Charged Analogue of Whittaker’s Interior Solution

Charged analogue of Whittaker’s interior solution is derived which possess constant gravitational mass density (ρ+3p). The solution joins smoothly to Nordstörm solution at the pressure free interface. The solution has increasing energy density away from the center which is unphysical however such model can very well represent the situations when density undergoes abrupt changes during the tug of war between the gravitational attraction and electrostatic repulsion.     

Phonon Dispersion in Polyadenylic Acid

A study of the normal modes of vibration and their dispersion in polyadenylic acid based on the Urey–Bradley force field is reported. It gives a better interpretation of FTIR spectra as compared with the valence force field. Characteristic features of dispersion curves such as regions of high density‐of‐states, repulsion, and character mixing of dispersive modes are discussed. Predictive valuzes of heat capacity as a function of temperature are reported.     

Phonon Dispersion in Polypyrrole

A study of the normal modes of vibration and their dispersion in polypyrrole (PPY) based on the Urey-Bradley force field is reported. It gives a fuller interpretation of previously reported FTIR spectra. Characterstic features of dispersion curves, such as regions of high density-of-states, repulsion, and character mixing of dispersive modes, are discussed. Predictive values of heat capacity as a function of temperature are reported.     

Stochastic Dynamics for Passage Times and Diffusion Approximations for Finite Capacity Storage Models with Different Kinds of Barriers

In this article, we discuss a number of storage models of finite capacity with random inputs, random outputs, and linear release policy. They form a class of one-dimensional master equations with separable kernels. For this class of problems, the integral equations for first overflow or first emptiness can be transformed exactly into ordinary differential equations. Analysis is done with separable kernel. For all the stochastic models, two barriers are considered: one at X = 0 and the other at X = k, and the barriers are treated as absorbing or reflecting. The imbedding method is used to derive a third order differential equation. We consider first passage times for overflow without or with emptiness of the dam. We also study the passage times for first emptiness with and without overflows. The expected amount of overflows in a given time is also calculated. Finally, by suitable statistical features, all these models are converted into diffusion process with drift. Closed form solutions are obtained for all the problems in terms of Laplace transform functions. For the diffusion process with drift first passage time density is arrived at by treating X = 0 and X = k as absorbing barriers. One of the barriers as reflecting is also studied.     

Stochastic Models for the Amount of Overflow in a Finite Dam with Random Inputs,Random Outputs,and Exponential Release Policy

In this article, we discuss finite dam models to study the expected amount of overflow in a given time. The inputs into the dam are taken as random and there are two types of outputs—one is random and the other is deterministic which is proportional to the content of the dam. The master equation for the expected amount of overflow is an one dimensional equation with separable kernel. For this class of master equation, the integral equation for the expected amount of overflow has been transformed exactly into ordinary differential equation with variable coefficients. The imbedding method is used to study the expected amount of overflow in a given time without emptiness in this period. We also consider the model for the expected amount of overflow in a given time with any number of emptiness of the dam in this period. The results are derived in the form of a third order differential Equation for the Laplace transformation function for the expected overflow. The closed form analytical solutions are obtained in terms of beta functions and degenerate hyper-geometric functions of two variables.     

Dinuclear gold(I)-N-heterocyclic carbene complexes: Synthesis,characterization, and catalytic application for hydrohydrazidation of terminal alkynes

Dinuclear gold(I)-N-heterocyclic carbene complexes were developed for the hydrohydrazidation of terminal alkynes. The gold(I)-N-heterocyclic carbene complexes 2a-2b were synthesized in good yields from silver complexes synthesized in situ, which in turn were obtained from the corresponding imidazolium salts with Ag₂O in dichloromethane as a solvent. The new air-stable gold(I)-NHC complexes, 2a - 2b, were characterized using NMR spectroscopy, elemental analysis, infrared, and mass spectroscopy studies. The gold(I) complex 2a was characterized using X-ray crystallography. Bis-N-heterocyclic carbene–based gold(I) complexes 2a - 2b exhibited excellent catalytic activities for hydrohydrazidation of terminal alkynes yielding acylhydrazone derivatives. The working catalytic system can be used in gram-scale synthesis. In addition, the catalytic reaction mechanism of the hydrohydrazidation of terminal alkynes by gold(I)-NHC complex was studied in detail using density functional theory.     

Bubble point measurements of binary mixtures formed by ethyl benzene with selected compounds at 95.35 kPa

Bubble point temperatures (at 95.35 kPa) over the entire composition range were measured for the binary mixtures formed by ethyl benzene with: acetyl acetone, o-, and p-cresols, 1-hexanol, and tetraethoxysilane, employing a Swietoslawski type ebulliometer. Wilson equation was used to represent the measured liquid phase composition versus bubble point temperature data, and the computed values of the vapor phase mole fractions, activity coefficients, and excess Gibbs free energy were tabulated and briefly discussed.     

Solid-state photochemical [2+2] cycloaddition in a hydrogen-bonded metal complex containing several parallel and crisscross C=C bonds

One-dimensional hydrogen-bonded complex [Zn(bpe)(2)(H(2)O)(4)](NO(3))(2).8/3 H(2)O.2/3 bpe (1, bpe=4,4'-bipyridylethylene) containing coordination complex cations [Zn(bpe)(2)(H(2)O)(4)](2+) with parallel and crisscross double bonds undergoes photochemical [2+2] cycloaddition in the solid state and produces tetrakis(4-pyridyl)cyclobutane (tpcb) in up to 100 % yield with rctt-tpcb (2a) as major and rtct-tpcb (2b) as minor product. The bpe ligands with crisscross conformation of C=C bonds appear to undergo pedal-like motion prior to photodimerization. Grinding single crystals to powder accelerates the pedal motion of crisscrossed olefins in the bpe ligands to parallel alignment and provides the rctt-cyclobutane stereoisomer 2a quantitatively. In addition, 100 % photodimerization of ground 1 indicates that the free bpe ligands, which are remote from each other in a pool of water, and NO(3)(-) ions moved toward each other to give a mixture of rctt- and rtct-tpcb isomers.     

Stoichiometric functionalization of gold nanoparticles in solution through a free radical polymerization approach

A new simple concept for the stoichiometrical functionalization of nanoparticles based on free radical polymerization of vinyl protected nanoparticles is presented. To demonstrate this concept 2-bis(4-vinylphenyl)disulfane was synthesized and used in the synthesis of gold nanoparticles, leading to 4-vinylthiophenol functionalized nanoparticles. Simple free radical polymerization of these particles initiated by 4,4'-azobis-(4-cyanopentanoic acid) delivered nanoparticles with a single carboxyl group. These monofunctionalized gold nanoparticles were utilized for chemical preparation of gold nanoparticle dimers as well as for construction of gold nanoparticle arrays via binding to polyallylamine.