Axiomatic results and dynamic processes for two weighted indexes under fuzzy transferable-utility behavior

<p style='text-indent:20px;'>By considering the supreme-utilities and the weights simultaneously under fuzzy behavior, we propose two indexes on fuzzy transferable-utility games. In order to present the rationality for these two indexes, we define extended reductions to offer several axiomatic results and dynamics processes. Based on different consideration, we also adopt excess functions to propose alternative formulations and related dynamic processes for these two indexes respectively.</p>

Densities, Viscosities and Excess Properties for Dimethyl Sulfoxide with Diethylene Glycol and Methyldiethanolamine at Different Temperatures

Densities and viscosities of the binary systems dimethylsulfoxide with diethylene glycol and methyldiethanolamine were measured at temperatures ranging from 293.15 to 313.15 K, at atmospheric pressure and over the entire composition range. The experimental density data was correlated as a function of composition using Belda’s and Herraez’s equations, and as a function of temperature and composition using the models of Emmerling et al. and Gonzalez-Olmos-Iglesias. The viscosity results were fitted to the Grunberg-Nissan, Heric-Brewer, Wilson, Noda, and Ishida and Eyring-NRTL equations. The values of viscosity deviation (), excess molar volume (VE), partial molar volumes ( and ) and apparent molar volume ( and ) were determined. The excess functions of the binary systems were fitted to the polynomial equations. The values of thermodynamic functions of activation of viscous flow were calculated and discussed.

Phase vapor–liquid equilibrium for the solutions of diethyl selenide and diethylzinc

Using a semi-empirical Wilson’s model, the vapor-liquid equilibrium in the “diethylzinc - diethyl selenide” system is described: the activity coefficients of the solution components, the separation coefficient, the excess functions of the solution (HE, GE, TSE) are calculated, and isothermal P-X diagrams are obtained. The parameters of the Wilson’s model were calculated on the basis of our data on measuring the temperature dependence for saturated vapor pressure of high-purity samples of diethylzinc, diethyl selenide and their equimolecular solution using iterations from the mathematical software package Mathsad 14. Peculiarities of intermolecular interaction in the “diethylzinc – diethyl selenide” system and the presence of a negative deviation from Raoul's law have been found. The studied system is homogeneous in the whole concentration range. The concentration dependence of the enthalpy of mixing is alternating for the researched temperature range (280-340 K).

Ultrasonic Investigation of Binary Solutions of Petrolium And Its Products

<p>Experiment values of densities and ultrasonic speed of petroleum product Gasoline (Petrol) and 2T Oil were taken in different volume concentrations from 5%, 10%------, and 95% at different temperatures from 298.15K to 318.15K having difference of 5K. From the experimental data, Apparent Molar Compressibility (<em>ϕ_K</em>), Relative Association (<em>R_A</em>), Solvation Number (<em>S_n</em>), Free Energy of Activation (<em>ΔE</em>), Excess Adiabatic Compressibility (<em>β_ad^E</em>), Excess Volume (<em>V^E</em>), Excess Free Length (<em>L_f^E</em>) have been computed. These parameters are used to focus light on the nature of component molecules of binary liquids and the excess functions are found to be sensitive to the nature and extent of the intermolecular interactions taking place in these binary mixtures.</p>

A weighted power distribution mechanism under fuzzy behavior systems

In real situations, players might represent administrative areas of different scales; players might have different activity abilities. Thus, we propose an extension of the Banzhaf-Owen index in the framework of fuzzy transferable-utility games by considering supreme-utilities and weights simultaneously, which we name the weighted fuzzy Banzhaf-Owen index. Here we adopt three existing notions from traditional game theory and reinterpret them in the framework of fuzzy transferable-utility games. The first one is that this weighted index could be represented as an alternative formulation in terms of excess functions. The second is that, based on an reduced game and related consistency, we offer an axiomatic result to present the rationality of this weighted index. Finally, we introduce two dynamic processes to illustrate that this weighted index could be reached by players who start from an arbitrary efficient payoff vector and make successive adjustments.

Thermodynamic Study on Density and Viscosity of Binary Mixtures of Ethyl acetoacetate with (C4-C9) Aliphatic Ketones at (303.15 and 308.15) K

Investigation on Density (ρ) and viscosity (η) of various binary mixtures of ethylacetoacetate and straight chain aliphatic ketones (butan-2-one, pentan-2- one, hexan-2-one, heptan-2-one, octan-2-one and nonan2-one) have been carried out over the entire solvents composition range at temperatures of 303.15K and 308.15K. From the data obtained, the excess molar volumes (V E ), the excess viscosity (η E ) and excess Gibbs free energy of activation for viscous flow (ΔG*E) have been calculated from the experimental density and viscosity measurements at the working temperatures. Excess molar volumes, V E results are negative and positive over the entire range of mole fractions and become more positive as the chain length increases. The excess viscosities, η E were both positive and negative over the entire mole fraction range. While the observed excess Gibbs free energies of activation of viscous flow, ΔG*E data are positive throughout the entire mole fraction range of solvents composition at all investigated temperatures. These observed results of the excess functions have been interpreted in terms of possible molecular interactions in the binary mixtures.

Recent studies on thermophysical properties of metallic alloys with PROSPECT: Excess properties to construct a solution model

We have developed the system PROSPECT for measuring thermophysical properties at high temperature. Precise thermophysical measurements provide accurate excess functions, which represent non-ideality of solutions. We use excess functions to discuss solution models on the basis of electronic structure and thermodynamics. Pd-Fe systems show positive excess volume VE with negative excess Gibbs energy GE. The phase diagrams of these systems have common features with those of other Pd-X and Pt-X systems (where X is Fe, Ni, Co, or Cu), which means they all have order-disorder transitions. The correlation between VE and GE is discussed in terms of the electronic structure of the alloys, and an energy diagram is proposed to understand this correlation. The excess heat capacity CpE of Fe-Ni melts is positive over a whole composition range and a wide temperature range. We estimate the temperature dependences of the excess enthalpy HE and excess entropy SE of Fe-Ni melts from CpE. The Lupis-Elliott rule is satisfied for HE and SE with positive CpE.