中国科学院数学与系统科学研究院期刊网

15 June 2002, Volume 45 Issue 6
    

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  • Temuer CHAOLU(1),Xiao Shan GAO
    Acta Mathematica Sinica, Chinese Series. 2002, 45(6): 1041-105. https://doi.org/10.12386/A2002sxxb0135
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    Abstract The relationship between nearly differential characteristic set and differential characterstic set of differential polynomial systems is investigated and the result that under some conditions the nearly differential characteristic set of differential polyno-mial system can be Wu's differential characteristic set is proved. So the characteristic set theory (Wu's method) of differential polynomial system is modified and the algo-rithm thus established greatly increases the efficiency of computation of differential characteristic set.
  • Shi Kun WANG,Di ZHAO
    Acta Mathematica Sinica, Chinese Series. 2002, 45(6): 1051-105. https://doi.org/10.12386/A2002sxxb0136
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    Abstract By introducing a pseudo-distance function on compact Riemann surfaces, we give a new type of Hadamard theorem.
  • Qing Liu YAO
    Acta Mathematica Sinica, Chinese Series. 2002, 45(6): 1057-106. https://doi.org/10.12386/A2002sxxb0137
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    Abstract The existence, nonexistence and multiplicity of positive solutions for a class of second-order three-point nonlinear boundary value problems are considered by using the Krasnosel'skii fixed point theorem of cone expansion-compression type.
  • Jing Hua YANG(1),Wen Ting TONG
    Acta Mathematica Sinica, Chinese Series. 2002, 45(6): 1065-106. https://doi.org/10.12386/A2002sxxb0138
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    Abstract In this paper, we investigate the difference between PS-ring and nonsingular ring, and obtain a formula of the homological dimensions.
  • Xian Bo ZHOU(1),Wei LIN(2)
    Acta Mathematica Sinica, Chinese Series. 2002, 45(6): 1069-107. https://doi.org/10.12386/A2002sxxb0139
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    Abstract In this paper, a formula for the Sobolev regularity index of scaling functions is given. It is proved that among the four-coefficient orthogonal filters the regularity of D4 wavelet is optimal. For the biorthogonal filters associated with B-spline functions, we increase the regularity of dual wavelets by using the lifting scheme.Keywords Wavelet regularity; Sobolev regularity index; Four-coefficient filters; Lifting scheme
  • Yao Chen ZHU
    Acta Mathematica Sinica, Chinese Series. 2002, 45(6): 1079-108. https://doi.org/10.12386/A2002sxxb0140
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    Abstract In the present note the algebraic independence of values of certain trigono-metric series in C with algebraic coefficients and of their derivatives at algebraic points is studied.
  • Jin Qing ZHANG
    Acta Mathematica Sinica, Chinese Series. 2002, 45(6): 1087-109. https://doi.org/10.12386/A2002sxxb0141
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    Abstract In this paper, we obtain several new fixed point theorems for discontinuous increasing operators in a wider Banach space than C[I, E] for a Banach space E. As applications, we investigate the existence of maximal and minimal solutions of nonlinear impulsive integral equations and differential equations with discontinuous terms in Banach spaces.
  • Ji Gen PENG,Zong Beng XU
    Acta Mathematica Sinica, Chinese Series. 2002, 45(6): 1099-110. https://doi.org/10.12386/A2002sxxb0142
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    Abstract This paper is concerned with the asymptotic behaviors of nonlinear semi-group of Lipschitz operators. A series of basic properties similar to those of linear semigroups are characterized. It is shown that the Dahlquist constant, which is a non-linear extension of logarithmic norm of a bounded linear operator, can be applied to characterize the asymptotic behaviours of nonlinear semigroup of Lipschitz operators. Moreover, in order to characterize the asymptotic behaviours of nonlinear semigroups much better, a novel quantity of nonlinear operator, named the generalized Dahlquist constant, is defined. Unlike Dahlqust constant only defined for Lipschitz operator, this new quantity can be defined well for nonlinear operator. As an application, a new result on global exponential stability of Hopfield-type neural networks is proved.
  • Zhong Kui LIU
    Acta Mathematica Sinica, Chinese Series. 2002, 45(6): 1107-111. https://doi.org/10.12386/A2002sxxb0143
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    Abstract A ring R is called right principally quasi-Baer (or simply right p.q.Baer) if the right annihilator of every principal right ideal of R is generated by an idempotent. It is shown that for a ring R with SJ(R)(?)C(R), R[[x, x-1]] is right p.q.Baer if and only if R is right p.q.Baer and any countable family of idempotents in R has a generalized join in I(R). It is also shown that a ring R is right p.q.Baer if and only if R[x, x-1] is right p.q.Baer.
  • Jin Lin SHI
    Acta Mathematica Sinica, Chinese Series. 2002, 45(6): 1113-112. https://doi.org/10.12386/A2002sxxb0144
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    Abstract Up to now, researches is the smooth linearization of differential equations have been restricted to a small neighborhood of the origin. A result of global smooth linearization is presented in this paper. The premise of the global topological lineariza-tion (the global smooth linearization) is that the existent domain of any solution is the whole real axis. So, this paper also discusses the generalization of the Wintner Theorem,
  • Qi Sheng LI(1),Wen Ting TONG(2
    Acta Mathematica Sinica, Chinese Series. 2002, 45(6): 1121-112. https://doi.org/10.12386/A2002sxxb0145
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    Abstract This paper studies weak cancellation of modules and weakly stable range condition of exchange rings, and some new charaterizations for the wsrl condition are given. For a module M with finite exchange property, it is shown that M satisfies outer weak cancellation if and only if M satisfies inner weak cancellation, which is also equivalent to that EndR(M) satisfies the wsrl condition.
  • Fu Gui SHI(1),Chong You ZHENG(
    Acta Mathematica Sinica, Chinese Series. 2002, 45(6): 1127-113. https://doi.org/10.12386/A2002sxxb0146
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    Abstract In this paper, some brief characterizations of pointwise uniformities on lattices are presented by means of remote-neighborhood mappings. A few pointwise metrization theorems are proved. Some separation axioms which are consistent with pointwise metric theorem are given.
  • Jin Bao JIAN(1),Yan Lian LAI(2
    Acta Mathematica Sinica, Chinese Series. 2002, 45(6): 1137-114. https://doi.org/10.12386/A2002sxxb0147
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    Abstract In this paper, inequality constrained programming problems are discussed, based on a combination technique of a system of linear equations and an auxiliary direction, a new feasible algorithm is presented, where the step size is found by a new line search. Under suitable conditions, only one system of linear equations needs to be solved for finding the direction dk when k is large enough. The algorithm isproved to possess global convergence, rate of superlinear convergence and quadratical convergence. Some preliminary numerical results are reported.
  • Xiao Hong FU
    Acta Mathematica Sinica, Chinese Series. 2002, 45(6): 1147-114. https://doi.org/10.12386/A2002sxxb0148
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    Abstract In this paper, we point out that in [1] the assumption of 1-Lipschitz on the unit sphere S1(H) can be replaced with a "locally 1-Lipschitz mapping".
  • Xiao Xia ZHANG(1),Lun Chuan ZH
    Acta Mathematica Sinica, Chinese Series. 2002, 45(6): 1149-115. https://doi.org/10.12386/A2002sxxb0149
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    Abstract Let G = (A, A) be a compact matrix quantum group, G the equivalent set of all finite, smooth, irreducible corepresentations of A. In this paper, via a special corepresentation V0 of A, we construct a pair of sets, and using the theory of Hilbert C*-module, we prove that they are exactly A and A respectively, where A corresponds to Baaj and Skandalis-construction. We also prove that for any a ? G there exists a projective operator pa in A such that dim(α) = dim(pα).
  • Shou LIN(1),You Cheng ZHOU(2),
    Acta Mathematica Sinica, Chinese Series. 2002, 45(6): 1157-116. https://doi.org/10.12386/A2002sxxb0150
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    Abstract In this paper we use the concept of point-star networks, discuss some proper-ties of π-images of metric spaces, establish the characterizations of sequentially quotient π-images and sequence-coveringπ-images of metric spaces, and generalize some corresponding results of Kofner J. A. and Tanaka Y.
  • Jie XIN,Jia Yun ZHOU
    Acta Mathematica Sinica, Chinese Series. 2002, 45(6): 1165-117. https://doi.org/10.12386/A2002sxxb0151
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    Abstract In this paper, we study perturbation and stability of frames and atomic decompositions for Banach spaces by utilizing the theory of frames, and improve on and generalize the results in [5] and [6].
  • Fang Gui WANG
    Acta Mathematica Sinica, Chinese Series. 2002, 45(6): 1171-117. https://doi.org/10.12386/A2002sxxb0152
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    Abstract In this note, we prove that if R is a reduced ring and A = R[T]/fR[T] is a finitely generated R-module, then f is a normal polynomial. Moreover, if R is connected, then the leading coefficient of / is a unit. It is also proved that a coherent connected ring with finite weak global dimension is a domain.
  • Yan Juan DENG(1),Hui Li LIU(2)
    Acta Mathematica Sinica, Chinese Series. 2002, 45(6): 1177-118. https://doi.org/10.12386/A2002sxxb0153
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    Abstract In this paper, we construct some 1-parameter families of rotation surfaces with constant mean curvature in a 3-dimensional Anti-de Sitter space.
  • Fu Cai LI,Chun Hong XIE
    Acta Mathematica Sinica, Chinese Series. 2002, 45(6): 1185-119. https://doi.org/10.12386/A2002sxxb0154
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    Abstract In this paper, a semi-linear reaction diffusion system with nonlocal source is considered, and existence and uniqueness of the classical solution are proved by establishing a comparison theorem and employing the Schauder fixed point theorem. The blow-up set and asymptotic behavior of solution are also obtained.
  • Yue Zhu WU(1),Dao Ji MENG(2)
    Acta Mathematica Sinica, Chinese Series. 2002, 45(6): 1197-120. https://doi.org/10.12386/A2002sxxb0155
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    Abstract Let L be a finite dimensional Lie algebra with a finite number of ideals over the complex number field. The paper obtains the struture of L. And the paper studies the Lie algebra L such that L = S + Cr + N, [S,r] = 0: When N is abelian, the sufficient and necessary conditions under which L has a finite number of ideals are found; when N is a Heisenberg algebra or metabelian algebra, the paper simplifies the problem to the case where N is abelian.
  • Jin Fa CHEN(1),Z. ANNIE(2)
    Acta Mathematica Sinica, Chinese Series. 2002, 45(6): 1207-121. https://doi.org/10.12386/A2002sxxb0156
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    Abstract In this article, we study the mth order neutral functional difference equations of mixed type: Am (xn + cxn-h + c*xn+h*) = k(qxn∧g + pxn+g*), k =±1. Where c,c*,p,q are real numbers and h,h*,g and g* are positive integer, and establish some new criteria for the oscillation of such equations. Our results in this paper improve on all theorems in [1], and answer an open problem offered by Grace S. R. in [1].
  • Zhi Shan DONG(1),Xiao Yun YANG
    Acta Mathematica Sinica, Chinese Series. 2002, 45(6): 1213-122. https://doi.org/10.12386/A2002sxxb0157
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    Abstract In this article, we give the sufficient conditions for the NA random variables without stationary distribution to satisfy the law of iterated logarithm and the law of large numbers. The proof is based on the maximal moment inequality and probability inequality provided by Shao.
  • Zi Qiu YUN
    Acta Mathematica Sinica, Chinese Series. 2002, 45(6): 1221-122. https://doi.org/10.12386/A2002sxxb0158
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    Abstract In this paper, we give a canonical example of sequential space whose sequen-tial order is greater than n. As applications, some results about sequential order of product spaces of sequential spaces are obtained.
  • Lu LIN
    Acta Mathematica Sinica, Chinese Series. 2002, 45(6): 1227-123. https://doi.org/10.12386/A2002sxxb0159
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    Abstract It is well known that the recent theory on seemingly unrelated statistical sys-tems focuses mainly on linear regression systems. In this paper, we originate a Bayes quasi-likelihood with auxiliary information in some seemingly unrelated nonlinear re-gression systems. The method for iteratively adding related error information and prior information to an estimator is obtained. The optimal properties of its score function and parameter estimation based on the Bayes risk are discussed. It is shown that the asymptotic Bayes risk of Bayes quasi-likelihood estimation with auxiliary information decreases gradually with the increase of auxiliary information.