A summation formula for appell’s functionF 2

The exact solution of number of problems in quantum mechanics has been given in terms of Appell’s functionF ₂; in an extension of this work I have given here a summation formula, which is as follows:

$$\begin{gathered} \sum\limits_{n = 0}^m {F_2 (a,} - n, - n;1;x,y) \hfill \\ = \frac{{(m + 1)(x - y)^{ - 1} }}{a}[F_2 (a - 1, - m, - m - 1;1,1;x,y) - \rightleftharpoons ] \hfill \\ \end{gathered} $$     

An existence theorem for a fractional control problem

Computational algorithms in mathematical programming have been much in use in the theory of optimal control (see, for example Refs. 1–2). In the present work, we use the algorithm devised by Dinkelback (Ref. 3) for a nonlinear fractional programming problem to prove an existence theorem for a control problem with the cost functional having a fractional form which subsumes the control problem considered by Lee and Marcus (Ref. 4) as a particular case.The author is thankful to the referee for suggestions.     

Energy transfer from acraflavine to rhodamine B in methanol and glycerol:water solution

Excitation energy transfer from acraflavine to rhodamine B in methanol at 300 K is found to be through the mechanism of exciton migration even though the acceptor concentration is about 10 times the donor concentration. The transfer is more efficient at 230 K. In glycerol: water solvent at 300 K the energy migration has been found to persist even upto the acceptor concentration about 50 times the donor concentration. Our results agree with those of Bojarski [2] in as much as the energy migration has been observed even though the acceptor concentration is greater than the donor concentration, but differ in the sense that the migration does not cease at the acceptor concentration 3 times the donor as observed by Bojarski. These effects have been attributed to facilitation of the exciton migration as in glassy media reported by us previously [14,15]. By a quantitative analysis of acceptor emission, we have concluded that the quantum efficiency of transfer is unity. Part of the acraflavine band has been found to transfer radiatively also.     

Kinetics of Oxidation of Phosphinic, Phenylphosphinic and Phosphorous Acid by Benzyltrimethylammonium Chlorobromate

The oxidation of lower phosphorus oxyacids by benzyltrimethylammonium chlorobromate (BTMACB) proceeds by a mechanism involving a hydride-ion transfer from oxyacids to the oxidant in the rate-determining step.     

Finite-temperature thermophysical properties of fcc-Ca

At an extreme environment, such as high-temperature and high-pressure, harmonic theory has obvious limitations, where the anharmonic effects are influential in determining bulk properties of the materials. In this regard, necessity for incorporating anharmonicity through vibrational contribution and thermally excited electrons to the total free energy at finite temperatures is illustrated taking an example of divalent fcc-Ca. In this regard, we have employed a coupling scheme of combining recently proposed mean-field potential (MFP) with the local pseudopotential to obtain vibrational contribution to the total free energy. To access the applicability of the present coupling scheme, we have calculated temperature variation of several thermodynamical properties. Static EOS, shock Hugoniot and temperature along principal Hugoniot are also estimated. Results are satisfactorily compared with the other theoretical and experimental data and the use of local pseudopotential in conjunction with the MFP approach is justified.     

Some solutions of the Einstein-Maxwell equations in general relativity

A solution of the Einstein-Maxwell equations corresponding to source-free electromagnetic field plus pure radiation is obtained. The solution is algebraically special. A particular case of the solution is considered which encompasses many known solutions. Among them is a radiating Ruban metric.     

A new general method for the introduction of the aldehyde function in aromatic compounds

Side chain bromination of aromatic amidomethylated compounds yields aldehydes.     

The Nimbus 7 LIMS version 6 radiance conditioning and temperature retrieval methods and results

The Nimbus 7 Limb Infrared Monitor of the Stratosphere (LIMS) experiment operated for just over 7 months in 1978/1979, as planned. Its version 5 (V5) dataset was archived for public use in 1983. Subsequently, several important improvements were realized about the LIMS instrument, its forward radiance model, and the line parameters (from HITRAN 92 or 96) for the gases that emit in its broadband spectral channels. In addition, the orbital attitude knowledge for LIMS was refined by comparing the slopes of the observed radiance profiles from its two CO₂ channels within the upper stratosphere through lower mesosphere. This approach also overcomes the usual requirement for absolute radiance calibrations in flight. The band model approximations employed for CO₂ and interfering O₃ and based on HITRAN for the 15-μm region are adequate for accurate retrievals of temperature versus pressure profiles T(p). Consequently, a reprocessed or Version 6 (V6) profile dataset was generated using these improved radiance conditioning methods (or Level 1) and the T(p) retrieval algorithm (or Level 2), and those updates are described briefly. In particular, the approach for V6 used all the radiance data ( vertical spacing), and the V6 retrievals are based on all the measured radiance profiles along an orbit. Precision and accuracy of the V6 T(p) data are improved over that for V5, most noticeably in the mesosphere. Profiles of geopotential height have also been generated as part of the V6 dataset from which one can analyze its horizontal gradients for the wind fields and higher dynamical quantities, rather than mapping the temperature fields first. The entire LIMS V6 profile dataset was archived at the NASA Goddard Distributed Active Archive Center (DAAC) in September 2002. The high quality of these V6 data demonstrates more fully the promise of the broadband, limb-infrared remote sensing technique for operational measurements of middle atmosphere T(p) from Earth-orbiting satellites.     

Antibacterial study of Eucalyptus grandis fabricated zinc oxide and magnesium doped zinc oxide nanoparticles and its characterization

Mg-doped zinc oxide and zinc oxide nanoparticles were prepared by using methanolic seed extract from the Eucalyptus grandis plant via a green approach. Phytoconstituents present in seed extract act as capping and stabilizing agents for the biosynthesis of nanoparticles. Doping of Mg to zinc oxide nanoparticles increases the bandgap energy, thus enhancing its chemical, physical and optical properties. Further, it was characterized by various techniques such as scanning electron microscopy giving morphological information about the wurtzite hexagonal structure of bio-synthesized nanoparticles. X-ray diffraction technique tells about the crystalline nature of particles and the average crystallite size for zinc oxide and doped zinc oxide nanoparticles. Mg as a dopant enhances the properties of nanoparticles, thus making it more efficiently applicable as an antibacterial agent against Escherichia coli, gram-negative bacteria.