15 September 1990, Volume 6 Issue 3

    

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  On The Injective Metrization for Infinite Collapsible Polyhedra

  Luo Maokang

  Acta Mathematica Sinica. 1990, 6(3): 193-205. https://doi.org/10.1007/BF02108199

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  Lattice-valued semicontinuous mappings play a basic and important role in solving the problems of L-fuzzy compactification theory, and make the previous work on weakly induced spaces and induced spaces determinatively generalized and strengthened. Moreover, we can describe the complete distributivity of lattices with them as well. In this paper, we give the mutually descriptive relation between lattice-valued semicontinuous mappings and the complete distributivity of lattices, and the construction theorems of open sets and closed sets in lattice-valued fully stratified spaces, weakly induced spaces and induced spaces (they are called S-spaces). Furthermore, we will investigate the structure of the co-topology of S-space, solve a series of interesting problems on product, N-compactness and metrization of S-spaces.
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  On Evaluating the Rate Function of Large Deviations for Jump Processes

  Chen Mufa, Lu Yungang

  Acta Mathematica Sinica. 1990, 6(3): 206-219. https://doi.org/10.1007/BF02108200

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  This is a sequel to our joint paper^[4] in which upper bound estimates for large deviations for Markov chains are studied. The purpose of this paper is to characterize the rate function of large deviations for jump processes. In particular, an explicit expression of the rate function is given in the case of the process being symmetrizable.
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  Coconvex Approximation of Continuous Functions

  Yu Xiangming

  Acta Mathematica Sinica. 1990, 6(3): 220-229. https://doi.org/10.1007/BF02108201

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  Suppose that f(x)∈C[-1,1], f(x) is convex in [0,1] and concave in [-1,0] with the new concept of regular convexity-turning points,we obtain the following estimates of Jackson type for coconvex approximation of f(x) by algebraic polynomials of degree ≤ n: .
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  Discrete Generalizations of Some N-Independent-Variable Integral Inequalities of Langenhop-Gollwitzer Type

  Yang Enhao

  Acta Mathematica Sinica. 1990, 6(3): 230-242. https://doi.org/10.1007/BF02108202

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  We establish some new n-independent-variable discrete inequalities which are analogous to some Langenhop-Gollwitzer type integral inequalities obtained by the present author in J. Math. Anal. Appl., 109 (1985), 171-181. An application to hyperbolic summary-difference equations in n variables is also sketched.
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  Qualitative Analysis of Van Der Pol Type Equation with Periodic Forcing Term

  Zheng Zhiming

  Acta Mathematica Sinica. 1990, 6(3): 243-256. https://doi.org/10.1007/BF02108203

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  In this paper we analyze the qualitative behaviour of the equation
  ,
  where ε is a small parameter. We divide the interval of parameter b into four sets of subintervals. A, B, C and D. For b∈A, B or D, we discuss the different structures of the attractors of the equation and their stabilities. When chaotic phenomena appear, we also estimate the entropy. For b∈C, the set of bifurcation intervals, we analyze the bifurcating type and get a series of consequences from the results of Newhouse and Palis.
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  Three Kinds of Constraints of Potential for KdV Hierarchy

  Zeng Yunbo, Li Yishen

  Acta Mathematica Sinica. 1990, 6(3): 257-272. https://doi.org/10.1007/BF02108204

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  Under three kinds of constraints of potential for KdV hierarchy,the two systems, stemming from the spatial part and the time part of the Lax pair for KdV hierarchy, are shown to be naturally consistent. For the former system, the constants of the motion are presented and the Painlevé property is examined.
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  Double Darboux Transformation for AKNS Hierarchy

  Gu Xinshen

  Acta Mathematica Sinica. 1990, 6(3): 273-288. https://doi.org/10.1007/BF02108205

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  In this paper we construct a double Darboux Transformation for AKNS hierarchy and give its decomposition theorem. A remarkable characteristic of the double Darboux Transformation—incommutativity is proved.