The piecewise algebraic variety is the set of all common zeros of multivariate splines. We show that solving a parametric piecewise algebraic variety amounts to solve a finite number of parametric polynomial systems c...The piecewise algebraic variety is the set of all common zeros of multivariate splines. We show that solving a parametric piecewise algebraic variety amounts to solve a finite number of parametric polynomial systems containing strict inequalities. With the regular decomposition of semi-algebraic systems and the partial cylindrical algebraic decomposition method, we give a method to compute the supremum of the number of torsion-free real zeros of a given zero-dimensional parametric piecewise algebraic variety, and to get distributions of the number of real zeros in every n-dimensional cell when the number reaches the supremum. This method also produces corresponding necessary and sufficient conditions for reaching the supremum and its distributions. We also present an algorithm to produce a necessary and sufficient condition for a given zero-dimensional parametric piecewise algebraic variety to have a given number of distinct torsion-free real zeros in every n-cell in the n-complex.展开更多
This paper proposes a new method for the construction of Bernstein-Bezier algebraic hypersurface on a simplex with prescribed topology. The method is based on the combinatorial patchworking of Viro method. The topolog...This paper proposes a new method for the construction of Bernstein-Bezier algebraic hypersurface on a simplex with prescribed topology. The method is based on the combinatorial patchworking of Viro method. The topology of the Viro Bernstein-Bezier algebraic hypersurface piece is also described.展开更多
A series of novel uracil and 5-fluorouracil-l-yl-acetic acid-colchicine derivatives（6a--6n） was synthe- sized via coupling and 5-fluorouracil（5-FU） with C-10 analogues of colchicine. The antitumor activities of th...A series of novel uracil and 5-fluorouracil-l-yl-acetic acid-colchicine derivatives（6a--6n） was synthe- sized via coupling and 5-fluorouracil（5-FU） with C-10 analogues of colchicine. The antitumor activities of the target compounds against human hepatocellular earcinoma（BEL7402） cells, human ovary carcinoma（A2780） cells, human lung adenocarcinoma（A549） cells and human breast carcinoma（MCF7） cells were tested in vitro, and the structure-activity relationship（SAR） of the compounds was also studied. The bioassay results demonstrate that most of the tested compounds display significant activity and particularly, compounds 6a, 6e, 6h and 61 show more potent cytotoxic activities than 5-fluorouracil and colchicine. The results show that the new derivatives of colchicine are potential suppressors on human cancer.展开更多
This paper proposes an improved algorithm to construct moving quadrics from moving planes that follow a tensor product surface with no base points, assuming that there are no moving planes of low degree following the ...This paper proposes an improved algorithm to construct moving quadrics from moving planes that follow a tensor product surface with no base points, assuming that there are no moving planes of low degree following the surface. These moving quadrics provide an efficient method to implicitize the tensor product surface which outperforms a previous approach by the present authors.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos. 10271022, 60373093,60533060)the Natural Science Foundation of Zhejiang Province (Grant No. Y7080068)the Foundation of Department of Education of Zhejiang Province (Grant Nos. 20070628 and Y200802999)
文摘The piecewise algebraic variety is the set of all common zeros of multivariate splines. We show that solving a parametric piecewise algebraic variety amounts to solve a finite number of parametric polynomial systems containing strict inequalities. With the regular decomposition of semi-algebraic systems and the partial cylindrical algebraic decomposition method, we give a method to compute the supremum of the number of torsion-free real zeros of a given zero-dimensional parametric piecewise algebraic variety, and to get distributions of the number of real zeros in every n-dimensional cell when the number reaches the supremum. This method also produces corresponding necessary and sufficient conditions for reaching the supremum and its distributions. We also present an algorithm to produce a necessary and sufficient condition for a given zero-dimensional parametric piecewise algebraic variety to have a given number of distinct torsion-free real zeros in every n-cell in the n-complex.
基金supported by National Natural Science Foundation of China (Grant Nos.11071031,60533060,11101366,10771189)the NSFC-Guangdong Joint Fund (Grant No. U0935004)the Zhejiang Provincial Natural Science Foundation (Grant Nos. Y7080068,Y6100126)
文摘This paper proposes a new method for the construction of Bernstein-Bezier algebraic hypersurface on a simplex with prescribed topology. The method is based on the combinatorial patchworking of Viro method. The topology of the Viro Bernstein-Bezier algebraic hypersurface piece is also described.
文摘A series of novel uracil and 5-fluorouracil-l-yl-acetic acid-colchicine derivatives（6a--6n） was synthe- sized via coupling and 5-fluorouracil（5-FU） with C-10 analogues of colchicine. The antitumor activities of the target compounds against human hepatocellular earcinoma（BEL7402） cells, human ovary carcinoma（A2780） cells, human lung adenocarcinoma（A549） cells and human breast carcinoma（MCF7） cells were tested in vitro, and the structure-activity relationship（SAR） of the compounds was also studied. The bioassay results demonstrate that most of the tested compounds display significant activity and particularly, compounds 6a, 6e, 6h and 61 show more potent cytotoxic activities than 5-fluorouracil and colchicine. The results show that the new derivatives of colchicine are potential suppressors on human cancer.
基金supported by the National Natural Science Foundation of China under Grant Nos.11271328and 11571338the Zhejiang Provincial Natural Science Foundation under Grant No.Y7080068
文摘This paper proposes an improved algorithm to construct moving quadrics from moving planes that follow a tensor product surface with no base points, assuming that there are no moving planes of low degree following the surface. These moving quadrics provide an efficient method to implicitize the tensor product surface which outperforms a previous approach by the present authors.
