relationship between the degree of substitution, DS, of the ester obtained, and the molar ratio Ac(2)O/AGU (anhydroglucose unit of the biopolymer); 100% efficiency means obtaining DS = 3 at Ac(2)O/AGU = 3. For all celluloses, the dependence of DS on Ac(2)O/AGU is described by an exponential decay equation: DS = DS(o) - Ae(-[(Ac2O/AGU)/B]); (A) and (B) are regression coefficients, and DS(o) is the calculated maximum degree of substitution, achieved under the conditions of each experiment. Values of (B) are clearly dependent on the cellulose employed: B((M-cotton)) > B((M-sisal)) > B((MCC)); they correlate qualitatively with the degree of polymerization of cellulose, and linearly with the aggregation number, N(agg), of the dissolved biopolymer, as calculated from static light scattering measurements: (B) = 1.709 + 0.034 N(agg). To our knowledge, this is the first report on the latter correlation; it shows the importance of the physical state of dissolved cellulose, and serves to explain, in part, the need to use distinct reaction conditions for MCC and fibrous celluloses, in particular Ac(2)O/AGU, time, temperature.

Some classes of semisimple group (and loop) algebras over finite fields

We determine the structure of the semisimple group algebra of certain groups over the rationals and over those finite fields where the Wedderburn decompositions have the least number of simple components We apply our work to obtain similar information about the loop algebras of mdecomposable RA loops and to produce negative answers to the isomorphism problem over various fields (C) 2010 Elsevier Inc All rights reserved

Differential response of AMPA and NMDA glutamate receptors of Purkinje cells to aging of the chicken cerebellum

Aging can lead to cognitive, affective, learning, memory and motor deficits. Since the cerebellum and glutamatergic neurotransmission are involved in several of those functions, the present work aimed at studying the expression of AMPA and NMDA glutamate receptor subunits in the chick cerebellum during aging. Young (30 days old) and aged (ca. 4 years old) chickens (Gallus gallus) were used in order to evaluate the expression of GluR1, GluR2/3 and NR1 subunits. The cerebella of young and aged chickens were subjected to immunohistochemical and immunoblotting techniques. Numbers of GluR1, GluR2/3 and NR1-positive cells and optical density of the immunoblotting data were analyzed and submitted to statistical analysis using ANOVA and the Bonferroni post hoc test. Mean density of Purkinje cells stained for Giemsa, GluR1, GluR2/3 and NR1 in the cerebellum all showed a statistically significant decrease in aged animals when compared to the young animals (Giemsa, P < 0.01; GluRs and NR1, P < 0.03). However, the ratio of GluR1 and GluR2/3-positive Purkinje cells in relation the total number of Purkinje cells found in each time point decreased with aging (ca. 10%), whereas the ratio of NR1-positive cells increased (ca. 9%). The immunoblotting data showed a significant decrease of GluR1 (ca. 66%) and GluR2/3 (ca. 55%) protein expression with aging, but did not reveal changes for NR1. Our data suggest that aging can lead to differential changes in the pattern of expression of glutamate receptor subunits, which can underlie at least part of the cognitive and motor disorders found in aged animals. (c) 2010 Elsevier Ireland Ltd. All rights reserved.

Influence of organic fertilization on the number of culturable diazotrophic endophytic bacteria isolated from sugarcane

The numbers of culturable diazotrophic endophytic bacteria (CDEB) from roots stems and leaves of sugarcane submitted to organic inorganic or no fertilization were compared In order to determine the size of the N(2) fixing populations the Most Probable Number technique (MPN) was used The quantification of diazotrophic bacteria by using the acetylene reduction assay (ARA) was more accurate than observing the bacterial growth in the vials to confirm N(2) fixing capability the detection of gene nifH was performed on a sample of 105 Isolated bacteria The production of extracellular enzymes involved in the penetration of the plants by the bacteria was also studied The results showed that organic fertilization enhances the number of CDEB when compared with conventional fertilization used throughout the growing season The maximum number of bacteria was detected in the roots Roots and stems presented the greatest number of CDEB in the middle of the cropping season and in leaves numbers varied according to the treatment Using two pairs of primers and two different methods the nifH gene was found in 104 of the 105 tested isolates Larger amounts of pectinase were released by isolates from sugarcane treated with conventional fertilizers (66%) whereas larger amounts of cellulase were released by strains isolated from sugarcane treated with organic fertilizers (80%) (C) 2010 Elsevier Masson SAS All rights reserved

A coupling cutting stock-lot sizing problem in the paper industry

An important production programming problem arises in paper industries coupling multiple machine scheduling with cutting stocks. Concerning machine scheduling: how can the production of the quantity of large rolls of paper of different types be determined. These rolls are cut to meet demand of items. Scheduling that minimizes setups and production costs may produce rolls which may increase waste in the cutting process. On the other hand, the best number of rolls in the point of view of minimizing waste may lead to high setup costs. In this paper, coupled modeling and heuristic methods are proposed. Computational experiments are presented.

Number of particle creation and decoherence in the nonideal dynamical Casimir effect at finite temperature

In this work we investigate the dynamical Casimir effect in a nonideal cavity by deriving an effective Hamiltonian. We first compute a general expression for the average number of particle creation, applicable for any law of motion of the cavity boundary, under the only restriction of small velocities. We also compute a general expression for the linear entropy of an arbitrary state prepared in a selected mode, also applicable for any law of motion of a slow moving boundary. As an application of our results we have analyzed both the average number of particle creation and linear entropy within a particular oscillatory motion of the cavity boundary. On the basis of these expressions we develop a comprehensive analysis of the resonances in the number of particle creation in the nonideal dynamical Casimir effect. We also demonstrate the occurrence of resonances in the loss of purity of the initial state and estimate the decoherence times associated with these resonances. Since our results were obtained in the framework of the perturbation theory, they are restricted, under resonant conditions, to a short-time approximation. (C) 2009 Elsevier Inc. All rights reserved.