Computing Generators of Free Modules over Orders in Group Algebras

Let E be a number field and G be a finite group. Let A be any O_E-order of full rank in the group algebra E[G] and X be a (left) A-lattice. We give a necessary and sufficient condition for X to be free of given rank d over A. In the case that the Wedderburn decomposition E[G] \cong \oplus_xM_x is explicitly computable and each M_x is in fact a matrix ring over a field, this leads to an algorithm that either gives elements \alpha_1,...,\alpha_d \in X such that X = A\alpha_1 \oplus ... \oplusA\alpha_d or determines that no such elements exist. Let L/K be a finite Galois extension of number fields with Galois group G such that E is a subfield of K and put d = [K : E]. The algorithm can be applied to certain Galois modules that arise naturally in this situation. For example, one can take X to be O_L, the ring of algebraic integers of L, and A to be the associated order A(E[G];O_L) \subseteq E[G]. The application of the algorithm to this special situation is implemented in Magma under certain extra hypotheses when K = E = \IQ.

Solvothermal synthesis of one-dimensional chalcogenides containing group 13 elements

The solvothermal synthesis and characterisation of [C6H16N2][GaS2]2 (1), [C6H16N2][Ga2Se3(Se2)] (2), and mixed-metal phases with composition [C6H16N2][Ga2–xInxSe3(Se2)] (0 < x < 2)(3–5), is described. These materials have been characterised by single-crystal and powder X-ray diffraction, thermogravimetric analysis and UV/Vis diffuse reflectance spectroscopy. The materials contain one-dimensional anionic chains. In 1, these chains consist of edge-linked GaS4 tetrahedra, whilst in 2–5, the chains contain perselenide (Se2)2– units and comprise alternating four-membered [M2Se2] and five-membered [M2Se3] rings (where M = Ga, In). Compounds 3–5 represent the first examples of ternary mixed-metal [M2Se3(Se2)]2– chains.

A NOTE ON FREE GROUPS IN THE RING OF FRACTIONS OF SKEW POLYNOMIAL RINGS

Let L be a function field over the rationals and let D denote the skew field of fractions of L[t; sigma], the skew polynomial ring in t, over L, with automorphism sigma. We prove that the multiplicative group D(x) of D contains a free noncyclic subgroup.

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

Locally nilpotent groups of units in tiled rings

We consider locally nilpotent subgroups of units in basic tiled rings A, over local rings O which satisfy a weak commutativity condition. Tiled rings are generalizations of both tiled orders and incidence rings. If, in addition, O is Artinian then we give a complete description of the maximal locally nilpotent subgroups of the unit group of A up to conjugacy. All of them are both nilpotent and maximal Engel. This generalizes our description of such subgroups of upper-triangular matrices over O given in M. Dokuchaev, V. Kirichenko, and C. Polcino Milies (2005) [3]. (C) 2010 Elsevier Inc. All rights reserved.

On invariant Rings of Sylow subgroups of finite classical groups

In this thesis we study the invariant rings for the Sylow p-subgroups of the nite classical groups. We have successfully constructed presentations for the invariant rings for the Sylow p-subgroups of the unitary groups GU(3; Fq2) and GU(4; Fq2 ), the symplectic group Sp(4; Fq) and the orthogonal group O+(4; Fq) with q odd. In all cases, we obtained a minimal generating set which is also a SAGBI basis. Moreover, we computed the relations among the generators and showed that the invariant ring for these groups are a complete intersection. This shows that, even though the invariant rings of the Sylow p-subgroups of the general linear group are polynomial, the same is not true for Sylow p-subgroups of general classical groups. We also constructed the generators for the invariant elds for the Sylow p-subgroups of GU(n; Fq2 ), Sp(2n; Fq), O+(2n; Fq), O-(2n + 2; Fq) and O(2n + 1; Fq), for every n and q. This is an important step in order to obtain the generators and relations for the invariant rings of all these groups.

The Yang-Lee edge singularity in spin models on connected and non-connected rings

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Reactivity of mesenteric and aortic rings from trained rats fed with high caloric diet

A strong association between the benefits of physical exercise on the cardiovascular disease with an improvement of the endothelium-derived relaxing factor production has been consistently shown. The purpose of this study was to evaluate the effect of exercise training associated with high caloric diet in the reactivity of rat mesenteric and aortic rings. Experimental protocol consisted of 4 weeks of high caloric diet consumption previous to 4 weeks of run training (1.2 km/h, 0% grade, in sessions of 60 min, 5 days/week). Concentrations of triglycerides, glucose, insulin and nitrite/nitrate levels were measured and atherogenic index was calculated. Concentration-response curves to acetylcholine (10 nM-100 mu M), sodium nitroprusside (100 pM-100 nM) and phenylephrine (1 nM-3 mu M) were obtained. Exercise training reduced body mass (6%) and triglyceride levels (about 54%), without changes in glucose and insulin concentrations. An improvement of endothelium-dependent relaxation responses to acetylcholine in mesenteric and aortic rings was observed in trained group. No changes were seen for sodium nitroprusside and phenylephrine. In conclusion, our study is the first to show clearly that run training promotes an improvement of the endothelium-dependent relaxing response in aorta and mesenteric rings from rats fed with high caloric diet and that is associated with increase of NO production. (c) 2006 Elsevier B.V. All rights reserved.

Alternant and BCH codes over certain rings

Alternant codes over arbitrary finite commutative local rings with identity are constructed in terms of parity-check matrices. The derivation is based on the factorization of x s - 1 over the unit group of an appropriate extension of the finite ring. An efficient decoding procedure which makes use of the modified Berlekamp-Massey algorithm to correct errors and erasures is presented. Furthermore, we address the construction of BCH codes over Zm under Lee metric.

Exercise training improves relaxation response and SOD-1 expression in aortic and mesenteric rings from high caloric diet-fed rats

Background. Obesity has been associated with a variety of disease such as type II diabetes mellitus, arterial hypertension and atherosclerosis. Evidences have shown that exercise training promotes beneficial effects on these disorders, but the underlying mechanisms are not fully understood. The aim of this study was to investigate whether physical preconditioning prevents the deleterious effect of high caloric diet in vascular reactivity of rat aortic and mesenteric rings. Methods. Male Wistar rats were divided into sedentary (SD); trained (TR); sedentary diet (SDD) and trained diet (TRD) groups. Run training (RT) was performed in sessions of 60 min, 5 days/week for 12 weeks (70-80% VO2max). Triglycerides, glucose, insulin and nitrite/nitrate concentrations (NOx -) were measured. Concentration- response curves to acetylcholine (ACh) and sodium nitroprusside (SNP) were obtained. Expression of Cu/Zn superoxide dismutase (SOD-1) was assessed by Western blotting. Results. High caloric diet increased triglycerides concentration (SDD: 216 ± 25 mg/dl) and exercise training restored to the baseline value (TRD: 89 ± 9 mg/dl). Physical preconditioning significantly reduced insulin levels in both groups (TR: 0.54 ± 0.1 and TRD: 1.24 ± 0.3 ng/ml) as compared to sedentary animals (SD: 0.87 ± 0.1 and SDD: 2.57 ± 0.3 ng/ml). On the other hand, glucose concentration was slightly increased by high caloric diet, and RT did not modify this parameter (SD: 126 ± 6; TR: 140 ± 8; SDD: 156 ± 8 and TRD 153 ± 9 mg/dl). Neither high caloric diet nor RT modified NO x - levels (SD: 27 ± 4; TR: 28 ± 6; SDD: 27 ± 3 and TRD: 30 ± 2 μM). Functional assays showed that high caloric diet impaired the relaxing response to ACh in mesenteric (about 13%), but not in aortic rings. RT improved the relaxing responses to ACh either in aortic (28%, for TR and 16%, to TRD groups) or mesenteric rings (10%, for TR and 17%, to TRD groups) that was accompanied by up-regulation of SOD-1 expression and reduction in triglycerides levels. Conclusion. The improvement in endothelial function by physical preconditioning in mesenteric and aortic arteries from high caloric fed-rats was directly related to an increase in NO bioavailability to the smooth muscle mostly due to SOD-1 up regulation. © 2008 de Moraes et al; licensee BioMed Central Ltd.

Quaternion orders over quadratic integer rings from arithmetic fuchsian groups

In this paper we show that the quaternion orders OZ[ √ 2] ≃ ( √ 2, −1)Z[ √ 2] and OZ[ √ 3] ≃ (3 + 2√ 3, −1)Z[ √ 3], appearing in problems related to the coding theory [4], [3], are not maximal orders in the quaternion algebras AQ( √ 2) ≃ ( √ 2, −1)Q( √ 2) and AQ( √ 3) ≃ (3 + 2√ 3, −1)Q( √ 3), respectively. Furthermore, we identify the maximal orders containing these orders.

A SURVEY ON FREE OBJECTS IN DIVISION RINGS AND IN DIVISION RINGS WITH AN INVOLUTION

Let D be a division ring with center k, and let D-dagger be its multiplicative group. We investigate the existence of free groups in D-dagger, and free algebras and free group algebras in D. We also go through the case when D has an involution * and consider the existence of free symmetric and unitary pairs in D-dagger.

Single-Molecule Junctions Based on Nitrile-Terminated Biphenyls: A Promising New Anchoring Group

We present a combined experimental and theoretical study of the electronic transport through single-molecule junctions based on nitrile-terminated biphenyl derivatives. Using a scanning tunneling microscope-based break-junction technique, we show that the nitrile-terminated compounds give rise to well-defined peaks in the conductance histograms resulting from the high selectivity of the N-Au binding. Ab initio calculations have revealed that the transport takes place through the tail of the LUMO. Furthermore, we have found both theoretically and experimentally that the conductance of the molecular junctions is roughly proportional to the square of the cosine of the torsion angle between the two benzene rings of the biphenyl core, which demonstrates the robustness of this structure-conductance relationship.

Modulus method and radial stretch map in the Heisenberg group

We develop a modulus method for surface families inside a domain in the Heisenberg group and we prove that the stretch map between two Heisenberg spherical rings is a minimiser for the mean distortion among the class of contact quasiconformal maps between these rings which satisfy certain boundary conditions.