The dynamics of satellites formation is of great interest for the space mission. This work discusses a more efficient model of the relative motion dynamics of satellites formation. The model is based on employing the ...The dynamics of satellites formation is of great interest for the space mission. This work discusses a more efficient model of the relative motion dynamics of satellites formation. The model is based on employing the concepts restricted three-body problem (R3BP) and for more accuracy, it considers the effects of both oblateness and radiation pressure on deputy relative motion w.r.t the chief satellite. A model of deputy relative motion w.r.t the chief satellite is derived in the local-vertical local-horizontal system and simplified assuming the concept of the circular restricted three-body problem (CR3BP). The deputy equations of motion were rewritten in the form of recurrence relations and solved numerically using the Lie series approach. Assuming that the formation is revolving around the Moon in the Earth-Moon system, the effects of both oblateness and radiation pressure on the deputy satellite orbit were assessed through a particular example of satellites formation. A comparison between the perturbed and unperturbed R3BP shows a significant difference in the deputy relative position that has to be considered for the formation dynamics.展开更多
We present an eight component integrable Hamiltonian hierarchy, based on a reduced seventh order matrix spectral problem, with the aim of aiding the study and classification of multicomponent integrable models and the...We present an eight component integrable Hamiltonian hierarchy, based on a reduced seventh order matrix spectral problem, with the aim of aiding the study and classification of multicomponent integrable models and their underlying mathematical structures. The zero-curvature formulation is the tool to construct a recursion operator from the spatial matrix problem. The second and third set of integrable equations present integrable nonlinear Schrödinger and modified Korteweg-de Vries type equations, respectively. The trace identity is used to construct Hamiltonian structures, and the first three Hamiltonian functionals so generated are computed.展开更多
Two types of Lie algebras are presented,from which two integrable couplings associated with the Tuisospectral problem are obtained,respectively.One of them possesses the Hamiltonian structure generated by a linearisom...Two types of Lie algebras are presented,from which two integrable couplings associated with the Tuisospectral problem are obtained,respectively.One of them possesses the Hamiltonian structure generated by a linearisomorphism and the quadratic-form identity.An approach for working out the double integrable couplings of the sameintegrable system is presented in the paper.展开更多
The Rosenberg problem is a typical but not too complicated problem of nonholonomic mechanical systems. The Lie-Mei symmetry and the conserved quantities of the Rosenberg problem are studied. For the Rosenberg problem,...The Rosenberg problem is a typical but not too complicated problem of nonholonomic mechanical systems. The Lie-Mei symmetry and the conserved quantities of the Rosenberg problem are studied. For the Rosenberg problem, the Lie and the Mei symmetries for the equation are obtained, the conserved quantities are deduced from them and then the definition and the criterion for the Lie-Mei symmetry of the Rosenberg problem are derived. Finally, the Hojman conserved quantity and the Mei conserved quantity are deduced from the Lie--Mei symmetry.展开更多
We present a differential geometric perspective of the IEP for symmetric matrices in the framework of a fibre bundle with structure group SO（n）. In particular, a Newton type algorithm is developed to construct a non...We present a differential geometric perspective of the IEP for symmetric matrices in the framework of a fibre bundle with structure group SO（n）. In particular, a Newton type algorithm is developed to construct a non singular symmetric matrix for given target eigenvalues using a singular symmetric matrix as the initial matrix for the iteration. Explicit computations are performed for 2 x 2 non singular symmetric matrix to illustrate the result.展开更多
Baum-Welch algorithm most likely results in underflow in practice. In some literatures, such as 'Scaling' algorithm was introduced to solve the problem. In applications, however, some mistakes were found in th...Baum-Welch algorithm most likely results in underflow in practice. In some literatures, such as 'Scaling' algorithm was introduced to solve the problem. In applications, however, some mistakes were found in the equations presented in these literatures. The practical calculations show that the original algorithm often results in poor or even none convergence and rather higher error rate in speech recognition. The mistakes in these literatures and brings forward the correct equations are analysed. The speech recognition system using the revised algorithm can converge well and has lower error rate.展开更多
Let A be a factor von Neumann algebra and Ф be a nonlinear surjective map from A onto itself. We prove that, if Ф satisfies that Ф（A）Ф（B） - Ф（B）Ф（A）＊ -- AB - BA＊ for all A, B ∈ A, then there exist a l...Let A be a factor von Neumann algebra and Ф be a nonlinear surjective map from A onto itself. We prove that, if Ф satisfies that Ф（A）Ф（B） - Ф（B）Ф（A）＊ -- AB - BA＊ for all A, B ∈ A, then there exist a linear bijective map ψA →A satisfying ψ（A）ψ（B） - ψ（B）ψ（A）＊ = AB - BA＊ for A, B ∈ A and a real functional h on A with h（0） -= 0 such that Ф（A） = ψ（A） ＋ h（A）I for every A ∈ A. In particular, if .4 is a type I factor, then, Ф（A） = cA ＋ h（A）I for every A ∈ .4, where c = ±1.展开更多
文摘The dynamics of satellites formation is of great interest for the space mission. This work discusses a more efficient model of the relative motion dynamics of satellites formation. The model is based on employing the concepts restricted three-body problem (R3BP) and for more accuracy, it considers the effects of both oblateness and radiation pressure on deputy relative motion w.r.t the chief satellite. A model of deputy relative motion w.r.t the chief satellite is derived in the local-vertical local-horizontal system and simplified assuming the concept of the circular restricted three-body problem (CR3BP). The deputy equations of motion were rewritten in the form of recurrence relations and solved numerically using the Lie series approach. Assuming that the formation is revolving around the Moon in the Earth-Moon system, the effects of both oblateness and radiation pressure on the deputy satellite orbit were assessed through a particular example of satellites formation. A comparison between the perturbed and unperturbed R3BP shows a significant difference in the deputy relative position that has to be considered for the formation dynamics.
文摘We present an eight component integrable Hamiltonian hierarchy, based on a reduced seventh order matrix spectral problem, with the aim of aiding the study and classification of multicomponent integrable models and their underlying mathematical structures. The zero-curvature formulation is the tool to construct a recursion operator from the spatial matrix problem. The second and third set of integrable equations present integrable nonlinear Schrödinger and modified Korteweg-de Vries type equations, respectively. The trace identity is used to construct Hamiltonian structures, and the first three Hamiltonian functionals so generated are computed.
基金National Natural Science Foundation of China under Grant No.10471139
文摘Two types of Lie algebras are presented,from which two integrable couplings associated with the Tuisospectral problem are obtained,respectively.One of them possesses the Hamiltonian structure generated by a linearisomorphism and the quadratic-form identity.An approach for working out the double integrable couplings of the sameintegrable system is presented in the paper.
文摘The Rosenberg problem is a typical but not too complicated problem of nonholonomic mechanical systems. The Lie-Mei symmetry and the conserved quantities of the Rosenberg problem are studied. For the Rosenberg problem, the Lie and the Mei symmetries for the equation are obtained, the conserved quantities are deduced from them and then the definition and the criterion for the Lie-Mei symmetry of the Rosenberg problem are derived. Finally, the Hojman conserved quantity and the Mei conserved quantity are deduced from the Lie--Mei symmetry.
文摘We present a differential geometric perspective of the IEP for symmetric matrices in the framework of a fibre bundle with structure group SO（n）. In particular, a Newton type algorithm is developed to construct a non singular symmetric matrix for given target eigenvalues using a singular symmetric matrix as the initial matrix for the iteration. Explicit computations are performed for 2 x 2 non singular symmetric matrix to illustrate the result.
文摘Baum-Welch algorithm most likely results in underflow in practice. In some literatures, such as 'Scaling' algorithm was introduced to solve the problem. In applications, however, some mistakes were found in the equations presented in these literatures. The practical calculations show that the original algorithm often results in poor or even none convergence and rather higher error rate in speech recognition. The mistakes in these literatures and brings forward the correct equations are analysed. The speech recognition system using the revised algorithm can converge well and has lower error rate.
基金supported by National Natural Science Foundation of China(10871111)the Specialized Research Fund for Doctoral Program of Higher Education(200800030059)(to Cui)Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education,Science and Technology(NRF-2009-0070788)(to Park)
文摘Let A be a factor von Neumann algebra and Ф be a nonlinear surjective map from A onto itself. We prove that, if Ф satisfies that Ф（A）Ф（B） - Ф（B）Ф（A）＊ -- AB - BA＊ for all A, B ∈ A, then there exist a linear bijective map ψA →A satisfying ψ（A）ψ（B） - ψ（B）ψ（A）＊ = AB - BA＊ for A, B ∈ A and a real functional h on A with h（0） -= 0 such that Ф（A） = ψ（A） ＋ h（A）I for every A ∈ A. In particular, if .4 is a type I factor, then, Ф（A） = cA ＋ h（A）I for every A ∈ .4, where c = ±1.
