A unified treatment of the groups SO(4) and SO(3,1)

The irreducible representations of the group SO(4) in which the SO(3) subgroup is reduced are studied by an explicit construction of the operators and the basis in the spinor representation. The basis function which is formally identical with that for the coupling of two angular momentaj ₁ andj ₂ is expressible in terms of a hypergeometric function and strongly resembles the one for the irreducible representations of the groups SO(3,1). For the Lorentz group, the bases for the unitary representations which require unphysical values ofj ₁ andj ₂ are found to be analytic continuation of those for SO(4). The realization of the unitary irreducible representations of the group SO(4) in the Hilbert space of these functions leads, for appropriate unphysical values ofj ₁,j ₂, to the Gelfand-Naimark formula for the principal and complementary series of the representations of SO(3;1). The matrix elements for finite transformations of SO(4) and SO(3,1) can be evaluated, in this approach, in a unified manner by using standard properties of the hypergeometric function. These turn out to be a finite sum of₃ F ₂-functions which, as expected, are polynomials for SO(4) and infinite series for SO(3,1). A number of special matrix elements are calculated from the general formula and these agree with the results obtained previously.The authors are deeply indebted to Professor S.Dutta Majumdar fo many important suggestions and clarifications.     

Anomaly in electron channeling due to imperfections produced thermally in a potassium chloride crystal

Lattice imperfections were produced in KCl crystals by a thermal process. The heat treated specimen was irradiated with 50 KeV electrons and the corresponding range of electrons in the crystal has been estimated. It was found that the electron range in the crystal depends upon the temperature of heat treatment, being a decreasing function of this temperature up to about 625 K, above which it becomes an increasing function. This anomaly has been explained in terms of dissolution of vacancies through dislocation loops.     

Use of zirconium phosphate as ion exchanger in some parent-daughter radioisotope separations

Zirconium phosphate as ion exchanger suitable for column operation has been prepared by mixing hot metaphosphoric acid solution with a solution of zirconium oxychloride when the white insoluble phosphate separated out which was dried and purified. The ratio of zirconium: phosphate was found to be 1:2. Separation of parent-daughter systems like¹¹⁵Cd-^115mIn,¹⁴⁴Ce-¹⁴⁴Pr and²¹⁰Pb-²¹⁰Bi were carried out with this exchanger. γ-ray spectrum of the separated^115mIn and the β-decay curve of¹⁴⁴Pr and²¹⁰Bi showed that all the daughter activities are radiochemically pure. The separation process in each case takes less than half an hour and the yield is quantitative.     

Biocompatibility of gold nanoparticles and their endocytotic fate inside the cellular compartment: a microscopic overview

Macrophages are one of the principal immune effector cells that play essential roles as secretory, phagocytic, and antigen-presenting cells in the immune system. In this study, we address the issue of cytotoxicity and immunogenic effects of gold nanoparticles on RAW264.7 macrophage cells. The cytotoxicity of gold nanoparticles has been correlated with a detailed study of their endocytotic uptake using various microscopy tools such as atomic force microscopy (AFM), confocal-laser-scanning microscopy (CFLSM), and transmission electron microscopy (TEM). Our findings suggest that Au(0) nanoparticles are not cytotoxic, reduce the production of reactive oxygen and nitrite species, and do not elicit secretion of proinflammatory cytokines TNF-alpha and IL1-beta, making them suitable candidates for nanomedicine. AFM measurements suggest that gold nanoparticles are internalized inside the cell via a mechanism involving pinocytosis, while CFLSM and TEM studies indicate their internalization in lysosomal bodies arranged in perinuclear fashion. Our studies thus underline the noncytotoxic, nonimmunogenic, and biocompatible properties of gold nanoparticles with the potential for application in nanoimmunology, nanomedicine, and nanobiotechnology.     

Monte Carlo calculation of hot electron drift velocity in silicon (100)-inversion layer by including three subbands

A Monte Carlo calculation of the drift velocity of hot electrons in quantized silicon inversion layers for (100)-oriented surface has been performed by considering the three lowest subbands. The intersubband and intervalley phonons conform to the surface Brillouin zone structure and are assumed to have bulk values of deformation potential constants. It is found that most of the electrons tend to occupy the E_0′ subband at about 10 kV cm^-1. The effect of surface-oxide-charge scattering is found to be quite important. The calculated curves show a change of slope at about 10 kV cm^-1 and do not show clear saturation. This is in contrast with the experimental curve which shows first a smooth variation and then tends to saturate.     

Experimental estimation of the interaction parameter eO for ZnN

The use of dislocation measurements in Zinc single crystals reveals the presence of a yield point or flow stress corresponding to a Stages I–II (elastic to elastic-plastic) transition. This is commonly attributed to the presence of interstitials such as N. The mathematical models of Seeger and Dorn and Rajnak are used to evaluate certain microstructural parameters. These correlate favourably with experimental values. The excess work done over that to overcome the Peierls and frictional forces is then calculated per pair of pinning interstitials and equated to the energy of formation of a molecule of Zn₃N₂ which is believed to form. The results show that this assumption does lead to the stochiometry Zn₃N₂, thus verifying mathematical parameters from different equations using work-energy concepts. Use of the mechanical equivalent J also seems to indicate a favourable correlation for the stochiometry of Zn₃N₂, and for e_O as calculated calorimetrically.     

Investigation of the problem of singularities in general relativity

Recently Addy and Datta have obtained a linearized solution for isentropic motions of a perfect fluid by assigning Cauchy data on the hypersurfacex ⁴=0 and by imposing a restriction on the equation of state. In the present paper we pursue this study and discuss the problem of singularities from the standpoint of a local observer for which a singularity is defined as a state with an infinite proper rest mass density. It is shown that for a closed universe with any distribution of matter whatsoever there occurred a singularity in the past in the nonrotating parts of the universe and it must recur in the future. Furthermore, the collapse of a rotating fluid to a singularity seems inevitable when the relativistic equation of state is considered.