15 March 1996, Volume 12 Issue 1

    

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  On Extension of Isometries in (F>)-Spaces

  Ding Guanggui, Huang Senzhong

  Acta Mathematica Sinica. 1996, 12(1): 1-9. https://doi.org/10.1007/BF02109385

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  An (F)-spaceE is said to be locally midpoint constricted (in short,Imp-constricted) if there exists some δ>0 such that D(A/2)<D(A) for every subset A of E with 0<D(A)≤δ,where D(A) denotes the diameter of A.Our main result goes as follow:Let E be an Imp-constricted (F)-space and U an open connected subset of E.Assume that T:U|→F is an isometry (i.e.,a distance-preserving map) which maps U onto an open subset of the (F)-spaceF.Then T can be extended to an affine homeomorphism from E toF.Also,some other results about the question whether each isometry between two (F)-spaces is affine are obtained.
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  Groups Whose Proper Subgroups are Baer Groups

  Xu Maoqian

  Acta Mathematica Sinica. 1996, 12(1): 10-17. https://doi.org/10.1007/BF02109386

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  In this paper we classify infinite soluble minimal non-nilpotent-groups,detemine the basic structure of infinite soluble minimal non-Baer-groups,and using famed Heineken-Mohamed-groups we construct an example of minimal non-Baer-group which is not minimal non-nilpotent-group.
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  Dirichlet Problems for the Quasilinear Second Order Subelliptic Equations

  Xu Chaojiang

  Acta Mathematica Sinica. 1996, 12(1): 18-32. https://doi.org/10.1007/BF02109387

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  In this paper,we study the Dirichlet problems for the following quasilinear second order sub-elliptic equation,
  
  whereX={X₁,...,X_m} is a system of real smooth vector fields which satisfies the Hörmander's condition,A_i,j,B_j,C∈C^∞(Ω×R) and (A_i,j (x,z)) is a positive definite matrix.We have proved the existence and the maximal regularity of solutions in the "non-isotropic" Hölder space associated with the system of vector fieldsX.
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  Hypothesis Testing for Arbitrarily Varying Source

  Fu Fangwei, Shen Shiyi

  Acta Mathematica Sinica. 1996, 12(1): 33-39. https://doi.org/10.1007/BF02109388

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  Hypothesis testing for arbitrarily varying source (AVS),which is to decide between the two hypotheses for the varying behavior of the distribution of AVS,is considered in this paper.We determine the best asymptotic exponent of the second kind of error probability when the first kind of error probability is fixed.This result generalizes the well-known lemma of Stein in statistics.As a corollary,Strassen's coding theorem for AVS is obtained.
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  Polar Duals of Rotors

  Ghandehari M.

  Acta Mathematica Sinica. 1996, 12(1): 40-42. https://doi.org/10.1007/BF02109389

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  Assume K is a rotor in a regular simplex of heihgt 1 in an n-dimensional Euclidean space.Let K^* denote the polar dual of K.Then the volume V(K^*) satisfies the inequality
  
  where ω_n denotes the volume of an n-dimensional unit ball.Equality holds if and only if K is a ball centered at the centroid of the simplex.
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  The Isotone Mappings on Ockham Algebras

  Fang Jie

  Acta Mathematica Sinica. 1996, 12(1): 43-48. https://doi.org/10.1007/BF02109390

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  In this paper we shall describe some algebraic concepts of Ockham algebras.We show that,if L,M∈K_1,1 then H(S(L),S(M)) S(H(L,M)).
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  Bounded Automorphisms of Surfaces

  Jiang Renfang

  Acta Mathematica Sinica. 1996, 12(1): 49-53. https://doi.org/10.1007/BF02109391

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  The equivalence among bounded homeomorphisms of a surface,reducible homeomorphisms of the surface,bounded automorphisms of the surface group,induced or exchange automorphisms of the surface group,and the stabilizer of the translation length function of the tree action is established.
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  On a Class of Nonlocal Bifurcation Concerning the Lorenz Attractor

  Qi Dongwen

  Acta Mathematica Sinica. 1996, 12(1): 54-70. https://doi.org/10.1007/BF02109392

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  In this paper,we consider a two-parameter family of systems E_ε in which E_ε has a contour consisting of a saddle point and two hyperbolic periodic orbits,i.e.,the situation is similar to that described by the Lorenz equations for parameters b=8/3,Σ=10,r=r₁≈24.06.For the generic unfolding E_ε of E_ε,we find three kinds of infinitely many bifurcation curves and establish the correspondence of the trajectories which stay forever in a sufficiently small neighborhood of the contour with symbolic systems of finite or countably infinite symbols;these results can be used to explain the turbulence behaviors appearing at the critical value r=r₁≈24.06 observed on computer for Lorenz equations in a precise mathematical way.
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  Realization of Fixed Point Sets

  Zhao Xuezhi

  Acta Mathematica Sinica. 1996, 12(1): 71-76. https://doi.org/10.1007/BF02109393

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  Let f:X→X be a selfmap of a compact connected polyhedron,and A a nonempty closed subset of X.In this paper,we shall deal with the question whether or not there is a map g:X→X homotopic to f such that the fixed point set Fixg of g equals A.We introduce a necessary condition for the existence of such a map g.It is shown that this condition is easy to check,and hence some sufficient conditions are obtained.
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  Extremal Problems of Bloch Function Spaces

  Zhang Shunyan, Wang Wei

  Acta Mathematica Sinica. 1996, 12(1): 77-88. https://doi.org/10.1007/BF02109394

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  Let f be analytic in a hyperbolic region Ω.The Bloch constant β_f of f is defined by ,where λ_Ω(z)|dz| is the Poincar émetric in Ω.Suppose Δ is hyperbolic and where .Then for allf withf(Ω)⊆Δ,we have β_f≤1/λ(Δ).In this paper we study the extremal functions defined by β_f=1/λ(Δ) and the existence of those functions.
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  Duck Solutions: A New Kind of Bifurcation Phenomenon in Relaxation Oscillations

  Li Cuiping

  Acta Mathematica Sinica. 1996, 12(1): 89-104. https://doi.org/10.1007/BF02109395

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  In this paper,we apply the asymptotic methods to the study of the evolution and vanishing of limit cycles of a one parameter family of differential equations.Some sufficient conditions are given to guarantee the existence of duck solutions and duck cycles.The abruptness of this evolution is illustrated by a computer-analysis study.
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  Topological Influence of the Presence of Fully-λ-Bases in Locally Convex Spaces

  Deheri G. M.

  Acta Mathematica Sinica. 1996, 12(1): 105-112. https://doi.org/10.1007/BF02109396

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  This article reveals the topological impact of full y-λ-bases in locally convex spaces where λ carries either the traditional normal topology or the fairly generalized Σμ-topology of Ruckle.It has been established that the generalized nuclearity of λ plays a significant role in influencing the topology of the space.Further,the equivalence of normal topology and the topology arising out of the full y-λ-base (λ being equipped with normal topology or Σμ-topology) has been investigated.