Using reproducing kernels for Hilbert spaces, we give best approximation for Weierstrass transform associated with spherical mean operator. Also, estimates of extremal functions are checked.
In this paper we consider the approximation for functions in some subspaces of L^2 by spherical means of their Fourier integrals and Fourier series on set of full measure. Two main theorems are obtained.
A comprehensive review of recent advances in study on thermodynamic models for real electrolyte solutions is presented. The differences between primitive and non-primitive electrolyte models are demonstrated. Some new...A comprehensive review of recent advances in study on thermodynamic models for real electrolyte solutions is presented. The differences between primitive and non-primitive electrolyte models are demonstrated. Some new thermodynamic models for electrolyte solutions based on the mean spherical approximation and perturbation theory are introduced. An extended scaled-particle theory and modified CleggPitzer equation are presented for physical and chemical absorption processes with mixed solvents, respectively. A pseudo one-component two-Yukawa equation of state is used for the aqueous two-phase extraction process in charged colloidal systems.展开更多
Based on statistical mechanics, a review of recent theoretical studies of real electrolyte solutions is presented from three aspects, namely, molecular simulation, mean spherical approximation (MSA), and perturbation ...Based on statistical mechanics, a review of recent theoretical studies of real electrolyte solutions is presented from three aspects, namely, molecular simulation, mean spherical approximation (MSA), and perturbation theory. Recent advances in studies of three kinds of electrostatic potentials of mean force, three kinds of internal energies (ion-ion, ion-dipole, and dipole-dipole interactions), and three kinds of electro-lyte models (primitive, non-primitive, and solvent primitive models) are introduced. The advantages and dis-advantages between primitive and non-primitive models, and between MSA and perturbation theory are dis-cussed. Some new equations of state (EOSs) based on MSA and perturbation theory for real electrolyte so-lutions are introduced. The one-Yukawa EOS and the two-Yukawa EOS for charged colloid systems are presented.展开更多
文摘Using reproducing kernels for Hilbert spaces, we give best approximation for Weierstrass transform associated with spherical mean operator. Also, estimates of extremal functions are checked.
文摘In this paper we consider the approximation for functions in some subspaces of L^2 by spherical means of their Fourier integrals and Fourier series on set of full measure. Two main theorems are obtained.
基金Supported by the Fundamental Research Fund of Tsinghua Universitof China (No. JZ 2002003)
文摘A comprehensive review of recent advances in study on thermodynamic models for real electrolyte solutions is presented. The differences between primitive and non-primitive electrolyte models are demonstrated. Some new thermodynamic models for electrolyte solutions based on the mean spherical approximation and perturbation theory are introduced. An extended scaled-particle theory and modified CleggPitzer equation are presented for physical and chemical absorption processes with mixed solvents, respectively. A pseudo one-component two-Yukawa equation of state is used for the aqueous two-phase extraction process in charged colloidal systems.
基金the Fundamental Research Fund of Tsinghua University of China (No. JZ 2002003)
文摘Based on statistical mechanics, a review of recent theoretical studies of real electrolyte solutions is presented from three aspects, namely, molecular simulation, mean spherical approximation (MSA), and perturbation theory. Recent advances in studies of three kinds of electrostatic potentials of mean force, three kinds of internal energies (ion-ion, ion-dipole, and dipole-dipole interactions), and three kinds of electro-lyte models (primitive, non-primitive, and solvent primitive models) are introduced. The advantages and dis-advantages between primitive and non-primitive models, and between MSA and perturbation theory are dis-cussed. Some new equations of state (EOSs) based on MSA and perturbation theory for real electrolyte so-lutions are introduced. The one-Yukawa EOS and the two-Yukawa EOS for charged colloid systems are presented.
