中国科学院数学与系统科学研究院期刊网

15 March 1997, Volume 40 Issue 2
    

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  • LiPing Huang
    Acta Mathematica Sinica, Chinese Series. 1997, 40(2): 161-166. https://doi.org/10.12386/A1997sxxb0019
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    Let F be a field, R an F-algebra with an involution, if any matrix over R has a singular value decomposition (SVD for short), then R is said to have the SVD property. This paper shows that: R is an F-algebra having the SVD property if and only if R is isomorphic to either R+ or R+(-1~1/-1) or the quaternion field (-1,-1/R+) over R+, where R+ is the set of all symmetric elements of R, and R+ is a Galois order closed field.
  • ZhaoYong Huang
    Acta Mathematica Sinica, Chinese Series. 1997, 40(2): 167-174. https://doi.org/10.12386/A1997sxxb0020
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    In this paper, we introduce the notion of Wn-modules and describe non-commutative coherent rings with finite FP-selfinjective dimension. The obtained results generalize the works of Stentrom and Bass. Finally we apply these results to extension closed categories of modules.
  • GuangXing Zeng,ZhiZhong Dai
    Acta Mathematica Sinica, Chinese Series. 1997, 40(2): 175-184. https://doi.org/10.12386/A1997sxxb0021
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    In this paper, by introducing the notion of a strongly real Hilbert ring, we show that (1) A ring A is a strqngly real Hilbert ring if and only if A[X] is a real Hilbert ring; and (2) A ring A is a strongly real Hilbert ring if and only if every real maximal ideal of A[X]contracts in A to a real maximal ideal. Thereby, the two main results listed in reference [1] are negated. Moreover, the so-called strictly real Hilbert rings are investigated; these rings are of significance for the discussion of the semialgebraic Nullstellensatz.
  • ChengKui Zhong
    Acta Mathematica Sinica, Chinese Series. 1997, 40(2): 185-190. https://doi.org/10.12386/A1997sxxb0022
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    This paper first generalizes Ekeland's variational principle and then considers the relation between (P.S.) condition and coercivity of functional.
  • Gang Li(1),JiPu Ma(2)
    Acta Mathematica Sinica, Chinese Series. 1997, 40(2): 191-201. https://doi.org/10.12386/A1997sxxb0023
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    In this paper, we provide nonlinear ergodic theorems and weak convergence theorems for commutative semigroups of asymptotically nonexpansive type mappings iu uniformly convex Banach spaces that satisfy opial's condition or have a Frechet differentiable norm.
  • YouNing Wang,JiZhi Liu

    Acta Mathematica Sinica, Chinese Series. 1997, 40(2): 202-206. https://doi.org/10.12386/A1997sxxb0024
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    An answer to the problem formulated by W. Fenchel[1] is obtained. A global property of spherical curves is given and applied to generalize Jacobi theorem on closed space curves.
  • HaiYun Zhou
    Acta Mathematica Sinica, Chinese Series. 1997, 40(2): 207-212. https://doi.org/10.12386/A1997sxxb0025
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    In the present paper we establish some surjectivity theorems for the operators A and C, where A is m-accretive and C is compact. Our results generalize and improve the main results of Zhu[5].
  • WeiYao Zeng(1),ZhuJun Jing(2)
    Acta Mathematica Sinica, Chinese Series. 1997, 40(2): 213-220. https://doi.org/10.12386/A1997sxxb0026
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    In this paper, by using the theory of exponential dichotomies and functional analystic method, we investigate the degenerate heteroclinic bifurcation of the systems whose unperturbed equations have not heteroclinic manifold. The sufficient condition assuring the existence of transversal heteroclinic orbits is given by making use of Melnikov vector.
  • DingGuo Wang
    Acta Mathematica Sinica, Chinese Series. 1997, 40(2): 221-226. https://doi.org/10.12386/A1997sxxb0027
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    Let M be a Γ-ring in the sense of Nobusawa.The ring M2=(RΓML) was defined by Kyuno. In this paper, first we characterise primitive ideals and the Jacobson radical of M2. Next, we introduce a new class of Γ-rings in which, for every homomorphic image, the Jacobson radical equals the simplicial radical. We shall call this the class of PM-Γ-rings. Relationships between PM properties of Γ-ring M and the corresponding properties of Γn,m-ring Mm,n, the right operator ring R of Γ-ring M, M-ring Γ and the ring M2 are established. Finally, we give a general version of Jacobson properties for Γ-rings, which includes also Jacobson property, Brown-McCoy property and PM property.
  • XiYu Liu
    Acta Mathematica Sinica, Chinese Series. 1997, 40(2): 227-234. https://doi.org/10.12386/A1997sxxb0028
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    This paper deals with a kind of superlinear boundary value problems with singularity. We prove continua to the solution set exist. Our corollary improves the main results of [1] to some extent, and we drop their main condition off.
  • YouLiang Hou,PeiDe Liu
    Acta Mathematica Sinica, Chinese Series. 1997, 40(2): 235-245. https://doi.org/10.12386/A1997sxxb0029
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    This paper discussed the complex measure dμ= ψdv where the complex valued function ψ∈ Lloc1 and some properties of conditional expectations and matin-gales with respect to the measure dμ. Then it proved that the maximal operators of the martingales are week (p, p) bounded and strong (p, p) bounded if ψsatisfies bp+(K) condition and that the square operators of the martingales are L2-bounded if ψ satisfies b∞+(K) ∩ a1(K) condition.
  • MaoAn Han
    Acta Mathematica Sinica, Chinese Series. 1997, 40(2): 246-252. https://doi.org/10.12386/A1997sxxb0030
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    The limit cycle bifurcations near a heteroclinic loop with two or three saddle points are studied. The uniqueness of limit cycles is proved uader a simple condition, and a necessary and sufficient condition for a limit cycle to exist is obtained. As an application to a codimension two bifurcation in a three dimensional system, the problem on the uniqueness of limit cycles near a heteroclinic loop of the deduced plane system is solved.
  • YuanSheng Tang
    Acta Mathematica Sinica, Chinese Series. 1997, 40(2): 253-258. https://doi.org/10.12386/A1997sxxb0031
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    In this paper, we construct some even continuous solutions of the Feigen-baum Function Equation. For every 0 < λ < 1, we give out some C∞-even-solutions of this equation.
  • Chen Lin,ZiKun Yan
    Acta Mathematica Sinica, Chinese Series. 1997, 40(2): 259-264. https://doi.org/10.12386/A1997sxxb0032
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    In this paper, we introduce the conceptions S∈ (Q) S∈ L(H) with σe(S) C σe(T) for every operator T quasisimilar to S, β(S) = {λ∈C : a neighbourhood U of λ such that (S -z) ○(V,H) is closed for every neighbour hood V of λ, V U}, characterize (Q) operators by means of β(S) and show that the family of (Q) operators includes many familiar operators (such as subdecompasable, M-hyponormal, semi-hyponormal operators, etc.) and is norm-dense in L(H).
  • HanXing Wang,YongLong Dai
    Acta Mathematica Sinica, Chinese Series. 1997, 40(2): 265-270. https://doi.org/10.12386/A1997sxxb0033
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    A Markov chain in markovian environment is studied in this paper. For this process we prove a limit law for the recurrence to small cylindrical sets. Moreover, we give a sufficient condition for the process being φ-mixing, and give a exponential estimation of the probability for the process to return to small cylindrical sets.
  • ShanChao Yang

    Acta Mathematica Sinica, Chinese Series. 1997, 40(2): 271-279. https://doi.org/10.12386/A1997sxxb0034
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    This paper gives two moment inequalities for σ-mixing and (ψ-mixing sequences. In the study of weighted sums, they are more useful than ones abtained by Shao Qiman in [6] and [7]. Here they are applied to discuss the rate of strong convergence for the nonparametric recursive kernel estimators and the strong consistency for the nonparametric weighted kernel estimators of regression function. The obtained results are much better.
  • JinDe Chao(1),YongKun Li(2)

    Acta Mathematica Sinica, Chinese Series. 1997, 40(2): 280-286. https://doi.org/10.12386/A1997sxxb0035
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    In this paper, higher dimensional periodic systems with delay of the form x'(t) = A(t,x(t))x(t) + f(t,x(t - r)) are considered, where the n x n matrix A(t, x) and the n-vector f(t,x) are continuous in (t,x) ∈ R × Rn, and A(t + T,x)-A(t,x), f(t + T, x) = f(t, x). Using fixed point method, some sufficient conditions to guarantee the existence and uniqueness of T periodic solution for the systems are obtained. The main results in [1-3] are extended and improved.
  • WeiPing Chao(1),JiPu Ma(2)
    Acta Mathematica Sinica, Chinese Series. 1997, 40(2): 287-295. https://doi.org/10.12386/A1997sxxb0036
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    We give some conditions of the pointwise continuity of the M-P inverses Ax+ of Ax, when Ax is pointwise continuous. Then some applications to integral equations are given in 3.
  • Jin Zou
    Acta Mathematica Sinica, Chinese Series. 1997, 40(2): 296-300. https://doi.org/10.12386/A1997sxxb0037
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    The main result of this paper is: suppose that A(ζ,η) satisfies A0, A1, A2, A3, A4, then Tb is bounded on L2(K) if and only if b eBMO(K). We apply this result to prove that the commutator of fractional integration with b is bounded on L2(K) if and only if b∈I-s(BMO), (-1 < s < 0), the commutator of singular integral transform with b is bounded on L2(K) if and only if b∈BMO(K), and the commutator of multiplier with b is bounded on L2(K) if b∈BMO(K).
  • YuanHuai Bai
    Acta Mathematica Sinica, Chinese Series. 1997, 40(2): 301-307. https://doi.org/10.12386/A1997sxxb0038
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    Let M be the ideal in Z[v] generated by v-1 and a odd prime p, U be a quantum algebra over A-Z[V]M with a symmetric Cartan matrix. Let k be algebraically closed field of characteristic zero. Consider a ring homomorphism A→k (v→ζ) and let Uk = U A k, Uk be infinitesimal quantum algebra of Uk,ζ be a primitive p-th root of 1. Let V and M be finite dimensional integrable Uk-modules. In this paper we show that Uk module isomorphisms V M ≌ M V when at least one of V or M is injective, or least one of V or M is trivial Uk module. Moreover, if V is indecomposable Uk module, M is indecomposable Uk module and M restricts to an indecomposable Uk module, then we show that V M is indecomposable Uk module. Finally, if V and M is Uk module isomorphisms and with unique simple submodule, we prove that the V and M also is Uk module isomorphisms, this shows Uk structure on indecomposable injective Uk module is unique.
  • HuanYin Chen
    Acta Mathematica Sinica, Chinese Series. 1997, 40(2): 308-312. https://doi.org/10.12386/A1997sxxb0039
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    In this paper, we study the structures of modules over group ring RG with KdimR ≤1, gl.dimR ≤ 2 or w.gl.dimR = 0. As applications, we give some characterizations of group rings with lower dimensional coefficient rings.
  • YongZhong Song
    Acta Mathematica Sinica, Chinese Series. 1997, 40(2): 313-318. https://doi.org/10.12386/A1997sxxb0040
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    Comparison theorems for nonnegative splittings of bounded linear operators have been presented by Marek and Szyld. Without detailed proofs, they also gave the hypotheses which provide strict inequalities for the comparisons. In this note, several counter examples are given which show that all the hypotheses by Marek and Szyld, which provide strict inequalities, are not sufficient. Then the corrected comparison theorems are proposed.