Initial-value problems and singularities in general relativity

Linearized solution of Datta in a non-symmetric and isentropic motion of a perfect fluid is studied by dealing with a Cauchy problem in co-moving coordinates in the framework of general relativity. The problem of singularities is discussed from the standpoint of a local observer both for rotating and non-rotating fluids. It is shown that, whatever the distribution of matter, a singularity which occurred in the past in both the rotating and non-rotating parts of the universe must occur again later after some finite proper time, if the universe is closed. A modification is incorporated in Penrose’s theorem by explicitly exhibiting that the universe defined by Penrose can possess a Cauchy hypersurface.     

Virtual LSPs at e+ e− colliders

Currently popular search strategies for supersymmetric particles may be significantly affected due to relatively light sneutrinos which decay dominantly into invisible channels. In certain cases the second lightest neutralino may also decay invisibly leading to two extra carriers of missing energy (in addition to the lightest supersymmetric particle (LSP) ) — the virtual LSPs (VLSPs). A tree lavel calculation shows that if the sneutrino mass happens to be in the small but experimentally allowed range (m _≈ν ≈ 45–55 GeV), these particles together with neutralino pairs may contribute significantly to the missing energy in the process e⁺e^? → γ+ E at LEP-2 energies as an enhancement over the Standard Model or the conventional MSSM predictions. It is further shown that a much larger region of the parameter space can be scanned at a high luminosity e⁺e^? collider at 500 GeV like the proposed NLC machine. Moreover, at both LEP-2 and NLC this process may play a complementary role to direct chargino searches, which may fail due to a near mass degeneracy of the chargino and the sneutrino. Formulae for the cross sections taking into account full mixings of the charginos and the neutralinos are derived. The signal remains observable even in the context of more restricted models based onN=1 SUGRA with common scalar and gaugino masses. A preliminary study of the QED radiative corrections due to soft multiple photon emission as well as hard collinear bremsstrahlung indicates that these corrections play a crucial role in estimating the background.     

First order quantum correction to the free energy of simple liquids

Using the perturbation theory of Weekset al the first order quantum correction to the free energy of a simple fluid characterised by a double Yukawa potential function has been expressed in a simple closed analytical form which allows numerical calculation simply on a desk calculator.     

Catalytic transfer reduction of conjugated alkenes and an imine using polymer-supported formates

An efficient and mild method for catalytic transfer hydrogenation of CC and CN double bonds with the aid of resin-supported formate (PSF) as the hydrogen donor and palladium acetate as the catalyst is reported.     

Synthesis,reduction, and reductive alkylation of a few tricyclic α,β-unsaturated ketones

Reduction and reductive alkylation of the tricyclic α,β-unsaturated ketones 9–12 afforded the saturated ketones 13–21 in high yields.     

An Inventory Model with Two-Component Demand Rate and Shortages

The article investigates a deterministic inventory system with two-component demand rate. The demand rate is stock-dependent down to a certain level and then constant. Shortages are allowed and are fully backlogged. The storage space is assumed to be limited. A flowchart is provided to solve a general system. To study the effects of changes in the system parameters on the average net profit a sensitivity analysis has been performed.     

Stereochemical evidence for single electron transfer mechanism in the reduction of cyclic ketones with alkoxyaluminium dichlorides

The stereochemical results of the reduction of cyclic ketones with alkoxyaluminium dichlorides do not conform to the conventional polar cyclic mechanism and may be explained by a single electron transfer mechanism.     

Fluid-dynamical representations of the Dirac equation

A relative kinetic mass operator is defined bym =c ⁻²·(E −eΦ), and it is shown that bt using it in a symmetric form one can correlate the (charge) velocity operatorα in the Dirac theory exactly with the general quantum mechanical momentum —ih∇. Then the net force, defined as the rate of change of the relative momentum with time, is exactly equal to the Lorentz force. The contribution due to the time variation of mass equals the negative of space variation of the scalar potential, the Newtonian force, whereas the time variation of the charge current absorbs the entire vector potential dependence. The analogous Euler equations can be written either in terms of the charge current or in terms of the mass current. For a many particle system one needs the usual net single particle parameters and the consideration of both the direct and exchange contributions of the two particle interaction. These Euler equations yield two different conditions of the stationary state. It is shown that the charge-current condition is necessary but not sufficient, whereas the mass-current condition retains the appropriate scalar potential dependence. These two conditions are compared for the spherically symmetric case. The charge density, charge current and relative mass current are tabulated for atomic spinors. Differences between the quantum and classical forces for the H ₂ ⁺ molecular ion exhibit the inadequacy of ordinary atomic spinor basis in forming molecular spinors.     

Analysis and merit of the constrained-component variation in dirac theory

It is shown that the constrained-component variation generally suggested by Rosicky and Mark is very fundamental, has consistent variational features and reproduces, as a special case, earlier variational results for atomic systems obtained by Drake and Goldman. Numerical merits and demerits of this method are qualitatively assessed.