15 March 1997, Volume 13 Issue 1

    

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  Images on Locally Separable Metric Spaces

  Lin Shou, Liu Chuan, Dai Mumin

  Acta Mathematica Sinica. 1997, 13(1): 1-8. https://doi.org/10.1007/BF02560519

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  In this paper internal characterization on certain quotient images of locally separable metric spaces are discussed. We obtain some descriptions of quotient s-images, pseudo-open s-images, quotient compact images and closed images of locally separable metric spaces, and establish some relations between these and certain quotient images of metric spaces by the local separability of suitable subspaces.
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  The Cobordism Classification of Involution on DOLD ManifoldP(1, 2l)

  Wu Zhende, Liu Zongze, Bai Ruipu

  Acta Mathematica Sinica. 1997, 13(1): 9-20. https://doi.org/10.1007/BF02560520

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  Supposing the smooth involution of the DOLD manifold P(1,2l) satisfies the following condition: the fiberation π:P(1,2l)×_T×(-1)S^∞→RP(∞) is totally nonhomologous to zero (cf. [1, p373]), this paper determines the classification of smooth involution on the DOLD manifold P(1,2l) totally.
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  Surface Billiards and Nonvanishing Lyapunov Exponents

  Cheng Jian

  Acta Mathematica Sinica. 1997, 13(1): 21-34. https://doi.org/10.1007/BF02560521

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  We study in this paper the billiards on surfaces with mix-valued Gaussian curvature and the condition which gives nonvanishing Lyapunov exponents of the system. We introduce a criterion upon which a small perturbation of the surface will also produce a system with positive Lyapunov exponents. Some examples of such surfaces are given in this article.
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  On Mori’s Theorem in Quasiconformal Theory

  Qiu Songliang

  Acta Mathematica Sinica. 1997, 13(1): 35-44. https://doi.org/10.1007/BF02560522

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  In this paper, it is proved that the Mori constant, the Hölder coefficient of the family QC_K (B) of K-quasiconformal self-mappings of the unit disk B with the origin fixed, is at most 46^1-1/K. It is also shown that the Hölder coefficient of the restriction of a map f∈QC_K(B) to the disk |z|≤ sin 25.7° is at most 16^1-1/K.
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  Some Characterizations of Weighted Herz-type Hardy Spaces and Their Applications

  Lu Shanzhen, Yang Dachun

  Acta Mathematica Sinica. 1997, 13(1): 45-58. https://doi.org/10.1007/BF02560523

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  In this paper, the authors first establish some new real-variable characterizations of Herz-type Hardy spaces and , where ω₁,ω₃ ∈ A₁-weight, 1<q<∞,n(1-1/q)≤α<∞ and 0<p<∞. Then, using these new characterizations, they investigate the convergence of a bounded set in these spaces, and study the boundedness of some potential operators on these spaces.
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  The Space of Strong Types and an Open Map Theorem

  Shen Yunfu

  Acta Mathematica Sinica. 1997, 13(1): 59-63. https://doi.org/10.1007/BF02560524

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  We define a new topology on the space of strong types on a subset A of a model of a given theory and prove that either . We also deduce an open map theorem.
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  Bifurcation of Limit Cycles and the Cusp of Order n

  Han Maoan

  Acta Mathematica Sinica. 1997, 13(1): 64-75. https://doi.org/10.1007/BF02560525

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  The author first investigates the limit cycles bifurcating from a center for general two dimensional systems, and then proves the conjecture that any unfolding of the cusp of order n has at most n-1 limit cycles.
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  Twisted Product and Cohomology

  Zheng Qibing

  Acta Mathematica Sinica. 1997, 13(1): 76-80. https://doi.org/10.1007/BF02560526

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  Let H be a Hopf algebra,H₁ be a sub-Hopf algebra of H, H₂ be the quotient Hopt algebra of H modular H₁. This paper gives a simplified complex by defining a new base for the cobar complex and proves that the cobar complex of H has the same cohomology algebra with a twisted product of the cobar complexes of H₁ and H₂.
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  Asymptotic Behaviour of the Phase in Non-Smooth Obstacle Scattering

  Chen Hua

  Acta Mathematica Sinica. 1997, 13(1): 81-89. https://doi.org/10.1007/BF02560527

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  In this paper, we study the asymptotic behaviour of the scattering phases(λ) of the Dirichlet Laplacian associated with obstacle Ω, where Ω is a bounded open subset of IRⁿ (n≥2) with non-smooth boundary ∂Ω and connected complement Ω_e =IRⁿ \Ω. We can prove that if Ω satisfies a certain geometrical condition, then , where depending only on n, and |·|_j (j/ = n-1, n) is aj-dimensional Lebesgue measure.
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  The Abundance of Strange Attractor in the Families of Nearby Singular Diffeomorphism

  Cao Yongluo

  Acta Mathematica Sinica. 1997, 13(1): 90-96. https://doi.org/10.1007/BF02560528

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  In this paper, we consider the families of nearby singular diffeomorphism and the measure of a set in the parameter space, such that for each point of the set the corresponding diffeomorphism possesses strange attractor. For some families of one-dimensional mapping satisfying certain transversality condition, we prove that there is a positive measure set in the parameter space, such that the system in the corresponding families of nearly singular diffeomorphism has strange attractor. Furthermore, we study the dynamics of this type of strange attractor.
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  The Whitehead Groups of Semigroups

  Song Guangtian

  Acta Mathematica Sinica. 1997, 13(1): 97-104. https://doi.org/10.1007/BF02560529

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  Let S be a semigroup with identity and zero, the category of finitely generated projective S-systems. In this paper, the Whitehead group K₁ S of S is defined to be K₀ Ω , where Ω is the loop category of , and the structure of K₁ S is given.
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  Oscillatory and Asymptotic Behaviour of Fourth Order Nonlinear Difference Equations

  Yan Jurang, Liu Bin

  Acta Mathematica Sinica. 1997, 13(1): 105-115. https://doi.org/10.1007/BF02560530

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  This paper considers a class of fourth order nonlinear difference equations Δ²(r_n Δ²(y_n ) + f(n,y_n )=0,n ∈N(n₀) where f(n, y) may be classified as superlinear, sublinear, strongly superlinear and strongly sublinear. In superlinear and sublinear cases, necessary and sufficient conditions are obtained for the difference equation to admit the existence of nonoscillatory solutions with special asymptotic properties. In strongly superlinear and strongly sublinear cases, sufficient conditions are given for all solutions to be oscillatory.
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  A Probabilistic Approach to the First Dirichlet Eigenvalue on Non-compact Riemannian Manifold

  Wang Fengyu

  Acta Mathematica Sinica. 1997, 13(1): 116-126. https://doi.org/10.1007/BF02560531

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  By using diffusion process with absorbing boundary, some lower bounds are obtained for the first Dirichlet eigenvalue of operator Δ+∇h on a non-compact complete Riemannian manifold. The resulting estimates contain McKean's estimate for ∇h=0. Moreover, the first Dirichlet eigenvalue for elliptic operators on R^d and the first mixed eigenvalue are also studied. Some examples show that our estimates can be sharp even for ∇h≠0.
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  On Cardinal Wavelets with Compact Support and Their Duals

  Liu Youming

  Acta Mathematica Sinica. 1997, 13(1): 127-132. https://doi.org/10.1007/BF02560532

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  Some people try to construct an orthonormal wavelet such that the corresponding scaling function φ(t) has the cardinal property,i.e. φ(n)= σ_n0, since such wavelets have many good applications. Unfortunately it is impossible to do so, except for a trivial case^[1]. In this work, a family of non-orthogonal cardinal wavelets with compact support is constructed and their duals are investigated.
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  Classification and Enumeration of Matched Free Response Matrices of Linear Finite Automata

  Dai Zongduo, Ye Dingfeng, Zhai Qibin, Ou Haiwen

  Acta Mathematica Sinica. 1997, 13(1): 133-144. https://doi.org/10.1007/BF02560533

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  If H and G are the transfer function matrix and the free response matrix of a linear finite automaton, then G is called a free response matrix matched to H. Given H, let G(H) be the set of all possible free response matrices matched to H. A classification and an enumeration on the set G(H) are given in this paper.