Fan-Browder type fixed point theorems are obtained for non-selfmaps on non-compact generalized convex product spaces and new existence problems of（partially） maximai element and equilibrium point are discussed as ap...Fan-Browder type fixed point theorems are obtained for non-selfmaps on non-compact generalized convex product spaces and new existence problems of（partially） maximai element and equilibrium point are discussed as applications of above results.展开更多
In this paper, a unified matrix recovery model was proposed for diverse corrupted matrices. Resulting from the separable structure of the proposed model, the convex optimization problem can be solved efficiently by ad...In this paper, a unified matrix recovery model was proposed for diverse corrupted matrices. Resulting from the separable structure of the proposed model, the convex optimization problem can be solved efficiently by adopting an inexact augmented Lagrange multiplier (IALM) method. Additionally, a random projection accelerated technique (IALM+RP) was adopted to improve the success rate. From the preliminary numerical comparisons, it was indicated that for the standard robust principal component analysis (PCA) problem, IALM+RP was at least two to six times faster than IALM with an insignificant reduction in accuracy; and for the outlier pursuit (OP) problem, IALM+RP was at least 6.9 times faster, even up to 8.3 times faster when the size of matrix was 2 000×2 000.展开更多
This paper discusses some properties of two classes Vk[α,β] and Rk[α,β ]. Sharp distortion theorem and radius of convexity and starlikeness are obtained. Hadamard product of functions in the classes are also studied.
A small cover is a closed manifold M^n with a locally standard （Z2）^n-action such that its orbit space is a simple convex polytope P^n. Let A^n denote an n-simplex and P（m） an m-gon. This paper gives formulas for ...A small cover is a closed manifold M^n with a locally standard （Z2）^n-action such that its orbit space is a simple convex polytope P^n. Let A^n denote an n-simplex and P（m） an m-gon. This paper gives formulas for calculating the number of D-J equivalent classes and equivariant homeomorphism classes of orientable small covers over the product space △^n1 × △^n2 × P（m）, where n1 is odd.展开更多
The non-probabilistic approach to fatigue life analysis was studied using the convex models-interval, ellipsoidal and multiconvex models. The lower and upper bounds of the fatigue life were obtained by using the secon...The non-probabilistic approach to fatigue life analysis was studied using the convex models-interval, ellipsoidal and multiconvex models. The lower and upper bounds of the fatigue life were obtained by using the second-order Taylor series and Lagrange multiplier method. The solving process for derivatives of the implicit life function was presented. Moreover, a median ellipsoidal model was proposed which can take into account the sample blind zone and almost impossibility of concurrence of some small probability events. The Monte Carlo method for multi-convex model was presented, an important alternative when the analytical method does not work. A project example was given. The feasibility and rationality of the presented approach were verified. It is also revealed that the proposed method is conservative compared to the traditional probabilistic method, but it is a useful complement when it is difficult to obtain the accurate probability densities of parameters.展开更多
基金Supported by the National Natural Science Foundation of China（10361005）
文摘Fan-Browder type fixed point theorems are obtained for non-selfmaps on non-compact generalized convex product spaces and new existence problems of（partially） maximai element and equilibrium point are discussed as applications of above results.
基金Supported by National Natural Science Foundation of China (No.51275348)College Students Innovation and Entrepreneurship Training Program of Tianjin University (No.201210056339)
文摘In this paper, a unified matrix recovery model was proposed for diverse corrupted matrices. Resulting from the separable structure of the proposed model, the convex optimization problem can be solved efficiently by adopting an inexact augmented Lagrange multiplier (IALM) method. Additionally, a random projection accelerated technique (IALM+RP) was adopted to improve the success rate. From the preliminary numerical comparisons, it was indicated that for the standard robust principal component analysis (PCA) problem, IALM+RP was at least two to six times faster than IALM with an insignificant reduction in accuracy; and for the outlier pursuit (OP) problem, IALM+RP was at least 6.9 times faster, even up to 8.3 times faster when the size of matrix was 2 000×2 000.
文摘This paper discusses some properties of two classes Vk[α,β] and Rk[α,β ]. Sharp distortion theorem and radius of convexity and starlikeness are obtained. Hadamard product of functions in the classes are also studied.
基金supported by the National Natural Science Foundation of China(No.11371118)the Specialized Research Fund for the Doctoral Program of Higher Education(No.20121303110004)the Natural Science Foundation of Hebei Province(No.A2011205075)
文摘A small cover is a closed manifold M^n with a locally standard （Z2）^n-action such that its orbit space is a simple convex polytope P^n. Let A^n denote an n-simplex and P（m） an m-gon. This paper gives formulas for calculating the number of D-J equivalent classes and equivariant homeomorphism classes of orientable small covers over the product space △^n1 × △^n2 × P（m）, where n1 is odd.
基金supported by the Program for New Century Excellent Talents in University of Chinathe Advanced Research Foundation of China (Grant No. 9140A27050109JB1112)
文摘The non-probabilistic approach to fatigue life analysis was studied using the convex models-interval, ellipsoidal and multiconvex models. The lower and upper bounds of the fatigue life were obtained by using the second-order Taylor series and Lagrange multiplier method. The solving process for derivatives of the implicit life function was presented. Moreover, a median ellipsoidal model was proposed which can take into account the sample blind zone and almost impossibility of concurrence of some small probability events. The Monte Carlo method for multi-convex model was presented, an important alternative when the analytical method does not work. A project example was given. The feasibility and rationality of the presented approach were verified. It is also revealed that the proposed method is conservative compared to the traditional probabilistic method, but it is a useful complement when it is difficult to obtain the accurate probability densities of parameters.
