In this paper we present systematic differential representations for the dynamical group SO(4).Theserepresentations include the left and the right differential representations and the left and the right adjoint differ...In this paper we present systematic differential representations for the dynamical group SO(4).Theserepresentations include the left and the right differential representations and the left and the right adjoint differentialrepresentations in both the group parameter space and its coset spaces.They are the generalization of the differentialrepresentations of the SO(3) rotation group in the Euler angles.These representations may find their applications in thestudy of the physical systems with SO(4) dynamical symmetry.展开更多
In this paper,with the aid of symbolic computation,we present a uniform method for constructing soliton solutions and periodic solutions to (2+1)-dimensional Toda lattice equation.
In order to fulfil the microgravity requirements for space experiments, improved technology for the microgravity environment is proposed, including that for raising the orbital altitude, optimizing the layout of the d...In order to fulfil the microgravity requirements for space experiments, improved technology for the microgravity environment is proposed, including that for raising the orbital altitude, optimizing the layout of the disturbance source, using IN-thrusters instead of 5 N-thrusters, etc. In addition, evaluation of the microgravity environment of the recoverable satellite was also conducted using on-orbit micro-vibration measurement, on-orbit experiment and data analysis technologies. The microgravity level of the SJ-l0 recoverable satellite in China is compared with the spacecraft used for carrying out space science experiments internationally. This paper describes the microgravity environment of the SJ- 10 recoverable satellite, and its importance for analysing space experimental results.展开更多
This paper present an implementation of＂modified cubic B-spline differential quadrature method （MCB-DQM）＂ proposed by Arora ＆ Singh （Applied Mathematics and Computation Vol. 224（1） （2013） 161-177） for numer...This paper present an implementation of＂modified cubic B-spline differential quadrature method （MCB-DQM）＂ proposed by Arora ＆ Singh （Applied Mathematics and Computation Vol. 224（1） （2013） 161-177） for numerical computation of Fokker-Planck equations. The modified cubic B-splines are used as set of basis functions in the differential quadrature to compute the weighting coefficients for the spatial derivatives, which reduces Fokker-Planck equation into system of first-order ordinary differential equations （ODEs）, in time. The well known SSP-RK43 scheme is then applied to solve the resulting system of ODEs. The efficiency of proposed method has been confirmed by three examples having their exact solutions. This shows that MCB-DQM results are capable of achieving high accuracy. Advantage of the scheme is that it can be applied very smoothly to solve the linear or nonlinear physical problems, and a very less storage space is required which causes less accumulation of numerical errors.展开更多
Let H be a Hilbert space and A ■ B(H) be a C~*-subalgebra. This paper is devoted to studying the set gP of generalized projections in A from a differential geometric point of view, and mainly focuses on geodesic curv...Let H be a Hilbert space and A ■ B(H) be a C~*-subalgebra. This paper is devoted to studying the set gP of generalized projections in A from a differential geometric point of view, and mainly focuses on geodesic curves. We prove that the space gP is a C~∞ Banach submanifold of A, and a homogeneous reductive space under the action of Banach Lie group U_A of A. Moreover, we compute the geodesics of gP in a standard fashion, and prove that any generalized projection in a prescribed neighbourhood of p∈gP can be joined with p by a unique geodesic curve in gP.展开更多
We recognize the stochastic collisions of dopamine contained phospholipid vesicle on carbon fiber nanoelectrode, extending the observation of discrete collision events on nanoelectrode to biologically relevant analyte...We recognize the stochastic collisions of dopamine contained phospholipid vesicle on carbon fiber nanoelectrode, extending the observation of discrete collision events on nanoelectrode to biologically relevant analytes. To decrease noise interference to the technique, the dimensions of nanoelectrode was systematically investigated and optimized. Scanning electron microscopy(SEM) further supported the comparable sizes of nanoelectrode and vesicles(~100 nm in diameter). Vesicles collision and rupture on the surface of nanoelectrode led to the dopamine release from vesicles, which could be electrochemically oxidized to dopamine-o-quinone and detected via voltammetry. The comparable size of the nanoelectrode with vesicles and fast voltammetry allowed differentiation of single collision events from the current magnitudes and peak widths in the electrochemical collision experiments, which shows the efficacy of the method to characterize vesicle samples. This work provides a foundation upon which quantitative sensor technology might be built for the detection of dopamine contained vesicles with high spatial and temporal resolution.展开更多
基金National Natural Science Foundation of China under Grant Nos.10205007,10226033,10375039,and 90503008the Nuclear Theory Research Program for NCET and Fund of HIRFL of China
文摘In this paper we present systematic differential representations for the dynamical group SO(4).Theserepresentations include the left and the right differential representations and the left and the right adjoint differentialrepresentations in both the group parameter space and its coset spaces.They are the generalization of the differentialrepresentations of the SO(3) rotation group in the Euler angles.These representations may find their applications in thestudy of the physical systems with SO(4) dynamical symmetry.
基金supported by Natural Science Foundation of Zhejiang Province under Grant No.Y104420
文摘In this paper,with the aid of symbolic computation,we present a uniform method for constructing soliton solutions and periodic solutions to (2+1)-dimensional Toda lattice equation.
文摘In order to fulfil the microgravity requirements for space experiments, improved technology for the microgravity environment is proposed, including that for raising the orbital altitude, optimizing the layout of the disturbance source, using IN-thrusters instead of 5 N-thrusters, etc. In addition, evaluation of the microgravity environment of the recoverable satellite was also conducted using on-orbit micro-vibration measurement, on-orbit experiment and data analysis technologies. The microgravity level of the SJ-l0 recoverable satellite in China is compared with the spacecraft used for carrying out space science experiments internationally. This paper describes the microgravity environment of the SJ- 10 recoverable satellite, and its importance for analysing space experimental results.
文摘This paper present an implementation of＂modified cubic B-spline differential quadrature method （MCB-DQM）＂ proposed by Arora ＆ Singh （Applied Mathematics and Computation Vol. 224（1） （2013） 161-177） for numerical computation of Fokker-Planck equations. The modified cubic B-splines are used as set of basis functions in the differential quadrature to compute the weighting coefficients for the spatial derivatives, which reduces Fokker-Planck equation into system of first-order ordinary differential equations （ODEs）, in time. The well known SSP-RK43 scheme is then applied to solve the resulting system of ODEs. The efficiency of proposed method has been confirmed by three examples having their exact solutions. This shows that MCB-DQM results are capable of achieving high accuracy. Advantage of the scheme is that it can be applied very smoothly to solve the linear or nonlinear physical problems, and a very less storage space is required which causes less accumulation of numerical errors.
基金supported by National Natural Science Foundation of China(Grant No.11371233)
文摘Let H be a Hilbert space and A ■ B(H) be a C~*-subalgebra. This paper is devoted to studying the set gP of generalized projections in A from a differential geometric point of view, and mainly focuses on geodesic curves. We prove that the space gP is a C~∞ Banach submanifold of A, and a homogeneous reductive space under the action of Banach Lie group U_A of A. Moreover, we compute the geodesics of gP in a standard fashion, and prove that any generalized projection in a prescribed neighbourhood of p∈gP can be joined with p by a unique geodesic curve in gP.
基金supported by the National Natural Science Foundation of China(21422508,31470960)Chinese Academy of Sciencessupport by the Deanship of Scientific Research,College of Science Research Center at King Saud University
文摘We recognize the stochastic collisions of dopamine contained phospholipid vesicle on carbon fiber nanoelectrode, extending the observation of discrete collision events on nanoelectrode to biologically relevant analytes. To decrease noise interference to the technique, the dimensions of nanoelectrode was systematically investigated and optimized. Scanning electron microscopy(SEM) further supported the comparable sizes of nanoelectrode and vesicles(~100 nm in diameter). Vesicles collision and rupture on the surface of nanoelectrode led to the dopamine release from vesicles, which could be electrochemically oxidized to dopamine-o-quinone and detected via voltammetry. The comparable size of the nanoelectrode with vesicles and fast voltammetry allowed differentiation of single collision events from the current magnitudes and peak widths in the electrochemical collision experiments, which shows the efficacy of the method to characterize vesicle samples. This work provides a foundation upon which quantitative sensor technology might be built for the detection of dopamine contained vesicles with high spatial and temporal resolution.
