Local cohomology in classical rings

The aim of this paper is to stablish the close connection between prime ideals and torsion theories in anon necessarily commutative noetherian ring. We introduce a new definition of support of a module and characterize some kinds of torsion theories in terms of prime ideals. Using the machinery introduced before, we prove a version of the Mayer-Vietoris Theorem for local cohomology and stablish a relationship between the classical dimension and the vanishing of the groups of local cohomology on a classical ring

Crossover to the KPZ equation

We characterize the crossover regime to the KPZ equation for a class of one-dimensional weakly asymmetric exclusion processes. The crossover depends on the strength asymmetry $an^{2-\gamma}$ ($a,\gamma>0$) and it occurs at $\gamma=1/2$. We show that the density field is a solution of an Ornstein-Uhlenbeck equation if $\gamma\in(1/2,1]$, while for $\gamma=1/2$ it is an energy solution of the KPZ equation. The corresponding crossover for the current of particles is readily obtained.Comment: Published by Annales Henri Poincare Volume 13, Number 4 (2012), 813-82

Extending structures I: the level of groups

Let $H$ be a group and $E$ a set such that $H \subseteq E$. We shall describe and classify up to an isomorphism of groups that stabilizes $H$ the set of all group structures that can be defined on $E$ such that $H$ is a subgroup of $E$. A general product, which we call the unified product, is constructed such that both the crossed product and the bicrossed product of two groups are special cases of it. It is associated to $H$ and to a system $\bigl((S, 1_S,\ast), \triangleleft, \, \triangleright, \, f \bigl)$ called a group extending structure and we denote it by $H \ltimes S$. There exists a group structure on $E$ containing $H$ as a subgroup if and only if there exists an isomorphism of groups $(E, \cdot) \cong H \ltimes S$, for some group extending structure $\bigl((S, 1_S,\ast), \triangleleft, \, \triangleright, \, f \bigl)$. All such group structures on $E$ are classified up to an isomorphism of groups that stabilizes $H$ by a cohomological type set ${\mathcal K}^{2}_{\ltimes} (H, (S, 1_S))$. A Schreier type theorem is proved and an explicit example is given: it classifies up to an isomorphism that stabilizes $H$ all groups that contain $H$ as a subgroup of index 2.Comment: 17 pages; to appear in Algebras and Representation Theor

Acclimatation de vitroplants de bananier Musa sp. en culture hydroponique: impact de différentes concentrations en cuivre sur la croissance des vitroplants

Acclimatation of Banana's Vitroplants (Musa sp.) in Hydroponic Culture: Effects of Different Concentrations Copper on Growth of Vitroplants. Constraints due to copper and consequences of its accumulation in acclimatized banana in vitroplants have been studied in hydroponic culture. 0-100- 500-1000 ppm copper was added to the nutrient medium in hydroponic culture. At 1000 ppm, copper was accumulated in the roots but not in the aerial parts. Surprisingly, biomass of shoots and roots was augmented significantly at this concentration (with leaves as an exception). Plant height was reduced strongly even at 100 ppm CuSO4, although the copper content in shoots and leaves was very low

On Iterated Twisted Tensor Products of Algebras

We introduce and study the definition, main properties and applications of iterated twisted tensor products of algebras, motivated by the problem of defining a suitable representative for the product of spaces in noncommutative geometry. We find conditions for constructing an iterated product of three factors, and prove that they are enough for building an iterated product of any number of factors. As an example of the geometrical aspects of our construction, we show how to construct differential forms and involutions on iterated products starting from the corresponding structures on the factors, and give some examples of algebras that can be described within our theory. We prove a certain result (called ``invariance under twisting'') for a twisted tensor product of two algebras, stating that the twisted tensor product does not change when we apply certain kind of deformation. Under certain conditions, this invariance can be iterated, containing as particular cases a number of independent and previously unrelated results from Hopf algebra theory.Comment: 44 pages, 21 figures. More minor typos corrections, one more example and some references adde

A numerical approach to analyze the performance of a PEF-Ohmic heating system in microbial inactivation of solid food

Pulsed Electric Fields (PEF) technology has been recently proposed as a new ohmic-heating system for the heat treatment of solid products in short periods (less than 1 min). However, similar to traditional ohmic heating, non-homogeneous distribution of temperature has been observed and cold points appeared in the interphase between the solid treated product and the electrodes, which can limit the technology for assuring food safety for treated solid products. In this investigation, a computational axisymmetric model of a lab-scale PEF system for a solid product (agar cylinder) was developed. This model was used to predict the temperature and the electric field distribution, treatment time, and the microbial inactivation (Salmonella Typhimurium 878) in the solid product after a PEF-ohmic treatment. Using a factorial analysis, a total of 8 process conditions with different settings of applied field strength levels (2.5–3.75 kV/cm), frequencies (100–200 Hz), and initial agar and electrode temperature (40–50°C) were simulated for the agar cylinder in order to identify the effect and optimal values of these parameters, which offer the most temperature homogeneity. The results showed that the initial temperature of the agar and the electrodes was of great importance in achieving the best temperature uniformity, limiting the occurrence of cold points, and therefore, improving the homogeneity in the level of inactivation of Salmonella Typhimurium 878 all over the agar cylinder. A treatment of 2.3 s would be enough at 3.75 kV/cm, 200 Hz with an initial temperature of 50°C of the agar and the electrodes, for a 5-Log10 reduction of Salmonella Typhimurium 878 in the whole product with a deviation of 9°C between the coldest and hottest point of the solid

A Comparison of Myoelectric Control Modes for an Assistive Robotic Virtual Platform

In this paper, we propose a daily living situation where objects in a kitchen can be grasped and stored in specific containers using a virtual robot arm operated by different myoelectric control modes. The main goal of this study is to prove the feasibility of providing virtual environments controlled through surface electromyography that can be used for the future training of people using prosthetics or with upper limb motor impairments. We propose that simple control algorithms can be a more natural and robust way to interact with prostheses and assistive robotics in general than complex multipurpose machine learning approaches. Additionally, we discuss the advantages and disadvantages of adding intelligence to the setup to automatically assist grasping activities. The results show very good performance across all participants who share similar opinions regarding the execution of each of the proposed control modes

Long time, large scale limit of the Wigner transform for a system of linear oscillators in one dimension

We consider the long time, large scale behavior of the Wigner transform W_\eps(t,x,k) of the wave function corresponding to a discrete wave equation on a 1-d integer lattice, with a weak multiplicative noise. This model has been introduced in Basile, Bernardin, and Olla to describe a system of interacting linear oscillators with a weak noise that conserves locally the kinetic energy and the momentum. The kinetic limit for the Wigner transform has been shown in Basile, Olla, and Spohn. In the present paper we prove that in the unpinned case there exists $\gamma_0>0$ such that for any $\gamma\in(0,\gamma_0]$ the weak limit of W_\eps(t/\eps^{3/2\gamma},x/\eps^{\gamma},k), as \eps\ll1, satisfies a one dimensional fractional heat equation $\partial_t W(t,x)=-\hat c(-\partial_x^2)^{3/4}W(t,x)$ with $\hat c>0$. In the pinned case an analogous result can be claimed for W_\eps(t/\eps^{2\gamma},x/\eps^{\gamma},k) but the limit satisfies then the usual heat equation