A Few Properties of Just Infinite Algebras

In this article we prove a few interesting properties of just infinite algebras. Bartholdi (2006 Bartholdi , L. ( 2006 ). Branch rings, thinned rings, tree enveloping rings . Israel J. Math. 154 : 93 – 139 .[Crossref], [Web of Science ®] , [Google Scholar]), defines a particular class of just infinite algebras and demonstrates various properties of these examples. One such property, which is tedious to prove for his specific examples, is primality. We prove here that, in fact, all just infinite algebras are prime. We then consider two corollaries of this theorem; one suggests a weaker definition of just infinite for finitely generated algebras and the other examines the specific case of just infinite algebras which also satisfy a polynomial identity.     

Anionic N-Fries rearrangement of N-alkyl-2-iodo anilides induced by iodine-magnesium exchange: application for synthesis of strained 1,2,3-trisubstituted indoles

A superior, mild, high-yielding one-pot process for rapid access to oxo anilides has been developed that involves three cascade reactions: iodine-magnesium exchange, regiospecific ortho N-Fries rearrangement, and in situ trapping of the formed aniline anion. Coupled with McMurry cyclization, the two-step process allows ready synthesis of strained 1,2,3-trisubstituted indoles regioselectively.     

Microsurface potential measurements: repulsive forces between polyelectrolyte brushes in the presence of multivalent counterions

We propose a new way to determine weak repulsive forces operative between colloidal particles by measuring the rate of slow coagulation. The rate of slow coagulation is directly related to the competition of the repulsion with thermal motion. Since the thermal forces are weak, measurements of the coagulation rate can lead to precise information on repulsive potentials having a magnitude of just a few kT. We demonstrate this novel way by studying colloidal spherical polyelectrolyte brush (SPB) particles in aqueous solution containing trivalent La3+ counterions. The particles consist of a monodisperse polystyrene core of 121 nm radius from which linear sodium poly(styrenesulfonate) (PSS) chains are densely grafted (contour length 48 nm). We determine the rate of coagulation by time-resolved simultaneous static and dynamic light scattering in the presence of LaCl3 (0.2 to 150 mM). Direct measurements of the repulsive force between macroscopic brush layers demonstrate that the potential is decaying exponentially with distance. This is in good agreement with a simple theoretical treatment that furthermore leads to the effective surface potential Psi0. The good agreement of data obtained by the novel microscopic method with direct macroscopic measurements underscores the general validity of our approach.     

Extraction procedures in gas chromatographic determination of pesticides

Pesticides are necessary for increasing agricultural productivity; however, their enormous use contaminates air, water and food. Among various organic pesticides, organochlorine pesticides (OCPs) are most persistent; and though their use is banned, they are still used illegally. In contrast to OCPs, organophosphorous pesticides are less persistent and used most extensively, while synthetic pyrethroid pesticides are the least toxic and used as insecticides. Extensive use of these pesticides is vulnerable to the ecosystem. Various extraction methods are used worldwide both by the regulatory bodies and private laboratories for the determination of multi-residue pesticides in leafy vegetables. This mini review presents an update on extraction procedure in gas chromatographic methods of pesticides analysis in various samples with special emphasis on leafy vegetables. We have covered six years of work from 2008–2013, discussing various extraction methods and their applications.     

Clairvoyant and adaptive signal detection in non-Gaussian clutter:a data-dependent threshold interpretation

This paper addresses the problem of signal detection in correlated non-Gaussian clutter modeled as a spherically invariant random process. The optimum strategy to detect a constant signal, with either known or unknown complex amplitude, embedded in correlated Gaussian clutter is given by comparing the whitening-matched filter output with a fixed threshold. When the clutter is non-Gaussian, the performance of the matched filter sensibly degrades. The optimum strategy is the classical whitening-matched filter output compared with a data-dependent threshold. This interpretation provides a deeper insight into the structure of the optimum detector and allows us to single out a family of suboptimum detectors based on a polynomial approximation of the data-dependent threshold. They are easy to implement and have performance that is really close to the optimal. The adaptive implementation of the polynomial detectors is also investigated, and their performance is analyzed by means of Monte Carlo simulation for various clutter scenarios     

On the derivation of coupled-line models from EM simulators and application to MoM analysis

This paper addresses the problem of deriving an actual coupled-line model from the "spot frequency" characteristics of transmission media derived by means of a numerical electromagnetic simulator. For a given set of coupled lines, possibly asymmetric and lossy, one of the main issues is to recover a model whose parameters are physically and practically meaningful. In order to satisfy the requirements, the model ought to basically yield a natural generalization of the well-known even/odd and c//spl pi/ modes for couples of lines, and collapse to a set of uncoupled lines when coupling is negligible. Hence, part of this study is devoted to discussing and evaluating models that satisfy such requirements. The end result is a Weissfloch-type equivalent circuit made up of uncoupled lines and input and output ideal transformers. The algorithm is then applied to the network parameters of coupled lines. The latter are evaluated by a full-wave method of moments approach, and a subsequent short-open calibration (SOC) procedure. Finally, a new algorithm is introduced that is able to evaluate and remove the contribution of the naked discontinuity due to ports, usually not directly available from the SOC routine.     

Liouville theorems for stable solutions of semilinear elliptic equations with convex nonlinearities

We extend our recent results on the classification of stable solutions of the equation −Δu=f(u)$-\Delta u=f\left(u\right)$ in R^N${\mathbb{R}}^N$, where f≥0$f\ge 0$ is a general convex, non-decreasing function.     

Analytical Characterization of Fatty Acids Composition of Datura alba Seed Oil by Gas Chromatography Mass Spectrometry

Methyl ester derivatives of fatty acids were analyzed for the determination of the constituents of Datura alba seed oil. Gas chromatography coupled to mass spectrometer was used for these analyses. Results delivered that there were saturated as well as unsaturated fatty acids in Datura alba seed oil. Total of 15 different fatty acid components were identified and quantified. Methyl linoleate was found in highest concentration (16.22%) among the identified analytes of interest. In addition methyl esters of Palmitic acid (6.59%), Oleic acid (5.41%) and Stearic acid (1.35%) were found. Concentrations of rest of the detected fatty acids were less than 1%. From the literature it appears that no such work has been performed for the determination of fatty acids in Datura alba seed oil.     

Mathematical modeling of flows through inelastic porous solids

We propose a framework, based on classical mixture theory, to describe the isothermal flow of an incompressible fluid through a deformable inelastic porous solid. The modeling of the behavior of the inelastic solid takes into account changes in the elastic response due to evolution in the microstructure of the material. We apply the model to a compression layer problem. The mathematical problem generated by the model is a free boundary problem.