We give a proof of an explicit formula for affine coodinates of points in the Sato’s infinite Grassmannian corresponding to tau-functions for the KdV hierarchy.
In this paper, we consider the generalized Korteweg-de-Vries (KdV) equations which are remarkable models of the water waves mechanics, the shallow water waves, the quantum mechanics, the ion acoustic waves in plasma, ...In this paper, we consider the generalized Korteweg-de-Vries (KdV) equations which are remarkable models of the water waves mechanics, the shallow water waves, the quantum mechanics, the ion acoustic waves in plasma, the electro-hydro-dynamical model for local electric field, signal processing waves through optical fibers, etc. We determine the useful and further general exact traveling wave solutions of the above mentioned NLDEs by applying the exp(−τ(ξ))-expansion method by aid of traveling wave transformations. Furthermore, we explain the physical significance of the obtained solutions of its definite values of the involved parameters with graphic representations in order to know the physical phenomena. Finally, we show that the exp(−τ(ξ))-expansion method is convenient, powerful, straightforward and provide more general solutions and can be helping to examine vast amount of travelling wave solutions to the other different kinds of NLDEs.展开更多
To understand the mechanism of fluoride removal from the simulated zinc sulfate solution by the La(III)-modified zeolite,the adsorbent was characterized by XRD,SEM and EDS.The effects of absorbent dose and contact tim...To understand the mechanism of fluoride removal from the simulated zinc sulfate solution by the La(III)-modified zeolite,the adsorbent was characterized by XRD,SEM and EDS.The effects of absorbent dose and contact time,the adsorption isotherms and the sorption kinetics were investigated.The experimental results were compatible with the Langmuir isotherm model.The theoretical maximum adsorption capacities are 20.83 and 23.04 mg/g at 303 and 313 K,respectively.And the physisorption is revealed using the Temkin isotherm model and the D-R isotherm model.The sorption process is more suitable by the pseudo-second-order kinetic models.Thermodynamic parameters such as standard free energy change(ΔGΘ<0 kJ/mol),standard enthalpy change(ΔHΘ=8.28 kJ/mol)and standard entropy change(ΔSΘ=0.030 kJ/(mol?K))indicate the spontaneity of adsorption and endothermic physical sorption.Furthermore,the fluoride concentration in the industrial zinc sulfate solution decreases from 98.05 to 44.09 mg/L with the adsorbent dosage of 15 g/L.展开更多
The adsorption equilibrium of a fluoride solution on 1-2 mm granular activated alumina modified by Fe2(SO4)3 solution was investigated.The experiments were conducted using a wide range of initial fluoride concentratio...The adsorption equilibrium of a fluoride solution on 1-2 mm granular activated alumina modified by Fe2(SO4)3 solution was investigated.The experiments were conducted using a wide range of initial fluoride concentrations(0.5 to 180 mg·L-1 at pH～7.0) and an adsorbent dose of 1.0 g·L-1.The application of Langmuir and Freundlich adsorption isotherm models(linear and nonlinear forms) generally showed that a single Langmuir or Freundlich equation cannot fit the entire concentration gap.Experimental data on low equilibrium concentrations(0.1 to 5.0 mg·L-1) was in line with both Langmuir and Freundlich isotherm models,whereas that of high equilibrium concentrations(5.0 to 150 mg·L-1) was more in line with the Freundlich isotherm model.A new LangmuirFreundlich function was used for the entire concentration gap,as well as for low and high concentrations.展开更多
The ZrB 2 particles firstly modified Mg_(94)Zn_(2.5)Y_(2.5)Mn 1 alloy.And the microstructures and mechanical performances of the modified alloys were studied systematically.The results showed that the moderate additio...The ZrB 2 particles firstly modified Mg_(94)Zn_(2.5)Y_(2.5)Mn 1 alloy.And the microstructures and mechanical performances of the modified alloys were studied systematically.The results showed that the moderate addition of ZrB 2 accelerated the development of long-period stacking ordered(LPSO)structure and refined the grain size.The grains in ZrB 2-modified alloys were nearly equiaxed with a homogeneous size.When 0.0075 wt%ZrB 2 was added,the as-cast alloy with the finest grains(24.87μm)presented desirable mechanical properties(especially ductility)with maximum tensile strength and ductility of 225 MPa and 17.5%,respectively.展开更多
This work proved that biomass-based polyols (sorbitol, xylitol, erythritol, glycerol and ethanediol) were able to be converted into high-value chemical (p-xylene) by catalytic cracking of polyols, alkylation of aromat...This work proved that biomass-based polyols (sorbitol, xylitol, erythritol, glycerol and ethanediol) were able to be converted into high-value chemical (p-xylene) by catalytic cracking of polyols, alkylation of aromatics, and the isomerization of xylenes over the SiO2-modified zeolites. Compared to the conventional HZSM-5 zeolite, the SiO2-containing zeolites considerably increased the selectivity and yield of p-xylene due to the reduction of external surface acidity and the narrowing of pore entrance. The influences of the methanol additive, reaction temperature, and types of polyols on the selectivity and yield of p-xylene were investigated in detail. Catalytic cracking of polyols with methanol significantly enhanced the production of p-xylene by the alkylation of toluene with methanol. The highest p-xylene yield of 10.9 C-mol% with a p-xylene/xylenes ratio of 91.1% was obtained over the 15wt%SiO2/HZSM-5 catalyst. The reaction pathway for the formation of p-xylene was addressed according to the study of the key reactions and the characterization of catalysts.展开更多
We investigate the dielectric and ferroelectric properties of Sr1-xBixTi1-xFex03 solid solutions （x =0, 0.05, 0.1, 0.15 and 0.2） together with their structures. Through the analysis of Rietveld refinement of powder ...We investigate the dielectric and ferroelectric properties of Sr1-xBixTi1-xFex03 solid solutions （x =0, 0.05, 0.1, 0.15 and 0.2） together with their structures. Through the analysis of Rietveld refinement of powder x-ray diffraction, a cubic structure in space group Pm3m is determined for all the compositions. An obvious dielectric relaxation peak differing from SrTiO3 is observed in the present ceramics. The peak temperature Tm increases with increasing x, and it approaches room temperature at x =0.2. The Vogel Fulcher law and Curie Weiss law fittings further confirm the relaxor ferroelectricity in the present ceramics.展开更多
This paper examines the existence of weak solutions to a class of the high-order Korteweg-de Vries(KdV)system in Rn.We first prove,by the Leray-Schauder principle and the vanishing viscosity method,that any initial da...This paper examines the existence of weak solutions to a class of the high-order Korteweg-de Vries(KdV)system in Rn.We first prove,by the Leray-Schauder principle and the vanishing viscosity method,that any initial data N-dimensional vector value function u0(x)in Sobolev space H^(s)(R^(n))(s≥1)leads to a global weak solution.Second,we investigate some special regularity properties of solutions to the initial value problem associated with the KdV type system in R^(2)and R^(3).展开更多
The time-fractional modified Korteweg-de Vries(KdV)equation is committed to establish exact solutions by employing the bifurcation method.Firstly,the phase portraits and related qualitative analysis are comprehensivel...The time-fractional modified Korteweg-de Vries(KdV)equation is committed to establish exact solutions by employing the bifurcation method.Firstly,the phase portraits and related qualitative analysis are comprehensively provided.Then,we give parametric expressions of different types of solutions matching with the corresponding orbits.Finally,solution profiles,3D and density plots of some solutions are presented with proper parametric choices.展开更多
文摘We give a proof of an explicit formula for affine coodinates of points in the Sato’s infinite Grassmannian corresponding to tau-functions for the KdV hierarchy.
文摘In this paper, we consider the generalized Korteweg-de-Vries (KdV) equations which are remarkable models of the water waves mechanics, the shallow water waves, the quantum mechanics, the ion acoustic waves in plasma, the electro-hydro-dynamical model for local electric field, signal processing waves through optical fibers, etc. We determine the useful and further general exact traveling wave solutions of the above mentioned NLDEs by applying the exp(−τ(ξ))-expansion method by aid of traveling wave transformations. Furthermore, we explain the physical significance of the obtained solutions of its definite values of the involved parameters with graphic representations in order to know the physical phenomena. Finally, we show that the exp(−τ(ξ))-expansion method is convenient, powerful, straightforward and provide more general solutions and can be helping to examine vast amount of travelling wave solutions to the other different kinds of NLDEs.
基金Projects(51474238,51674301)supported by the National Natural Science Foundation of China
文摘To understand the mechanism of fluoride removal from the simulated zinc sulfate solution by the La(III)-modified zeolite,the adsorbent was characterized by XRD,SEM and EDS.The effects of absorbent dose and contact time,the adsorption isotherms and the sorption kinetics were investigated.The experimental results were compatible with the Langmuir isotherm model.The theoretical maximum adsorption capacities are 20.83 and 23.04 mg/g at 303 and 313 K,respectively.And the physisorption is revealed using the Temkin isotherm model and the D-R isotherm model.The sorption process is more suitable by the pseudo-second-order kinetic models.Thermodynamic parameters such as standard free energy change(ΔGΘ<0 kJ/mol),standard enthalpy change(ΔHΘ=8.28 kJ/mol)and standard entropy change(ΔSΘ=0.030 kJ/(mol?K))indicate the spontaneity of adsorption and endothermic physical sorption.Furthermore,the fluoride concentration in the industrial zinc sulfate solution decreases from 98.05 to 44.09 mg/L with the adsorbent dosage of 15 g/L.
基金Supported by the Major National Science and Technology Special Project on Treatment and Control of Water Pollution(2009ZX07425-006)the State Key laboratory of Environmental Simulation and Pollution Control (09K04ESPCT)
文摘The adsorption equilibrium of a fluoride solution on 1-2 mm granular activated alumina modified by Fe2(SO4)3 solution was investigated.The experiments were conducted using a wide range of initial fluoride concentrations(0.5 to 180 mg·L-1 at pH～7.0) and an adsorbent dose of 1.0 g·L-1.The application of Langmuir and Freundlich adsorption isotherm models(linear and nonlinear forms) generally showed that a single Langmuir or Freundlich equation cannot fit the entire concentration gap.Experimental data on low equilibrium concentrations(0.1 to 5.0 mg·L-1) was in line with both Langmuir and Freundlich isotherm models,whereas that of high equilibrium concentrations(5.0 to 150 mg·L-1) was more in line with the Freundlich isotherm model.A new LangmuirFreundlich function was used for the entire concentration gap,as well as for low and high concentrations.
基金support of Shanxi key laboratory of advanced magnesium-based material,Na-tional Natural Science Foundation of China(No.51474153 and 51574175)Ph.D.Programs Foundation of Ministry of Education of China(20111402110004)。
文摘The ZrB 2 particles firstly modified Mg_(94)Zn_(2.5)Y_(2.5)Mn 1 alloy.And the microstructures and mechanical performances of the modified alloys were studied systematically.The results showed that the moderate addition of ZrB 2 accelerated the development of long-period stacking ordered(LPSO)structure and refined the grain size.The grains in ZrB 2-modified alloys were nearly equiaxed with a homogeneous size.When 0.0075 wt%ZrB 2 was added,the as-cast alloy with the finest grains(24.87μm)presented desirable mechanical properties(especially ductility)with maximum tensile strength and ductility of 225 MPa and 17.5%,respectively.
基金supported by the National Key R&D Program of China (No.2018YFB1501404)
文摘This work proved that biomass-based polyols (sorbitol, xylitol, erythritol, glycerol and ethanediol) were able to be converted into high-value chemical (p-xylene) by catalytic cracking of polyols, alkylation of aromatics, and the isomerization of xylenes over the SiO2-modified zeolites. Compared to the conventional HZSM-5 zeolite, the SiO2-containing zeolites considerably increased the selectivity and yield of p-xylene due to the reduction of external surface acidity and the narrowing of pore entrance. The influences of the methanol additive, reaction temperature, and types of polyols on the selectivity and yield of p-xylene were investigated in detail. Catalytic cracking of polyols with methanol significantly enhanced the production of p-xylene by the alkylation of toluene with methanol. The highest p-xylene yield of 10.9 C-mol% with a p-xylene/xylenes ratio of 91.1% was obtained over the 15wt%SiO2/HZSM-5 catalyst. The reaction pathway for the formation of p-xylene was addressed according to the study of the key reactions and the characterization of catalysts.
基金Supported by the National Natural Science Foundation of China under Grant Nos 51332006,11274270,and 51272233
文摘We investigate the dielectric and ferroelectric properties of Sr1-xBixTi1-xFex03 solid solutions （x =0, 0.05, 0.1, 0.15 and 0.2） together with their structures. Through the analysis of Rietveld refinement of powder x-ray diffraction, a cubic structure in space group Pm3m is determined for all the compositions. An obvious dielectric relaxation peak differing from SrTiO3 is observed in the present ceramics. The peak temperature Tm increases with increasing x, and it approaches room temperature at x =0.2. The Vogel Fulcher law and Curie Weiss law fittings further confirm the relaxor ferroelectricity in the present ceramics.
文摘This paper examines the existence of weak solutions to a class of the high-order Korteweg-de Vries(KdV)system in Rn.We first prove,by the Leray-Schauder principle and the vanishing viscosity method,that any initial data N-dimensional vector value function u0(x)in Sobolev space H^(s)(R^(n))(s≥1)leads to a global weak solution.Second,we investigate some special regularity properties of solutions to the initial value problem associated with the KdV type system in R^(2)and R^(3).
基金Project supported by the Natural Science Foundation of Shandong Province (Grant No.ZR2021MA084)the Natural Science Foundation of Liaocheng University (Grant No.318012025)Discipline with Strong Characteristics of Liaocheng University–Intelligent Science and Technology (Grant No.319462208)。
文摘The time-fractional modified Korteweg-de Vries(KdV)equation is committed to establish exact solutions by employing the bifurcation method.Firstly,the phase portraits and related qualitative analysis are comprehensively provided.Then,we give parametric expressions of different types of solutions matching with the corresponding orbits.Finally,solution profiles,3D and density plots of some solutions are presented with proper parametric choices.
