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.
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.
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)〗|≠SE,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.
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)〗|≠SE,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.
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.
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.
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.
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.
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
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
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.