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.     

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.     

Parity Proofs of the Kochen–Specker Theorem Based on the 120-Cell

It is shown how the 300 rays associated with the antipodal pairs of vertices of a 120-cell (a four-dimensional regular polytope) can be used to give numerous “parity proofs” of the Kochen–Specker theorem ruling out the existence of noncontextual hidden variables theories. The symmetries of the 120-cell are exploited to give a simple construction of its Kochen–Specker diagram, which is exhibited in the form of a “basis table” showing all the orthogonalities between its rays. The basis table consists of 675 bases (a basis being a set of four mutually orthogonal rays), but all the bases can be written down from the few listed in this paper using some simple rules. The basis table is shown to contain a wide variety of parity proofs, ranging from 19 bases (or contexts) at the low end to 41 bases at the high end. Some explicit examples of these proofs are given, and their implications are discussed.     

Yang-Mills theory and Tamagawa numbers: the fascination of unexpected links in mathematics

Atiyah and Bott used equivariant Morse theory applied to theYang–Mills functional to calculate the Betti numbers ofmoduli spaces of vector bundles over a Riemann surface, rederivinginductive formulae obtained from an arithmetic approach whichinvolved the Tamagawa number of SL_n. This article attempts tosurvey and extend our understanding of this link between Yang–Millstheory and Tamagawa numbers, and to explain how methods usedover the last three decades to study the singular cohomologyof moduli spaces of bundles on a smooth projective curve over can be adapted to the setting of ¹-homotopy theory to studythe motivic cohomology of these moduli spaces over an algebraicallyclosed field.     

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.     

Hydrogen Bonding in Liquid Water and in the Hydration Shell of Salts

A near‐IR spectral study on pure water and aqueous salt solutions is used to investigate stoichiometric concentrations of different types of hydrogen‐bonded water species in liquid water and in water comprising the hydration shell of salts. Analysis of the thermodynamics of hydrogen‐bond formation signifies that hydrogen‐bond making and breaking processes are dominated by enthalpy with non‐negligible heat capacity effects, as revealed by the temperature dependence of standard molar enthalpies of hydrogen‐bond formation and from analysis of the linear enthalpy–entropy compensation effects. A generalized method is proposed for the simultaneous calculation of the spectrum of water in the hydration shell and hydration number of solutes. Resolved spectra of water in the hydration shell of different salts clearly differentiate hydrogen bonding of water in the hydration shell around cations and anions. A comparison of resolved liquid water spectra and resolved hydration‐shell spectra of ions highlights that the ordering of absorption frequencies of different kinds of hydrogen‐bonded water species is also preserved in the bound state with significant changes in band position, band width, and band intensity because of the polarization of water molecules in the vicinity of ions.