A CR-structure on a 2n +1-manifold gives a conformal class of Lorentz metrics on the Fefferman S1-bundle. This analogy is carried out to the quarternionic conformal 3-CR structure (a generalization of quaternionic CR-...A CR-structure on a 2n +1-manifold gives a conformal class of Lorentz metrics on the Fefferman S1-bundle. This analogy is carried out to the quarternionic conformal 3-CR structure (a generalization of quaternionic CR- structure) on a 4n + 3 -manifold M. This structure produces a conformal class [g] of a pseudo-Riemannian metric g of type (4n + 3,3) on M × S3. Let (PSp(n +1,1), S4n+3) be the geometric model obtained from the projective boundary of the complete simply connected quaternionic hyperbolic manifold. We shall prove that M is locally modeled on (PSp(n +1,1), S4n+3) if and only if (M × S3 ,[g]) is conformally flat (i.e. the Weyl conformal curvature tensor vanishes).展开更多
In the present article we propose a simple equality involving the Dirac operator and the Maxwell operators under chiral approach. This equality establishes a direct connection between solutions of the two systems and ...In the present article we propose a simple equality involving the Dirac operator and the Maxwell operators under chiral approach. This equality establishes a direct connection between solutions of the two systems and moreover, we show that it is valid when the natural relation between the frequency of the electromagnetic wave and the energy of the Dirac particle is fulfilled if the electric field E is parallel to the magnetic field H. Our analysis is based on the quaternionic form of the Dirac equation and on the quaternionic form of the Maxwell equations. In both cases these reformulations are completely equivalent to the traditional form of the Dirac and Maxwell systems. This theory is a new quantum mechanics (QM) interpretation. The below research proves that the QM represents the electrodynamics of the curvilinear closed chiral waves. It is entirely according to the modern interpretation and explains the particularities and the results of the quantum field theory. Also this work may help to clarify the controversial relation between Maxwell and Dirac equations while presenting an original way to derive the Dirac equation from the chiral electrodynamics, leading, perhaps, to novel conception in interactions between matter and electromagnetic fields. This approach may give a reinterpretation of Majorana equation, neutrino mass, violation of Heinsenberg’s measurement-disturbation relationship and mass generation in systems like graphene devices.展开更多
This paper deals with the problem of the type triangle open_H f+f^p=O inquaternionic Heisenberg group,where triangle open_H is the quaternionic Heisenberg Laplacian.Itis proved that,under suitable conditions on p and/...This paper deals with the problem of the type triangle open_H f+f^p=O inquaternionic Heisenberg group,where triangle open_H is the quaternionic Heisenberg Laplacian.Itis proved that,under suitable conditions on p and/,the only solution of triangle open_H f+f^p=O.展开更多
In this paper, a series of bicomplex representation methods of quaternion division algebra is introduced. We present a new multiplication concept of quaternion matrices, a new determinant concept, a new inverse concep...In this paper, a series of bicomplex representation methods of quaternion division algebra is introduced. We present a new multiplication concept of quaternion matrices, a new determinant concept, a new inverse concept of quaternion matrix and a new similar matrix concept. Under the new concept system, many quaternion algebra problems can be transformed into complex algebra problems to express and study. These concepts can perfect the theory of [J.L. Wu, A new representation theory and some methods on quaternion division algebra, JP Journal of Algebra, 2009, 14(2): 121-140] and unify the complex algebra and quaternion division algebra.展开更多
This paper aims to present, in a unified manner, algebraic techniques for linear equations which are valid on both the algebras of quaternions and split quaternions. This paper, introduces a concept of v-quaternion, s...This paper aims to present, in a unified manner, algebraic techniques for linear equations which are valid on both the algebras of quaternions and split quaternions. This paper, introduces a concept of v-quaternion, studies the problem of v-quaternionic linear equations by means of a complex representation and a real representation of v-quaternion matrices, and gives two algebraic methods for solving v-quaternionic linear equations. This paper also gives a unification of algebraic techniques for quaternionic and split quaternionic linear equations in quaternionic and split quaternionic mechanics.展开更多
This paper aims to present, in a unified manner, the algebraic techniques of eigen-problem which are valid on both the quaternions and split quaternions. This paper studies eigenvalues and eigenvectors of the v-quater...This paper aims to present, in a unified manner, the algebraic techniques of eigen-problem which are valid on both the quaternions and split quaternions. This paper studies eigenvalues and eigenvectors of the v-quaternion matrices by means of the complex representation of the v-quaternion matrices, and derives an algebraic technique to find the eigenvalues and eigenvectors of v-quaternion matrices. This paper also gives a unification of algebraic techniques for eigenvalues and eigenvectors in quaternionic and split quaternionic mechanics.展开更多
In this paper, by means of an isomorphism, we express the Clifford algebra Cl<sub>5,3</sub> as hyperquaternion algebra H ⊗H ⊗H ⊗H (a four-fold tensor product of quaternion alg...In this paper, by means of an isomorphism, we express the Clifford algebra Cl<sub>5,3</sub> as hyperquaternion algebra H ⊗H ⊗H ⊗H (a four-fold tensor product of quaternion algebras) and we provide the hyperquaternionic approach to the inner product null space (IPNS) representation of conic sections.展开更多
The functions studied in the paper are the quaternion-valued functions of a quaternionic variable.It is shown that the left slice regular functions and right slice regular functions are related by a particular involut...The functions studied in the paper are the quaternion-valued functions of a quaternionic variable.It is shown that the left slice regular functions and right slice regular functions are related by a particular involution,and that the intrinsic slice regular functions play a central role in the theory of slice regular functions.The relation between left slice regular functions,right slice regular functions and intrinsic slice regular functions is revealed.As an application,the classical Laplace transform is generalized naturally to quaternions in two different ways,which transform a quaternion-valued function of a real variable to a left or right slice regular function.The usual properties of the classical Laplace transforms are generalized to quaternionic Laplace transforms.展开更多
In order to effectively restore color noisy images with the mixture of Gaussian noise and impulse noise,a new algorithm is proposed using the quaternion-based holistic processing idea for color images.First,a color im...In order to effectively restore color noisy images with the mixture of Gaussian noise and impulse noise,a new algorithm is proposed using the quaternion-based holistic processing idea for color images.First,a color image is represented by a pure quaternion matrix.Secondly,according to the different characteristics of the Gaussian noise and the impulse noise,an algorithm based on quaternion directional vector order statistics is used to detect the impulse noise. Finally,the quaternion optimal weights non-local means filter （QOWNLMF）for Gaussian noise removal is improved for the mixed noise removal.The detected impulse noise pixels are not considered in the calculation of weights.Experimental results on five standard images demonstrate that the proposed algorithm performs better than the commonly used robust outlyingness ratio-nonlocal means （ROR-NLM）algorithm and the optimal weights mixed filter （OWMF）.展开更多
The traditional algorithms for formation flying satellites treat the satellite position and attitude sepa- rately. A novel algorithm combining satellite attitude with position is proposed. The principal satellite traj...The traditional algorithms for formation flying satellites treat the satellite position and attitude sepa- rately. A novel algorithm combining satellite attitude with position is proposed. The principal satellite trajectory is obtained by dual quaternion interpolation, then the relative position and attitude of the deputy satellite are ob- tained by dual quaternion modeling on the principal satellite. Through above process, relative position and atti- tude are unified. Compared with the orbital parameter and the quaternion methods, the simulation result proves that the algorithm can unify position and attitude, and satisfy the precision requirement of formation flying satel- lites.展开更多
Generally unitary solution to the system of martix equations over the quaternion field [X mA ns =B ns ,X nn C nt =D nt ] is considered. A necessary and sufficient condition for the existence o...Generally unitary solution to the system of martix equations over the quaternion field [X mA ns =B ns ,X nn C nt =D nt ] is considered. A necessary and sufficient condition for the existence of and the expression for the generally unitary solution of the system are derived.展开更多
The simultaneous diagonalization by congruence of pairs of Hermitian quaternion matrices is discussed. The problem is reduced to a parallel one on complex matrices by using the complex adjoint matrix related to each q...The simultaneous diagonalization by congruence of pairs of Hermitian quaternion matrices is discussed. The problem is reduced to a parallel one on complex matrices by using the complex adjoint matrix related to each quaternion matrix. It is proved that any two semi-positive definite Hermitian quaternion matrices can be simultaneously diagonalized by congruence.展开更多
In this paper, by using the matrix representation of the generalized quaternion algebra, we discussed solution problem for two classes of the first_degree algebraic equation of the generalized quaternion and obtained ...In this paper, by using the matrix representation of the generalized quaternion algebra, we discussed solution problem for two classes of the first_degree algebraic equation of the generalized quaternion and obtained critical conditions on existence of a unique solution, infinitely many solutions or nonexistence any solution for the two classes algebraic equation.展开更多
A 6-degree of freedom （6-DOF） aircraft wing position and pose automatic adjustment method is presented to improve ARJ21 wing-fuselage connection precision and efficiency. Wing position and pose are adjusted by three...A 6-degree of freedom （6-DOF） aircraft wing position and pose automatic adjustment method is presented to improve ARJ21 wing-fuselage connection precision and efficiency. Wing position and pose are adjusted by three pillars which are driven by six high-precision servo motors. During the adjustment process, wing is tracked and positioned by laser tracker. Wing initial position and pose are calibrated by using the measurement coordinates of assembly reference points. Wing target position and pose are calculated according to wing initial, fuselage position and pose, and relative position and pose requirements between wing and fuselage for the connection. Combining Newton-Euler method with quaternion position and pose analyzing method, the inverse kinematics of servo motors, together with the adjustment system dynamics is obtained. Wing quintic polynomial trajectory planning algorithm based on quatemion is proposed; the initial, target position and pose need to be solved and the intermediate moving path is uncertain. Simulation results show that the adjustment method has good dynamic characteristics and satisfies engineering requirements. Preliminary engineering application indicates that ARJ21 wing adjustment efficiency and precision are improved by using the proposed method.展开更多
A Kalman filter used in strapdown AHRS (Attitude Heading Reference System) based on micro machined inertial sensors is introduced. The composition and principle of the system are described. The attitude algorithm and ...A Kalman filter used in strapdown AHRS (Attitude Heading Reference System) based on micro machined inertial sensors is introduced. The composition and principle of the system are described. The attitude algorithm and error model of the system are derived based on the quaternion formulation. The real time quaternion based Kalman filter is designed. Simulation results show that accuracy of the system is better than 0.04 degree without disturbance of lateral acceleration and reduced to 0.44 degree with l...展开更多
文摘A CR-structure on a 2n +1-manifold gives a conformal class of Lorentz metrics on the Fefferman S1-bundle. This analogy is carried out to the quarternionic conformal 3-CR structure (a generalization of quaternionic CR- structure) on a 4n + 3 -manifold M. This structure produces a conformal class [g] of a pseudo-Riemannian metric g of type (4n + 3,3) on M × S3. Let (PSp(n +1,1), S4n+3) be the geometric model obtained from the projective boundary of the complete simply connected quaternionic hyperbolic manifold. We shall prove that M is locally modeled on (PSp(n +1,1), S4n+3) if and only if (M × S3 ,[g]) is conformally flat (i.e. the Weyl conformal curvature tensor vanishes).
文摘In the present article we propose a simple equality involving the Dirac operator and the Maxwell operators under chiral approach. This equality establishes a direct connection between solutions of the two systems and moreover, we show that it is valid when the natural relation between the frequency of the electromagnetic wave and the energy of the Dirac particle is fulfilled if the electric field E is parallel to the magnetic field H. Our analysis is based on the quaternionic form of the Dirac equation and on the quaternionic form of the Maxwell equations. In both cases these reformulations are completely equivalent to the traditional form of the Dirac and Maxwell systems. This theory is a new quantum mechanics (QM) interpretation. The below research proves that the QM represents the electrodynamics of the curvilinear closed chiral waves. It is entirely according to the modern interpretation and explains the particularities and the results of the quantum field theory. Also this work may help to clarify the controversial relation between Maxwell and Dirac equations while presenting an original way to derive the Dirac equation from the chiral electrodynamics, leading, perhaps, to novel conception in interactions between matter and electromagnetic fields. This approach may give a reinterpretation of Majorana equation, neutrino mass, violation of Heinsenberg’s measurement-disturbation relationship and mass generation in systems like graphene devices.
文摘This paper deals with the problem of the type triangle open_H f+f^p=O inquaternionic Heisenberg group,where triangle open_H is the quaternionic Heisenberg Laplacian.Itis proved that,under suitable conditions on p and/,the only solution of triangle open_H f+f^p=O.
文摘In this paper, a series of bicomplex representation methods of quaternion division algebra is introduced. We present a new multiplication concept of quaternion matrices, a new determinant concept, a new inverse concept of quaternion matrix and a new similar matrix concept. Under the new concept system, many quaternion algebra problems can be transformed into complex algebra problems to express and study. These concepts can perfect the theory of [J.L. Wu, A new representation theory and some methods on quaternion division algebra, JP Journal of Algebra, 2009, 14(2): 121-140] and unify the complex algebra and quaternion division algebra.
文摘This paper aims to present, in a unified manner, algebraic techniques for linear equations which are valid on both the algebras of quaternions and split quaternions. This paper, introduces a concept of v-quaternion, studies the problem of v-quaternionic linear equations by means of a complex representation and a real representation of v-quaternion matrices, and gives two algebraic methods for solving v-quaternionic linear equations. This paper also gives a unification of algebraic techniques for quaternionic and split quaternionic linear equations in quaternionic and split quaternionic mechanics.
文摘This paper aims to present, in a unified manner, the algebraic techniques of eigen-problem which are valid on both the quaternions and split quaternions. This paper studies eigenvalues and eigenvectors of the v-quaternion matrices by means of the complex representation of the v-quaternion matrices, and derives an algebraic technique to find the eigenvalues and eigenvectors of v-quaternion matrices. This paper also gives a unification of algebraic techniques for eigenvalues and eigenvectors in quaternionic and split quaternionic mechanics.
文摘In this paper, by means of an isomorphism, we express the Clifford algebra Cl<sub>5,3</sub> as hyperquaternion algebra H ⊗H ⊗H ⊗H (a four-fold tensor product of quaternion algebras) and we provide the hyperquaternionic approach to the inner product null space (IPNS) representation of conic sections.
基金supported by NSFC(12071422)Zhejiang Province Science Foundation of China(LY14A010018)。
文摘The functions studied in the paper are the quaternion-valued functions of a quaternionic variable.It is shown that the left slice regular functions and right slice regular functions are related by a particular involution,and that the intrinsic slice regular functions play a central role in the theory of slice regular functions.The relation between left slice regular functions,right slice regular functions and intrinsic slice regular functions is revealed.As an application,the classical Laplace transform is generalized naturally to quaternions in two different ways,which transform a quaternion-valued function of a real variable to a left or right slice regular function.The usual properties of the classical Laplace transforms are generalized to quaternionic Laplace transforms.
基金The National Natural Science Foundation of China(No.61572258,61173141,61271312,61232016,61272421)the Natural Science Foundation of Jiangsu Province(No.BK2012858,BK20151530)+1 种基金the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(No.13KJB520015)Open Fund of Jiangsu Engineering Center of Network Monitoring(No.KJR1404)
文摘In order to effectively restore color noisy images with the mixture of Gaussian noise and impulse noise,a new algorithm is proposed using the quaternion-based holistic processing idea for color images.First,a color image is represented by a pure quaternion matrix.Secondly,according to the different characteristics of the Gaussian noise and the impulse noise,an algorithm based on quaternion directional vector order statistics is used to detect the impulse noise. Finally,the quaternion optimal weights non-local means filter （QOWNLMF）for Gaussian noise removal is improved for the mixed noise removal.The detected impulse noise pixels are not considered in the calculation of weights.Experimental results on five standard images demonstrate that the proposed algorithm performs better than the commonly used robust outlyingness ratio-nonlocal means （ROR-NLM）algorithm and the optimal weights mixed filter （OWMF）.
基金Supported by the National Natural Science Foundation of China(60974107)the Research Foundation of Nanjing University of Aeronautics and Astronautics(2010219)~~
文摘The traditional algorithms for formation flying satellites treat the satellite position and attitude sepa- rately. A novel algorithm combining satellite attitude with position is proposed. The principal satellite trajectory is obtained by dual quaternion interpolation, then the relative position and attitude of the deputy satellite are ob- tained by dual quaternion modeling on the principal satellite. Through above process, relative position and atti- tude are unified. Compared with the orbital parameter and the quaternion methods, the simulation result proves that the algorithm can unify position and attitude, and satisfy the precision requirement of formation flying satel- lites.
文摘Generally unitary solution to the system of martix equations over the quaternion field [X mA ns =B ns ,X nn C nt =D nt ] is considered. A necessary and sufficient condition for the existence of and the expression for the generally unitary solution of the system are derived.
文摘The simultaneous diagonalization by congruence of pairs of Hermitian quaternion matrices is discussed. The problem is reduced to a parallel one on complex matrices by using the complex adjoint matrix related to each quaternion matrix. It is proved that any two semi-positive definite Hermitian quaternion matrices can be simultaneously diagonalized by congruence.
文摘In this paper, by using the matrix representation of the generalized quaternion algebra, we discussed solution problem for two classes of the first_degree algebraic equation of the generalized quaternion and obtained critical conditions on existence of a unique solution, infinitely many solutions or nonexistence any solution for the two classes algebraic equation.
基金Basic Scientific Research Projects of Nanjing University of Aeronautics & Astronautics (NS 2010128)
文摘A 6-degree of freedom （6-DOF） aircraft wing position and pose automatic adjustment method is presented to improve ARJ21 wing-fuselage connection precision and efficiency. Wing position and pose are adjusted by three pillars which are driven by six high-precision servo motors. During the adjustment process, wing is tracked and positioned by laser tracker. Wing initial position and pose are calibrated by using the measurement coordinates of assembly reference points. Wing target position and pose are calculated according to wing initial, fuselage position and pose, and relative position and pose requirements between wing and fuselage for the connection. Combining Newton-Euler method with quaternion position and pose analyzing method, the inverse kinematics of servo motors, together with the adjustment system dynamics is obtained. Wing quintic polynomial trajectory planning algorithm based on quatemion is proposed; the initial, target position and pose need to be solved and the intermediate moving path is uncertain. Simulation results show that the adjustment method has good dynamic characteristics and satisfies engineering requirements. Preliminary engineering application indicates that ARJ21 wing adjustment efficiency and precision are improved by using the proposed method.
文摘A Kalman filter used in strapdown AHRS (Attitude Heading Reference System) based on micro machined inertial sensors is introduced. The composition and principle of the system are described. The attitude algorithm and error model of the system are derived based on the quaternion formulation. The real time quaternion based Kalman filter is designed. Simulation results show that accuracy of the system is better than 0.04 degree without disturbance of lateral acceleration and reduced to 0.44 degree with l...
