Stimulated scattering of light in a laser produced magnetoplasma

This note considers stimulated scattering of laser light in the ordinary mode by magnetosonic waves in a plasma. Problems of three-wave decay interaction and modulation instability are investigated. The growth rates and thresholds are obtained analytically. Application to laser-plasma interaction is discussed.     

Replacement of native copper in superoxide dismutase with copper-64 without much loss in its enzymatic activity

Superoxide dismutase, containing copper and zinc, has been labeled with copper-64 by incubating the prepared apoenzyme with cupric(65) chloride at room temperature. No significant loss in the enzymatic activity was observed after labeling. The incorporation of copper-64 was ascertained by starch gel electrophoresis and high performance liquid chromatography. The labeling efficiency was found to be >95%.     

Quasi-Baer module hulls and applications

Let V be a module with $S=\mathrm{End}(V)$. V is called a quasi-Baer module if for each ideal J of S, $r_V(J)=eV$ for some $e^2=e\in S$. On the other hand, V is called a Rickart module if for each $?\in S$, $\mathrm{Ker}(?)=eV$ for some $e^2=e\in S$. For a module N, the quasi-Baer module hull $\mathbf{qB}(N)$ (resp., the Rickart module hull $\mathbf{Ric}(N)$) of N, if it exists, is the smallest quasi-Baer (resp., Rickart) overmodule, in a fixed injective hull $E(N)$ of N. In this paper, we initiate the study of quasi-Baer and Rickart module hulls. When a ring R is semiprime and ideal intrinsic over its center, it is shown that every finitely generated projective R-module has a quasi-Baer hull. Let R be a Dedekind domain with F its field of fractions and let $\{K_i|i\in \mathrm{\Lambda }\}$ be any set of R-submodules of $F_R$. For an R-module $M_R$ with ${\mathrm{Ann}}_R(M)\ne 0$, we show that $M_R\oplus {({?}_{i\in \mathrm{\Lambda }}{K}_i)}_R$ has a quasi-Baer module hull if and only if $M_R$ is semisimple. This quasi-Baer hull is explicitly described. An example such that $M_R\oplus {({?}_{i\in \mathrm{\Lambda }}{K}_i)}_R$ has no Rickart module hull is constructed. If N is a module over a Dedekind domain for which $N/t(N)$ is projective and ${\mathrm{Ann}}_R(t(N))\ne 0$, where $t(N)$ is the torsion submodule of N, we show that the quasi-Baer hull $\mathbf{qB}(N)$ of N exists if and only if $t(N)$ is semisimple. We prove that the Rickart module hull also exists for such modules N. Furthermore, we provide explicit constructions of $\mathbf{qB}(N)$ and $\mathbf{Ric}(N)$ and show that in this situation these two hulls coincide. Among applications, it is shown that if N is a finitely generated module over a Dedekind domain, then N is quasi-Baer if and only if N is Rickart if and only if N is Baer if and only if N is semisimple or torsion-free. For a direct sum $N_R$ of finitely generated modules, where R is a Dedekind domain, we show that N is quasi-Baer if and only if N is Rickart if and only if N is semisimple or torsion-free. Examples exhibiting differences between the notions of a Baer hull, a quasi-Baer hull, and a Rickart hull of a module are presented. Various explicit examples illustrating our results are constructed.     

Solvability of a class of boundary value problems in the space of convergent sequences

We consider two types of infinite systems of second-order differential equations with boundary conditions in the Banach sequence space c. For each system, sufficient conditions are provided for the existence of solutions. Our approach is based on the use of measure of noncompactness concept and the application of Darbo’s theorem for condensing operators. Some examples are presented to illustrate the obtained results.     

Practical,high-yield synthesis of thiol-terminated diacetylenes for formation of conductive monolayers

Self-assembled monolayers of thiol terminated conjugated diacetylenes can be cross-linked using ultraviolet light to form highly conjugated polydiacetylenic conductive monolayers [1]; however, the reported syntheses of the diacetylene monomers present numerous problems that prevent the wide spread application of these in functional materials. We report a redesigned four-step synthesis that proceeds in 75–80% overall yields and allows gram scale production of an array of thiol terminated conjugated diacetylenes, thereby allowing examination and application of these low-dimensional conductive materials.     

Preparation of gelatin/poly(vinyl alcohol) film modified by methyl methacrylate and gamma irradiation

The properties of gelatin–polyvinyl alcohol (G–PVA) blend films were improved by methyl methacrylate (MMA) and γ irradiation for a practical viewpoint. The films were prepared by the casting method, modified by glycerol and MMA monomer, and their mechanical properties were also studied. The gelatin-based films were successfully prepared using γ irradiation (3.1 kGy) and gelatin: PVA = 97:3 (w/w) as optimized. Tensile properties of the films were studied and thermal properties of the films were characterized by thermogravimetric analysis and dynamic mechanical analysis pointed out that MMA treated both gelatin films, and G–PVA blend films showed less thermal degradation than untreated films. In addition, structural and morphological features of the gelatin-based films were examined by Fourier transform infrared and scanning electron microscopy, respectively. The ultimate results of the present study showed remarkable enhancement in tensile properties (> 40%) and a reduction in elongation at break of the films, thanks to the MMA addition and γ irradiation.