The present work extends the search of Jacobi elliptic function solutions for the multi-component modified Korteweg-de Vries equations. When the modulum m →1, those periodic solutions degenerate as the corresponding ...The present work extends the search of Jacobi elliptic function solutions for the multi-component modified Korteweg-de Vries equations. When the modulum m →1, those periodic solutions degenerate as the corresponding solitary wave and shock wave ones. Especially, exact solutions for the three-component system are presented in detail and graphically.展开更多
Polypiperazine-amide membranes were modified with poly(ethyleneimine)(PEI) by self-assembled method,through which PEI molecules were fixed on the membrane surface by ionic interaction. In the experiments,the PEI conce...Polypiperazine-amide membranes were modified with poly(ethyleneimine)(PEI) by self-assembled method,through which PEI molecules were fixed on the membrane surface by ionic interaction. In the experiments,the PEI concentration ranged from 50 to 2000 mg·L-1while the depositing time was fixed at 20 min. The results showed that low PEI concentration resulted in a slight increase of pure water flux, which was attributed to the enhanced membrane surface hydrophilicity. The PEI adsorption on membrane surface had less effect on the rejections to neutral PEG and sucrose, but improved the rejections to divalent cationic ions and methylene blue as the result of reversion of the membrane surface charge from negative to positive according to the XPS analysis and zeta potential measurements. The membrane modified at PEI = 1500 mg·L-1exhibited high rejection to methylene blue(MB) and is potential to be applied in the treatment of effluents containing positively charged dyes.展开更多
In the present paper, we established a traveling wave solution by using modified Kudryashov method for the space-time fractional nonlinear partial differential equations. The method is used to obtain the exact solutio...In the present paper, we established a traveling wave solution by using modified Kudryashov method for the space-time fractional nonlinear partial differential equations. The method is used to obtain the exact solutions for different types of the space-time fractional nonlinear partial differential equations such as, the space-time fractional coupled equal width wave equation(CEWE) and the space-time fractional coupled modified equal width wave equation(CMEW), which are the important soliton equations. Both equations are reduced to ordinary differential equations by the use of fractional complex transform and properties of modified Riemann–Liouville derivative. We plot the exact solutions for these equations at different time levels.展开更多
基金supported by National Natural Science Foundation of China under Grant Nos. 60772023 and 60372095the Key Project of the Ministry of Education under Grant No. 106033+3 种基金the Open Fund of the State Key Laboratory of Software Development Environment under Grant No. SKLSDE-07-001Beijing University of Aeronautics and Astronautics,the National Basic Research Program of China (973 Program) under Grant No. 2005CB321901the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No. 20060006024the Ministry of Education
文摘The present work extends the search of Jacobi elliptic function solutions for the multi-component modified Korteweg-de Vries equations. When the modulum m →1, those periodic solutions degenerate as the corresponding solitary wave and shock wave ones. Especially, exact solutions for the three-component system are presented in detail and graphically.
基金Support by the National High Technology Research and Development Program of China(863 Program)(2012AA03A608)the Open Foundation of Zhejiang Provincial Top Key Academic Discipline of Applied Chemistry and Eco-Dyeing&Finishing Engineering(YR2012012)
文摘Polypiperazine-amide membranes were modified with poly(ethyleneimine)(PEI) by self-assembled method,through which PEI molecules were fixed on the membrane surface by ionic interaction. In the experiments,the PEI concentration ranged from 50 to 2000 mg·L-1while the depositing time was fixed at 20 min. The results showed that low PEI concentration resulted in a slight increase of pure water flux, which was attributed to the enhanced membrane surface hydrophilicity. The PEI adsorption on membrane surface had less effect on the rejections to neutral PEG and sucrose, but improved the rejections to divalent cationic ions and methylene blue as the result of reversion of the membrane surface charge from negative to positive according to the XPS analysis and zeta potential measurements. The membrane modified at PEI = 1500 mg·L-1exhibited high rejection to methylene blue(MB) and is potential to be applied in the treatment of effluents containing positively charged dyes.
文摘In the present paper, we established a traveling wave solution by using modified Kudryashov method for the space-time fractional nonlinear partial differential equations. The method is used to obtain the exact solutions for different types of the space-time fractional nonlinear partial differential equations such as, the space-time fractional coupled equal width wave equation(CEWE) and the space-time fractional coupled modified equal width wave equation(CMEW), which are the important soliton equations. Both equations are reduced to ordinary differential equations by the use of fractional complex transform and properties of modified Riemann–Liouville derivative. We plot the exact solutions for these equations at different time levels.
