Theorems of the Alternative over Indefinite Inner Product Spaces

In this paper, we study the Farkas alternative over indefinite inner product spaces using the recently proposed indefinite matrix product.     

Principal bundles on the affine line

We prove that any principal bundle on the affine line over a perfect field with a reductive group as structure group comes from the base field by base change.     

Some polishing experiments on copper in a hyperbolic cell

Some polishing experiments have been carried out on copper anodes in a hyperbolic cell designed by Gilmont and Walton, using orthophosphoric acid as the electrolyte. The results obtained have been compared to those obtained in similar experiments in a Hull cell. It has been found that very similar bands of different reflectivity and polishes are found to form in both the cells. These bands shift with time and a study of such displacements has been made. The results are briefly discussed.     

Analysis of a model for transport of charged particles in a random magnetic field

A model for the transport of charged particles in a random magnetic field is a Volterra integrodifferential equation with a long-range kernel. The integrodifferential equation is solved numerically with the method of Bellman, Kalaba, and Lockett (“Numerical Inversion of the Laplace Transform,” Elsevier, New York, 1966). The results are shown to be in excellent agreement with analytical asymptotic results.     

New methods for the Preparation of Nitrosyl Chloride

A pure sample of nitrosyl chloride has been prepared either by reaction of phosphorus trichloride with concentrated nitric acid or by reaction of phosphorus trichloride with sodium nitrate in presence of water. The nitrosyl chloride gas has been characterized by i.r. spectral data and elemental analysis.     

Photophysical Studies on the Interaction of Acridinedione Dyes with Universal Protein Denaturant: Guanidine Hydrochloride

Photophysical studies of photoinduced electron transfer (PET) and non-PET based acridinedione dyes with guanidine hydrochloride (GuHCl) were carried out in water and methanol. Addition of GuHCl to photoinduced electron transfer (PET) based acridinedione dye (ADR 1) results in a fluorescence enhancement, whereas a non-PET based dye (ADR 2) shows no significant change in the fluorescence intensity and lifetime. Addition of GuHCl to ADR 1 dye in methanol results in single exponential decay behaviour, on the contrary a biexponential decay pattern was observed on the addition of GuHCl in water. Absorption and emission spectral studies of ADR 1 dye interaction with GuHCl reveals that the dye molecule is not in the protonated form in aqueous GuHCl solution, and the dye is confined to two distinguishable microenvironment in the aqueous phase. A large variation in the microenvironment around the dye molecule is created on the addition of GuHCl and this was ascertained by time-resolved area normalized emission spectroscopy (TRANES) and time-resolved emission spectroscopy (TRES). The dye molecule prefers to reside in the hydrophobic microenvironment, rather in the hydrophilic aqueous phase is well emphasized by time-resolved fluorescence lifetime studies. The mechanism of fluorescence enhancement of ADR 1 dye by GuHCl is attributed to the suppression of the PET process occuring through space.     

On the repetitive operation of a self-switched transversely excited atmosphere CO<Subscript>2</Subscript> laser

The repetition rate capability of self-switched transversely excited atmosphere (TEA) CO₂ laser was studied for different gas flow configurations. For an optimized gas flow configuration, repetitive operation was achieved at a much smaller gas replenishment factor between two successive pulses when compared with repetitive systems energized by conventional pulsers.     

Influence of Sm<Superscript>3+</Superscript> ion in structural,morphological, and electrochemical properties of LiMn<Subscript>2</Subscript>O<Subscript>4</Subscript> synthesized by microwave calcination

LiSm_xMn_2–xO₄ samples were synthesized via co-precipitation technique. The structural properties of the synthesized materials were studied using X-ray diffraction analysis and it confirmed the cubic spinel structure for all the compounds. The lattice parameter of LiMn₂O₄ was observed to be 8.2347 Ǻ and it decreased with Sm³⁺ concentration, due to the shrinkage in cell volume aided by higher binding energy between Sm-O bond. The SEM micrographs were analyzed using Image processing software (Image-J) to ascertain the pore and grain properties. The microwave synthesis had been observed to control the bulk grain formation and had yielded lesser porous and nanoparticles. The particle size distributions obtained through photocross correlation laser diffraction analysis had shown that LiMn₂O₄ with 60 nm and Sm-doped compounds with ∼30 nm, respectively. The cyclic voltammetry studies had revealed the decrease in electrocatalytic behavior in the initial cycle for compounds doped with Sm³⁺ ion. The initial capacities of LiMn₂O₄, LiSm_0.05Mn_1.95O₄ and LiSm_0.10Mn_1.90O₄ substituted compounds were observed to be 134.87 mAhg⁻¹, 132.22 mAhg⁻¹ and 126.41 mAhg⁻¹, respectively. The cells were simulated using 1D model namely Dualfoil5.1 program. The simulated results coincide well with the measured results. The cycle life studies reveal 93% capacity retention of samarium-0.05-doped samples when compared with 78.4% of the LiMn₂O₄.