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Acta Mathematicae Applicatae Sinica(English Series) 2000 Vol.16

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(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.  
Abstract974)      PDF(pc) (330KB)(279)       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.
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(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.  
Abstract22)      PDF(pc) (330KB)(325)       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.
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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.  
Abstract18)      PDF(pc) (657KB)(384)       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.
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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.  
Abstract837)      PDF(pc) (657KB)(273)       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.
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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.  
Abstract7)      PDF(pc) (234KB)(271)       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.
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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.  
Abstract718)      PDF(pc) (234KB)(374)       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.
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Delay systems and optimal control
Xiao Ling XIANG, Hua Wu KUANG
Acta Mathematicae Applicatae Sinica(English Series)    2000, 16 (1): 27-35.  
Abstract28)      PDF(pc) (470KB)(320)       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.
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Delay systems and optimal control
Xiao Ling XIANG, Hua Wu KUANG
Acta Mathematicae Applicatae Sinica(English Series)    2000, 16 (1): 27-35.  
Abstract540)      PDF(pc) (470KB)(549)       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.
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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.  
Abstract584)      PDF(pc) (286KB)(323)       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.
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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.  
Abstract37)      PDF(pc) (286KB)(237)       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.
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Cubic Lienard equation with quadradic damping(I)
Yu Quan WANG, Zhu Jun JING
Acta Mathematicae Applicatae Sinica(English Series)    2000, 16 (1): 42-52.  
Abstract27)      PDF(pc) (521KB)(305)       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.
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Cubic Lienard equation with quadradic damping(I)
Yu Quan WANG, Zhu Jun JING
Acta Mathematicae Applicatae Sinica(English Series)    2000, 16 (1): 42-52.  
Abstract825)      PDF(pc) (521KB)(236)       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.
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A class of generalized cyclic codes
Zhuo Jun LIU, Dong Dai LIN
Acta Mathematicae Applicatae Sinica(English Series)    2000, 16 (1): 53-58.  
Abstract1367)      PDF(pc) (313KB)(298)       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.
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A class of generalized cyclic codes
Zhuo Jun LIU, Dong Dai LIN
Acta Mathematicae Applicatae Sinica(English Series)    2000, 16 (1): 53-58.  
Abstract0)      PDF(pc) (313KB)(269)       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.
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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.  
Abstract29)      PDF(pc) (684KB)(217)       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.
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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.  
Abstract800)      PDF(pc) (684KB)(305)       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.
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(Inverse Radon transform with one-dimensional wavelet transform)
Gang Rong LIANG
Acta Mathematicae Applicatae Sinica(English Series)    2000, 16 (1): 70-77.  
Abstract607)      PDF(pc) (344KB)(313)       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
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(Inverse Radon transform with one-dimensional wavelet transform)
Gang Rong LIANG
Acta Mathematicae Applicatae Sinica(English Series)    2000, 16 (1): 70-77.  
Abstract43)      PDF(pc) (344KB)(252)       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
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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.  
Abstract811)      PDF(pc) (588KB)(267)       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.
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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.  
Abstract19)      PDF(pc) (588KB)(303)       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.
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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.  
Abstract29)      PDF(pc) (280KB)(283)       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.
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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.  
Abstract792)      PDF(pc) (280KB)(363)       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.
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Inverse monoids of graphs
Wei Ming LI
Acta Mathematicae Applicatae Sinica(English Series)    2000, 16 (1): 93-99.  
Abstract22)      PDF(pc) (457KB)(265)       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.
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Inverse monoids of graphs
Wei Ming LI
Acta Mathematicae Applicatae Sinica(English Series)    2000, 16 (1): 93-99.  
Abstract726)      PDF(pc) (457KB)(295)       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.
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On the homogenization of degenerate parabolic equations
Huai Yu JIAN
Acta Mathematicae Applicatae Sinica(English Series)    2000, 16 (1): 100-110.  
Abstract21)      PDF(pc) (475KB)(596)       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.
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On the homogenization of degenerate parabolic equations
Huai Yu JIAN
Acta Mathematicae Applicatae Sinica(English Series)    2000, 16 (1): 100-110.  
Abstract803)      PDF(pc) (475KB)(256)       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.
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The local time process of a circular Brownian motion
Kai Nan XIANG
Acta Mathematicae Applicatae Sinica(English Series)    2000, 16 (1): 111-112.  
Abstract470)      PDF(pc) (81KB)(506)       Save
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The local time process of a circular Brownian motion
Kai Nan XIANG
Acta Mathematicae Applicatae Sinica(English Series)    2000, 16 (1): 111-112.  
Abstract2)      PDF(pc) (81KB)(335)       Save
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(On testing for no effect of the predictor on response)
Li Xing ZHU, Lam Yeh
Acta Mathematicae Applicatae Sinica(English Series)    2000, 16 (2): 113-121.  
Abstract654)      PDF(pc) (452KB)(336)       Save
In this paper,one of them being a cusum test proposed by Buckley is studied further.This test can be extended to treating the non-normal and time series cases.A Kolmogorov-Smirnov type test is suggested and studied too.The main observation is the link between the statistic and the Brownian bridge.Some small sample experiments are conducted to examine the power of the tests.In some non-normal cases the power is encouraging.
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(On testing for no effect of the predictor on response)
Li Xing ZHU, Lam Yeh
Acta Mathematicae Applicatae Sinica(English Series)    2000, 16 (2): 113-121.  
Abstract3)      PDF(pc) (452KB)(231)       Save
In this paper,one of them being a cusum test proposed by Buckley is studied further.This test can be extended to treating the non-normal and time series cases.A Kolmogorov-Smirnov type test is suggested and studied too.The main observation is the link between the statistic and the Brownian bridge.Some small sample experiments are conducted to examine the power of the tests.In some non-normal cases the power is encouraging.
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(Uniform machine scheduling with machine available constraints)
Yong HE
Acta Mathematicae Applicatae Sinica(English Series)    2000, 16 (2): 122-129.  
Abstract1)      PDF(pc) (530KB)(222)       Save
In this paper,we consider a uniform machine scheduling problem with nonsimultaneous available times.We prove that LPT algorithm has a worst case bound in the interval (1.52,5/3).We tighten this bound when the machine speed ratio is small or m=2.Furthermore,we present a linear compound algorithm QLC with a worst case bound of 6/5 for a two-machine system.
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(Uniform machine scheduling with machine available constraints)
Yong HE
Acta Mathematicae Applicatae Sinica(English Series)    2000, 16 (2): 122-129.  
Abstract638)      PDF(pc) (530KB)(412)       Save
In this paper,we consider a uniform machine scheduling problem with nonsimultaneous available times.We prove that LPT algorithm has a worst case bound in the interval (1.52,5/3).We tighten this bound when the machine speed ratio is small or m=2.Furthermore,we present a linear compound algorithm QLC with a worst case bound of 6/5 for a two-machine system.
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(Hausdorff dimension of cutset of complex valued Rademacher series)
Min WU
Acta Mathematicae Applicatae Sinica(English Series)    2000, 16 (2): 140-148.  
Abstract12)      PDF(pc) (314KB)(248)       Save
Cutsets of series form an important class of fractal sets.In this paper,the author obtains the Hausdoff dimension of cutset of complex valued Rademacher series
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(Hausdorff dimension of cutset of complex valued Rademacher series)
Min WU
Acta Mathematicae Applicatae Sinica(English Series)    2000, 16 (2): 140-148.  
Abstract437)      PDF(pc) (314KB)(327)       Save
Cutsets of series form an important class of fractal sets.In this paper,the author obtains the Hausdoff dimension of cutset of complex valued Rademacher series
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(Functional law of iterated logarithm for additive functionals of reversible Markov processes)
Li Ming WU
Acta Mathematicae Applicatae Sinica(English Series)    2000, 16 (2): 149-161.  
Abstract6)      PDF(pc) (582KB)(253)       Save
Using the forward-backward martingale decomposition and the martingale limit theorems,we establish the functional law of iterated logarithm for an additive functional (A_t) of a reversible Markov process,under the minimal condition that σ~2(A)=(lim)〖DD(X〗t→∞〖DD)〗EA~2_t/t exists in R.We extend also the previous remarkable functional central limit theorem of Kipnis and Varadhan.
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(Functional law of iterated logarithm for additive functionals of reversible Markov processes)
Li Ming WU
Acta Mathematicae Applicatae Sinica(English Series)    2000, 16 (2): 149-161.  
Abstract624)      PDF(pc) (582KB)(408)       Save
Using the forward-backward martingale decomposition and the martingale limit theorems,we establish the functional law of iterated logarithm for an additive functional (A_t) of a reversible Markov process,under the minimal condition that σ~2(A)=(lim)〖DD(X〗t→∞〖DD)〗EA~2_t/t exists in R.We extend also the previous remarkable functional central limit theorem of Kipnis and Varadhan.
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(Improved estimation of the generalized precision under the entropy loss)
Xiao Qian SUN, Yun Jia PENG
Acta Mathematicae Applicatae Sinica(English Series)    2000, 16 (2): 162-170.  
Abstract841)      PDF(pc) (422KB)(323)       Save
Let X_1,…,X_n be a random sample from multivariate normal distribution N_p(μ,Σ),where μ∈R~p and Σ is a positive definite matrix,both μ and Σ being unknown.It is shown that for the entropy loss L(δ,|Σ|~(-1))=δ/|Σ|~(-1)-log(δ/|Σ|~(-1))-1,the best affine equivariant estimator of the generalized precision |Σ|~(-1) is inadmissible and three classes of improved estimators are given.
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(Improved estimation of the generalized precision under the entropy loss)
Xiao Qian SUN, Yun Jia PENG
Acta Mathematicae Applicatae Sinica(English Series)    2000, 16 (2): 162-170.  
Abstract894)      PDF(pc) (422KB)(126)       Save
Let X_1,…,X_n be a random sample from multivariate normal distribution N_p(μ,Σ),where μ∈R~p and Σ is a positive definite matrix,both μ and Σ being unknown.It is shown that for the entropy loss L(δ,|Σ|~(-1))=δ/|Σ|~(-1)-log(δ/|Σ|~(-1))-1,the best affine equivariant estimator of the generalized precision |Σ|~(-1) is inadmissible and three classes of improved estimators are given.
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(A primal-dual interior point method for parametric semidefinite programming problems)
Zhe Min WANG, Kun Ping ZNOU, Zheng Hai HUANG
Acta Mathematicae Applicatae Sinica(English Series)    2000, 16 (2): 171-179.  
Abstract0)      PDF(pc) (432KB)(235)       Save
On the basis of primal-dual approach,we present in this paper an interior point method that gives parametric ε-approximate solutions to parametric semi-definite programming problems.The method is finite,and the number of its iterations is quasi-polynomially bounded.
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(A primal-dual interior point method for parametric semidefinite programming problems)
Zhe Min WANG, Kun Ping ZNOU, Zheng Hai HUANG
Acta Mathematicae Applicatae Sinica(English Series)    2000, 16 (2): 171-179.  
Abstract778)      PDF(pc) (432KB)(277)       Save
On the basis of primal-dual approach,we present in this paper an interior point method that gives parametric ε-approximate solutions to parametric semi-definite programming problems.The method is finite,and the number of its iterations is quasi-polynomially bounded.
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