The vapor-liquid equilibrium of Dimethyl Carbonate-Methanol-Furfural under atmospheric pressure from DMC-CH 3OH,DMCC 5H 4O 2,CH 3OH-C 5H 4O 2 binary systematic VLE data is calculated,by using C ++(VC6.0) pr...The vapor-liquid equilibrium of Dimethyl Carbonate-Methanol-Furfural under atmospheric pressure from DMC-CH 3OH,DMCC 5H 4O 2,CH 3OH-C 5H 4O 2 binary systematic VLE data is calculated,by using C ++(VC6.0) programming language and Wilson equation.It provided important VLE data to set up mathematic models of extraction-rectifying separation of DMC and methanol by using furfural as extraction reagent.So the results can be used for chemical engineering calculation.展开更多
An attempt was made on applying the Wilson equation to predict the thermodynamic proper- ties of ternary liquid alloys.The activity of each component in ternary liquid alloys was found to be conveniently calculated fr...An attempt was made on applying the Wilson equation to predict the thermodynamic proper- ties of ternary liquid alloys.The activity of each component in ternary liquid alloys was found to be conveniently calculated from the equation with the related binary bimolecular interaction parameters.The calculated values are in fair agreement with experimental data,and are veri- fied to be reliable by the criterion of classical thermodynamics.展开更多
An attempt was made to use the Wilson equation to predict the thermodynamic properties of the FeO-CaO-SiO2 melts at 1673 and 1873K. The activities of component FeO in the ternary melts at a given temperature were foun...An attempt was made to use the Wilson equation to predict the thermodynamic properties of the FeO-CaO-SiO2 melts at 1673 and 1873K. The activities of component FeO in the ternary melts at a given temperature were found to be conveniently calculated from the equation only with related binary parameters at different temperatures.The predicted values are in agreement with the ternary experimental data.展开更多
In this paper we study the solutions and stability of the generalized Wilson＇s functional equation fc f（xty）dtt（t） ＋ fc f（xtσ（y））dtt（t） =2f（x）g（y）, x,y C G, where G is a locally compact group, a is a ...In this paper we study the solutions and stability of the generalized Wilson＇s functional equation fc f（xty）dtt（t） ＋ fc f（xtσ（y））dtt（t） =2f（x）g（y）, x,y C G, where G is a locally compact group, a is a continuous involution of G and # is an idempotent complex measure with compact support and which is a-invariant. We show that ∫Gg（xty）dp（t） ＋ fcg（xta（y））dp（t） = 2g（x）g（y） if f = 0 and fcf（t.）dp（t） =0, where [fcf（t.）dp（t）]（x） = fc f（tx）dμ（t）. We also study some stability theorems of that equation and we establish the stability on noncommutative groups of the classical Wilson＇s functional equation f（xy） ＋ X（y）f（xa（y）） = 2f（x）g（y） x, y C G, where X is a unitary character of G.展开更多
The aim of this paper is to investigate the superstability problem for the pexiderized trigonometric functional equation∑ v∈Φ∫Kf（xkv（y）k^-1）dwK（k）= Φ g（x）h（y）, x, y ∈ G,where G is any topological group...The aim of this paper is to investigate the superstability problem for the pexiderized trigonometric functional equation∑ v∈Φ∫Kf（xkv（y）k^-1）dwK（k）= Φ g（x）h（y）, x, y ∈ G,where G is any topological group, K is a compact subgroup of G, ωK is the normalized Haar measure of K, Φ is a finite group of K-invariant morphisms of G and f, g, h are continuous complex-valued functions.Consequently, we have generalized the results of stability for d＇Alembert＇s and Wilson＇s equations by R. Badora, J. Baker, B. Bouikhalene, P. Gavruta, S. Kabbaj, Pl. Kannappan, G. H.Kim, J.M. Rassias, A. Roukbi, L. Sz′ekelyhidi, D. Zeglami, etc.展开更多
KF or K2CO3 was added into the 1-butanol-water system and two phases were formed： water-rich phase （water phase） and 1-butanol-rich phase （1-butanol phase）. The liquid liquid equilibrium （LLE） data for 1-butano...KF or K2CO3 was added into the 1-butanol-water system and two phases were formed： water-rich phase （water phase） and 1-butanol-rich phase （1-butanol phase）. The liquid liquid equilibrium （LLE） data for 1-butanol-water-KF and 1-butanol-water-K2CO3 systems were measured at 25℃ and showed that 1-butanol phase contained negligible salt and water phase contained negligible 1-butanol when the concentrations of KF and K2CO3 in the water phase were equal to or higher than 27.11% and 31.68% , respectively. Thus water could be separated efficiently from 1-butanol-water by adding KF or K2CO3 into the system. A theoretical calculation of LLE data was calculated by using the Pitzer theory to get water activity in the water phase, and by the models, such as the Wilson, NRTL or the UNIQUAC for the 1-butanol phase. For 1-hutanol-water-KF system, the experimental data were found in good agreement with the calculated results by using Pitzer theory and Wilson equa tion, while for 1-butanol-water-K2CO3 system, the experimental data were found in good agreement with the calculated results by using Pitzer theory and UNIQUAC eauation.展开更多
This work investigates three nonlinear equations that describe waves on the oceans which are the Kadomtsev Petviashvili-modified equal width(KP-MEW)equation,the coupled Drinfel’d-Sokolov-Wilson(DSW)equation,and the B...This work investigates three nonlinear equations that describe waves on the oceans which are the Kadomtsev Petviashvili-modified equal width(KP-MEW)equation,the coupled Drinfel’d-Sokolov-Wilson(DSW)equation,and the Benjamin-Ono(BO)equation using the modified(G′/G^(2))-expansion approach.The solutions of proposed equations by modified(G′/G^(2))-expansion approach can be trigonometric,hyperbolic,or rational solutions.As a result,some new exact solutions are obtained and plotted.展开更多
文摘The vapor-liquid equilibrium of Dimethyl Carbonate-Methanol-Furfural under atmospheric pressure from DMC-CH 3OH,DMCC 5H 4O 2,CH 3OH-C 5H 4O 2 binary systematic VLE data is calculated,by using C ++(VC6.0) programming language and Wilson equation.It provided important VLE data to set up mathematic models of extraction-rectifying separation of DMC and methanol by using furfural as extraction reagent.So the results can be used for chemical engineering calculation.
文摘An attempt was made on applying the Wilson equation to predict the thermodynamic proper- ties of ternary liquid alloys.The activity of each component in ternary liquid alloys was found to be conveniently calculated from the equation with the related binary bimolecular interaction parameters.The calculated values are in fair agreement with experimental data,and are veri- fied to be reliable by the criterion of classical thermodynamics.
文摘An attempt was made to use the Wilson equation to predict the thermodynamic properties of the FeO-CaO-SiO2 melts at 1673 and 1873K. The activities of component FeO in the ternary melts at a given temperature were found to be conveniently calculated from the equation only with related binary parameters at different temperatures.The predicted values are in agreement with the ternary experimental data.
文摘In this paper we study the solutions and stability of the generalized Wilson＇s functional equation fc f（xty）dtt（t） ＋ fc f（xtσ（y））dtt（t） =2f（x）g（y）, x,y C G, where G is a locally compact group, a is a continuous involution of G and # is an idempotent complex measure with compact support and which is a-invariant. We show that ∫Gg（xty）dp（t） ＋ fcg（xta（y））dp（t） = 2g（x）g（y） if f = 0 and fcf（t.）dp（t） =0, where [fcf（t.）dp（t）]（x） = fc f（tx）dμ（t）. We also study some stability theorems of that equation and we establish the stability on noncommutative groups of the classical Wilson＇s functional equation f（xy） ＋ X（y）f（xa（y）） = 2f（x）g（y） x, y C G, where X is a unitary character of G.
文摘The aim of this paper is to investigate the superstability problem for the pexiderized trigonometric functional equation∑ v∈Φ∫Kf（xkv（y）k^-1）dwK（k）= Φ g（x）h（y）, x, y ∈ G,where G is any topological group, K is a compact subgroup of G, ωK is the normalized Haar measure of K, Φ is a finite group of K-invariant morphisms of G and f, g, h are continuous complex-valued functions.Consequently, we have generalized the results of stability for d＇Alembert＇s and Wilson＇s equations by R. Badora, J. Baker, B. Bouikhalene, P. Gavruta, S. Kabbaj, Pl. Kannappan, G. H.Kim, J.M. Rassias, A. Roukbi, L. Sz′ekelyhidi, D. Zeglami, etc.
文摘KF or K2CO3 was added into the 1-butanol-water system and two phases were formed： water-rich phase （water phase） and 1-butanol-rich phase （1-butanol phase）. The liquid liquid equilibrium （LLE） data for 1-butanol-water-KF and 1-butanol-water-K2CO3 systems were measured at 25℃ and showed that 1-butanol phase contained negligible salt and water phase contained negligible 1-butanol when the concentrations of KF and K2CO3 in the water phase were equal to or higher than 27.11% and 31.68% , respectively. Thus water could be separated efficiently from 1-butanol-water by adding KF or K2CO3 into the system. A theoretical calculation of LLE data was calculated by using the Pitzer theory to get water activity in the water phase, and by the models, such as the Wilson, NRTL or the UNIQUAC for the 1-butanol phase. For 1-hutanol-water-KF system, the experimental data were found in good agreement with the calculated results by using Pitzer theory and Wilson equa tion, while for 1-butanol-water-K2CO3 system, the experimental data were found in good agreement with the calculated results by using Pitzer theory and UNIQUAC eauation.
文摘This work investigates three nonlinear equations that describe waves on the oceans which are the Kadomtsev Petviashvili-modified equal width(KP-MEW)equation,the coupled Drinfel’d-Sokolov-Wilson(DSW)equation,and the Benjamin-Ono(BO)equation using the modified(G′/G^(2))-expansion approach.The solutions of proposed equations by modified(G′/G^(2))-expansion approach can be trigonometric,hyperbolic,or rational solutions.As a result,some new exact solutions are obtained and plotted.
