Bozek(1980)has introduced a class of solvable Lie groups Gn with arbitrary odd dimension to construct irreducible generalized symmetric Riemannian space such that the identity component of its full isometry group is s...Bozek(1980)has introduced a class of solvable Lie groups Gn with arbitrary odd dimension to construct irreducible generalized symmetric Riemannian space such that the identity component of its full isometry group is solvable.In this article,the authors provide the set of all left-invariant minimal unit vector fields on the solvable Lie group Gn,and give the relationships between the minimal unit vector fields and the geodesic vector fields,the strongly normal unit vectors respectively.展开更多
In this paper, a method of orbit determination is presented according to the principle of unit vector method (UVM). The model and arithmetic are improved and it not only suits initial orbit determination with short ar...In this paper, a method of orbit determination is presented according to the principle of unit vector method (UVM). The model and arithmetic are improved and it not only suits initial orbit determination with short arc data, it also suits orbit improvement with data longer. It is also suitable for orbit of any eccentricity and any inclination. It omits most partial derivatives of all the elements which must be calculated in classical differential orbit improvement (DOI), so, it is more efficient than DOI, and the accuracy of orbit determination and convergence of algorithm are also improved appreciably.展开更多
Based on the unit quaternion decomposition of rotation matrix, this paper puts forward an algorithm to estimate motion parameters from the space position vectors of 3D feature points. Rotation matrix’s representation...Based on the unit quaternion decomposition of rotation matrix, this paper puts forward an algorithm to estimate motion parameters from the space position vectors of 3D feature points. Rotation matrix’s representation with the unit quaternion has no singular points, so the unit quaternion-based estimation method is of more practical importance, and the algorithm in this paper does not need iteration computation compared to those unit quaternion-based methods proposed by Horn(1987) and Su, et al.(1989). Solution’s uniqueness analysis of the algorithm and simulation experiment results are also presented, it can be seen that performance of our method is satisfactory.展开更多
Downhole working conditions of sucker rod pumping wells are automatically identified on a computer from the analysis of dynamometer cards. In this process, extraction of feature parameters and pattern classification a...Downhole working conditions of sucker rod pumping wells are automatically identified on a computer from the analysis of dynamometer cards. In this process, extraction of feature parameters and pattern classification are two key steps. The dynamometer card is firstly divided into four parts which include different production information according to the "four point method" used in actual oilfield production, and then the moment invariants for pattern recognition are extracted. An improved support vector machine (SVM) method is used for pattern classification whose error penalty parameter C and kernel function parameter g are optimally chosen by the particle swarm optimization (PSO) algorithm. The simulation results show the method proposed in this paper has good classification results.展开更多
Certain locally optimal tests for deterministic components in vector time series have associated sampling distributions determined by a linear combination of Beta variates. Such distributions are nonstandard and must ...Certain locally optimal tests for deterministic components in vector time series have associated sampling distributions determined by a linear combination of Beta variates. Such distributions are nonstandard and must be tabulated by Monte Carlo simulation. In this paper, we provide closed form expressions for the mean and variance of several multivariate test statistics, moments that can be used to approximate unknown distributions. In particular, we find that the two-moment Inverse Gaussian approximation provides a simple and fast method to compute accurate quantiles and p-values in small and asymptotic samples. To illustrate the scope of this approximation we review some standard tests for deterministic trends and/or seasonal patterns in VARIMA and structural time series models.展开更多
The Wigner-Seitz unit cell (rhombus) for a honeycomb lattice fails to establish a k-vector in the 2D space, which is required for the Bloch electron dynamics. Phonon motion cannot be discussed in the triangular coordi...The Wigner-Seitz unit cell (rhombus) for a honeycomb lattice fails to establish a k-vector in the 2D space, which is required for the Bloch electron dynamics. Phonon motion cannot be discussed in the triangular coordinates, either. In this paper, we propose a rectangular 4-atom unit cell model, which allows us to discuss the electron and phonon (wave packets) motion in the k-space. The present paper discusses the band structure of graphene based on the rectangular 4-atom unit cell model to establish an appropriate k-vector for the Bloch electron dynamics. To obtain the band energy of a Bloch electron in graphene, we extend the tight-binding calculations for the Wigner-Seitz (2-atom unit cell) model of Reich et al. (Physical Review B, 66, Article ID: 035412 (2002)) to the rectangular 4-atom unit cell model. It is shown that the graphene band structure based on the rectangular 4-atom unit cell model reveals the same band structure of the graphene based on the Wigner-Seitz 2-atom unit cell model;the π-band energy holds a linear dispersion (ε−k ) relations near the Fermi energy (crossing points of the valence and the conduction bands) in the first Brillouin zone of the rectangular reciprocal lattice. We then confirm the suitability of the proposed rectangular (orthogonal) unit cell model for graphene in order to establish a 2D k-vector responsible for the Bloch electron (wave packet) dynamics in graphene.展开更多
基金supported by the National Natural Science Foundation of China (Nos. 12001007,12201358)the Natural Science Foundation of Shandong Province (No. ZR2021QA051)+1 种基金the Natural Science Foundation of Anhui Province (No. 1908085QA03)Starting Research Funds of Shandong University of Science and Technology (Nos. 0104060511817, 0104060540626)
文摘Bozek(1980)has introduced a class of solvable Lie groups Gn with arbitrary odd dimension to construct irreducible generalized symmetric Riemannian space such that the identity component of its full isometry group is solvable.In this article,the authors provide the set of all left-invariant minimal unit vector fields on the solvable Lie group Gn,and give the relationships between the minimal unit vector fields and the geodesic vector fields,the strongly normal unit vectors respectively.
文摘In this paper, a method of orbit determination is presented according to the principle of unit vector method (UVM). The model and arithmetic are improved and it not only suits initial orbit determination with short arc data, it also suits orbit improvement with data longer. It is also suitable for orbit of any eccentricity and any inclination. It omits most partial derivatives of all the elements which must be calculated in classical differential orbit improvement (DOI), so, it is more efficient than DOI, and the accuracy of orbit determination and convergence of algorithm are also improved appreciably.
基金"863"High Technology Research and Development Program of China under Grant 863-306-03-01
文摘Based on the unit quaternion decomposition of rotation matrix, this paper puts forward an algorithm to estimate motion parameters from the space position vectors of 3D feature points. Rotation matrix’s representation with the unit quaternion has no singular points, so the unit quaternion-based estimation method is of more practical importance, and the algorithm in this paper does not need iteration computation compared to those unit quaternion-based methods proposed by Horn(1987) and Su, et al.(1989). Solution’s uniqueness analysis of the algorithm and simulation experiment results are also presented, it can be seen that performance of our method is satisfactory.
基金support from the Key Project of the National Natural Science Foundation of China (61034005)Postgraduate Scientific Research and Innovation Projects of Basic Scientific Research Operating Expenses of Ministry of Education (N100604001)
文摘Downhole working conditions of sucker rod pumping wells are automatically identified on a computer from the analysis of dynamometer cards. In this process, extraction of feature parameters and pattern classification are two key steps. The dynamometer card is firstly divided into four parts which include different production information according to the "four point method" used in actual oilfield production, and then the moment invariants for pattern recognition are extracted. An improved support vector machine (SVM) method is used for pattern classification whose error penalty parameter C and kernel function parameter g are optimally chosen by the particle swarm optimization (PSO) algorithm. The simulation results show the method proposed in this paper has good classification results.
文摘Certain locally optimal tests for deterministic components in vector time series have associated sampling distributions determined by a linear combination of Beta variates. Such distributions are nonstandard and must be tabulated by Monte Carlo simulation. In this paper, we provide closed form expressions for the mean and variance of several multivariate test statistics, moments that can be used to approximate unknown distributions. In particular, we find that the two-moment Inverse Gaussian approximation provides a simple and fast method to compute accurate quantiles and p-values in small and asymptotic samples. To illustrate the scope of this approximation we review some standard tests for deterministic trends and/or seasonal patterns in VARIMA and structural time series models.
文摘The Wigner-Seitz unit cell (rhombus) for a honeycomb lattice fails to establish a k-vector in the 2D space, which is required for the Bloch electron dynamics. Phonon motion cannot be discussed in the triangular coordinates, either. In this paper, we propose a rectangular 4-atom unit cell model, which allows us to discuss the electron and phonon (wave packets) motion in the k-space. The present paper discusses the band structure of graphene based on the rectangular 4-atom unit cell model to establish an appropriate k-vector for the Bloch electron dynamics. To obtain the band energy of a Bloch electron in graphene, we extend the tight-binding calculations for the Wigner-Seitz (2-atom unit cell) model of Reich et al. (Physical Review B, 66, Article ID: 035412 (2002)) to the rectangular 4-atom unit cell model. It is shown that the graphene band structure based on the rectangular 4-atom unit cell model reveals the same band structure of the graphene based on the Wigner-Seitz 2-atom unit cell model;the π-band energy holds a linear dispersion (ε−k ) relations near the Fermi energy (crossing points of the valence and the conduction bands) in the first Brillouin zone of the rectangular reciprocal lattice. We then confirm the suitability of the proposed rectangular (orthogonal) unit cell model for graphene in order to establish a 2D k-vector responsible for the Bloch electron (wave packet) dynamics in graphene.
