Semi-tensor product of matrices is a generalization of conventional matrix product for the case when the two factor matrices do not meet the dimension matching condition. It was firstly proposed about ten years ago. S...Semi-tensor product of matrices is a generalization of conventional matrix product for the case when the two factor matrices do not meet the dimension matching condition. It was firstly proposed about ten years ago. Since then it has been developed and applied to several different fields. In this paper we will first give a brief introduction. Then give a survey on its applications to dynamic systems, to logic, to differential geometry, to abstract algebra, respectively.展开更多
Under certain conditions, the dynamic equations of membrane shells and the dynamic equations of flexural shells are obtained from dynamic equations of Koiter shells by the method of asymptotic analysis.
An exact de Sitter solution of scalar-tensor gravity is found in our recent work, in which the non-minimal coupling scalar is rolling along a non-constant potential. Based on this solution, a dust-filled FRW universe ...An exact de Sitter solution of scalar-tensor gravity is found in our recent work, in which the non-minimal coupling scalar is rolling along a non-constant potential. Based on this solution, a dust-filled FRW universe is explored in frame of scalar-tensor gravity in this article. The effective dark energy induced by the sole non-minimal scalar can be quintessence-like, phantom-like, and more significantly, can cross the phantom divide. The rich and varied properties of scalar-tensor gravity even with only one scalar is shown.展开更多
基金Supported partly by National Natural Science Foundation of China under Grant No. 60221301 and 60334040 .Dedicated to Academician Han-Fu Chen on the occasion of his 70th birthday.
文摘Semi-tensor product of matrices is a generalization of conventional matrix product for the case when the two factor matrices do not meet the dimension matching condition. It was firstly proposed about ten years ago. Since then it has been developed and applied to several different fields. In this paper we will first give a brief introduction. Then give a survey on its applications to dynamic systems, to logic, to differential geometry, to abstract algebra, respectively.
基金the National Natural Science Foundation of China (No.10071024).
文摘Under certain conditions, the dynamic equations of membrane shells and the dynamic equations of flexural shells are obtained from dynamic equations of Koiter shells by the method of asymptotic analysis.
基金supported by the Program for Professor of Special Appointment(Eastern Scholar)at Shanghai Institutions of Higher Learningthe National Education Foundation of China(Grant No.200931271104)+2 种基金the National Natural Science Foundation of China(Grant Nos.11075106,11275128,11203006 and 11303003)Shandong Provincial Natural Science Foundation of China(Grant Nos.ZR2012AQ029 and ZR2013AM002)Nature Science Foundation of Zhejiang Province(Grant No.Y6110778)
文摘An exact de Sitter solution of scalar-tensor gravity is found in our recent work, in which the non-minimal coupling scalar is rolling along a non-constant potential. Based on this solution, a dust-filled FRW universe is explored in frame of scalar-tensor gravity in this article. The effective dark energy induced by the sole non-minimal scalar can be quintessence-like, phantom-like, and more significantly, can cross the phantom divide. The rich and varied properties of scalar-tensor gravity even with only one scalar is shown.
