We calculate the transverse Ward-Takahashi relation for the vector vertex in momentum space at one-loop order in four-dimensional Abelian gauge theory. We demonstrate explicitly that the result is exactly the same as ...We calculate the transverse Ward-Takahashi relation for the vector vertex in momentum space at one-loop order in four-dimensional Abelian gauge theory. We demonstrate explicitly that the result is exactly the same as that derived by using one-loop vector vertex calculations.展开更多
Recently we have proposed anew method combininginterior and exterior approaches to solve linear programming problems. This method uses an interior point, and from there connected to the vertex of the so called station...Recently we have proposed anew method combininginterior and exterior approaches to solve linear programming problems. This method uses an interior point, and from there connected to the vertex of the so called station cone which is also a solution of the dual problem. This allows us to determine the entering vector and the new station cone. Here in this paper, we present a new modified algorithm for the case, when at each iteration we determine a new interior point. The new building interior point moves toward the optimal vertex. Thanks to the shortened from both inside and outside, the new version allows to find quicker the optimal solution. The computational experiments show that the number of iterations of the new modified algorithm is significantly smaller than that of the second phase of the dual simplex method.展开更多
The conditions for G1 continuity between two adjacent bicubic B-spline surfaces with double interior knots along their common boundary curve are obtained in this paper, which are directly represented by the control po...The conditions for G1 continuity between two adjacent bicubic B-spline surfaces with double interior knots along their common boundary curve are obtained in this paper, which are directly represented by the control points of the two B-spline surfaces. As stated by Shi Xi-quan and Zhao Yan, a local scheme of constructing G1 continuous B-spline surface models with single interior knots does not exist; we may achieve a local scheme of (true) G1 continuity over an arbitrary B-spline surface network using these conditions.展开更多
文摘We calculate the transverse Ward-Takahashi relation for the vector vertex in momentum space at one-loop order in four-dimensional Abelian gauge theory. We demonstrate explicitly that the result is exactly the same as that derived by using one-loop vector vertex calculations.
文摘Recently we have proposed anew method combininginterior and exterior approaches to solve linear programming problems. This method uses an interior point, and from there connected to the vertex of the so called station cone which is also a solution of the dual problem. This allows us to determine the entering vector and the new station cone. Here in this paper, we present a new modified algorithm for the case, when at each iteration we determine a new interior point. The new building interior point moves toward the optimal vertex. Thanks to the shortened from both inside and outside, the new version allows to find quicker the optimal solution. The computational experiments show that the number of iterations of the new modified algorithm is significantly smaller than that of the second phase of the dual simplex method.
基金973 Foundation of China (G19980306007) National Natural Science Foundation of China (G1999014115, 60473108) Outstanding Young Teacher Foundation of Educational Department of China (60073038) Doctoral Program Foundation of Educational Department of China.
文摘The conditions for G1 continuity between two adjacent bicubic B-spline surfaces with double interior knots along their common boundary curve are obtained in this paper, which are directly represented by the control points of the two B-spline surfaces. As stated by Shi Xi-quan and Zhao Yan, a local scheme of constructing G1 continuous B-spline surface models with single interior knots does not exist; we may achieve a local scheme of (true) G1 continuity over an arbitrary B-spline surface network using these conditions.
