15 January 2000, Volume 16 Issue 1
    

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  • Original Articles
    (Global smooth resolvability for a model equations of fluid flow in a pipe)
    Fa Gui LIU
    Acta Mathematicae Applicatae Sinica(English Series). 2000, 16(1): 1-014.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this article the author considers the Cauchy problem for a model equations of fluid flow in a pipe,and under certain hypotheses on the initial data,the global smooth resolvability and the blow-up phenomena are obtained.
  • 论文
    (Global smooth resolvability for a model equations of fluid flow in a pipe)
    Fa Gui LIU
    Acta Mathematicae Applicatae Sinica(English Series). 2000, 16(1): 1-014.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this article the author considers the Cauchy problem for a model equations of fluid flow in a pipe,and under certain hypotheses on the initial data,the global smooth resolvability and the blow-up phenomena are obtained.
  • 论文
    Measures and their dimension spectrums for cookie-cutter sets in R~d
    Jin Rong LIANG, Zu Guo YU, Fu Yao REN
    Acta Mathematicae Applicatae Sinica(English Series). 2000, 16(1): 9-21.
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    The characteristics of cookie-cutter sets in R~d are investigated.A Bowen's formula for the Hausdorff dimension of a cookie-cutter set in terms of the pressure function is derived.The existence of self-similar measures,conformal measures and Gibbs measures on cookie-cutter sets is proved.The dimension spectrum of each of these measures is analyzed.In addition,the locally uniformly α-dimensional condition and the fractal Plancherel Theorem for these measures are shown.Finally,the existence of order-two density for the Hausdorff measure of a cookie-cutter set is proved.
  • Original Articles
    Measures and their dimension spectrums for cookie-cutter sets in R~d
    Jin Rong LIANG, Zu Guo YU, Fu Yao REN
    Acta Mathematicae Applicatae Sinica(English Series). 2000, 16(1): 9-21.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    The characteristics of cookie-cutter sets in R~d are investigated.A Bowen's formula for the Hausdorff dimension of a cookie-cutter set in terms of the pressure function is derived.The existence of self-similar measures,conformal measures and Gibbs measures on cookie-cutter sets is proved.The dimension spectrum of each of these measures is analyzed.In addition,the locally uniformly α-dimensional condition and the fractal Plancherel Theorem for these measures are shown.Finally,the existence of order-two density for the Hausdorff measure of a cookie-cutter set is proved.
  • 论文
    Super efficiency and its scalarization in topological vector space
    Yu Hua HU, Xun Hua GONG
    Acta Mathematicae Applicatae Sinica(English Series). 2000, 16(1): 22-26.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper,we give a characterization of super efficiency,and obtain a scalarization result for super efficiency in locally convex locally bounded topological vector spaces.The proof given here is substantially different from that given by Borwein and Zhuang.
  • Original Articles
    Super efficiency and its scalarization in topological vector space
    Yu Hua HU, Xun Hua GONG
    Acta Mathematicae Applicatae Sinica(English Series). 2000, 16(1): 22-26.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper,we give a characterization of super efficiency,and obtain a scalarization result for super efficiency in locally convex locally bounded topological vector spaces.The proof given here is substantially different from that given by Borwein and Zhuang.
  • 论文
    Delay systems and optimal control
    Xiao Ling XIANG, Hua Wu KUANG
    Acta Mathematicae Applicatae Sinica(English Series). 2000, 16(1): 27-35.
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    In this paper,we generalize Gronwall lemma to the case with time lags and use them to study delay controlled systems.For delay controlled systems associated with C_0-semigroup and analytic semigroup,we obtain the existences of mild solutions and optimals control.Lastly,an example is given to illustrate our abstract results.
  • Original Articles
    Delay systems and optimal control
    Xiao Ling XIANG, Hua Wu KUANG
    Acta Mathematicae Applicatae Sinica(English Series). 2000, 16(1): 27-35.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper,we generalize Gronwall lemma to the case with time lags and use them to study delay controlled systems.For delay controlled systems associated with C_0-semigroup and analytic semigroup,we obtain the existences of mild solutions and optimals control.Lastly,an example is given to illustrate our abstract results.
  • Original Articles
    A feasible and superlinear algorithm for inequality constrained minimization problems
    Xu Yifan, Wei WANG
    Acta Mathematicae Applicatae Sinica(English Series). 2000, 16(1): 36-41.
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    In this paper,a new algorithm for inequality constrained optimization problems is presented.The algorithm is feasible and is globally and superlinearly convergent under some weaker assumptions-without strict complementary condition.
  • 论文
    A feasible and superlinear algorithm for inequality constrained minimization problems
    Xu Yifan, Wei WANG
    Acta Mathematicae Applicatae Sinica(English Series). 2000, 16(1): 36-41.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper,a new algorithm for inequality constrained optimization problems is presented.The algorithm is feasible and is globally and superlinearly convergent under some weaker assumptions-without strict complementary condition.
  • 论文
    Cubic Lienard equation with quadradic damping(I)
    Yu Quan WANG, Zhu Jun JING
    Acta Mathematicae Applicatae Sinica(English Series). 2000, 16(1): 42-52.
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    Applying Hopf bifurcation theory and qualitative theory,we give the conditions of the existence and uniqueness of one limit cycle and the existence of two limit cycles for the general cubic Lienard equation.Numerical simulation results with one and two limit cycles are given to demonstrate the theoretical results.
  • Original Articles
    Cubic Lienard equation with quadradic damping(I)
    Yu Quan WANG, Zhu Jun JING
    Acta Mathematicae Applicatae Sinica(English Series). 2000, 16(1): 42-52.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Applying Hopf bifurcation theory and qualitative theory,we give the conditions of the existence and uniqueness of one limit cycle and the existence of two limit cycles for the general cubic Lienard equation.Numerical simulation results with one and two limit cycles are given to demonstrate the theoretical results.
  • Original Articles
    A class of generalized cyclic codes
    Zhuo Jun LIU, Dong Dai LIN
    Acta Mathematicae Applicatae Sinica(English Series). 2000, 16(1): 53-58.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper,we discuss how to construct a class of generalized cyclic codes,denoted by GCC.It is well known that a cyclic code is generated by a factor of x~n-1.Clearly,any monic polynomial g(x) with degree less than n could be considered as a factor of some polynomial of degree n.Similarly the construction of cyclic codes,we explain how g(x) can generate a GCC.Meanwhile,as related to cyclic codes,experiments show that GCC can anlays produce a better parameter and/or give more linear codes.On the basis the of concept of GCC,we can also construct a linear code of [90,76,5]_2.
  • 论文
    A class of generalized cyclic codes
    Zhuo Jun LIU, Dong Dai LIN
    Acta Mathematicae Applicatae Sinica(English Series). 2000, 16(1): 53-58.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper,we discuss how to construct a class of generalized cyclic codes,denoted by GCC.It is well known that a cyclic code is generated by a factor of x~n-1.Clearly,any monic polynomial g(x) with degree less than n could be considered as a factor of some polynomial of degree n.Similarly the construction of cyclic codes,we explain how g(x) can generate a GCC.Meanwhile,as related to cyclic codes,experiments show that GCC can anlays produce a better parameter and/or give more linear codes.On the basis the of concept of GCC,we can also construct a linear code of [90,76,5]_2.
  • 论文
    Modefied optimization layer by layer algorithm for learning multilayer perceptrons
    De Gang LIU, Xiang Sun ZHANG
    Acta Mathematicae Applicatae Sinica(English Series). 2000, 16(1): 59-69.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper a modified learning procedure is presented which tries to find a weight change vector at each trial iteration in the OLL algorithm more efficiently.The proposed learning procedure can save expensive computation efforts and yield better convergence rate as compared to the original OLL learning algorithms especially for large scale networks.The improved OLL learning algorithm is applied to the time series prediction problems presented by the OLL authors,and demonstrates a faster learning capability.
  • Original Articles
    Modefied optimization layer by layer algorithm for learning multilayer perceptrons
    De Gang LIU, Xiang Sun ZHANG
    Acta Mathematicae Applicatae Sinica(English Series). 2000, 16(1): 59-69.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper a modified learning procedure is presented which tries to find a weight change vector at each trial iteration in the OLL algorithm more efficiently.The proposed learning procedure can save expensive computation efforts and yield better convergence rate as compared to the original OLL learning algorithms especially for large scale networks.The improved OLL learning algorithm is applied to the time series prediction problems presented by the OLL authors,and demonstrates a faster learning capability.
  • Original Articles
    (Inverse Radon transform with one-dimensional wavelet transform)
    Gang Rong LIANG
    Acta Mathematicae Applicatae Sinica(English Series). 2000, 16(1): 70-77.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper,the wavelet inverse formula of Radon transform is obtained with one-dimensional wavelet.The convolution back-projection method of Radon transform is derived from this inverse formula.An asymptotic relation between wavelet inverse formula of Radon transform and convolution-back projection algorithm of Radon transform in 2 dimensions is established
  • 论文
    (Inverse Radon transform with one-dimensional wavelet transform)
    Gang Rong LIANG
    Acta Mathematicae Applicatae Sinica(English Series). 2000, 16(1): 70-77.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper,the wavelet inverse formula of Radon transform is obtained with one-dimensional wavelet.The convolution back-projection method of Radon transform is derived from this inverse formula.An asymptotic relation between wavelet inverse formula of Radon transform and convolution-back projection algorithm of Radon transform in 2 dimensions is established
  • Original Articles
    Hamiltonian decomposition of Cayley graphs of orders p~2 and pq
    Hai Zhu LI, Jian Fang WANG, Liang SUN
    Acta Mathematicae Applicatae Sinica(English Series). 2000, 16(1): 78-86.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper,it is proved that any connected Cayley graph on an abelian group of order pq or p~2 has a hamiltonian decomposition,where p and q are odd primes.This result answers partially a conjecture of Alspach concerning hamiltonian decomposition of 2k-regular connected Cayley graphs on abelian groups.
  • 论文
    Hamiltonian decomposition of Cayley graphs of orders p~2 and pq
    Hai Zhu LI, Jian Fang WANG, Liang SUN
    Acta Mathematicae Applicatae Sinica(English Series). 2000, 16(1): 78-86.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper,it is proved that any connected Cayley graph on an abelian group of order pq or p~2 has a hamiltonian decomposition,where p and q are odd primes.This result answers partially a conjecture of Alspach concerning hamiltonian decomposition of 2k-regular connected Cayley graphs on abelian groups.
  • 论文
    A second-order periodic boundary value problem with singular and discontinuous nonlinearity
    Hui Zhao LI, Da Qing JIANG
    Acta Mathematicae Applicatae Sinica(English Series). 2000, 16(1): 87-92.
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    In this paper,we study a nonlinear second-order periodic boundary value problem,in which the equation has a singular and discontinuous nonlinearity.By using perturbation techniques and comparison principles,we obtain the existence of solutions for this problem.
  • Original Articles
    A second-order periodic boundary value problem with singular and discontinuous nonlinearity
    Hui Zhao LI, Da Qing JIANG
    Acta Mathematicae Applicatae Sinica(English Series). 2000, 16(1): 87-92.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper,we study a nonlinear second-order periodic boundary value problem,in which the equation has a singular and discontinuous nonlinearity.By using perturbation techniques and comparison principles,we obtain the existence of solutions for this problem.
  • 论文
    Inverse monoids of graphs
    Wei Ming LI
    Acta Mathematicae Applicatae Sinica(English Series). 2000, 16(1): 93-99.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper we first present a combinatorial characterization of an inverse monoid of a graph.Then using this we prove that a bipartite graph with an inverse monoid is uniquely K_2,and that a graph G has an inverse monoid if and only if the join of G and a complete graph also has an inverse monoid.
  • Original Articles
    Inverse monoids of graphs
    Wei Ming LI
    Acta Mathematicae Applicatae Sinica(English Series). 2000, 16(1): 93-99.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper we first present a combinatorial characterization of an inverse monoid of a graph.Then using this we prove that a bipartite graph with an inverse monoid is uniquely K_2,and that a graph G has an inverse monoid if and only if the join of G and a complete graph also has an inverse monoid.
  • 论文
    On the homogenization of degenerate parabolic equations
    Huai Yu JIAN
    Acta Mathematicae Applicatae Sinica(English Series). 2000, 16(1): 100-110.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    The homogenization of the nonlinear degenerate parabolic equations,_tb(u)-diva(x/ε,t/ε,u,u)=f(x,t),is studied,where a(y,t,μ,λ) is periodic in (y,t) and b may be a nonlinear function whose prototype is |u|~r sign u with r>0.
  • Original Articles
    On the homogenization of degenerate parabolic equations
    Huai Yu JIAN
    Acta Mathematicae Applicatae Sinica(English Series). 2000, 16(1): 100-110.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    The homogenization of the nonlinear degenerate parabolic equations,_tb(u)-diva(x/ε,t/ε,u,u)=f(x,t),is studied,where a(y,t,μ,λ) is periodic in (y,t) and b may be a nonlinear function whose prototype is |u|~r sign u with r>0.
  • Original Articles
    The local time process of a circular Brownian motion
    Kai Nan XIANG
    Acta Mathematicae Applicatae Sinica(English Series). 2000, 16(1): 111-112.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
  • 论文
    The local time process of a circular Brownian motion
    Kai Nan XIANG
    Acta Mathematicae Applicatae Sinica(English Series). 2000, 16(1): 111-112.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
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