In this paper, we prove that the best rational approximation of a given analytic function in Orlicz space L~*(G), where G = {|z|≤∈}, converges to the Pade approximants of the function as the measure of G approaches ...In this paper, we prove that the best rational approximation of a given analytic function in Orlicz space L~*(G), where G = {|z|≤∈}, converges to the Pade approximants of the function as the measure of G approaches zero.展开更多
In density-based topological design, one expects that the final result consists of elements either black （solid material） or white （void）, without any grey areas. Moreover, one also expects that the optimal topolo...In density-based topological design, one expects that the final result consists of elements either black （solid material） or white （void）, without any grey areas. Moreover, one also expects that the optimal topology can be obtained by starting from any initial topology configuration. An improved structural topological optimization method for multidisplacement constraints is proposed in this paper. In the proposed method, the whole optimization process is divided into two optimization adjustment phases and a phase transferring step. Firstly, an optimization model is built to deal with the varied displacement limits, design space adjustments, and reasonable relations between the element stiffness matrix and mass and its element topology variable. Secondly, a procedure is proposed to solve the optimization problem formulated in the first optimization adjustment phase, by starting with a small design space and advancing to a larger deign space. The design space adjustments are automatic when the design domain needs expansions, in which the convergence of the proposed method will not be affected. The final topology obtained by the proposed procedure in the first optimization phase, can approach to the vicinity of the optimum topology. Then, a heuristic algorithm is given to improve the efficiency and make the designed structural topology black/white in both the phase transferring step and the second optimization adjustment phase. And the optimum topology can finally be obtained by the second phase optimization adjustments. Two examples are presented to show that the topologies obtained by the proposed method are of very good 0/1 design distribution property, and the computational efficiency is enhanced by reducing the element number of the design structural finite model during two optimization adjustment phases. And the examples also show that this method is robust and practicable.展开更多
This is a survey paper about a selection of results in complex algebraic geometry that appeared in the recent and less recent litterature,and in which rational homogeneous spaces play a prominent role.This selection i...This is a survey paper about a selection of results in complex algebraic geometry that appeared in the recent and less recent litterature,and in which rational homogeneous spaces play a prominent role.This selection is largely arbitrary and mainly refiects the interests of the author.展开更多
Among several implicitization methods, the method based on resultant computation is a simple and direct one, but it often brings extraneous factors which are difficult to remove. This paper studies a class of rational...Among several implicitization methods, the method based on resultant computation is a simple and direct one, but it often brings extraneous factors which are difficult to remove. This paper studies a class of rational space curves and rational surfaces by implicitization with univaxiate resultant computations. This method is more efficient than the other algorithms in finding implicit equations for this class of rational curves and surfaces.展开更多
基金This research is suported by National Science foundation Grant.
文摘In this paper, we prove that the best rational approximation of a given analytic function in Orlicz space L~*(G), where G = {|z|≤∈}, converges to the Pade approximants of the function as the measure of G approaches zero.
基金supported by the National Natural Science Foundation of China (10872036)the High Technological Research and Development Program of China (2008AA04Z118)the Airspace Natural Science Foundation (2007ZA23007)
文摘In density-based topological design, one expects that the final result consists of elements either black （solid material） or white （void）, without any grey areas. Moreover, one also expects that the optimal topology can be obtained by starting from any initial topology configuration. An improved structural topological optimization method for multidisplacement constraints is proposed in this paper. In the proposed method, the whole optimization process is divided into two optimization adjustment phases and a phase transferring step. Firstly, an optimization model is built to deal with the varied displacement limits, design space adjustments, and reasonable relations between the element stiffness matrix and mass and its element topology variable. Secondly, a procedure is proposed to solve the optimization problem formulated in the first optimization adjustment phase, by starting with a small design space and advancing to a larger deign space. The design space adjustments are automatic when the design domain needs expansions, in which the convergence of the proposed method will not be affected. The final topology obtained by the proposed procedure in the first optimization phase, can approach to the vicinity of the optimum topology. Then, a heuristic algorithm is given to improve the efficiency and make the designed structural topology black/white in both the phase transferring step and the second optimization adjustment phase. And the optimum topology can finally be obtained by the second phase optimization adjustments. Two examples are presented to show that the topologies obtained by the proposed method are of very good 0/1 design distribution property, and the computational efficiency is enhanced by reducing the element number of the design structural finite model during two optimization adjustment phases. And the examples also show that this method is robust and practicable.
文摘This is a survey paper about a selection of results in complex algebraic geometry that appeared in the recent and less recent litterature,and in which rational homogeneous spaces play a prominent role.This selection is largely arbitrary and mainly refiects the interests of the author.
基金supported by the Natural Science Foundation of China under Grant No. 10901163the Knowledge Innovation Program of the Chinese Academy of Sciences
文摘Among several implicitization methods, the method based on resultant computation is a simple and direct one, but it often brings extraneous factors which are difficult to remove. This paper studies a class of rational space curves and rational surfaces by implicitization with univaxiate resultant computations. This method is more efficient than the other algorithms in finding implicit equations for this class of rational curves and surfaces.
