In this paper, Remes algorithm is applied to compute the numerical solution of the best chebyshev approximation from varisolvent family. Feasibility and convergence of the algorithm are discussed carefully.
Hollow nanomaterials have attracted signifi- cant attention because of their high chemical and thermal stability, high specific surface area, high porosity, low density, and good biocompatibility. These state-of-the-a...Hollow nanomaterials have attracted signifi- cant attention because of their high chemical and thermal stability, high specific surface area, high porosity, low density, and good biocompatibility. These state-of-the-art nanomaterials have been shown to efficiently adsorb heavy metals, and volatile hazardous substances, photodegrade persistent organic pollutants, and other compounds, and inactivate bacteria. Such properties have enabled the use of these materials for environmental remediation, such as in water/wastewater treatment, soil remediation, air purifica- tion, and substance monitoring, etc. Hollow nanomaterials showed higher photocatalytic activity than those without hollow structure owing to their high active surface area, reduced diffusion resistance, and improved accessibility. And, the Doping method could improve the photocatalytic performance of hollow nanomaterials further under visible light. Moreover, the synthetic mechanisms and methods of these materials are important because their size and morphology help to determine their precise properties. This article reviews the environmental applications and potential risks of these materials, in addition to their syntheses. Finally, an outlook into the development of these materials is provided.展开更多
We propose a class of iteration methods searching the best approximately generalized polynomial, which has parallel computational function and converges to the exact solution quadratically. We first transform it into ...We propose a class of iteration methods searching the best approximately generalized polynomial, which has parallel computational function and converges to the exact solution quadratically. We first transform it into a special system of nonlinear equations with constraint, then by using to certain iteration method, we combine the two basic processes of the Remes method into a whole such that the iterative process of the system of nonlinear equations and the computation of the solution to the system of linear equations proceed alternately. A lot of numerical examples show that this method not only has good convergence property but also always converges to the exact solution of the problem accurately and rapidly for almost all initial approximations .展开更多
文摘In this paper, Remes algorithm is applied to compute the numerical solution of the best chebyshev approximation from varisolvent family. Feasibility and convergence of the algorithm are discussed carefully.
文摘Hollow nanomaterials have attracted signifi- cant attention because of their high chemical and thermal stability, high specific surface area, high porosity, low density, and good biocompatibility. These state-of-the-art nanomaterials have been shown to efficiently adsorb heavy metals, and volatile hazardous substances, photodegrade persistent organic pollutants, and other compounds, and inactivate bacteria. Such properties have enabled the use of these materials for environmental remediation, such as in water/wastewater treatment, soil remediation, air purifica- tion, and substance monitoring, etc. Hollow nanomaterials showed higher photocatalytic activity than those without hollow structure owing to their high active surface area, reduced diffusion resistance, and improved accessibility. And, the Doping method could improve the photocatalytic performance of hollow nanomaterials further under visible light. Moreover, the synthetic mechanisms and methods of these materials are important because their size and morphology help to determine their precise properties. This article reviews the environmental applications and potential risks of these materials, in addition to their syntheses. Finally, an outlook into the development of these materials is provided.
文摘We propose a class of iteration methods searching the best approximately generalized polynomial, which has parallel computational function and converges to the exact solution quadratically. We first transform it into a special system of nonlinear equations with constraint, then by using to certain iteration method, we combine the two basic processes of the Remes method into a whole such that the iterative process of the system of nonlinear equations and the computation of the solution to the system of linear equations proceed alternately. A lot of numerical examples show that this method not only has good convergence property but also always converges to the exact solution of the problem accurately and rapidly for almost all initial approximations .
