15 April 2001, Volume 17 Issue 4
    

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  • 论文
    (Percentage points and power of a K-S type test for linearity in autoregressive time series
    Min CHEN, Guo Fu WU
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(4): 433-442.
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    The empirical upper percentage points of the null distribution of a Kolmogorov-Smirnov type test for checking linearity in autoregressive models are tabulated in this paper,and the good power property of the test is demonstrated.
  • Original Articles
    (Percentage points and power of a K-S type test for linearity in autoregressive time series
    Min CHEN, Guo Fu WU
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(4): 433-442.
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    The empirical upper percentage points of the null distribution of a Kolmogorov-Smirnov type test for checking linearity in autoregressive models are tabulated in this paper,and the good power property of the test is demonstrated.
  • 论文
    On the edge-binding number of some plane graphs
    Lin ZHong LIU, Zhong Fu ZHANG, Jian Fang Wang
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(4): 443-448.
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    Let G(V) be a simple graph,the edge-binding number b_1(G) of G is defined as b_1(G)=min〖JB({〗〖SX(〗|N(S)|〖〗|S|〖SX)〗|≠SE,N(S)≠E〖JB)}〗,where N(S) denotes the adjacent edges set of S.In this paper,we obtained the edge-binding number of outer plane graphs,Halin graph and tree.
  • Original Articles
    On the edge-binding number of some plane graphs
    Lin ZHong LIU, Zhong Fu ZHANG, Jian Fang Wang
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(4): 443-448.
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    Let G(V) be a simple graph,the edge-binding number b_1(G) of G is defined as b_1(G)=min〖JB({〗〖SX(〗|N(S)|〖〗|S|〖SX)〗|≠SE,N(S)≠E〖JB)}〗,where N(S) denotes the adjacent edges set of S.In this paper,we obtained the edge-binding number of outer plane graphs,Halin graph and tree.
  • 论文
    Comparison of variance estimators for the ratio estimator based on small sample)
    Huai Zhen QIN, Li Li LI
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(4): 449-456.
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    This paper sheds light on an open problem put forward by Cochran.The comparison between two commonly used variance estimators v_1(〖AKR∧〗) and v_2(〖AKR∧〗) of the ratio estimator 〖AKR∧〗 for population ratio R from small sample selected by simple random sampling is made following the idea of the estimated loss approach (See [2]).Considering the superpopulation model under which the ratio estimator (〖AKY-〗)〖DD(〗∧〖DD)〗_R for population mean 〖AKY-〗 is the best linear unbised one,the necessary and sufficient conditions for v_1(〖AKR∧〗)〖DD(〗u〖DD)〗v_2(〖AKR∧〗) and v_2(〖AKR∧〗)〖DD(〗u〖DD)〗v_1(〖AKR∧〗) are obtained with ignored the sampling fraction f.For a substantial f,several rigorous sufficient conditions for v_2(〖AKR∧〗)〖DD(〗u〖DD)〗v_1(〖AKR∧〗) are derived.
  • Original Articles
    Comparison of variance estimators for the ratio estimator based on small sample)
    Huai Zhen QIN, Li Li LI
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(4): 449-456.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    This paper sheds light on an open problem put forward by Cochran.The comparison between two commonly used variance estimators v_1(〖AKR∧〗) and v_2(〖AKR∧〗) of the ratio estimator 〖AKR∧〗 for population ratio R from small sample selected by simple random sampling is made following the idea of the estimated loss approach (See [2]).Considering the superpopulation model under which the ratio estimator (〖AKY-〗)〖DD(〗∧〖DD)〗_R for population mean 〖AKY-〗 is the best linear unbised one,the necessary and sufficient conditions for v_1(〖AKR∧〗)〖DD(〗u〖DD)〗v_2(〖AKR∧〗) and v_2(〖AKR∧〗)〖DD(〗u〖DD)〗v_1(〖AKR∧〗) are obtained with ignored the sampling fraction f.For a substantial f,several rigorous sufficient conditions for v_2(〖AKR∧〗)〖DD(〗u〖DD)〗v_1(〖AKR∧〗) are derived.
  • 论文
    (Estimating hazard ratios in nested case-control studies by Mantel-Haenszel method)
    Zhong Zhan ZHANG
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(4): 457-468.
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    In this article,a class of Mantel-Haenszel type estimators of hazard ratios in proportional hazards model is presented for simple nested case-control study.The estimators have the form of the Mantel-Haenszel estimator of odds ratios,and it is shown that the estimators are dually consistent,and asymptotically normal.Dually consistently estimated covariance matrices of the proposed estimators are also developed.An example is given to illustrate the estimators.
  • Original Articles
    (Estimating hazard ratios in nested case-control studies by Mantel-Haenszel method)
    Zhong Zhan ZHANG
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(4): 457-468.
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    In this article,a class of Mantel-Haenszel type estimators of hazard ratios in proportional hazards model is presented for simple nested case-control study.The estimators have the form of the Mantel-Haenszel estimator of odds ratios,and it is shown that the estimators are dually consistent,and asymptotically normal.Dually consistently estimated covariance matrices of the proposed estimators are also developed.An example is given to illustrate the estimators.
  • 论文
    A class of nonlocal singularly perturbed problems for nonlinear hyperbolic differential equation
    Jia Qi MO
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(4): 469-475.
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    The nonlocal singularly perturbed problems for the hyperbolic differential equation are considered.Under suitable conditions,using the fixed point theorem,the asymptotic behavior of solution for the initial boundary value problems is studied
  • Original Articles
    A class of nonlocal singularly perturbed problems for nonlinear hyperbolic differential equation
    Jia Qi MO
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(4): 469-475.
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    The nonlocal singularly perturbed problems for the hyperbolic differential equation are considered.Under suitable conditions,using the fixed point theorem,the asymptotic behavior of solution for the initial boundary value problems is studied
  • Original Articles
    On generalized Hamiltonian systems
    Dai Zhan CHENG, Xie Wei MIN, Li Zhi LIAO, Da Yong CAI
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(4): 475-483.
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    The purpose of this paper is to explore an extension of some fundamental properties of the Hamiltonian systems to a more general case.We first extend symplectic group to a general N-group,G_N,and prove that it has certain similar properties.A particular property of G_N is that as a Lie group dim(G_N)≥1.Certain properties of its Lie-algebra g_N are investigated.The results obtained are used to investigate the structure-preserving systems,which generalize the property of symplectic form preserving of Hamiltonian system to a covariant tensor field preserving of certain dynamic systems.The results provide a theoretical benchmark of applying symplectic algorithm to a considerably larger class of structure-preserving systems.
  • 论文
    On generalized Hamiltonian systems
    Dai Zhan CHENG, Xie Wei MIN, Li Zhi LIAO, Da Yong CAI
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(4): 475-483.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    The purpose of this paper is to explore an extension of some fundamental properties of the Hamiltonian systems to a more general case.We first extend symplectic group to a general N-group,G_N,and prove that it has certain similar properties.A particular property of G_N is that as a Lie group dim(G_N)≥1.Certain properties of its Lie-algebra g_N are investigated.The results obtained are used to investigate the structure-preserving systems,which generalize the property of symplectic form preserving of Hamiltonian system to a covariant tensor field preserving of certain dynamic systems.The results provide a theoretical benchmark of applying symplectic algorithm to a considerably larger class of structure-preserving systems.
  • 论文
    Exponential attractors of the Ginzburg-Landau-BBM equations in an unbounded domain
    Zheng De DAI, Mu Rong JIANG
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(4): 484-493.
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    In this paper,the existence of the exponential attractors for the Ginzburg-Landau-BBM equations in an unbounded domain is proved by using weighted function and squeezing property.
  • Original Articles
    Exponential attractors of the Ginzburg-Landau-BBM equations in an unbounded domain
    Zheng De DAI, Mu Rong JIANG
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(4): 484-493.
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    In this paper,the existence of the exponential attractors for the Ginzburg-Landau-BBM equations in an unbounded domain is proved by using weighted function and squeezing property.
  • 论文
    A fixed-parameter-tractable algorithm for set packing
    Chuan Lin ZHANG , Wei Jia JIA , Jian Er CHEN
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(4): 494-502.
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    The PARAMETERIZED SET PACKING problem asks,for an input consisting of a collection C of n finite sets with |c|≤m for any c∈C and a positive integer k,whether C contains at least k mutually disjoint sets.We give a fixed-parameter-tractable algorithm for this problem that runs in times ○(f(k,m)+g(k,m)n),where f(k,m)=(m－2)〖KF(〗m－1〖KF)〗k~4〖JB([〗〖SX(〗k~(m－2)(m－1)~(m－1)b_m〖〗e~(m－2)〖SX)〗〖JB)]〗~k,g(k,m)=(m+1)(m－2)k〖KF(〗m－1〖KF)〗〖JB([〗〖SX(〗k~(m－2)(m－1)~(m－1)b_m〖〗e~(m－2)〖SX)〗〖JB)]〗~k+m,where,b_m is the minimal positive root of m-degree equation x~m=∑〖DD(〗m－1〖〗i=1〖DD)〗(〖SX(B〗m〖〗i〖SX)〗)x~(m－i) and e=∑〖DD(〗+∞〖〗i=0〖DD)〗〖SX(〗1〖〗i!〖SX)〗=2.7182818.In particular,this gives an ○(k~4(5.7k)~k+[k(5.7k)~k+3]n) algorithm to construct mutually k disjoint sets if {c}≤3 for any c∈C.
  • Original Articles
    A fixed-parameter-tractable algorithm for set packing
    Chuan Lin ZHANG , Wei Jia JIA , Jian Er CHEN
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(4): 494-502.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    The PARAMETERIZED SET PACKING problem asks,for an input consisting of a collection C of n finite sets with |c|≤m for any c∈C and a positive integer k,whether C contains at least k mutually disjoint sets.We give a fixed-parameter-tractable algorithm for this problem that runs in times ○(f(k,m)+g(k,m)n),where f(k,m)=(m－2)〖KF(〗m－1〖KF)〗k~4〖JB([〗〖SX(〗k~(m－2)(m－1)~(m－1)b_m〖〗e~(m－2)〖SX)〗〖JB)]〗~k,g(k,m)=(m+1)(m－2)k〖KF(〗m－1〖KF)〗〖JB([〗〖SX(〗k~(m－2)(m－1)~(m－1)b_m〖〗e~(m－2)〖SX)〗〖JB)]〗~k+m,where,b_m is the minimal positive root of m-degree equation x~m=∑〖DD(〗m－1〖〗i=1〖DD)〗(〖SX(B〗m〖〗i〖SX)〗)x~(m－i) and e=∑〖DD(〗+∞〖〗i=0〖DD)〗〖SX(〗1〖〗i!〖SX)〗=2.7182818.In particular,this gives an ○(k~4(5.7k)~k+[k(5.7k)~k+3]n) algorithm to construct mutually k disjoint sets if {c}≤3 for any c∈C.
  • 论文
    Subspace subcodes of generalized Reed-Solomon codes
    Jie CUI , Jun Ying PEI
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(4): 503-508.
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    In this paper,the subspace subcodes of generalized Reed-Solomon codes are introduced and the fomulas to compute the dimensions of these codes are given.
  • Original Articles
    Subspace subcodes of generalized Reed-Solomon codes
    Jie CUI , Jun Ying PEI
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(4): 503-508.
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    In this paper,the subspace subcodes of generalized Reed-Solomon codes are introduced and the fomulas to compute the dimensions of these codes are given.
  • 论文
    Some extremal properties of the integral of Legendre polynomials
    Ying Guang SHI, Zi Yu Wang
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(4): 509-516.
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    Some extremal properties of the integral of Legendre polynomials are given,which are of independent interest.Meanwhile they show that a conjecture of P.Erd〖AKo¨〗s(1995) is plausible and maybe provides some means to prove this conjecture.
  • Original Articles
    Some extremal properties of the integral of Legendre polynomials
    Ying Guang SHI, Zi Yu Wang
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(4): 509-516.
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    Some extremal properties of the integral of Legendre polynomials are given,which are of independent interest.Meanwhile they show that a conjecture of P.Erd〖AKo¨〗s(1995) is plausible and maybe provides some means to prove this conjecture.
  • 论文
    A note on finite element wavelets
    Qiu Hui Shen , Han Lin CHEN
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(4): 517-525.
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    The main purpose of this note is to make a correction of the error in the main result of [1].These coefficients are very important for the properties of wavelets,such as vanishing moments and regularity.
  • Original Articles
    A note on finite element wavelets
    Qiu Hui Shen , Han Lin CHEN
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(4): 517-525.
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    The main purpose of this note is to make a correction of the error in the main result of [1].These coefficients are very important for the properties of wavelets,such as vanishing moments and regularity.
  • 论文
    (On the convergence of sequential number-theoretic method for optimization)
    Yao Chen Zhu
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(4): 532-538.
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    In the present note the convergence problem of the sequential number-theoretic method for optimization proposed by Fang and Wang is studied,the convergence criteria and the estimation of errors concerning this algorithm are given.
  • 论文
    (On the convergence of sequential number-theoretic method for optimization)
    Yao Chen Zhu
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(4): 532-538.
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    In the present note the convergence problem of the sequential number-theoretic method for optimization proposed by Fang and Wang is studied,the convergence criteria and the estimation of errors concerning this algorithm are given.
  • Original Articles
    (On the convergence of sequential number-theoretic method for optimization)
    Yao Chen Zhu
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(4): 532-538.
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    In the present note the convergence problem of the sequential number-theoretic method for optimization proposed by Fang and Wang is studied,the convergence criteria and the estimation of errors concerning this algorithm are given.
  • Original Articles
    (On the convergence of sequential number-theoretic method for optimization)
    Yao Chen Zhu
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(4): 532-538.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In the present note the convergence problem of the sequential number-theoretic method for optimization proposed by Fang and Wang is studied,the convergence criteria and the estimation of errors concerning this algorithm are given.
  • 论文
    Model selection for canonical correlation analysis
    Lin Cheng ZHAO, Li Min Peng , Yao Hua WU
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(4): 539-549.
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    In this paper,we study a general criterion for estimating the rank of canonical correlation matrix (CCM).Besides the strong consistency,we give the exponential-type bounds under certain conditions on the probability of wrong detection of the rank of CCM.On the basis of this criterion,we give two methods to determine the multiplicities of canonical correlation coefficients.And the strong consistency of them is established.
  • Original Articles
    Model selection for canonical correlation analysis
    Lin Cheng ZHAO, Li Min Peng , Yao Hua WU
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(4): 539-549.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper,we study a general criterion for estimating the rank of canonical correlation matrix (CCM).Besides the strong consistency,we give the exponential-type bounds under certain conditions on the probability of wrong detection of the rank of CCM.On the basis of this criterion,we give two methods to determine the multiplicities of canonical correlation coefficients.And the strong consistency of them is established.
  • 论文
    Completely positive matrices of order five
    Chang Qing XU
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(4): 550-562.
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    This paper gives an effective criterion for any doubly nonnegative matrix A of order 5 whose associated graph is isomorphic neither to K_5 (the complete graph) nor to K_5－e (a subgraph of K_5 obtained by cutting off an edge from it) to be completely positive.
  • Original Articles
    Completely positive matrices of order five
    Chang Qing XU
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(4): 550-562.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    This paper gives an effective criterion for any doubly nonnegative matrix A of order 5 whose associated graph is isomorphic neither to K_5 (the complete graph) nor to K_5－e (a subgraph of K_5 obtained by cutting off an edge from it) to be completely positive.
  • 论文
    Hamiltonian decomposition of complete bipartite r-hypergraphs
    Jirimutu , Jian Fang WANG
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(4): 563-566.
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    In this paper,we give the concepts for bipergraph and Hamiltonian paths and cycles of a hypergraph,and prove that the complete bipartite 3-hypergraph with q vertices in each part is Hamiltonian decomposable where q is a prime.
  • Original Articles
    Hamiltonian decomposition of complete bipartite r-hypergraphs
    Jirimutu , Jian Fang WANG
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(4): 563-566.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper,we give the concepts for bipergraph and Hamiltonian paths and cycles of a hypergraph,and prove that the complete bipartite 3-hypergraph with q vertices in each part is Hamiltonian decomposable where q is a prime.
  • 论文
    Enumeration of maps on the projective plane
    Rong Xia HAO, Jun Liang CAI , Yan Pei LIU
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(4): 567-573.
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    The enumerative functional equation of maps by the number of inner faces,the valency of root face and the number of non-rooted vertices on the projective plane is studied.An explicit expression for the generating function by the number of inner faces and the number of non-rooted vertices is obtained.From this result,the enumeration of rooted maps by the number of edges discussed in [1] is obtained as a corollary.
  • Original Articles
    Enumeration of maps on the projective plane
    Rong Xia HAO, Jun Liang CAI , Yan Pei LIU
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(4): 567-573.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    The enumerative functional equation of maps by the number of inner faces,the valency of root face and the number of non-rooted vertices on the projective plane is studied.An explicit expression for the generating function by the number of inner faces and the number of non-rooted vertices is obtained.From this result,the enumeration of rooted maps by the number of edges discussed in [1] is obtained as a corollary.
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