Opacity Calculations for Dense Plasmas

A code has been developed for calculating opacities of hot dense plasmas. This uses the average atom model to calculate the frequency dependent opacities with contributions from bound‐bound, bound‐free, free‐free and scattering processes. In this paper, we report work in three areas. Firstly, we present the enhanced absorption found in certain photon energy regions with the use of screening coefficients with l‐splitting in comparison to those obtained without l‐splitting. Secondly, we have generalized the code to allow mixture of elements, albeit without molecular effects. Thirdly, we compare our code results with other codes and experimental data.     

Confidence ellipsoids based on a general family of shrinkage estimators for a linear model with non-spherical disturbances

This paper considers a general family of Stein rule estimators for the coefficient vector of a linear regression model with nonspherical disturbances, and derives estimators for the Mean Squared Error (MSE) matrix, and risk under quadratic loss for this family of estimators. The confidence ellipsoids for the coefficient vector based on this family of estimators are proposed, and the performance of the confidence ellipsoids under the criterion of coverage probability and expected volumes is investigated. The results of a numerical simulation are presented to illustrate the theoretical findings, which could be applicable in the area of economic growth modeling.     

A new method for the calculation of Sommerfeld screening parameter σ1 in x-ray spectra

The paper describes a new method for the calculation of the Sommerfeld screening parameter σ₁. It requires neither the knowledge of the energy separations of spin doublet levels nor is it based on the application of the Hertz law. The only data required for the calculation are the experimental energy values of the level concerned for the series of elements belonging to the same subshell in which the element in the question is situated. As an illustration the values of σ₁ are calculated for the L ₁, L ₂ and L ₃ levels for elements belonging to the 4f subshell and these are found to be in excellent agreement with those published earlier by Gokhale and Misra. The method brings out the constancy of σ₁ (L ₂ L ₃)−σ₁(L ₁) in a natural way and may thus be regarded as providing theoretical explanation of the Hertz law.     

Synthesis and Properties of Mixed Ligand Complexes of Diorganotin(IV): Part(VII) – Synthesis and Characterisation of Some Antibacterial Dibenzoylmethane Diorganotin(IV)‐O‐alkyl Trithiophosphates

A series of some new mixed ligand complexes have been synthesized with an objective for evaluation as antimicrobials. Reactions of diorganotin(IV) dichloride with dibenzoyl methane and O‐alkyl trithiophosphates in a 1:1:1 molar ratio in refluxing benzene yield products of the type [PhCOCHCOPh]R₂Sn‐[SSH(S)POR'] [where R = Me, Bu, Ph; R' = Me, Et, Prⁱ, Buⁱ, Ph]. The newly synthesized complexes are light yellow colored crystalline solids, non‐volatile, soluble in common organic solvents, monomeric in nature and highly sensitive towards atmospheric moisture. These complexes are characterized by elemental analysis, IR and multinuclear NMR (¹H, ³¹P and ¹¹⁹Sn) spectral studies. Spectral studies of these complexes indicate that dibenzoyl methane and O‐alkyl trithiophosphate moieties are bidentate and the central tin atom is hexacoordinated in nature. A few of these compounds were tested for their antibacterial activity using standard drugs.     

Fixed-width confidence intervals for contrasts in the means

The sequential procedure developed by Bhargava and Srivastava (1973, J. Roy. Statist. Soc. Ser. B, 35, 147–152) to construct fixed-width confidence intervals for contrasts in the means is further analyzed. Second-order approximations for the first two moments of the stopping time and the coverage probability associated with the sequential procedure, are obtained. A lower bound for the number of additional observations after stopping is derived, which ensures the mxact probability of coverage. Moreover, two-stage, three-stage and modified sequential procedures are proposed for the same estimation problem. Relative advantages and disadvantages of these sampling schemes are discussed and their properties are studied.     

A threefold superstructure of the anti‐epileptic drug phenytoin sodium as a mixed methanol solvate hydrate

Phenytoin sodium, a salt of 5,5‐diphenylimidazolidine‐2,4‐dione, or phenytoin, is commercially available in various dosage forms for its anti‐epileptic properties to treat and prevent seizures. The title compound, poly[aquatris(μ₃‐4,4‐diphenyl‐2,5‐dioxoimidazolidin‐1‐ido)trimethanoltrisodium(I)], [Na₃(C₁₅H₁₁N₂O₂)₃(CH₄O)₃(H₂O)_1.08]_n, a methanol solvate and hydrate of phenytoin sodium, forms a modulated crystal structure that consists of a supercell made up of three close‐to‐identical repeat units. Each of the basic fragments consists of one phenytoin anion, a sodium cation, and either a methanol, or a methanol and a water molecule coordinated to the sodium ion, yielding a formula unit of Na(C₁₅H₁₁N₂O₂)(CH₃OH)_x(H₂O)_y for each of the three segments (x, y = 0 or 1; x + y = 1 or 2). Modulation along the b axis is introduced due to the presence or absence of water or methanol molecules at sodium and by the alternating torsion angles of one of the two phenytoin phenyl rings. Individual segments within the asymmetric unit are linked by covalent Na—O and Na—N bonds, with each sodium ion coordinated to one anionic amide N atom and three keto O atoms. The Na—N and one of the Na—O bonds connect (C₁₅H₁₁N₂O₂)·Na units along the modulation direction, creating an infinite [(C₁₅H₁₁N₂O₂)·Na] chain that is further stabilized by intramolecular N—H…O hydrogen bonding parallel to [010]. The second Na—O bond connects this chain with a symmetry‐equivalent copy of itself created by a screw‐axis operation, yielding double strands of [(C₁₅H₁₁N₂O₂)·Na] chains. Two of these double strands, propagating in opposite directions, constitute the content of the unit cell. Neighboring double strands are connected with each other to form layers perpendicular to the a axis, tethered together via O—H…O hydrogen bonds involving the water and methanol molecules. In addition to modulation, each of the repeat units also exhibits disorder of the modulated segments. Phenyl rings of each repeat unit are rotationally disordered, and sodium‐coordinated methanol and water molecules are also positionally disordered and/or partially occupied. The solvated structure reported here, while not matching the patterns reported for any of the known forms of phenytoin sodium, does provide a first insight into the complications and complexities involved in resolving the structure of anhydrous phenytoin sodium.     

Vibrational dynamics and heat capacity in poly(L‐lactic acid)

Poly(L ‐lactic acid) (PLLA) (? CH(CH₃) ? COO? )_n is a biodegradable polymer, which exhibits many applications in the biomedical field and where thermoplastics are employed. A comprehensive study of the normal modes and their dispersion in PLLA using Wilson′s GF matrix method as modified by Higgs is being reported. Assignments of calculated normal modes have been made and characteristic features of dispersion curves are discussed. Heat capacity has been calculated via density‐of‐states using Debye relation in the temperature range 10–250 K, which is in fairly good agreement with the experimental data. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 175–182, 2010     

O-Alkyl Trithiophosphate Derivatives of Triorganotin(IV) and S-Alkyl Trithiophosphate Derivatives of Diorganotin(IV) Chloride

Reactions of triorganotin chlorides with potassium salt of O-alkyl trithiophosphate [ROP(S)(SK)₂; R = Me, Prⁱ, Ph] in 2:1 molar ratio in anhydrous benzene yield triorganotin O-alkyl trithiophosphate of the type ROP(S) [SSnR′₃]₂ R = Me, Prⁱ; Ph, R′ = Prⁿ, Buⁿ, Ph] which are found to be monomeric in nature. These complexes are soluble in common organic solvents. Similar reactions of diorganotin chloride with dipotassium salt of S-alkyl trithiophosphate yield diorganotin-S-alkyl trithiophosphate of the type [(RS)P(O)S₂]₂SnR′₂; R = Me, Prⁱ; R′ = Me, Et, Ph, which also are found to be monomeric in nature and are soluble in common organic solvents. The newly synthesized derivatives have been characterized by physicochemical and spectroscopic techniques, IR, NMR (¹H, ³¹P, and ¹¹⁹Sn).