Necessary and sufficient condition for hydrostatic equilibrium in general relativity

We present explicit examples to show that the `compatibility criterion' is capable of providing a {\em necessary} and {\em sufficient} condition for any regular configuration to be compatible with the state of hydrostatic equilibrium. This conclusion is drawn on the basis of the finding that the $M-R$ relation gives the necessary and sufficient condition for dynamical stability of equilibrium configurations only when the compatibility criterion for these configurations is appropriately satisfied. In this regard, we construct an appropriate sequence composed of core-envelope models on the basis of compatibility criterion, such that each member of this sequence satisfies the extreme case of causality condition $v = c = 1$ at the centre. The maximum stable value of $u \simeq 0.3389$ (which occurs for the model corresponding to the maximum value of mass in the mass-radius relation) and the corresponding central value of the local adiabatic index, $(\Gamma_1)_0 \simeq 2.5911$, of this model are found fully consistent with those of the corresponding {\em absolute} values, $u_{\rm max} \leq 0.3406$, and $(\Gamma_1)_0 \leq 2.5946$, which impose strong constraints on these parameters of such models. In addition to this example, we also study dynamical stability of pure adiabatic polytropic configurations on the basis of variational method for the choice of the `trial function', $\xi =re^{\nu/4}$, as well as the mass-central density relation, since the compatibility criterion is appropriately satisfied for these models. The results of this example provide additional proof in favour of the statement regarding compatibility criterion mentioned above.Comment: 31 pages (double-spaced) revtex style, 1 figure in `ps' forma

Shell Model Description of 102−108^{102-108}Sn Isotopes

We have performed shell model calculations for neutron deficient even $^{102-108}$Sn and odd $^{103-107}$Sn isotopes in $sdg_{7/2}h_{11/2}$ model space using two different interactions. The first set of interaction is due to Brown {\it et al.} and second is due to Hoska {\it et al}. The calculations have been performed using doubly magic $^{100}$Sn as core and valence neutrons are distributed over the single particle orbits 1$g_{7/2}$, 2$d_{5/2}$, 2$d_{3/2}$, 3$s_{1/2}$ and 1$h_{11/2}$. In more recent experimental work for $^{101}$Sn [Phys. Rev. Lett. {\bf 105} (2010) 162502], the g.s. is predicted as 5/2$^+$ with excited 7/2$^+$ at 172 keV. We have also performed another two set of calculations by taking difference in single particle energies of 2$d_{5/2}$ and 1$g_{7/2}$ orbitals by 172 keV. The present state-of-the-art shell model calculations predicts fair agreements with the experimental data. These calculations serve as a test of nuclear shell model in the region far from stability for unstable Sn isotopes near the doubly magic $^{100}$Sn core.Comment: Int. J. Mod. Phys. E accepted for publicatio

Dynamical stability of strange quark stars

We show that the mass-radius $(M-R)$ relation corresponding to the MIT bag models of strange quark matter (SQM) and the models obtained by Day et al (1998) do not provide the necessary and sufficient condition for dynamical stability for the equilibrium configurations, since such configurations can not even fulfill the necessary condition of hydrostatic equilibrium provided by the exterior Schwarzschild solution. These findings will remain unaltered and can be extended to any other sequence of pure SQM. This study explicitly show that although the strange quark matter might exist in the state of zero pressure and temperature, but the models of pure strange quark `stars' can not exist in the state of hydrostatic equilibrium on the basis of General Relativity Theory. This study can affect the results which are claiming that various objects like - RX J1856.5-3754, SAX J1808.4-3658, 4U 1728-34, PSR 0943+10 etc. might be strange stars.Comment: 7 pages (including 6 tables and 1 figure) in MNRAS styl

Hydrostatic equilibrium of insular, static, spherically symmetric, perfect fluid solutions in general relativity

An analysis of insular solutions of Einstein's field equations for static, spherically symmetric, source mass, on the basis of exterior Schwarzschild solution is presented. Following the analysis, we demonstrate that the {\em regular} solutions governed by a self-bound (that is, the surface density does not vanish together with pressure) equation of state (EOS) or density variation can not exist in the state of hydrostatic equilibrium, because the source mass which belongs to them, does not represent the `actual mass' appears in the exterior Schwarzschild solution. The only configuration which could exist in this regard is governed by the homogeneous density distribution (that is, the interior Schwarzschild solution). Other structures which naturally fulfill the requirement of the source mass, set up by exterior Schwarzschild solution (and, therefore, can exist in hydrostatic equilibrium) are either governed by gravitationally-bound regular solutions (that is, the surface density also vanishes together with pressure), or self-bound singular solutions (that is, the pressure and density both become infinity at the centre).Comment: 16 pages (including 1 table); added section 5; accepted for publication in Modern Physics Letters

KINETIC ENERGY RECOVERY SYSTEM (KERS)

Kinetic Energy Recovery System (KERS) is a system for recovering the moving vehicle's kinetic energy under braking and also to convert the usual loss in kinetic energy into gain in kinetic energy. When riding a bicycle, a great amount of kinetic energy is lost while braking, making start up fairly strenuous. Here we used mechanical kinetic energy recovery system by means of a flywheel to store the energy which is normally lost during braking, and reuse it to help propel the rider when starting. The rider can charge the flywheel when slowing or descending a hill and boost the bike when accelerating or climbing a hill. The flywheel increases maximum acceleration and nets 10% pedal energy savings during a ride where speeds are between 12.5 and 15 mph

Markers of Oxidative Stress in Generalized Anxiety Psychiatric Disorder: Therapeutic Implications

There is growing evidence that oxidative stress contributes to the pathogenesis of anxiety disorders. Our aim was to measure oxidative stress in anxiety disorders subjects, and assesses the potential confounding influences of anti anxiety therapy. Serum malondialdehyde and antioxidant levels were estimated in patients at the time of presentation and also after anti- anxiety therapy for 3 months. During the period of study no antioxidant/s was given to the patients and control subjects. Serum malondialdehyde levels were significantly higher in the anxiety disorders patients in comparison to control cases. Also, the antioxidant activity of enzymes super oxide dismutase, glutathione and non enzymatic antioxidant levels of vitamins E and C were significantly lower in patients compared to controls at the initial presentation. After 3 months of anti anxiety treatment all the above parameters showed reversal in the respective levels of serum malondialdehyde and antioxidant activity. Anti anxiety medications results in reduced oxidative stress which indicates that oxidative stress is not the cause, but rather a consequence, of anxiety disorders

Lipid Peroxidation and Thymidine Phosphorylase expression in Prostate Carcinoma

Aim: To understand the association between markers of oxidative stress and angiogenesis in relation to disease progression, clinical stage and cytological grade in patho-physiology of prostate carcinoma.Patients and Methods: Case control study comprised of 50 prostate carcinoma patients along with 20 age and sex-matched healthy subjects as controls. Levels of malondialdehyde were measured to study the oxidative stress status in the study subjects. Angiogenesis was evaluated by studying the activity of Thymidine Phosphorylase/Platelet derived endothelial cell growth factor.Results: The levels of markers of oxidative stress along with the activity of thymidine phosphorylase were found to be significantly higher in the study subjects in comparison to healthy controls. The results indicate oxidative stress and angiogenesis activity increase progressively with the increase in staging and progression of disease.Conclusion: Oxidative stress and expression of angiogenesis activity points clearly that with the progression of oxidative stress there is a simultaneous progression of angiogenesis in relation to disease progression, clinical stage and cytological grade in the pathophysiology of prostate carcinoma