Variable electrical and thermal conductivity in the theory of generalized thermoelastic diffusion

This paper deals with the problem of a thermoelastic half-space with a permeating substance in contact with the bounding plane in the context of the theory of generalized thermoelastic diffusion with one relaxation time and with variable electrical and thermal conductivity. The bounding surface of the half-space is taken to be traction free and subjected to a time dependent thermal shock. The solution is obtained in the Laplace transform domain by a direct approach. A numerical technique is employed to obtain the solution in the physical domain. It is found that there exist two coupled waves, one of which is elastic and the other is thermal, and a third wave affects diffusion mainly. A comparison is made with the results obtained in a thermoelastic medium with and without diffusion in the following cases : (a) the electrical and thermal conductivities have constant values, (b) the presence of magnetic field and (c) the generalized theory in thermoelasticity.     

Two-carbon homologation of ketones via sily ketene acetals: Synthesis of α,β-unsaturated acids and α-trimethylsilyl δ-ketoacids

The reaction of C,O,O-tris(trimethylsilyl)ketene acetal 1 with saturated, cyclic and aromatic ketones 2 proceeds smoothly in the presence of titanium chloride to give (E)-α,β-unsaturated carboxylic acids 3 with fairly good stereoselectivity. With α,β-unsaturated ketones 4, α-trimethylsilyl δ-ketoacids 5 (syn + anti) are obtained according to Michael-type 1,4 addition. These diastereoisomers are separated and the configurations of 5a are achieved by X-ray molecular analysis.     

Synthesis of New Spirocyclopropane and Oxadiazole Products

In explorations of synthesis and chemistry of spiroheterocycles, we found that the reaction of 2‐diazopropane with arylidene‐benzofuran‐2(3H)‐one and arylidene‐benzofuran‐3(2H)‐one derivatives generated the spirocyclopropane products. In addition to the expected cycloadducts, an unexpected oxadiazole was formed in some cases. The structures of the obtained adducts have been assigned by means of spectroscopic methods.     

Spatial Stability for the Quasi-Static Problem in Thermoelastic Diffusion Theory

In this paper we derive some spatial stability results for the quasi-static problem in thermoelastic diffusion theory for anisotropic media. The coupled system of equations of thermoelasticity with diffusion is a coupling of an elliptic equation with two parabolic equations. It poses some new mathematical difficulties. Here we study the exponential spatial decay of solutions. An upper bound for the amplitude in terms of the boundary and initial conditions is obtained. The extension of the spatial stability results is also treated.     

A Solvent-Stable Metalloprotease Produced by <Emphasis Type="Italic">Pseudomonas aeruginosa</Emphasis> A2 Grown on Shrimp Shell Waste and Its Application in Chitin Extraction

A solvent-stable protease-producing bacterium was isolated and identified as Pseudomonas aeruginosa A2. The strain was found to produce high level of protease activity when grown in media containing only fresh shrimp waste (FSW) or shrimp waste powder (SWP), indicating that it can obtain its carbon, nitrogen, and salts requirements directly from shrimp waste. Maximum protease activities 17,000 and 12,000 U/mL were obtained with 80 g/L SWP and 135 g/L FSW, respectively. The optimum temperature and pH for protease activity were 60 °C and 8.0, respectively. The crude protease, at different enzyme/substrate (E/S) ratio, was tested for the deproteinization of shrimp waste to produce chitin. The crude enzyme of P. aeruginosa A2 was found to be effective in the deproteinization of shrimp waste. The protein removals after 3 h hydrolysis at 40 °C with an E/S ratio of 0.5 and 5 U/mg protein were about 56% and 85%, respectively. ¹³C CP/MAS-NMR spectral analysis of the chitin prepared by treatment with the crude protease was carried out and was found to be similar to that of the commercial α-chitin. These results suggest that enzymatic deproteinization of shrimp waste by A2 protease could be applicable to the chitin production process.     

Sur les distributions covariantes dans les algèbres de Lie réductives

We study the possibility of factoring a covariant distribution on reductive Lie algebras as finite sum of products of an invariant distribution by a covariant polynomial.     

A theory of thermoelastic diffusion materials with voids

In the first part of this paper, we derive the equations of the linear theory of thermoelastic diffusion in porous media based on the concept of volume fraction. Then, we establish a reciprocal relation which leads to reciprocity, uniqueness and continuous dependence theorems for anisotropic materials. Finally, we prove the existence of a generalized solution by means of the semigroup of linear operators theory.     

Separation of Coadjoint Orbits of Generalized Diamond Lie Groups

Mathematical Notes - Let $$G$$ be a type I connected and simply connected generalized diamond Lie group defined as the semidirect product of a $$d$$ -dimensional Abelian Lie group $$N$$ with...