With thermal Bose–Fermi mapping method, we investigate the Tonks–Girardeau gas at finite temperature. It is shown that at low temperature, the Tonks gas displays the Fermi-like density profiles, and with the increas...With thermal Bose–Fermi mapping method, we investigate the Tonks–Girardeau gas at finite temperature. It is shown that at low temperature, the Tonks gas displays the Fermi-like density profiles, and with the increase in temperature, the Tonks gas distributes in wider region. The reduced one-body density matrix is diagonal dominant in the whole temperature region, and the off-diagonal elements shall vanish rapidly with the deviation from the diagonal part at high temperature.展开更多
We in this paper give necessary and sufficient conditions for the existence of the general solution to the system of matrix equations A1X1 = C1, AXiB1 ＋ X2B2 = C3, A2X2 ＋ A3X3B= C2 and X3B3 = C4 over the quaternion ...We in this paper give necessary and sufficient conditions for the existence of the general solution to the system of matrix equations A1X1 = C1, AXiB1 ＋ X2B2 = C3, A2X2 ＋ A3X3B= C2 and X3B3 = C4 over the quaternion algebra H, and present an expression of the general solution to this system when it is solvable. Using the results, we give some necessary and sufficient conditions for the system of matrix equations AX = C, XB = C over H to have a reducible solution as well as the representation of such solution to the system when the consistency conditions are met. A numerical example is also given to illustrate our results. As another application, we give the necessary and sufficient conditions for two associated electronic networks to have the same branch current and branch voltage and give the expressions of the same branch current and branch voltage when the conditions are satisfied.展开更多
The multibody system transfer matrix method(MSTMM),a novel dynamics approach developed during the past three decades,has several advantages compared to conventional dynamics methods.Some of these advantages include av...The multibody system transfer matrix method(MSTMM),a novel dynamics approach developed during the past three decades,has several advantages compared to conventional dynamics methods.Some of these advantages include avoiding global dynamics equations with a system inertia matrix,utilizing low‐order matrices independent of system degree of freedom,high computational speed,and simplicity of computer implementation.MSTMM has been widely used in computer modeling,simulations,and performance evaluation of approximately 150 different complex mechanical systems.In this paper,the following aspects regarding MSTMM are reviewed:basic theory,algorithms,simulation and design software,and applications.Future research directions and generalization to more applications in various fields of science,technology,and engineering are discussed.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.11004007)the Fundamental Research Funds for the Central Universities of China
文摘With thermal Bose–Fermi mapping method, we investigate the Tonks–Girardeau gas at finite temperature. It is shown that at low temperature, the Tonks gas displays the Fermi-like density profiles, and with the increase in temperature, the Tonks gas distributes in wider region. The reduced one-body density matrix is diagonal dominant in the whole temperature region, and the off-diagonal elements shall vanish rapidly with the deviation from the diagonal part at high temperature.
基金This research was supported by the National Natural Science Foundation of China （11571220）, the Science and Technology Foundation of Guizhou Province （LKB [2013] 11）, the Natural Sciences and Engineering Research Council of Canada （NSERC） （RGPIN 312386-2015）, and the Macao Science and Technology Development Fund （003/2015/A1）.
文摘We in this paper give necessary and sufficient conditions for the existence of the general solution to the system of matrix equations A1X1 = C1, AXiB1 ＋ X2B2 = C3, A2X2 ＋ A3X3B= C2 and X3B3 = C4 over the quaternion algebra H, and present an expression of the general solution to this system when it is solvable. Using the results, we give some necessary and sufficient conditions for the system of matrix equations AX = C, XB = C over H to have a reducible solution as well as the representation of such solution to the system when the consistency conditions are met. A numerical example is also given to illustrate our results. As another application, we give the necessary and sufficient conditions for two associated electronic networks to have the same branch current and branch voltage and give the expressions of the same branch current and branch voltage when the conditions are satisfied.
基金National Program on Key Basic Research Project of China,Grant/Award Number:613308Science Challenge Project,Grant/Award Number:TZ2016006‐0104+3 种基金Natural Science Foundation of China Government,Grant/Award Number:11472135supported by the National Program on Key Basic Research Project of China(973 Program,No.613308)the Science Challenge Project(No.TZ2016006‐0104)the Natural Science Foundation of China Government(No.11472135).
文摘The multibody system transfer matrix method(MSTMM),a novel dynamics approach developed during the past three decades,has several advantages compared to conventional dynamics methods.Some of these advantages include avoiding global dynamics equations with a system inertia matrix,utilizing low‐order matrices independent of system degree of freedom,high computational speed,and simplicity of computer implementation.MSTMM has been widely used in computer modeling,simulations,and performance evaluation of approximately 150 different complex mechanical systems.In this paper,the following aspects regarding MSTMM are reviewed:basic theory,algorithms,simulation and design software,and applications.Future research directions and generalization to more applications in various fields of science,technology,and engineering are discussed.
