Mathematical Model for Impact of Media on Cleanliness Drive in India

A mathematical model on cleanliness drive in India is analysed for active cleaners and passive cleaners. Cleanliness and endemic equilibrium points are found. Local and global stability of these equilibrium points are discussed using Routh-Hurwitz criteria and Lyapunov function respectively. Impact of media (as a control) is studied on passive cleaners to become active. Numerical simulation of the model is carried out which indicates that with the help of media transfer rate to active cleaners from passive cleaners is higher

Exact Kohn-Sham versus Hartree-Fock in momentum-space: examples of two-fermion systems

The question of how density functional theory (DFT) compares with Hartree-Fock (HF) for the computation of momentum-space properties is addressed in relation to systems for which (near) exact Kohn-Sham (KS) and HF one-electron matrices are known. This makes it possible to objectively compare HF and exact KS and hence to assess the potential of DFT for momentum space studies. The systems considered are the Moshinsky atom, the Hooke's atom and light two-electron ions, for which expressions for correlated density-matrices or momentum densities have been derived in closed-form. The results obtained show that it is necessary to make a distinction between true and approximate DFT.Comment: 30 pages, accepted for publication in J. Chem. Phys. (2006

Pseudospectral Calculation of the Wavefunction of Helium and the Negative Hydrogen Ion

We study the numerical solution of the non-relativistic Schr\"{o}dinger equation for two-electron atoms in ground and excited S-states using pseudospectral (PS) methods of calculation. The calculation achieves convergence rates for the energy, Cauchy error in the wavefunction, and variance in local energy that are exponentially fast for all practical purposes. The method requires three separate subdomains to handle the wavefunction's cusp-like behavior near the two-particle coalescences. The use of three subdomains is essential to maintaining exponential convergence. A comparison of several different treatments of the cusps and the semi-infinite domain suggest that the simplest prescription is sufficient. For many purposes it proves unnecessary to handle the logarithmic behavior near the three-particle coalescence in a special way. The PS method has many virtues: no explicit assumptions need be made about the asymptotic behavior of the wavefunction near cusps or at large distances, the local energy is exactly equal to the calculated global energy at all collocation points, local errors go down everywhere with increasing resolution, the effective basis using Chebyshev polynomials is complete and simple, and the method is easily extensible to other bound states. This study serves as a proof-of-principle of the method for more general two- and possibly three-electron applications.Comment: 23 pages, 20 figures, 2 tables, Final refereed version - Some references added, some stylistic changes, added paragraph to matrix methods section, added last sentence to abstract

On the evaluation of some three-body variational integrals

Stable recursive relations are presented for the numerical computation of the integrals $$\int d{\bf r}_1 d{\bf r}_2 r_1^{l-1} r_2^{m-1} r_{12}^{n-1} \exp{\{-\alpha r_1 -\beta r_2 -\gamma r_{12}\}}$$ ($l$, $m$ and $n$ integer, $\alpha$, $\beta$ and $\gamma$ real) when the indices $l$, $m$ or $n$ are negative. Useful formulas are given for particular values of the parameters $\alpha$, $\beta$ and $\gamma$.Comment: 12 pages, 1 figure (PS) and 3 tables. Old figures 2 and 3 replaced by Tables I and III. A further table added. Paper enlarged giving some tips on the convergence of quadrature

Corrections to the Nonrelativistic Ground Energy of a Helium Atom

Considering the nuclear motion, the authors give out the nonrelativistic ground energy of a helium atom by using a simple but effective variational wave function with a flexible parameter $k$. Based on this result, the relativistic and radiative corrections to the nonrelativistic Hamiltonian are discussed. The high precision value of the helium ground energy is evaluated to be -2.90338 a.u., and the relative error is 0.00034%.Comment: 8 pages, no figures, 2 table

The First Caltech-Jodrell Bank VLBI Survey. II. λ = 18 Centimeter Observations of 25 Sources

We report λ-18 cm VLBI observations made in 1991 September of a further 25 objects from the first Caltech-Jodrell Bank VLBI Survey (the CJ1 survey). The CJ1 sample is a complete, flux-density limited sample of 135 radio sources with total flux density at λ-6 cm between 0.7 and 1.3 Jy. These observations complete the λ-18 cm part of the survey. Together with the results of Paper I (Polatidis et al.), we have now observed 81 CJ1 sources at λ-18 cm. later papers in the series will present λ-6 cm observations and the analysis and interpretation of the results

Evaluation of antioxidative, proteolytic, and ace inhibitory activities of potential probiotic lactic acid bacteria isolated from traditional fermented food products

Probiotic lactic acid bacteria (LAB) have been engrossed in plentiful food fermentations, known to man for millennia. The current investigation was aimed at investigating technical attributes, such as production of bioactive peptides, particularly ACE-I activity (anti-hypertensive property), proteolytic activity, and antioxidant activities of the potential probiotic LAB strains isolated from a diverse dairy and non-dairy based fermented foods. Among all ten LAB isolates, PFC21, isolated from sauerkraut, exhibited the highest antioxidative potential and showed maximum free radical scavenging ability using both ABTS (83.8±3.77%) and DPPH (59.4±2.18%) assays. It was followed by PD2 (dosa batter isolate) that showed (79.4±1.61%) activity in ABTS assay. PD2 revealed the highest proteolytic activity during 24 h and 48 h (with 0.82 and 1.12 absorbance, respectively) of fermentation at 37 °C; followed by a curd isolate, PC6, and PFC21 with 0.99 and 0.90 absorbance, respectively, at 48 h incubation. Furthermore, PD2 also showed the significantly (P<0.05) highest (49.39%) ACE inhibition followed by PFC21 (41.38%). These fascinating results led us to further evaluate the potential probiotic strains with regard to their utilization in the production of healthy quality foods with additional technical advantages

Theory and applications of atomic and ionic polarizabilities

Atomic polarization phenomena impinge upon a number of areas and processes in physics. The dielectric constant and refractive index of any gas are examples of macroscopic properties that are largely determined by the dipole polarizability. When it comes to microscopic phenomena, the existence of alkaline-earth anions and the recently discovered ability of positrons to bind to many atoms are predominantly due to the polarization interaction. An imperfect knowledge of atomic polarizabilities is presently looming as the largest source of uncertainty in the new generation of optical frequency standards. Accurate polarizabilities for the group I and II atoms and ions of the periodic table have recently become available by a variety of techniques. These include refined many-body perturbation theory and coupled-cluster calculations sometimes combined with precise experimental data for selected transitions, microwave spectroscopy of Rydberg atoms and ions, refractive index measurements in microwave cavities, ab initio calculations of atomic structures using explicitly correlated wave functions, interferometry with atom beams, and velocity changes of laser cooled atoms induced by an electric field. This review examines existing theoretical methods of determining atomic and ionic polarizabilities, and discusses their relevance to various applications with particular emphasis on cold-atom physics and the metrology of atomic frequency standards.Comment: Review paper, 44 page