15 April 2003, Volume 19 Issue 4
    

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  • 论文
    Stability and Existence of Multidimensional Subsonic Phase Transitions
    Ya Guang WANG, Zhou Ping XIN
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(4): 529-558.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    The purpose of this paper is to prove the uniform stability of multidimensional subsonic phase transitions satisfying the viscosity-capillarity criterion in a van der Waals fluid, and further to establish the local existence of phase transition solutions.
  • Original Articles
    Stability and Existence of Multidimensional Subsonic Phase Transitions
    Ya Guang WANG, Zhou Ping XIN
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(4): 529-558.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    The purpose of this paper is to prove the uniform stability of multidimensional subsonic phase transitions satisfying the viscosity-capillarity criterion in a van der Waals fluid, and further to establish the local existence of phase transition solutions.
  • 论文
    A Global Solution to a Two-dimensional Riemann Problem Involving Shocks as Free Boundaries
    Yu Xi ZHANG
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(4): 559-572.
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    We present a global solution to a Riemann problem for the pressure gradient system of equations. The Riemann problem has initially two shock waves and two contact discontinuities. The angle between the two shock waves is set initially to be close to 180 degrees. The solution has a shock wave that is usually regarded as a free boundary in the self-similar variable plane. Our main contribution in methodology is handling the tangential oblique derivative boundary values.
  • Original Articles
    A Global Solution to a Two-dimensional Riemann Problem Involving Shocks as Free Boundaries
    Yu Xi ZHANG
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(4): 559-572.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    We present a global solution to a Riemann problem for the pressure gradient system of equations. The Riemann problem has initially two shock waves and two contact discontinuities. The angle between the two shock waves is set initially to be close to 180 degrees. The solution has a shock wave that is usually regarded as a free boundary in the self-similar variable plane. Our main contribution in methodology is handling the tangential oblique derivative boundary values.
  • 论文
    On Stability and Trajectory Boundedness in Mean-square Sense for ARMA Processes
    Han Fu CHEN
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(4): 573-580.
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    For the multidimensional ARMA system A(z)y k = C(z)w k it is shown that stability (det A(z) ≠ 0, ?z : |z| ≤ 1) of A(z) is equivalent to the trajectory boundedness in the mean square sense (MSS) lim sup/n→∞ ‖y_k‖~2 < ∞ a.s., which, as a rule, is a consequence of a successful stochastic adaptive control leading the closed-loop of an ARMAX system to a steady state ARMA system. In comparison with existing results the stability condition imposed on C(z) is no longer needed. The only structural requirement on the system is that det A(z) and det C(z) have no unstable common factor.
  • Original Articles
    On Stability and Trajectory Boundedness in Mean-square Sense for ARMA Processes
    Han Fu CHEN
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(4): 573-580.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    For the multidimensional ARMA system A(z)y k = C(z)w k it is shown that stability (det A(z) ≠ 0, ?z : |z| ≤ 1) of A(z) is equivalent to the trajectory boundedness in the mean square sense (MSS) lim sup/n→∞ ‖y_k‖~2 < ∞ a.s., which, as a rule, is a consequence of a successful stochastic adaptive control leading the closed-loop of an ARMAX system to a steady state ARMA system. In comparison with existing results the stability condition imposed on C(z) is no longer needed. The only structural requirement on the system is that det A(z) and det C(z) have no unstable common factor.
  • 论文
    Correlation and Entanglement
    Shun Long LUI, You Feng LUO
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(4): 581-598.
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    In quantum mechanics, it is long recognized that there exist correlations between observables which are much stronger than the classical ones. These correlations are usually called entanglement, and cannot be accounted for by classical theory. In this paper, we will study correlations between observables in terms of covariance and the Wigner-Yanase correlation, and compare their merits in characterizing entanglement. We will show that the Wigner-Yanase correlation has some advantages over the conventional covariance
  • Original Articles
    Correlation and Entanglement
    Shun Long LUI, You Feng LUO
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(4): 581-598.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In quantum mechanics, it is long recognized that there exist correlations between observables which are much stronger than the classical ones. These correlations are usually called entanglement, and cannot be accounted for by classical theory. In this paper, we will study correlations between observables in terms of covariance and the Wigner-Yanase correlation, and compare their merits in characterizing entanglement. We will show that the Wigner-Yanase correlation has some advantages over the conventional covariance
  • 论文
    Delete-group Jackknife Estimate in Partially Linear Regression Models with Heteroscedasticity
    Jin Hong YOU, Ge Mai CHEN
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(4): 599-610.
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    Consider a partially linear regression model with an unknown vector parameter β, an unknown function g(·), and unknown heteroscedastic error variances. Chen, You~([23]) proposed a semiparametric generalized least squares estimator (SGLSE) forβ, which takes the heteroscedasticity into account to increase efficiency. For inference based on this SGLSE, it is necessary to construct a consistent estimator for its asymptotic covariance matrix. However, when there exists within-group correlation, the traditional delta method and the delete-1 jackknife estimation fail to offer such a consistent estimator. In this paper, by deleting grouped partial residuals a delete-group jackknife method is examined. It is shown that the delete-group jackknife method indeed can provide a consistent estimator for the asymptotic covariance matrix in the presence of within-group correlations. This result is an extension of that in [21].
  • Original Articles
    Delete-group Jackknife Estimate in Partially Linear Regression Models with Heteroscedasticity
    Jin Hong YOU, Ge Mai CHEN
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(4): 599-610.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Consider a partially linear regression model with an unknown vector parameter β, an unknown function g(·), and unknown heteroscedastic error variances. Chen, You~([23]) proposed a semiparametric generalized least squares estimator (SGLSE) forβ, which takes the heteroscedasticity into account to increase efficiency. For inference based on this SGLSE, it is necessary to construct a consistent estimator for its asymptotic covariance matrix. However, when there exists within-group correlation, the traditional delta method and the delete-1 jackknife estimation fail to offer such a consistent estimator. In this paper, by deleting grouped partial residuals a delete-group jackknife method is examined. It is shown that the delete-group jackknife method indeed can provide a consistent estimator for the asymptotic covariance matrix in the presence of within-group correlations. This result is an extension of that in [21].
  • 论文
    A Class of Cone Bounded Quasiconvex Mappings in Topological Vector Spaces
    Yu Da HU, Ling CHEN
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(4): 611-620.
    DOI:5
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    Within the context of cone-ordered topological vector spaces, this paper introduces the concepts of cone bounded point and cone bounded set for vector set. With their aid, a class of new cone quasiconvex mappings in topological vector spaces is defined, and their fundamental properties are presented. The relationships between the cone bounded quasiconvex mapping defined in this paper and cone convex mapping, and other known cone quasiconvex mapping are also discussed.
  • Original Articles
    A Class of Cone Bounded Quasiconvex Mappings in Topological Vector Spaces
    Yu Da HU, Ling CHEN
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(4): 611-620.
    DOI:5
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Within the context of cone-ordered topological vector spaces, this paper introduces the concepts of cone bounded point and cone bounded set for vector set. With their aid, a class of new cone quasiconvex mappings in topological vector spaces is defined, and their fundamental properties are presented. The relationships between the cone bounded quasiconvex mapping defined in this paper and cone convex mapping, and other known cone quasiconvex mapping are also discussed.
  • 论文
    Ruin Probabilities under a Markovian Risk Model
    Han Xing WANG, Da Fan FANG, Mao Ning TANG
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(4): 621-630.
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    In this paper, a Markovian risk model is developed, in which the occurrence of the claims is described by a point process {N(t)}_(t≥0) with N(t) being the number of jumps of a Markov chain during the interval [0, t]. For the model, the explicit form of the ruin probability Ψ(0) and the bound for the convergence rate of the ruin probability Ψ(u) are given by using the generalized renewal technique developed in this paper. Finally, we prove that the ruin probability Ψ(u) is a linear combination of some negative exponential functions in a special case when the claims are exponentially distributed and the Markov chain has an intensity matrix (q_(ij))_(i,j∈E such that q_m = q_(m1) and q_i = q_(i(i+1)), 1 ≤ i ≤ m–1.
  • Original Articles
    Ruin Probabilities under a Markovian Risk Model
    Han Xing WANG, Da Fan FANG, Mao Ning TANG
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(4): 621-630.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, a Markovian risk model is developed, in which the occurrence of the claims is described by a point process {N(t)}_(t≥0) with N(t) being the number of jumps of a Markov chain during the interval [0, t]. For the model, the explicit form of the ruin probability Ψ(0) and the bound for the convergence rate of the ruin probability Ψ(u) are given by using the generalized renewal technique developed in this paper. Finally, we prove that the ruin probability Ψ(u) is a linear combination of some negative exponential functions in a special case when the claims are exponentially distributed and the Markov chain has an intensity matrix (q_(ij))_(i,j∈E such that q_m = q_(m1) and q_i = q_(i(i+1)), 1 ≤ i ≤ m–1.
  • 论文
    On the Existence of Positive Periodic Solutions for Neutral Functional Differential Equation with Multiple Deviating Arguments
    Shi Ping LU, Wei Gao GE
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(4): 631-640.
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    By means of an abstract continuation theory for k-set contraction and continuation theorem of coincidence degree principle, some criteria are established for the existence of positive periodic solutions of following neutral functional differential equation dN/dt = N(t) [a(t)-β(t)N(t)-∑from j = 1 to n of b_j (t)N(t-σ_j(t))-∑from i=1 to m of c_i(t)N'(t-τ_i(t))].
  • Original Articles
    On the Existence of Positive Periodic Solutions for Neutral Functional Differential Equation with Multiple Deviating Arguments
    Shi Ping LU, Wei Gao GE
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(4): 631-640.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    By means of an abstract continuation theory for k-set contraction and continuation theorem of coincidence degree principle, some criteria are established for the existence of positive periodic solutions of following neutral functional differential equation dN/dt = N(t) [a(t)-β(t)N(t)-∑from j = 1 to n of b_j (t)N(t-σ_j(t))-∑from i=1 to m of c_i(t)N'(t-τ_i(t))].
  • 论文
    The Invariance Principle for Linear Processes Generated by a Negatively Associated Sequence and Its Applications
    Chuan Rong LU
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(4): 641-646.
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    In this paper, we obtain the invariance principle for linear processes generated by a negatively associated sequence.
  • Original Articles
    The Invariance Principle for Linear Processes Generated by a Negatively Associated Sequence and Its Applications
    Chuan Rong LU
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(4): 641-646.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, we obtain the invariance principle for linear processes generated by a negatively associated sequence.
  • 论文
    Time-risk Discount Valuation of Life Contracts
    Dian Fa CHEN, George Xiang
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(4): 647-662.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper a new approach is developed to value life insurance contracts by means of the method of backward stochastic differential equation. Such a valuation may relax certain market limitations. Following this approach, the values of single decrement policies are studied and Thiele's-type PDEs for general life insurance contracts are derived
  • Original Articles
    Time-risk Discount Valuation of Life Contracts
    Dian Fa CHEN, George Xiang
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(4): 647-662.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper a new approach is developed to value life insurance contracts by means of the method of backward stochastic differential equation. Such a valuation may relax certain market limitations. Following this approach, the values of single decrement policies are studied and Thiele's-type PDEs for general life insurance contracts are derived
  • 论文
    Dynamical Behaviors in a Two-dimensional Map
    Yu CHANG , Xu Dong LI
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(4): 663-676.
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    We consider the dynamics of a two-dimensional map proposed by Maynard Smith as a population model. The existence of chaos in the sense of Marotto's theorem is first proved, and the bifurcations of periodic points are studied by analytic methods. The numerical simulations not only show the consistence with the theoretical analysis but also exhibi the complex dynamical behaviors.
  • Original Articles
    Dynamical Behaviors in a Two-dimensional Map
    Yu CHANG , Xu Dong LI
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(4): 663-676.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    We consider the dynamics of a two-dimensional map proposed by Maynard Smith as a population model. The existence of chaos in the sense of Marotto's theorem is first proved, and the bifurcations of periodic points are studied by analytic methods. The numerical simulations not only show the consistence with the theoretical analysis but also exhibi the complex dynamical behaviors.
  • 论文
    The Existence of Silnikov's Orbit in Four-dimensional Duffing's Systems
    Wei LI , Peng Cheng XU
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(4): 677-690.
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    The existence of Silnikov's orbits in a four-dimensional dynamical system is discussed. The existence of Silnikov's orbit resulting in chaotic dynamics is established by the fiber structure of invariant manifold and high-dimensional Melnikov method. Numerical simulations are given to demonstrate the theoretical analysis
  • Original Articles
    The Existence of Silnikov's Orbit in Four-dimensional Duffing's Systems
    Wei LI , Peng Cheng XU
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(4): 677-690.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    The existence of Silnikov's orbits in a four-dimensional dynamical system is discussed. The existence of Silnikov's orbit resulting in chaotic dynamics is established by the fiber structure of invariant manifold and high-dimensional Melnikov method. Numerical simulations are given to demonstrate the theoretical analysis
  • 论文
    Periodic Solution of a Nonautonomous Diffusive Food Chain System of Three Species with Time Delays
    Zheng Qiu ZHANG, Xian Wu ZENG, Zhi Cheng WANG
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(4): 691-702.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for a nonautonomous diffusive food chain system of three species. { dx_1(t)/dt = x_1(t)[r_1(t)-a_(11)(t)x_1(t)-a_(12)(t)_2(t)]+D_1(t)[y(t)-x_1(t)],dx_2(t)/dt = x_2(t)[-r_2(t)+a(21)(t)x_1(t-τ_1)-a_(22)(t)x_2(t)-a_(23)(t)x_3(t)], dx_3(t)/dt = x_3(t)[-r_3(t)+a_(32)(t)x_2(t-τ_2)-a_(33)(t)x_3(t)], dy(t)/dt = y(t)[r_4(t) -a_(44)(t)y(t)]+D_2(t)[x_1(t)-y(t)], is established, where r_i (t), a_(ii) (t) (i = 1, 2, 3, 4), D_i (t) (i = 1, 2), a_(12)(t), a_(21)(t), a_(23)(t) and a_(32)(t) are all positive periodic continuous functions with period w > 0, τ_i (i = 1, 2) are positive constants.
  • Original Articles
    Periodic Solution of a Nonautonomous Diffusive Food Chain System of Three Species with Time Delays
    Zheng Qiu ZHANG, Xian Wu ZENG, Zhi Cheng WANG
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(4): 691-702.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for a nonautonomous diffusive food chain system of three species. { dx_1(t)/dt = x_1(t)[r_1(t)-a_(11)(t)x_1(t)-a_(12)(t)_2(t)]+D_1(t)[y(t)-x_1(t)],dx_2(t)/dt = x_2(t)[-r_2(t)+a(21)(t)x_1(t-τ_1)-a_(22)(t)x_2(t)-a_(23)(t)x_3(t)], dx_3(t)/dt = x_3(t)[-r_3(t)+a_(32)(t)x_2(t-τ_2)-a_(33)(t)x_3(t)], dy(t)/dt = y(t)[r_4(t) -a_(44)(t)y(t)]+D_2(t)[x_1(t)-y(t)], is established, where r_i (t), a_(ii) (t) (i = 1, 2, 3, 4), D_i (t) (i = 1, 2), a_(12)(t), a_(21)(t), a_(23)(t) and a_(32)(t) are all positive periodic continuous functions with period w > 0, τ_i (i = 1, 2) are positive constants.
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