In this paper,we investigate some properties of dual complex numbers,dual complex vectors,and dual complex matrices.First,based on the magnitude of the dual complex number,we study the Young inequality,the Hölder...In this paper,we investigate some properties of dual complex numbers,dual complex vectors,and dual complex matrices.First,based on the magnitude of the dual complex number,we study the Young inequality,the Hölder inequality,and the Minkowski inequality in the setting of dual complex numbers.Second,we define the p-norm of a dual complex vector,which is a nonnegative dual number,and show some related properties.Third,we study the properties of eigenvalues of unitary matrices and unitary triangulation of arbitrary dual complex matrices.In particular,we introduce the operator norm of dual complex matrices induced by the p-norm of dual complex vectors,and give expressions of three important operator norms of dual complex matrices.展开更多
This paper presents the application of dual-number matrix to the formulation of Jacobian equations of robot with redundancy, the analytical technique that is based on the dual-number matrices, a 3 × 3 matrix with...This paper presents the application of dual-number matrix to the formulation of Jacobian equations of robot with redundancy, the analytical technique that is based on the dual-number matrices, a 3 × 3 matrix with dualnumber elements, and the dual-number transformation method. Dual-number matrices make possible a concise representation of joint parameters. In particular, the method can effectively be used for direct determination of Jacobian matrices. It is shown that the proposed procedure contributes a simplified approach to the formulation of robotic kinematics, dynamics and control system modelling.展开更多
A dual-jet consisting of a wall jet and an offset jet has been numerically simulated using lattice Boltzmann method to examine the effects of jet spacing between two jet centerlines,defined as s.The Reynolds number ba...A dual-jet consisting of a wall jet and an offset jet has been numerically simulated using lattice Boltzmann method to examine the effects of jet spacing between two jet centerlines,defined as s.The Reynolds number based on jet-exit-width dis set to be Re = 56 and the jet spacing is set to be less than or equal 10 times the jet-exitwidth.Computational results reveal that the flow field displays periodic vortex shedding when the jet spacing is in the range of 9≤s/d ≤ 10,while it remains steady with two counter-rotating vortices in the converging region when s/d ≤ 8.When s/d = 9,the power spectral analyses indicate that the vortex shedding phenomenon has specific frequency.The significant oscillation stresses induced by the periodic components of velocities are found to mainly exist in the inner shear layer regions,implying stronger momentum transfer occuring in these regions.展开更多
The dual algorithm for minimax problems is further studied in this paper.The resulting theoretical analysis shows that the condition number of the corresponding Hessian of the smooth modified Lagrange function with ch...The dual algorithm for minimax problems is further studied in this paper.The resulting theoretical analysis shows that the condition number of the corresponding Hessian of the smooth modified Lagrange function with changing parameter in the dual algorithm is proportional to the reciprocal of the parameter,which is very important for the efficiency of the dual algorithm.At last,the numerical experiments are reported to validate the analysis results.展开更多
As is known to all, nitrogen not only plays an important role in the industrial development of human society but also plays an important part in the proteins that constitute the essence of life[1]. In 1910, the Haber-...As is known to all, nitrogen not only plays an important role in the industrial development of human society but also plays an important part in the proteins that constitute the essence of life[1]. In 1910, the Haber-Bosch process was first used to synthesize ammonia.展开更多
基金the National Natural Science Foundation of China(Grant No.11871051).
文摘In this paper,we investigate some properties of dual complex numbers,dual complex vectors,and dual complex matrices.First,based on the magnitude of the dual complex number,we study the Young inequality,the Hölder inequality,and the Minkowski inequality in the setting of dual complex numbers.Second,we define the p-norm of a dual complex vector,which is a nonnegative dual number,and show some related properties.Third,we study the properties of eigenvalues of unitary matrices and unitary triangulation of arbitrary dual complex matrices.In particular,we introduce the operator norm of dual complex matrices induced by the p-norm of dual complex vectors,and give expressions of three important operator norms of dual complex matrices.
文摘This paper presents the application of dual-number matrix to the formulation of Jacobian equations of robot with redundancy, the analytical technique that is based on the dual-number matrices, a 3 × 3 matrix with dualnumber elements, and the dual-number transformation method. Dual-number matrices make possible a concise representation of joint parameters. In particular, the method can effectively be used for direct determination of Jacobian matrices. It is shown that the proposed procedure contributes a simplified approach to the formulation of robotic kinematics, dynamics and control system modelling.
基金supported by the National Natural Science Foundation of China(No.11402124)the Natural Science Foundation of Jiangsu Province(No.BK20140985)+1 种基金the Natural Science Foundation of Jiangsu Higher Education Institutions of China(No.14KJB130002)the Startup Foundation for Introducing Talent of NUIST(No.2013x031)
文摘A dual-jet consisting of a wall jet and an offset jet has been numerically simulated using lattice Boltzmann method to examine the effects of jet spacing between two jet centerlines,defined as s.The Reynolds number based on jet-exit-width dis set to be Re = 56 and the jet spacing is set to be less than or equal 10 times the jet-exitwidth.Computational results reveal that the flow field displays periodic vortex shedding when the jet spacing is in the range of 9≤s/d ≤ 10,while it remains steady with two counter-rotating vortices in the converging region when s/d ≤ 8.When s/d = 9,the power spectral analyses indicate that the vortex shedding phenomenon has specific frequency.The significant oscillation stresses induced by the periodic components of velocities are found to mainly exist in the inner shear layer regions,implying stronger momentum transfer occuring in these regions.
文摘The dual algorithm for minimax problems is further studied in this paper.The resulting theoretical analysis shows that the condition number of the corresponding Hessian of the smooth modified Lagrange function with changing parameter in the dual algorithm is proportional to the reciprocal of the parameter,which is very important for the efficiency of the dual algorithm.At last,the numerical experiments are reported to validate the analysis results.
基金supported by the National Key R&D Program of China(2017YFA0208300 and 2017YFA0700104)the National Natural Science Foundation of China(21671180 and 21406184)+2 种基金the Chengdu International Science and Technology Cooperation Fund(2020GH0200069HZ)the funding support from CAS Fujian Institute of Innovationfinancially supported by the DNL Cooperation Fund(DNL201918)。
文摘As is known to all, nitrogen not only plays an important role in the industrial development of human society but also plays an important part in the proteins that constitute the essence of life[1]. In 1910, the Haber-Bosch process was first used to synthesize ammonia.
