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

Kinetic Characterization and Partial Purification of Peroxidase in Eucalyptus F1 Hybrids

A differential pattern of peroxidase (E.C. 1.1.11.7) has been observed in reciprocal F1 hybrids of Eucalyptus (FRI-4 and FRI-5) produced using parental combination of E. tereticornis and E. camaldulensis. The hybrids were characterized for the qualitative, kinetic parameters (total and specific activity, units, Km and Vmax) and partial purification of peroxidase. The qualitative study showed the presence of high molecular weight peroxidase isoforms i.e. 260 KD, 250 KD and 110KD bands. A strong maternal inheritance was observed for 260 KD loci in FRI-5. Kinetic characterization of peroxidase revealed that F1 genotypes had efficient peroxidase system over their parental combination resulting in 8 -10 times more heterotic vigour. The FRI-5 genotypes were found to be having efficient peroxidase system with lowest Km values (0.12mM-0.17mM) and higher Vmax values ranging from 0.07-0.14mM min-1mg prot-1. The study revealed the role of maternal inheritance and was found that better genotypes are produced when superior parents are used as seed parent. The results suggest the efficient use of peroxidase marker for the identification of the better genotypes in forest tree species. &nbsp

The spectrum of endstates of gravitational collapse with tangential stresses

The final state--black hole or naked singularity--of the gravitational collapse of a marginally bound matter configuration in the presence of tangential stresses is classified, in full generality, in terms of the initial data and equation of state. If the tangential pressure is sufficiently strong, configurations that would otherwise evolve to a spacelike singularity, result in a locally naked singularity, both in the homogeneous and in the general, inhomogeneous density case.Comment: 9 pages, revtex4; accepted for publication in Phys. Rev.

Quantitative Determination and Source Variation of Rutin in Fagopyrum Tataricum

Buckwheat (Fagopyrum sp.) is a traditional crop of Uttarakhand (India) known for its high Rutin content, a bioflavonoid with significant medicinal properties. This study explores the quantitative measurement of Rutin in various buckwheat varieties grown in different regions of Uttarakhand using Thin Layer Chromatography (TLC) and High-Performance Thin Layer Chromatography (HPTLC). Twelve seed sources of Fagopyrum tataricum from the Garhwal and Kumaon regions, along with Fagopyrum esculentum seeds for comparison, were collected. Preliminary phytochemical screening of the extracts revealed the presence of flavonoids, alkaloids, tannins, and carbohydrates, with methanolic extracts showing higher concentrations. TLC analysis was employed to determine the most effective solvent system for Rutin separation, leading to the identification of three samples with substantial Rutin content. HPTLC was then used for quantitative Rutin assessment, with a calibration curve established using standard Rutin solutions. The three selected samples, along with the standard, were applied to HPTLC plates, and the Rutin content was measured based on peak areas and peak heights. The sample collected from Joshimath, Uttarakhand, known as "JOG," exhibited the highest Rutin content. This study provides valuable insights into the phytochemical composition of buckwheat varieties in Uttarakhand, which can inform the development of high-quality functional foods. Rutin, a potent antioxidant with various health benefits, underscores the significance of buckwheat as a naturally occurring functional food source. The results contribute to understanding the Rutin-rich potential of buckwheat grown in Uttarakhand and its applications in functional foods and nutraceuticals. Further research in this field can promote the cultivation and utilization of buckwheat as a source of this valuable bioactive compound with numerous health benefits

The final fate of spherical inhomogeneous dust collapse II: Initial data and causal structure of singularity

Further to results in [9], pointing out the role of initial density and velocity distributions towards determining the final outcome of spherical dust collapse, the causal structure of singularity is examined here in terms of evolution of the apparent horizon. We also bring out several related features which throw some useful light towards understanding the nature of this singularity, including the behaviour of geodesic families coming out and some aspects related to the stability of singularity.Comment: Latex file, uses epsf.sty, 15 pages and 3 eps figures. Paragraph on role of smooth functions rewritten. Four references added. To appear in Classical & Quantum Gravit

Phytochemical Analysis And Evaluation Of Antioxidant Activity In Fagopyrum Esculentum

Herbal nutraceutical products have become increasingly popular in recent years, particularly in the dermatology and cosmetics fields, because of their potential to prevent skin photodamage and their photoprotective qualities against UV radiation. Standardized herbal extracts are necessary for modern phytopharmaceutics and phytocosmetics, and buckwheat herb, which is high in flavonoids, has shown promise as an antioxidant source. The objective of the research is to ascertain the existence of various nutraceutical components in buckwheat, such as proteins, carbohydrates, sterols, alkaloids, saponins, and tannins, both quantitatively and qualitatively. The study assesses possible interactions between these components, food, and prescribed medications as the body of research on their health benefits grows. Through a variety of phytochemical tests, the results show the high antioxidant and nutraceutical qualities of Fagopyrum esculentum, with methanolic extracts showing greater activity than water extracts. Notably, the study highlights the high antioxidant activity, alkaloids, flavonoids, tannins, and phenolic compounds of F. esculentum as potential major food supplement. This study offers a biochemical justification for its application in ethnopharmacology and as a nutraceutical to improve health and prevent a variety of ailment

Singularities in gravitational collapse with radial pressure

We analyze spherical dust collapse with non-vanishing radial pressure, $\Pi$, and vanishing tangential stresses. Considering a barotropic equation of state, $\Pi=\gamma\rho$, we obtain an analytical solution in closed form---which is exact for $\gamma=-1,0$, and approximate otherwise---near the center of symmetry (where the curvature singularity forms). We study the formation, visibility, and curvature strength of singularities in the resulting spacetime. We find that visible, Tipler strong singularities can develop from generic initial data. Radial pressure alters the spectrum of possible endstates for collapse, increasing the parameter space region that contains no visible singularities, but cannot by itself prevent the formation of visible singularities for sufficiently low values of the energy density. Known results from pressureless dust are recovered in the $\gamma=0$ limit.Comment: to appear in GRG; LaTeX, 22 pages, 2 eps figure

Long term effect of INM on aonla (Emblica officinalis) and soil quality under rainfed hot semi-arid environment

The experiment was conducted on seven and eight years old aonla (Emblica officinalis Gaertn) tree of NA-7 to study the influence of various levels of organic (FYM and biofertilizers) and inorganic (NPK) sources of nutrients on morphometrix, productivity and quality attributes of aonla and soil quality during 2009-10 and 2010-11 under hot semi-arid ecosystem. Significant improvement was recorded in soil quality by application of different combinations of NPK, FYM and biofertilizers. The vegetative growth, yield and quality of aonla were influenced significantly by different sources of nutrients. The maximum vegetative growth was recorded in the plants which were applied with standard doses of NPK which was followed by farmyard manure plus 50% of the standard dose of NPK. The maximum mean yield per plant (48.45 kg) was recorded in the plants treated with standard doses of NPK followed by FYM + 50% of standard dose of NPK (45.27 kg). TSS, total sugar, vitamin C and total phenols were influenced considerably by the application of different organic sources of nutrients being highest in T5 (FYM + Azotobactor + VAM) treatment. The soil properties in terms of pH and EC declined whereas hydraulic conductivity, organic carbon increased from their initial values with the application of various organic sources of nutrient in different combinations, while pH, EC, hydraulic conductivity, bulk density and organic carbon of the basin soil treated with standard dose of NPK were not improved considerably