We apply the dynamic programming methods to compute the analytical solution of the dynamic mean-variance optimization problem affected by an exogenous liability in a multi-periods market model with singular second mom...We apply the dynamic programming methods to compute the analytical solution of the dynamic mean-variance optimization problem affected by an exogenous liability in a multi-periods market model with singular second moment matrixes of the return vector of assets. We use orthogonai transformations to overcome the difficulty produced by those singular matrixes, and the analytical form of the efficient frontier is obtained. As an application, the explicit form of the optimal mean-variance hedging strategy is also obtained for our model.展开更多
In this paper orthogonal matrix polynomials with respect to a right matrix moment functional an introduced. Basic results, important examples and applications to the approximation of matrix integrals are studied. Erro...In this paper orthogonal matrix polynomials with respect to a right matrix moment functional an introduced. Basic results, important examples and applications to the approximation of matrix integrals are studied. Error bounds for the proposed matrix quadrature rules are given.展开更多
In this paper basic results for a theory of orthogonal matrix polynomials with respect to a conjugate bilinear matrix moment functional are proposed. Properties of orthogonal matrix polynomial sequences including a th...In this paper basic results for a theory of orthogonal matrix polynomials with respect to a conjugate bilinear matrix moment functional are proposed. Properties of orthogonal matrix polynomial sequences including a three term matrix relationship are given. Positive definite conjugate bilinear matrix moment functionals are introduced and a characterization of positive definiteness in terms of a block Haenkel moment matrix is established. For each positive definite conjugate bilinear matrix moment functional an associated matrix inner product is defined.展开更多
An accurate electric dipole moment function(EDMF) is obtained for the carbon monoxide(CO) molecule(X1+Σ)by fitting the experimental rovibrational transitional moments. Additionally, an accurate ab initio EDMF is foun...An accurate electric dipole moment function(EDMF) is obtained for the carbon monoxide(CO) molecule(X1+Σ)by fitting the experimental rovibrational transitional moments. Additionally, an accurate ab initio EDMF is found using the highly accurate, multi-reference averaged coupled-pair functional(ACPF) approach with the basis set, aug-cc-p V6 Z, and a finite-field with ±0.005 a.u.(The unit a.u. is the abbreviation of atomic unit). This ab initio EDMF is very consistent with the fitted ones. The vibrational transition matrix moments and the Herman–Wallis factors, calculated with the Rydberg–Klein–Rees(RKR) potential and the fitted and ab initio EDMFs, are compared with experimental measurements. The consistency of these line intensities with the high-resolution transmission(HITRAN) molecular database demonstrates the improved accuracy of the fitted and ab initio EDMFs derived in this work.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
Recently, the diverse properties of Rydberg atoms, which probably arise from its large electric dipole moment （EDM）, have been explored. In this paper, we report electric dipole moments along with Stark energies and...Recently, the diverse properties of Rydberg atoms, which probably arise from its large electric dipole moment （EDM）, have been explored. In this paper, we report electric dipole moments along with Stark energies and charge densities of lithium Rydberg states in the presence of electric fields, calculated by matrix diagonalization. Huge electric dipole moments are discovered. In order to check the validity of the EDMs, we also use these electric dipole moments to calculate the Stark energies by numerical integration. The results agree with those calculated by matrix diagonalization.展开更多
The concepts of random Markov matrix, Markov branching chain in randomenvironment (MBCRE) and Laplace functional of Markov branching chain in random environment (LFMBCRE)are introduced. The properties of LFMBCRE and t...The concepts of random Markov matrix, Markov branching chain in randomenvironment (MBCRE) and Laplace functional of Markov branching chain in random environment (LFMBCRE)are introduced. The properties of LFMBCRE and the explicit formulas of momentsof MBCRE are given.展开更多
基金National Basic Research Program of China (973 Program No.2007CB814903)National Natural Science Foundation of China (No.70671069)
文摘We apply the dynamic programming methods to compute the analytical solution of the dynamic mean-variance optimization problem affected by an exogenous liability in a multi-periods market model with singular second moment matrixes of the return vector of assets. We use orthogonai transformations to overcome the difficulty produced by those singular matrixes, and the analytical form of the efficient frontier is obtained. As an application, the explicit form of the optimal mean-variance hedging strategy is also obtained for our model.
文摘In this paper orthogonal matrix polynomials with respect to a right matrix moment functional an introduced. Basic results, important examples and applications to the approximation of matrix integrals are studied. Error bounds for the proposed matrix quadrature rules are given.
文摘In this paper basic results for a theory of orthogonal matrix polynomials with respect to a conjugate bilinear matrix moment functional are proposed. Properties of orthogonal matrix polynomial sequences including a three term matrix relationship are given. Positive definite conjugate bilinear matrix moment functionals are introduced and a characterization of positive definiteness in terms of a block Haenkel moment matrix is established. For each positive definite conjugate bilinear matrix moment functional an associated matrix inner product is defined.
基金supported by the National Natural Science Foundation of China(Grant Nos.11374217 and 11474207)
文摘An accurate electric dipole moment function(EDMF) is obtained for the carbon monoxide(CO) molecule(X1+Σ)by fitting the experimental rovibrational transitional moments. Additionally, an accurate ab initio EDMF is found using the highly accurate, multi-reference averaged coupled-pair functional(ACPF) approach with the basis set, aug-cc-p V6 Z, and a finite-field with ±0.005 a.u.(The unit a.u. is the abbreviation of atomic unit). This ab initio EDMF is very consistent with the fitted ones. The vibrational transition matrix moments and the Herman–Wallis factors, calculated with the Rydberg–Klein–Rees(RKR) potential and the fitted and ab initio EDMFs, are compared with experimental measurements. The consistency of these line intensities with the high-resolution transmission(HITRAN) molecular database demonstrates the improved accuracy of the fitted and ab initio EDMFs derived in this work.
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.
基金supported by the National Basic Research Program of China(Grant No.2012CB921603)the National Natural Science Foundation of China(GrantNos.61378039,61078013,61178009,and 11274209)+3 种基金the Program for Changjiang Scholars and Innovative Research Team in University,China(Grant No.IRT13076)the Fund for Fostering Talents in Basic Science of the National Natural Science Foundation of China(Grant No.J1210036)the Natural Science Foundation of Shanxi Province,China(Grant No.2012011003-2)the Shanxi International Collaboration Program,China(Grant No.2010081046)
文摘Recently, the diverse properties of Rydberg atoms, which probably arise from its large electric dipole moment （EDM）, have been explored. In this paper, we report electric dipole moments along with Stark energies and charge densities of lithium Rydberg states in the presence of electric fields, calculated by matrix diagonalization. Huge electric dipole moments are discovered. In order to check the validity of the EDMs, we also use these electric dipole moments to calculate the Stark energies by numerical integration. The results agree with those calculated by matrix diagonalization.
文摘The concepts of random Markov matrix, Markov branching chain in randomenvironment (MBCRE) and Laplace functional of Markov branching chain in random environment (LFMBCRE)are introduced. The properties of LFMBCRE and the explicit formulas of momentsof MBCRE are given.
