Genericity aspects in gravitational collapse to black holes and naked singularities

We investigate here the genericity and stability aspects for naked singularities and black holes that arise as the final states for a complete gravitational collapse of a spherical massive matter cloud. The form of the matter considered is a general Type I matter field, which includes most of the physically reasonable matter fields such as dust, perfect fluids and such other physically interesting forms of matter widely used in gravitation theory. We first study here in some detail the effects of small pressure perturbations in an otherwise pressure-free collapse scenario, and examine how a collapse evolution that was going to the black hole endstate would be modified and go to a naked singularity, once small pressures are introduced in the initial data. This allows us to understand the distribution of black holes and naked singularities in the initial data space. Collapse is examined in terms of the evolutions allowed by Einstein equations, under suitable physical conditions and as evolving from a regular initial data. We then show that both black holes and naked singularities are generic outcomes of a complete collapse, when genericity is defined in a suitable sense in an appropriate space.Comment: 24 pages, 6 figures, some changes in text and figures to match the version accepted for publication by IJMP

Stability of Naked Singularity arising in gravitational collapse of Type I matter fields

Considering gravitational collapse of Type I matter fields, we prove that, given an arbitrary $C^{2}$- mass function $\textit{M}(r,v)$ and a $C^{1}$- function $h(r,v)$ (through the corresponding $C^{1}$- metric function $\nu(t,r)$), there exist infinitely many choices of energy distribution function $b(r)$ such that the `true' initial data ($\textit{M},h(r,v)$) leads the collapse to the formation of naked singularity. We further prove that the occurrence of such a naked singularity is stable with respect to small changes in the initial data. We remark that though the initial data leading to both black hole and naked singularity form a "big" subset of the true initial data set, their occurrence is not generic. The terms `stability' and `genericity' are appropriately defined following the theory of dynamical systems. The particular case of radial pressure $p_{r}(r)$ has been illustrated in details to get clear picture of how naked singularity is formed and how, it is stable with respect to initial data.Comment: 16 pages, no figure, Latex, submitted to Praman

Antibacterial and antioxidant properties of macrocyclic Schiff bases with vanadium (V) complexes

Macrocyclic Schiff bases have been synthesized by the condensation of acetyl acetone with semicarbazide hydrochloride and thiosemicarbazide in presence of methanol. Further, their oxovanadium complexes have been synthesized by using vanadium acetylacetone. The structural assignment of these compounds has been made on the basis of MP, TLC, MW determination,  conductivities, elemental analysis and UV, IR and 1HNMR spectral datas. The synthesized compounds were screened for their in vitro growth inhibiting activity against different strains of bacteria viz., Staphylococcus aureus, Bacillus licheniformis, Escherichia coli and Micrococcus luteus (ATCC) and were compared with the standard antibiotic oflaxocin. Also in-vitro antioxidant activity of all compounds was determined by nitric acid free radical scavanging assay

An improved magnetic field simulator - MAGFLD.

An improved two-dimensional simulator MAGFLD has been developed which is useful for the design and simulation of periodic permanent magnet (PPM) focusing system for linear beam tubes. At present, input is possible only through the input file, which is very simple and user friendly. A complete PPM circuit is generated using the coordinates of first pole piece, first magnet, gun adapter (if the structure is a-periodic) and the region of computation. Small mesh units of either square or rectangular shapes can be used with mesh refinement capability in one or more regions in any or both directions for better accuracy of the solution. Materials with different magnetic permeability can be modeled by defining a characteristic value for each mesh point of the geometry. The effective potential value at each point in the region of interest is calculated based on the vector potential model by using the 5-point finite difference method and the solution is achieved by over relaxation technique for faster convergence. This package has an interface with EGUN to model the electron gun and collector under the influence of magnetic field. Versatile color graphics are capable of plotting both axial magnetic field and flux lines along with the magnetic circuit. MAGFLD has been validated against some published data and experimental results

A comparison of soft and hard thresholding by using discrete wavelet transforms

This paper  about to reduce the  noise by Adaptive time-frequency Block Thresholding procedure using discrete wavelet transform to achieve better SNR of the audio signal. .  Discrete-wavelet transforms based algorithms are used for audio signal denoising. The resulting algorithm is robust to variations of signal structures such as short transients and long harmonics.  Analysis is done on noisy speech signal corrupted by white noise at 0dB, 5dB, 10dB and 15dB signal to noise ratio levels. Here both hard thresholding and soft thresholding are used for denoising. Simulation & results are performed in MATLAB 7.10.0 (R2010a).  In this paper we are comparing results of soft thresholding and hard thresholding

Theoretical studies on β-lactam antibiotics. VI. Conformational analysis and structure-activity relationships of penicillin sulfoxides and cephalosporins

Conformational energy calculations were carried out on penicillin α- and β-sulfoxides and Δ2- and Δ3- cephalosporins, in order to identify the structural features governing their biological activity. Results on penicillin α-sulfoxide indicated that in its favoured conformation, the orientation of the aminoacyl group was different from the one required for biological activity. Penicillin a sulfoxide, like penicillin sulfide, favoured two conformations of nearly equal energies, but separated by a much higher energy barrier. The reduced activity of the sulfoxides despite the nonplanarity of their lactam peptide indicated that the orientations of the aminoacyl and carboxyl groups might also govern biological activity. Δ3- cephalosporins favoured two conformations of nearly equal energies, whereas Δ2-cephalosporins favoured only one conformation. The lactam peptide was moderately nonplanAr in the former, but nearly planar in the latter. The differences in the.preferred orientations of the carboxyl group between penicillins and cephalosporins were correlated with the resistance of cephalosporins to penicillinases