Torsion theories induced from commutative subalgebras

We begin a study of torsion theories for representations of finitely generated algebras U over a field containing a finitely generated commutative Harish-Chandra subalgebra Gamma. This is an important class of associative algebras, which includes all finite W-algebras of type A over an algebraically closed field of characteristic zero, in particular, the universal enveloping algebra of gl(n) (or sl(n)) for all n. We show that any Gamma-torsion theory defined by the coheight of the prime ideals of Gamma is liftable to U. Moreover, for any simple U-module M, all associated prime ideals of M in Spec Gamma have the same coheight. Hence, the coheight of these associated prime ideals is an invariant of a given simple U-module. This implies the stratification of the category of U-modules controlled by the coheight of the associated prime ideals of Gamma. Our approach can be viewed as a generalization of the classical paper by Block (1981) [4]; it allows, in particular, to study representations of gl(n) beyond the classical category of weight or generalized weight modules. (C) 2011 Elsevier B.V. All rights reserved.

On the manifold structure of the set of unparameterized embeddings with low regularity

Given manifolds M and N, with M compact, we study the geometrical structure of the space of embeddings of M into N, having less regularity than C(infinity) quotiented by the group of diffeomorphisms of M.

BASS CYCLIC UNITS AS FACTORS IN A FREE GROUP IN INTEGRAL GROUP RING UNITS

Marciniak and Sehgal showed that if u is a non-trivial bicyclic unit of an integral group ring then there is a bicyclic unit v such that u and v generate a non-abelian free group. A similar result does not hold for Bass cyclic units of infinite order based on non-central elements as some of them have finite order modulo the center. We prove a theorem that suggests that this is the only limitation to obtain a non-abelian free group from a given Bass cyclic unit. More precisely, we prove that if u is a Bass cyclic unit of an integral group ring ZG of a solvable and finite group G, such that u has infinite order modulo the center of U(ZG) and it is based on an element of prime order, then there is a non-abelian free group generated by a power of u and a power of a unit in ZG which is either a Bass cyclic unit or a bicyclic unit.

Maslov index in semi-Riemannian submersions

We study focal points and Maslov index of a horizontal geodesic gamma : I -> M in the total space of a semi-Riemannian submersion pi : M -> B by determining an explicit relation with the corresponding objects along the projected geodesic pi omicron gamma : I -> B in the base space. We use this result to calculate the focal Maslov index of a (spacelike) geodesic in a stationary spacetime which is orthogonal to a timelike Killing vector field.

Curvature Estimates for Submanifolds in Warped Products

We give estimates of the intrinsic and the extrinsic curvature of manifolds that are isometrically immersed as cylindrically bounded submanifolds of warped products. We also address extensions of the results in the case of submanifolds of the total space of a Riemannian submersion.

Pseudo Focal Points Along Lorentzian Geodesics and Morse Index

Given a Lorentzian manifold (M,g), a geodesic gamma in M and a timelike Jacobi field Y along gamma, we introduce a special class of instants along gamma that we call Y-pseudo conjugate (or focal relatively to some initial orthogonal submanifold). We prove that the Y-pseudo conjugate instants form a finite set, and their number equals the Morse index of (a suitable restriction of) the index form. This gives a Riemannian-like Morse index theorem. As special cases of the theory, we will consider geodesics in stationary and static Lorentzian manifolds, where the Jacobi field Y is obtained as the restriction of a globally defined timelike Killing vector field.

COMPARISON RESULTS FOR CONJUGATE AND FOCAL POINTS IN SEMI-RIEMANNIAN GEOMETRY VIA MASLOV INDEX

We prove an estimate on the difference of Maslov indices relative to the choice of two distinct reference Lagrangians of a continuous path in the Lagrangian Grassmannian of a symplectic space. We discuss some applications to the study of conjugate and focal points along a geodesic in a semi-Riemannian manifold.

Crítica ao fundacionismo cartesiano com base no argumento contra a linguagem privada

This assignment ains to prove the pertinency of using the wittgenstein´s argument against private language as a criticism to cartesian fundacionism. Therefore, I want to demonstrate in the first chaper the conceptual viability of facing the cartesian argument of cogito not as a simple silogism but as an exemple of a private experience (process of thinking). At the second chaper, the subordination of the argument against private language give us the idea that rules can only be followed by means of corrections givem by a linguistic community that is external to the private subject, in a way to be unviable the assumption that is possible to name an internal experience without searching external rules of the use of terms. At the chaper 3 the pertinency of the hypothesis raised by A. Kenny, about the overtaking of the argument against private language can be extended to the idea of epistemic and ontologic privacy that would lend validity to the fundacion present at the argument at the cartesian cogito. In oder to become evident the pertinency of use of Wittgenstein´s argument agaist Descartes´ fundation, it´s necessary, at the chaper 3, to demonstrate the impertinency of the objection to the A. Kenny´s hypothesis, based on the experiency of the thought of the brain at the recipient, to make clear the incompatibility existing between the cartesian idea of cogito and Wittgenstein´s notion that language is an activitie followed by rules, wich correction criterion may be external and intersubjective

Quantitative distribution of gibberellins and indole-acetic acid in pea (Pisum sativum L.) seedlings

The objective was to determine the distribution in pea seedling of GA (by thin layer chromatography) and IAA (by HPLC). Three samples of 30 7/day-old seedlings were sectioned into: apical meristem + plumular hook; stem elongation zone; stem non-elongation zone; cotyledons; root non-elongation zone; root tip. The material was frozen in liquid N and stored at -80 degrees C. The stem elongation zone, the apical meristem+plumular hook and the root tip had low IAA, whereas the stem non-elongation zone and root non-elongation zone had high IAA content. The stem elongation zone and apical meristem plumular hook had high GA, while root non-elongation zone had the lowest GA content.

Senna occidentalis Link. (Caesalpiniaceae) imbibition curves for NaCl osmotic potential levels up to 0.6 MPa

An investigation is reported on the statistical model of imbibition curves of the seeds of Senna occidentalis Link. (Caesalpiniaceae), up to Phase II (start of root emission) in osmotic potential levels (0; -0.2; -0.4 and -0.6 MPa), induced NaCl or PEG 6000. The statistical model for both solutions was y = a [1 b exp(-cx)] where y is the fresh matter of seed in g, and x the time of evaluation in h. The analysis of variance of the estimated parameters, showed that with the NaCl solution, the -0.4 and -0.6 MPa levels differed significantly from the 0 and -0.2 MPa levels, and that with the PEG solution, the -0.6 MPa differed from the rest. Prolongation of Phase II occurred as the potential decreased, with both solutions. More reduction in water uptake and prolongation of this phase occurred with the PEG treatment.

EFFECT OF WATER POTENTIAL ON GERMINATION OF SEEDS OF STYLOSANTHES-GUIANENSIS (AUBL) SW

Effect of water potential on germination of seeds of Slylosanthes guianensis (Aubl.) Sw. To evaluate the water potential effect on germination of S. guianensis two experiments were performed.The first one used osmotic pre-treatment in the imbibition phase and after this period (14 h) the seeds were germinated on filter paper moistened with distilled water. In the second experiment, besides the imbibition phase, seeds were kept in a range of water potentials during all the process. The potentials ranged from 0 to -18 bars, with 3 bars increments, induced by mannitol or by polyethylene glycol. Each treatment was replicated 3 times with 100 seeds per replication. The seeds pre-treated during imbibition had high germination percentage, the highest being the ones in polhyetylene glycol. In the second experiment the polyethylene glycol solutions reduced dramatically the germination percentage in relation to mannitol. From -12 bars on germination ceased in the polyethylene glycol treatments, while in mannitol solution there was 52,67% of germination, in the same water potential.

Effects of some mineral deficiencies on the development of the soybean plant, Glycine max (L.) Merril cv Santa Rosa

The present work studies Ca, B and Zn omission on the development of soybean plants (Glycine max (L.) Merrill cv Santa Rosa). The experiment was carried out as hydroponic culture, viith complete Hoagland & Arnon nutrient solution nr. 2 (C), lacking calcium (-Ca), lacking boron (-B) or lacking zinc (-Zn), a total of 4 treatments. Seven samplings were made to determine: total dry matter (g), root dry matter (g), stem dry matter (g) and leaf dry matter (g). Results showed that Ca and B omissions decreased dry weight. Lack of Zn did not affect dry weight.