The Shapley value as the maximizer of expected Nash welfare

We provide an alternative interpretation of the Shapley value in TU games as the unique maximizer of expected Nash welfare.     

Positron annihilation studies of defects and interfaces in ZnS nanostructures of different crystalline and morphological features

Nanostructures of ZnS, both particles and rods, were synthesized through solvothermal processes and characterized by x-ray diffraction and high resolution transmission electron microscopy. Positron lifetime and Doppler broadening measurements were made to study the features related to the defect nanostructures present in the samples. The nanocrystalline grain surfaces and interfaces, which trapped significant fractions of positrons, gradually disappeared during grain growth, as indicated by the decreasing fraction of orthopositronium atoms. The crystal vacancies present within the grains also trapped positrons. These vacancies further agglomerated into clusters during the thermal treatment given to effect grain growth. The positron lifetime was remarkably large at extremely small grain sizes (approximately 1.5 nm) and this was attributed to the occurrence of quantum confinement effects, as verified through optical absorption measurements. Positron lifetimes in ZnS nanorods increased with increasing content of cubic phase in the samples and this observation is assigned to the annihilation of positrons in sites with increased cubic unit cell volume. The Doppler broadened spectra also indicated qualitative changes consistent with these observations.     

Synthesis, crystal structure, spectroscopic and photoluminescence studies of manganese(II), cobalt(II), cadmium(II), zinc(II) and copper(II) complexes with a pyrazole derived Schiff base ligand

Varying coordination modes of the Schiff base ligand H₂L [5-methyl-1-H-pyrazole-3-carboxylic acid (1-pyridin-2-yl-ethylidene)-hydrazide] towards different metal centers are reported with the syntheses and characterization of four mononuclear Mn(II), Co(II), Cd(II) and Zn(II) complexes, [Mn(H₂L)(H₂O)₂](ClO₄)₂(MeOH) (1), [Co(H₂L)(NCS)₂] (2), [Cd(H₂L)(H₂O)₂](ClO₄)₂ (3) and [Zn(H₂L)(H₂O)₂](ClO₄)₂ (4), and a binuclear Cu(II) complex, [Cu₂(L)₂](ClO₄)₂ (5). In the complexes 1-4 the neutral ligand serves as a 3N,2O donor where the pyridine ring N, two azomethine N and two carbohydrazine oxygen atoms are coordinatively active, leaving the pyrazole-N atoms inactive. In the case of complex 5, each ligand molecule behaves as a 4N,O donor utilizing the pyridine N, one azomethine N, the nitrogen atom proximal to the azomethine of the remaining pendant arm and one pyrazole-N atom to one metal center and the carbohydrazide oxygen atom to the second metal center. The complexes 1-4 are pentagonal bipyramidal in geometry. In each case, the ligand molecule spans the equatorial plane while the apical positions are occupied by water molecules in 1, 3 and 4 and two N bonded thiocyanate ions in 2. In complex 5, the two Cu(II) centers have almost square pyramidal geometry (τ = 0.05 for Cu1 and 0.013 for Cu2). Four N atoms from a ligand molecule form the basal plane and the carbohydrazide oxygen atom of a second ligand molecule sits in the apex of the square pyramid. All the complexes have been X-ray crystallographically characterized. The Zn(II) and Cd(II) complexes show considerable fluorescence emission while the remaining complexes and the ligand molecule are fluorescent silent.     

Three-dimensional free convection MHD flow in a vertical channel through a porous medium with heat source and chemical reaction

An analysis is made to study the three-dimensional MHD free convection flow in a vertical channel through a porous medium with heat source and chemical reaction. The flow phenomenon is characterized by magnetic parameters (M), Darcy number (K _p ), Reynolds number (R _e ), source parameter (S), Grashof number for heat transfer (G _r ), Grashof number for mass transfer (G _c ), Prandtl number (P _r ), Schmidt number (S _c ), and chemical reaction parameter (K _c ). Approximate solutions of the velocity, temperature, and concentration are obtained using a perturbation technique. The effect of these parameters on the velocity, temperature and concentrations distribution is discussed and some interesting results are presented.     

Secondary benzylation with benzyl alcohols catalyzed by a high-valent heterobimetallic Ir-Sn complex

A highly efficient secondary benzylation procedure has been demonstrated using a high-valent heterobimetallic complex [Ir2(COD)2(SnCl3)2(Cl)2(mu-Cl)2] 1 as the catalyst in 1,2-dichloroethane to afford the corresponding benzylated products in moderate to excellent yields. The reaction was performed not only with carbon nucleophiles (arenes and heteroarenes) but also with oxygen (alcohol), nitrogen (amide and sulfonamide), and sulfur (thiol) nucleophiles. Mechanistic investigation showed the intermediacy of the ether in this reaction. An electrophilic mechanism is proposed from Hammett correlation.     

Preferential binding of the magnesium ion by anthraquinone based chromogenic receptors

Two new anthraquinone based receptors have been synthesized. A colour change for both these receptors could be detected when group IIA metal ions were added in DMF solution at room temperature. No such colour change was noticed for group IA metal ions. Association constants for these receptors towards Mg²⁺, Ca²⁺, Sr²⁺ and Ba²⁺ were evaluated by systematic spectrophotomeric titrations and they follow the order K_Mg(II) ? K_Ca(II) > K_Sr(II) ? K_Ba(II). The association constants for L₁ were found to be higher than those for L₂ toward group IIA metal ions. Ab initio quantum chemical calculations have been performed to rationalize these observed results. X-ray structural analysis shows a helical structure for one of the receptor molecules.     

Dislocation structure of α<Subscript>2</Subscript>/β two-phase Ti-21.4Al-5.6Nb alloy

An electron microscopic analysis of the dislocation structure of two-phase α₂/β Ti-21.4 at % Al-5.6 at % Nb alloy deformed at ambient temperature was performed. It was established that after deformation, the microstructure of the α₂ phase consists of mobile a-superdislocations in the basal and prism planes and of 2c + a-superdislocations in the pyramidal planes. Some dislocations with the Burgers vector [0001] in the prism planes were also observed. Deformation transfer from the α₂ to the β phase occurs only due to a-super-dislocations with a Burgers vector corresponding to the Burgers orientation relations between these phases. The reasons for the increase in plasticity in two-phase Ti₃Al with Nb alloys are discussed.