The equation of limit cycles has been discussed in [1]. On the basis of [2—4], some problems of analytic theory of limit cycles are solved in this note for the autonomous differential system E(α) in the real plane w...The equation of limit cycles has been discussed in [1]. On the basis of [2—4], some problems of analytic theory of limit cycles are solved in this note for the autonomous differential system E(α) in the real plane with a single parameter α:展开更多
By using the iterative method in functional theory, an analytic expression of the Poisson-Boltzmann equation (PB eq.), which describes the distribution of the potential of electrical double layer of a spherical micell...By using the iterative method in functional theory, an analytic expression of the Poisson-Boltzmann equation (PB eq.), which describes the distribution of the potential of electrical double layer of a spherical micelle, has been carried out under the general potential condition for the first time. The method also can give the radius, the surface potential, and the thickness of the layer.展开更多
The iterative method in functional analysis is applied to looking for asolution of the Poisson-Boltzmann equation in order to describe the problems of the distribution ofthe potentials in the electric double layer (ED...The iterative method in functional analysis is applied to looking for asolution of the Poisson-Boltzmann equation in order to describe the problems of the distribution ofthe potentials in the electric double layer (EDL) inside the water pool for a cylindrical inversemicelle. Potentials as a function of the position of a particular point in EDL are computed, whichdisplay a quantitative agreement with those from earlier calculation of Debye and Huckel in the caseof low potentials. But it is also shown that in the higher-potential range the iterativecalculations can give more accurate results. These results indicate the utility of this functionalanalysis technique in the description of the properties of EDL for a cylindrical inverse micelle.展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘The equation of limit cycles has been discussed in [1]. On the basis of [2—4], some problems of analytic theory of limit cycles are solved in this note for the autonomous differential system E(α) in the real plane with a single parameter α:
基金We wish to thank to the National Natural Science Foundation of China(to grant No,29903006 and 29973023)the Visiting Scholar Foundation of Key Laboratory in University of China for financial suppor.
文摘By using the iterative method in functional theory, an analytic expression of the Poisson-Boltzmann equation (PB eq.), which describes the distribution of the potential of electrical double layer of a spherical micelle, has been carried out under the general potential condition for the first time. The method also can give the radius, the surface potential, and the thickness of the layer.
基金This work was supported by the National Natural Science Foundation of China (Grant Nos.20473034 and 20573048) the Open Project Program of the Key Laboratory of Industrial Biotechnology, Ministry of Education of China (Grant No. KLIB-KF200504).
文摘The iterative method in functional analysis is applied to looking for asolution of the Poisson-Boltzmann equation in order to describe the problems of the distribution ofthe potentials in the electric double layer (EDL) inside the water pool for a cylindrical inversemicelle. Potentials as a function of the position of a particular point in EDL are computed, whichdisplay a quantitative agreement with those from earlier calculation of Debye and Huckel in the caseof low potentials. But it is also shown that in the higher-potential range the iterativecalculations can give more accurate results. These results indicate the utility of this functionalanalysis technique in the description of the properties of EDL for a cylindrical inverse micelle.
