Ab-initio nonrelativistic and relativistic Hartree-Fock calculations for both closed- and open-shell molecules using GTO basis

Computer programs forab-initio Hartree-Fock and Dirac-Hartree-Fock calculations on closed- and open-shell atoms and molecules have been indigenously developed. Sample results of high quality are given for Li, Be, LiH and Be₂. As a byproduct of these calculations the importance of considering relativistic effects in the investigation of the elusive bound-state structure of Be₂ is clearly indicated.     

On the effective computation of the inertia of a non-hermitian matrix

Summary given a complex lower Hessenberg matrixA with unit codiagonal, a hermitian matrixH is constructed such that, ifH is non-singular InA= InH. IfA is real,H is real symmetric. Classical results of Fujiwara on the root-separation problem and of Schwarz on the eigenvalue-separation problem are included as special cases.The authors' research was conducted at the Universidade Estadual de Campinas and supported by the Fundação de Amparo à Pesquisa do Estado de São Paulo, Brasil, under grant n⁰ 78/0490.     

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.     

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.