Within the framework of the first-order Born approximation, the triple differential cross sections （TDCSs） for simultaneous ionization and excitation of helium are calculated. The wave function of the ejected electr...Within the framework of the first-order Born approximation, the triple differential cross sections （TDCSs） for simultaneous ionization and excitation of helium are calculated. The wave function of the ejected electron is chosen to be orthogonal or non-orthogonal to the wave function of the bound electron before ionization. It is found that the orthogonality has a strong effect on the TDCS, especially when plane waves and Coulomb waves are used to describe the projectile and the ejected electron.展开更多
Round inductosyn is widely used in inertial navigation test equipment, and its accuracy has significant effect on the general accuracy of the equipment. Four main errors of round inductosyn,i.e. the first-order long-p...Round inductosyn is widely used in inertial navigation test equipment, and its accuracy has significant effect on the general accuracy of the equipment. Four main errors of round inductosyn,i.e. the first-order long-period (360°) harmonic error, the second-order long-period harmonic error, the first-order short-period harmonic error and the second-order short-period harmonic error, are described, and the orthogonality of these four kinds of errors is studied. An error separating technology is proposed to separate these four kinds of errors, and in the process of separating the short-period harmonic errors, the arrangement in the order of decimal part of the angle pitch number can be omitted. The effectiveness of the technology proposed is proved through measuring and adjusting the angular errors.展开更多
This paper introduced a dynamical system (neural networks) algorithm for solving a least squares problem with orthogonality constraints, which has wide applications in computer vision and signal processing. A rigorous...This paper introduced a dynamical system (neural networks) algorithm for solving a least squares problem with orthogonality constraints, which has wide applications in computer vision and signal processing. A rigorous analysis for the convergence and stability of the algorithm was provided. Moreover, a so called zero extension technique was presented to keep the algorithm always convergent to the needed result for any randomly chosen initial data. Numerical experiments illustrate the effectiveness and efficiency of the algorithm.展开更多
Let X be a Minkowski plane, i.e., a real two dimensional normed linear space. We use projections to give a definition of the angle Aq（x, y） between two vectors x and y in X, such that x is Birkhoff orthogonal to y i...Let X be a Minkowski plane, i.e., a real two dimensional normed linear space. We use projections to give a definition of the angle Aq（x, y） between two vectors x and y in X, such that x is Birkhoff orthogonal to y if and only if Aq（x,y）=π/2. Some other properties of this angle are also discussed.展开更多
In this paper, we present various notions and aspects of orthogonality in normed spaces. Characterizations and generalizations of orthogonality are also consid- ered. Results on orthogonality of the range and the kern...In this paper, we present various notions and aspects of orthogonality in normed spaces. Characterizations and generalizations of orthogonality are also consid- ered. Results on orthogonality of the range and the kernel of elementary operators and the operators implementing them also are given.展开更多
In this paper, we reexamine the method of successive approximation presented by Prof. Chien Wei-zangfor solving the problem of large deflection of a circular plate, and find that the method could be regarded as the me...In this paper, we reexamine the method of successive approximation presented by Prof. Chien Wei-zangfor solving the problem of large deflection of a circular plate, and find that the method could be regarded as the method of strained parameters in the singular perturbation theory. In terms of the parameter representing the ratio of the center deflection to the thickness of the plate, we make the asymptotic expansions of the deflection, membrane stress and the parameter of load as in Ref. [1], and then give the orthogonality conditions (i.e. the solvability conditions) for the resulting equations, by which the stiffness characteristics of the plate could be determined. It is pointed out that with the solutions for the small deflection problem of the circular plate and the orthogonality conditions, we can derive the third order approximate relations between the parameter of load and the center deflection and the first-term approximation of membrane stresses at the center and edge of the plate without solving the differential equations. For some special cases (i.e. under uniform load, under compound toad, with different boundary conditiors), we deduce the specific expressions and obtain the results in agreement with the previous ones given by Chien Wei-zang, Yeh kai-yuan and Hwang Chien in Refs. [1 - 4J.展开更多
Abstract. Let {L（Ln^（A,λ）（x）}n≥0 be the sequence of monic Laguerre matrix polynomials defined on [0,∞） byLn^（A,λ）（x）=n!/（-λ）^n ∑nk-0（-λ）^k/k!（n-k）!（A＋I）n[（A＋I）k]^-1x^k,where A ∈ C^r×...Abstract. Let {L（Ln^（A,λ）（x）}n≥0 be the sequence of monic Laguerre matrix polynomials defined on [0,∞） byLn^（A,λ）（x）=n!/（-λ）^n ∑nk-0（-λ）^k/k!（n-k）!（A＋I）n[（A＋I）k]^-1x^k,where A ∈ C^r×r. It is known that {Ln^（A,λ）（x）}n≥0 is orthogonal with respect to a matrix moment functional when A satisfies the spectral condition that Re（z） 〉 -1 for every z E or（a）. In this note we show that forA such that σ（A） does not contain negative integers, the Laguerre matrix polynomials Ln^（A,λ）（x） are orthogonal with respect to a non-diagonal SobolevLaguerre matrix moment functional, which extends two cases： the above matrix case and the known scalar case.展开更多
For square contingency tables with ordered categories, the present paper gives several theorems that the symmetry model holds if and only if the generalized linear diagonals-parameter symmetry model for cell probabili...For square contingency tables with ordered categories, the present paper gives several theorems that the symmetry model holds if and only if the generalized linear diagonals-parameter symmetry model for cell probabilities and for cumulative probabilities and the mean nonequality model of row and column variables hold. It also shows the orthogonality of statistic for testing goodness-of-fit of the symmetry model. An example is given.展开更多
The orthogonality of eigenvector is a precondition to compute the dynamic responses of linear multi-rigid-flexible-body system using the classical modal analysis method. For a linear multi-rigid-flexible-body system, ...The orthogonality of eigenvector is a precondition to compute the dynamic responses of linear multi-rigid-flexible-body system using the classical modal analysis method. For a linear multi-rigid-flexible-body system, the eigenfunction does not satisfy the orthogonality under ordinary meaning. A new concept--augmented eigenvector is introduced, which is used to overcome the orthogonality problem of eigenvectors of linear multi-rigid-flexible-body system. The constitution method and the orthogonality of augmented eigenvector are expatiated. After the orthogonality of augmented eigenvector is acquired, the coupling of coordinates in dynamics equations can be released, which makes it possible to analyze exactly the dynamic responses of linear multi-rigid-flexible-body system using the classical modal analysis method.展开更多
An implicit algorithm of Bi-penalty approximation with orthogonality projection for the numerical simulation of Bingham fluid flow problems is proposed in this paper. A Newton fluid flow with two kinds of artificial v...An implicit algorithm of Bi-penalty approximation with orthogonality projection for the numerical simulation of Bingham fluid flow problems is proposed in this paper. A Newton fluid flow with two kinds of artificial viscosity subjected to the inequality constraint is introduced to approximate the Bingham fluid flow. This approach can effectively simulate the Bingham fluid flow with floating rigid cores or fixing rigid cores.展开更多
基金Project supported by the Anhui University Doctoral Research Starting Foundation,China(Grant Nos.02303319 and 33190203)the National Natural Science Foundation of China(Grant No.11274219)
文摘Within the framework of the first-order Born approximation, the triple differential cross sections （TDCSs） for simultaneous ionization and excitation of helium are calculated. The wave function of the ejected electron is chosen to be orthogonal or non-orthogonal to the wave function of the bound electron before ionization. It is found that the orthogonality has a strong effect on the TDCS, especially when plane waves and Coulomb waves are used to describe the projectile and the ejected electron.
文摘Round inductosyn is widely used in inertial navigation test equipment, and its accuracy has significant effect on the general accuracy of the equipment. Four main errors of round inductosyn,i.e. the first-order long-period (360°) harmonic error, the second-order long-period harmonic error, the first-order short-period harmonic error and the second-order short-period harmonic error, are described, and the orthogonality of these four kinds of errors is studied. An error separating technology is proposed to separate these four kinds of errors, and in the process of separating the short-period harmonic errors, the arrangement in the order of decimal part of the angle pitch number can be omitted. The effectiveness of the technology proposed is proved through measuring and adjusting the angular errors.
基金National Natural Science Foundation of China (No. 1990 10 18)
文摘This paper introduced a dynamical system (neural networks) algorithm for solving a least squares problem with orthogonality constraints, which has wide applications in computer vision and signal processing. A rigorous analysis for the convergence and stability of the algorithm was provided. Moreover, a so called zero extension technique was presented to keep the algorithm always convergent to the needed result for any randomly chosen initial data. Numerical experiments illustrate the effectiveness and efficiency of the algorithm.
文摘Let X be a Minkowski plane, i.e., a real two dimensional normed linear space. We use projections to give a definition of the angle Aq（x, y） between two vectors x and y in X, such that x is Birkhoff orthogonal to y if and only if Aq（x,y）=π/2. Some other properties of this angle are also discussed.
基金National Council for Science and Technology (NCST) of KenyaDAAD-Germany for the financial support
文摘In this paper, we present various notions and aspects of orthogonality in normed spaces. Characterizations and generalizations of orthogonality are also consid- ered. Results on orthogonality of the range and the kernel of elementary operators and the operators implementing them also are given.
基金Project supported by the National Natural Science Foundation of China
文摘In this paper, we reexamine the method of successive approximation presented by Prof. Chien Wei-zangfor solving the problem of large deflection of a circular plate, and find that the method could be regarded as the method of strained parameters in the singular perturbation theory. In terms of the parameter representing the ratio of the center deflection to the thickness of the plate, we make the asymptotic expansions of the deflection, membrane stress and the parameter of load as in Ref. [1], and then give the orthogonality conditions (i.e. the solvability conditions) for the resulting equations, by which the stiffness characteristics of the plate could be determined. It is pointed out that with the solutions for the small deflection problem of the circular plate and the orthogonality conditions, we can derive the third order approximate relations between the parameter of load and the center deflection and the first-term approximation of membrane stresses at the center and edge of the plate without solving the differential equations. For some special cases (i.e. under uniform load, under compound toad, with different boundary conditiors), we deduce the specific expressions and obtain the results in agreement with the previous ones given by Chien Wei-zang, Yeh kai-yuan and Hwang Chien in Refs. [1 - 4J.
基金Supported by the National Natural Science Foundation of China(No.10571122)the Beijing Natural Science Foundation(No.1052006)+1 种基金the Project of Excellent Young Teachersthe Doctoral Programme Foundation of National Education Ministry of China
文摘Abstract. Let {L（Ln^（A,λ）（x）}n≥0 be the sequence of monic Laguerre matrix polynomials defined on [0,∞） byLn^（A,λ）（x）=n!/（-λ）^n ∑nk-0（-λ）^k/k!（n-k）!（A＋I）n[（A＋I）k]^-1x^k,where A ∈ C^r×r. It is known that {Ln^（A,λ）（x）}n≥0 is orthogonal with respect to a matrix moment functional when A satisfies the spectral condition that Re（z） 〉 -1 for every z E or（a）. In this note we show that forA such that σ（A） does not contain negative integers, the Laguerre matrix polynomials Ln^（A,λ）（x） are orthogonal with respect to a non-diagonal SobolevLaguerre matrix moment functional, which extends two cases： the above matrix case and the known scalar case.
文摘For square contingency tables with ordered categories, the present paper gives several theorems that the symmetry model holds if and only if the generalized linear diagonals-parameter symmetry model for cell probabilities and for cumulative probabilities and the mean nonequality model of row and column variables hold. It also shows the orthogonality of statistic for testing goodness-of-fit of the symmetry model. An example is given.
文摘The orthogonality of eigenvector is a precondition to compute the dynamic responses of linear multi-rigid-flexible-body system using the classical modal analysis method. For a linear multi-rigid-flexible-body system, the eigenfunction does not satisfy the orthogonality under ordinary meaning. A new concept--augmented eigenvector is introduced, which is used to overcome the orthogonality problem of eigenvectors of linear multi-rigid-flexible-body system. The constitution method and the orthogonality of augmented eigenvector are expatiated. After the orthogonality of augmented eigenvector is acquired, the coupling of coordinates in dynamics equations can be released, which makes it possible to analyze exactly the dynamic responses of linear multi-rigid-flexible-body system using the classical modal analysis method.
文摘An implicit algorithm of Bi-penalty approximation with orthogonality projection for the numerical simulation of Bingham fluid flow problems is proposed in this paper. A Newton fluid flow with two kinds of artificial viscosity subjected to the inequality constraint is introduced to approximate the Bingham fluid flow. This approach can effectively simulate the Bingham fluid flow with floating rigid cores or fixing rigid cores.
