A Characterization of Nash Equilibrium for the Games with Random Payoffs

We consider a two-player random bimatrix game where each player is interested in the payoffs which can be obtained with certain confidence. The payoff function of each player is defined using a chance constraint. We consider the case where the entries of the random payoff matrix of each player jointly follow a multivariate elliptically symmetric distribution. We show an equivalence between the Nash equilibrium problem and the global maximization of a certain mathematical program. The case where the entries of the payoff matrices are independent normal/Cauchy random variables is also considered. The case of independent normally distributed random payoffs can be viewed as a special case of a multivariate elliptically symmetric distributed random payoffs. As for Cauchy distribution, we show that the Nash equilibrium problem is equivalent to the global maximization of a certain quadratic program. Our theoretical results are illustrated by considering randomly generated instances of the game.     

Mechanoluminescence Study of Europium Doped CaZrO<Subscript>3</Subscript> Phosphor

Behaviour displayed by mechanoluminescence (ML) in CaZrO₃:Eu³⁺ doped phosphors with variable concentration of europium ions are described. When the ML is excited impulsively by the impact of a load on the phosphors the ML intensity increases with time, attains a maximum value and then it decreases. In the ML intensity versus time curve, the peak increases and shifts towards shorter time values with increasing impact velocities. Sample was synthesized by combustion synthesis method with variable concentration of Eu³⁺ ions (0.1, 0.2, 0.5, 1, 1.5 mol%) and characterized by X-ray diffraction technique. The total ML intensity I_T is defined as the area below the ML intensity versus time curve. Initially I_T increases with impact velocity V₀ of the load and then it attains a saturation value for higher values of impact velocities which follow the relation I_T = I_T ⁰ exp.(?V_c/V₀) where I_T ⁰ and V_c are constants. Total ML intensity increases linearly with the mass of the phosphors for higher impact velocities. The ML intensity I_m, corresponding to the peak of ML intensity versus time curve increases linearly with the impact velocities. The time t_m, is found to be linearly related to 1000/V₀. The mechanoluminescence induced by impulsive excitation in europium doped CaZrO₃ phosphors plays a significance role in the understanding of biological sensors and display device application.     

Comparative study of travelling-wave and numerical solutions for the coupled short pulse （CSP） equation

The Lie symmetry analysis is performed for the coupled short plus (CSP) equation. We derive the infinitesimals that admit the classical symmetry group. Five types arise depending on the nature of the Lie symmetry generator. In all types, we find reductions in terms of system of ordinary differential equations, and exact solutions of the CSP equation are derived, which are compared with numerical solutions using the classical fourth-order Runge-Kutta scheme.     

Bis-spirochromanones as potent inhibitors of Mycobacterium tuberculosis: synthesis and biological evaluation

Molecular Diversity - On the basis of reported antimycobacterial property of chroman-4-one pharmacophore, a series of chemically modified bis-spirochromanones were synthesized starting from...     

Reactive sensing of gold (III) by coumarin tethered fluorescent probe through alkyne activation

A novel strategy, involving anchoring and un-anchoring of coumarin based fluorophore, has been established for the selective detection of Au³⁺ species. Selective sensing of Gold (Au³⁺) was triggered due to alkynophilicity of gold ions to create lateral fluorescence of a latent fluorophore. The 4-methyl-2-oxo-2H-chromen-7-yl 2-(2-phenylethynyl) benzoate (CEB) probe was synthesized by reacting 7-hydroxy-4-methylcoumarin with iodo-benzoic acid. CEB probe has an absorption at 300 nm and 335 nm which decreases gradually and new absorption appeared at 406 nm due to Au³⁺ promoted ester hydrolysis selectively over other metal ions with great sensitivity, which accompanies a turn on fluorescence change produced by 7-hydroxy coumarin. The principle behind this sensing strategy is activation of triple bond induced uniquely by Au⁺³ ions leading to cascade and delivers active fluorophore. The sensing mechanism was proposed and supported by ¹H NMR, MS and TD-DFT experiments. The density functional theory (DFT) and time dependent density functional theory (TD-DFT) theoretical results of the CEB-probe and Au³⁺ reaction is in good agreement with the experimental results. Additionally, probe could be well incorporated onto the test strips for effective detection of Au^3+.     

Reaction of Oximes of α-Diketones with Diphosphorous Tetraiodide for Preparation of Oxadiazoles and Nitriles

The utility of diphosphorous tetraiodide as a new, mild, condensing agent for synthesis of oxadiazole is described. These data indicate the simple dehydration of oximes to 1,2,5-oxadiazole as well as the rearrangements of oximes to normal Beckmann product 1,2,4-oxadiazole. However, mono-oxime of benzil undergoes abnormal Beckman rearrangement to benzaldehyde as major product. The described method is simple and important for the synthesis of the oxadiazoles as well as for nitriles.     

Role of diet and trace elements in lithogenesis of renal calculi

Twenty eight stones were characterized for chemical composition and structure. The concentrations of trace elements were determined using INAA while EDXRF was used for determining the calcium contents of the stones. Twenty stones were found to be mainly composed of calcium, six were mixed type and the remaining two were of uric acid type. The concentrations of trace elements namely Zn, Sr, Fe and Cr were lower in uric acid stones as compared to calcium based stones. Diet analysis of 310 patients who were treated for renal stones showed a diet rich in calcium and oxalate and decreased water consumption.

     

Influence of Molecular Separation on Through-Space Intervalence Transient Charge Transfer in Metal–Organic Frameworks with Cofacially arranged Redox Pairs

We demonstrate direct evidence of photoinduced through-space intervalence charge transfer (IVCT) between two cofacially arranged redox-active pairs in metal–organic frameworks and their dynamic variation with their molecular separation. Two homologous MOFs [Co₂(NDC)₂(DPTTZ)₂]. DPTTZ. DMF, 1 and [Co₂(BDC)₂(DPTTZ)₂]. DMF, 2 (where NDC=naphthalene dicarboxylate, BDC=benzene dicarboxylate, DPTTZ=N, N′-di(4-pyridyl)thiazolo-[5,4-d]thiazole, DMF=N, N′-dimethyl formamide) are considered for this, whose intra-dimer distance of redox-active DPTTZ ligands differs ca. 1 Å from one system to another. Spectroelectrochemical study detects the formation of IVCT band at the NIR region between cofacially oriented DPTTZ molecules in both MOFs. Transient spectroscopy shows faster charge separation as well as charge recombination when intra-dimer distance is lesser (in MOF 2 ) due to stronger electronic coupling. We quantify the extent of IVCT by charge transfer integral calculation; and also by optical pump terahertz probe spectroscopy, where MOF 2 shows three times higher carrier mobility due to lesser inter-DPTTZ distance than MOF 1 . These findings reveal a more localized aspect of through-space IVCT between cofacially organized redox-active pair in a three-dimensional framework.     

An efficient diethyl ether-based soxhlet protocol to quantify faecal sterols from catchment waters

A study was conducted to evaluate the efficiency and reproducibility of a diethyl ether-based soxhlet extraction procedure for faecal sterols occurring from catchment waters. Water samples spiked with a mixture of faecal sterols were filtered and analytes were extracted using the diethyl ether-based soxhlet method and the Bligh and Dyer chloroform extraction process. For diethyl ether-based soxhlet extraction procedure, solvent extracts were saponified with 100 microL of 10% KOH in methanol (100 degrees C/120 min) and then acidified with 60 microL of 6M HCl. Lipid contents were extracted by ethanol (0.5 mL) from the saponification products. The lipid extracts were then reacted with 100 microL of bis(trimethyl)trifluoroacetamide (BSTFA) containing 1% trimethyl chlorosilane (100 degrees C/60 min) to form the trimethylsilyl (TMS) derivatives. The derivatised extracts were then analyzed by gas chromatography-mass spectrometry. For sterol concentrations ranging from 35 to 175 microg mL(-1), the soxhlet-based extraction process yielded the following recovery efficiencies for coprostanol (101%), epicoprostanol (97%), cholesterol (97%), dihydrocholesterol (97%) and 5alpha-cholestane (111%), whereas the Bligh and Dyer process yielded recoveries of 32, 41, 0, 36 and 51%, respectively. The results suggested that the diethyl ether-based soxhlet extraction method was more efficient and reproducible than the Bligh and Dyer chloroform extraction process for the analyses of trace levels of faecal sterols from water samples. Moreover, it was revealed that the diethyl ether-based soxhlet extraction method used less solvent and was logistically easier.     

Efficient Elemental Iodine Catalyzed One-Pot Synthesis of 2,4,5-Triarylimidazoles

Elemental iodine is used as an efficient catalyst for the synthesis of 2,4,5-triarylimidazoles in excellent yields via condensation of benzoin, ammonium acetate, and aromatic aldehydes. This is a simple, one-pot, high yielding technique using cheap, non-toxic iodine in catalytic amounts.