中国科学院数学与系统科学研究院期刊网

01 April 1998, Volume 41 Issue 3
    

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  • JiXiang Chen
    Acta Mathematica Sinica, Chinese Series. 1998, 41(3): . https://doi.org/10.12386/A1998sxxb0120
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    K.A. Hardie and K.H. Kamps investigated the track homotopy category H B over a fixed space B (). They have introduced two pairs of adjoint functors: P B┤N B and m *┤m *, where P B: H BH B and m *:H AH B for a fixed map m: AB. We have introduced a split fibration of categories L:H bH B and proved L┤J, J┤L in . This paper firstly extends P B┤N B to P b *┤N Bb # for any fixed map b: B. Moreover we also extend these results to obtain two pairs of adjoint functors involving track homotopy categories H b and H b where H b is the dual of H b.One of our results is N b┤P b. This differs from P B┤N B.
  • GuangWen Zhai
    Acta Mathematica Sinica, Chinese Series. 1998, 41(3): . https://doi.org/10.12386/A1998sxxb0121
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    In this paper we study the hybrid problem of the Waring Goldbach problem (k=2 ) and the Piatetski Shapiro prime number theorem, thus deepen the classical result of Hua Luokeng.
  • TongSuo Wu
    Acta Mathematica Sinica, Chinese Series. 1998, 41(3): . https://doi.org/10.12386/A1998sxxb0119
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    In this paper, we study endomorphism rings of regular modules. Sufficient conditions are given to P such that  End R(P) has one in it′s stable range.
  • YuePing Jiang
    Acta Mathematica Sinica, Chinese Series. 1998, 41(3): . https://doi.org/10.12386/A1998sxxb0118
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    The discrete criterion of any non elementary Mbius groups in several dimensions is given by using the generalised Jrgensen's inequality.
  • HongYun Xiong,XiMin Rong
    Acta Mathematica Sinica, Chinese Series. 1998, 41(3): . https://doi.org/10.12386/A1998sxxb0092
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    Let {E i:i∈I} be a family of Archimedean Riesz spaces. The Riesz product space is denoted by  Π i∈IE i . The main result in this paper is the following conclusion: there exists a completely regular Hausdorff space X such that  Π i∈IE i  is Riesz isomorphic to C(X) if and only if for every i∈I there exists a completely regular Hausdorff space X i  such that E i  is Riesz isomorphic to C(X i ).
  • LiPing Huang
    Acta Mathematica Sinica, Chinese Series. 1998, 41(3): . https://doi.org/10.12386/A1998sxxb0093
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    Let H F be the generalized quaternion division algebra over a field F with  char F≠2. By using the adjoint matrix and the method of repersentation matrix, this paper obtains several necessary and sufficient conditions for existence of a solution or a unique solution to the matrix equation ki=0A iXB i=E over H F, and gives some explicit formulas of solutions.
  • AiNong Fang
    Acta Mathematica Sinica, Chinese Series. 1998, 41(3): . https://doi.org/10.12386/A1998sxxb0094
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    In this paper, a distortion theorem and some equicontinuity and compactness theorems are obtained for the homeomorphism f with the sphere dilatation H(x,f)∈L loc (D).
  • EnHao Yang
    Acta Mathematica Sinica, Chinese Series. 1998, 41(3): . https://doi.org/10.12386/A1998sxxb0096
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    Nonlinear integral and discrete inequalities are obtained which related to some recent generalizations of Ou Iang integral inequality given by B.G. Pachpatte in . As special cases some new inequalities with the power nonlinearity are derived from our main results. To convey the usefulness of the results obtained, boundedness of solutions to a certain nonlinear difference equation is also discussed.
  • ZongMing Guo,ZuoDong Yang

    FanPing Zeng
    Acta Mathematica Sinica, Chinese Series. 1998, 41(3): . https://doi.org/10.12386/A1998sxxb0099
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    Let P and AC be two primary sequences with  min {P,AC}RLR ∞, ρ(P) and ρ(AC) be the eigenvalues of P and AC, respectively. Let f∈C 0(I,I) be a unimodal expanding map with expanding constant λ and m be a nonegative integer. It is proved that f has the kneading sequence K(f)(RC) *m *P if λ(ρ(P)) 1/2 m , and K(f)>(RC) *m * AC*E for any shift maximal sequence E if λ>(ρ(AC)) 1/2 m .The value of (ρ(P)) 1/2 m  or (ρ(AC)) 1/2 m  is the best possible in the sense that the related conclusion may not be true if it is replaced by any smaller one.
  • ChunQin Zhou,YuanDi Wang
    Acta Mathematica Sinica, Chinese Series. 1998, 41(3): . https://doi.org/10.12386/A1998sxxb0100
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    In this paper a weak solution to the heat flow for p harmonic maps are constructed. Nonuniqueness results for such solutions are also given when the first data u 0(x) is a weakly p harmonic map but not a weakly stationary harmonic map.
  • Bo Zhou,BoLian Liu
    Acta Mathematica Sinica, Chinese Series. 1998, 41(3): . https://doi.org/10.12386/A1998sxxb0098
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    Let D n,s (t) be the set of n by n Boolean matrices with s-cycle positive elements on exactly t rows, stn. We derive a upper bound for the convergent indices of matrices in D n,s (t) when s=1 or s is prime. We prove that this upper bound can be attained except the case that t>n-s(n-1)+1/4-3/2, and s and n are not comprime. And we give partial characterizations of the matrices in D n,s (t) whose convergent indices attain this upper bound.
  • ShaoKuan Li
    Acta Mathematica Sinica, Chinese Series. 1998, 41(3): . https://doi.org/10.12386/A1998sxxb0105
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    In this paper the conditions for partial matrix can completing invertible operator with one entry of its inverse are specified and all solutions of problem are obtained. The problem of completing invertible self adjoint operator of partial matrix and discussed.
  • ChengKui Zhong(1),Ke Shi(2)
    Acta Mathematica Sinica, Chinese Series. 1998, 41(3): . https://doi.org/10.12386/A1998sxxb0106
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    In this paper, we construct a new index by use of the canonical representation of Z 2×Z 2 group over a product space. This index satisfies the general properties of the usual index, but does not satisfy the dimension property. As an application, we obtain two abstract critical point theorems.
  • Wei He(1),MaoKang Luo(2)
    Acta Mathematica Sinica, Chinese Series. 1998, 41(3): . https://doi.org/10.12386/A1998sxxb0101
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    In this paper, we investigate the zero dimensional property for locales, the main results are following: (1) The pointwise characterization of joins of nuclei in a locale is given, the relationship between compactness of a locale A and compactness of N(A) is obtained.(2) The compact zero dimensional refletion of a zero dimensional localeis obtained in much simple form. (3) The category theory characterization of the category of zero dimensional locales is obtained.
  • PeiYong Zhu
    Acta Mathematica Sinica, Chinese Series. 1998, 41(3): . https://doi.org/10.12386/A1998sxxb0102
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    In this paper, we first prove a group of equivalent characterizations of hereditarily σ metacompact spaces. By the one of characterizations we obtain two Tychonoff product theorems and the theorem on σ product. Finally, we show that the above Tychononoff product theorems do not hold if hereditarily σ metacompact is replaced by σ metacompact.
  • BingRen Li,MinLi Li
    Acta Mathematica Sinica, Chinese Series. 1998, 41(3): . https://doi.org/10.12386/A1998sxxb0103
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    V. Pták has given the detailed discussion for a unital Banach * algebra in . In this paper, we will generalize his results to the general case. In particular, we introduce the concept of a positive linear functional with positive extension, and describe its characterizations.
  • HongQing Chen
    Acta Mathematica Sinica, Chinese Series. 1998, 41(3): . https://doi.org/10.12386/A1998sxxb0104
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    In this paper, we study the oscillations of first order neutral delay differential equations with both positive and negative coefficients of the form d dt [x(t)+px(t-τ)-rx(t-ρ)]+qx(t-s)-hx(t-v)=0where the coefficients and the delays are positive constants. We obtain a necessary and sufficient condition with several changeable parameters and a series of sufficient criteria for the equations and a necessary and sufficient condition in a certain from for the equation to be oscillatory. Some necessary and sufficient conditions and sufficient criteria contain and further improve some corresponding results of the former authors.
  • PingZhi Yuan(1)(2)

    Acta Mathematica Sinica, Chinese Series. 1998, 41(3): . https://doi.org/10.12386/A1998sxxb0107
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    Let d be a positive square free number, h(d) the class number of the field Q(d). In this paper, we prove that: if a,n>2, k>1 are positive integers with 1+4k 2n =da 2 and a<0.9k 25n  or that every prime factor p of n and q of k satisfies (p,q-1)=1. Then h(d)≡0 ( mod n) with the only exception (a,d,k,n)=(5,41,2,4). Meanwhile, we conjecture that the condition (p,q-1)=1 of the above result is not needed.
  • JianJun Deng(1),TiJun Xiao(2),
    Acta Mathematica Sinica, Chinese Series. 1998, 41(3): . https://doi.org/10.12386/A1998sxxb0108
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    In this paper, our main result is that if A is the generator of a holomorphic regularized semigroup, then A is also the generator of some regularized cosine function.
  • YaoTian Shen
    Acta Mathematica Sinica, Chinese Series. 1998, 41(3): . https://doi.org/10.12386/A1998sxxb0116
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    In this paper, we describe the asymptotic behavior, as λ+∞ , of axially symmetric solutions u λ for the problem: u∧(-Δu+λ(u,n)n) =0 , |u|=1 , x∈B 1 and u=(x 1,x 2,0) , x∈B 1 , where B 1 is the unit ball in R 2 , u=(u 1,u 2,u 3) , n=(0,0,1) . We prove here that u λ convergent u ∞ in H 2(B 1\B ε, R 3) .
  • LiBo Luo
    Acta Mathematica Sinica, Chinese Series. 1998, 41(3): . https://doi.org/10.12386/A1998sxxb0117
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    We prove the Vaught's conjecture and obtain a complete classification for unitary selations.
  • NanQing Ding(1),JianLong Chen(
    Acta Mathematica Sinica, Chinese Series. 1998, 41(3): . https://doi.org/10.12386/A1998sxxb0109
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    The purpose of this paper is to give characterizations of relative covers and envelopes. As an application, it is shown that for any ring R , if 0  A  B  C  0 is an exact sequence of left R modules, where both A and C have flat covers, then B has a flat cover.
  • JinQi Li(1),DingGuo Wang(2)
    Acta Mathematica Sinica, Chinese Series. 1998, 41(3): . https://doi.org/10.12386/A1998sxxb0110
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    Tet C, D be coalgebras. This paper show that if C and D are Morita Takeuchi equivalence then the lattice of subcoalgebras of C is isomorphism the lattice of subcoalgebras of D. If the right  Γ  comodules M Γ , N Γ  are quasi finite, then (h - Γ (M,M),h - Γ (N,N);h - Γ (N,M), h - Γ (M,N); f,g) is a Morita Takeuchi context. We give some conditions making the M T context is equivalence. Finally, we give a method to construct M T context from a M T context.
  • YongXiang Li
    Acta Mathematica Sinica, Chinese Series. 1998, 41(3): . https://doi.org/10.12386/A1998sxxb0111
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    In this paper, the supersolution and subsolution method is applied to periodic solution problems for semilinear evolution equations in ordered Banach spaces. The results on the existence of maximal periodic solution and minimal periodic solution are obtained by using the characteristics of positive operators semigroups and the monotone iteration scheme. This paper generalizes and extends the relevant results in ordinary differential equations and partial differential equations.
  • JianCheng Zou
    Acta Mathematica Sinica, Chinese Series. 1998, 41(3): . https://doi.org/10.12386/A1998sxxb0115
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    A new framework is set up to study the stability of bifurcation problems using Wassermann's idea of (r,s) stability in singularity theory. Transversality conditions are used to characterize the stability
  • XiGeng Chen(1),MaoHua Le(2)
    Acta Mathematica Sinica, Chinese Series. 1998, 41(3): . https://doi.org/10.12386/A1998sxxb0112
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    Let n be a positive integer. In this paper, under the assumption of the generalized Riemann conjecture, we prove that if and only if n =1,2,4,6,10,18,22,30,42,58, 70,78,102,130,190,210,330,462, then the equation xy+yz+zx=n has no positive integer solution (x,y,z) .
  • ZhongLi Wei

    Acta Mathematica Sinica, Chinese Series. 1998, 41(3): . https://doi.org/10.12386/A1998sxxb0113
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    This paper investigates the existence of positive solutions of singular boundary value problems of negative exponent Emden Fowler equations. A necessary and sufficient condition for the existence of C positive solutions as well as C 1 positive solutions is given by means of the method of lower and upper solutions with the fixed point theorems.
  • FanLiang Kong
    Acta Mathematica Sinica, Chinese Series. 1998, 41(3): . https://doi.org/10.12386/A1998sxxb0114
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    In this paper, with the Doob decomposition of B valued asymptotic martingles, we study the strong and weak law of large number for B valued asymptotic martingles in Banach space B , which is RNP and the dual separable, and give a series of result and proof.
  • JunDe Wu(1),RongLu Li(2),WenBo
    Acta Mathematica Sinica, Chinese Series. 1998, 41(3): . https://doi.org/10.12386/A1998sxxb0097
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    Let (E,T) be a separated locally convex space. The main results obtained in this paper are:(1) If (E,T) is sub separable, then AE is a relatively weakly compact set A is a relatively weakly countable compact set A is a relatively weakly sequentially compact set. (2) If (E,T) is strongly sub separable and (E *, β(E *,E)) is a barrelled space, then AE is a relatively weakly compact set A is a relatively weakly countable compact set A is a relatively weakly sequentially compact set.
  • JunYi Guo,Rong Wu
    Acta Mathematica Sinica, Chinese Series. 1998, 41(3): . https://doi.org/10.12386/A1998sxxb0122
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    We start from a super-Brownian motion with the branching mechanism presented by Dawson and Vinogradov. Its behaviour near extinction is studied in this paper and the main result is that the diameter of the support tends to zero almost surely at the time of extinction.
  • FengYu Wang
    Acta Mathematica Sinica, Chinese Series. 1998, 41(3): . https://doi.org/10.12386/A1998sxxb0123
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    Let τ D denote the lifetime of a diffusion process on domain DR d. This paper presents a sufficient condition for the exponential moment of τ D to be finite. Here,both of the domain and the diffusion operator are in general. As an application, the Gao′s result (1995) for conditioned diffusions is improved.
  • YangMing Li
    Acta Mathematica Sinica, Chinese Series. 1998, 41(3): 583-058. https://doi.org/10.12386/A1998sxxb0124
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    In this paper, we point out an