1989年, 第2卷, 第4期　刊出日期：1989-10-15

  

• 全选
  |

论文
• Select
  ON THE FOUNDATION OF ALGEBRAIC DIFFERENTIAL GEOMETRY

  Wu Wenjun (Wu Wen-tsun)

  Journal of Systems Science and Complexity. 1989, 2(4): 289-312.

  摘要 ( ) PDF全文 ( )   可视化   收藏

  An algebraic differential variety is defined as the zero-set of a differential polynomial set, and algebraic differential geometry is devoted to the study of such varieties. We give various decomposition formulas for the structures of such zero-sets which imply inparticular, the unique decomposition of an algebraic differential variety into its irreducible components. These formulas will find applications in various directions including mechanical theorem-proving of differential geometries.
• Select
  RELATIVE TREND AND ITS TEST

  Chen Keh-wei;Zheng Zhongguo

  Journal of Systems Science and Complexity. 1989, 2(4): 313-316.

  摘要 ( ) PDF全文 ( )   可视化   收藏

  In this paper we develop tests using L-statistic for a constant relative trend against a convex ordered relative trend. Unbiasedness of the test is obtained. For a certain path of trends,the score function can be chosen so that the sequence of the constructed tests is locally asymptotically most powerful. An example is given to illustrate the results.
• Select
  EB RULES FOR SELECTING THE BEST EXPONENTIAL POPULATION

  Gao Jiti

  Journal of Systems Science and Complexity. 1989, 2(4): 317-324.

  摘要 ( ) PDF全文 ( )   可视化   收藏

  In this paper, we obtain empirical Bayes(EB)procedures for selecting the best among k different exponential populations(the form of the conditional probability density e.g. each population is f_4(x_i/b_i)=b_i exp(-b_ix_i),x_i,b_i∈(0,∞),i=1,2,…,k).These rules are based on the EB estimators of b_i. We show that, under the squared error loss, the Bayes risk of the EB estimators converges to the related minimum Bayes risks with rates of conver-gence at Jeast of order O(n~(-q)). Further, for the selection problem, the rates of convergence of the proposed selection rules are shown to be at least of order O(n~((-q)/2) where q can be arbitrarily close to 1/5 or 1 under suitable conditions.
• Select
  ON A CONJECTURE OF HARMONIOUS GRAPH

  Liu Bolian;Zhang Xiankun

  Journal of Systems Science and Complexity. 1989, 2(4): 325-328.

  摘要 ( ) PDF全文 ( )   可视化   收藏

  Let the coronas C_n⊙K_1 be the polygons with one additional end-point for eachvertex.Thom Grace conjectured that C_n⊙K_1 are harmonious for n even. In this paper, a proof of his conjecture is given.
• Select
  AN IMPROVEMENT ON ESTIMATE OF d_0/d~* FOR STARLIKE FUNCTIONS

  Chen Yueqing

  Journal of Systems Science and Complexity. 1989, 2(4): 329-336.

  摘要 ( ) PDF全文 ( )   可视化   收藏

  Let S~* be the class of starlike functions in unit disc. For f∈S~*, denote its radius of convexity by r_0 and let d_0=\[min_}{\|z\|=r_0}\]|f(z)|, d~*=inf{|β||f(z)≠β,|z|<1}. In this paper we prove d_0/d~*≥0.45, thus improving the result of d_0/d~*≥0.38 by McCarty,C.P.and Tepper,D.E.and d_0/d~*≥0.41 by Huang Xinzhong.
• Select
  LOCAL AND GLOBAL BIFURCATIONS AND APPLICATIONS IN A PREDATOR-PREY SYSTEM WITH SEVERAL PARAMETERS

  Jing Zhujun

  Journal of Systems Science and Complexity. 1989, 2(4): 337-352.

  摘要 ( ) PDF全文 ( )   可视化   收藏

  A predator-prey system, depending on several parameters, is investigated forbifurcation of equilibria, Hopf bifurcation, global bifurcation occurring saddle connection, and global existence and nonexistence of limit cycles, and changes of the topological structure of trajectory as parameters are varied.
• Select
  IMPLICIT DEGREES AND CHVATAL'S CONDITION FOR HAMILTONICITY

  Zhu Yongjin;Gao Jingzhen

  Journal of Systems Science and Complexity. 1989, 2(4): 353-363.

  摘要 ( ) PDF全文 ( )   可视化   收藏

  Based on the ideas in[9], an integer d~0(v), called the implicit degree of v which satisfies d~0(v)≥d(v), is associated with each vertex v of a graph G. It is proved that if the implicit degree sequence d_1~0,d_2~0,…,d_n~0(where d_1~0≤d_2~0≤…≤d_n~0) of a simple graph G on n≥3 vertices satisfies d_i~0≤i
• Select
  FRAMING BORDISM GROUPS OF FRAMED IMMERSED SUBMANIFOLDS

  Li Guisong

  Journal of Systems Science and Complexity. 1989, 2(4): 364-368.

  摘要 ( ) PDF全文 ( )   可视化   收藏

  We prove that the n~(th) framing bordism group of framed immersed submanifolds in a manifold N, which is denoted by Δ_n(N), is canonically isomorphic to the normalbordism group Ω_n(N,-TN).
• Select
  AN EMPIRICAL BAYES TWO-SIDED TEST PROBLEM FOR CONTINUOUS ONE-PARAMETER EXPONENTIAL FAMILIES

  Wei Laisheng

  Journal of Systems Science and Complexity. 1989, 2(4): 369-384.

  摘要 ( ) PDF全文 ( )   可视化   收藏

  An empirical Bayes(EB) two-sided test problem about the continuous one-parameter exponential family has been discussed. We construct the EB test decision rule and prove its asymptotical optimality. Further, we get its convergence rates O(n~(-(λ(s-2))/(2s+1)) under suitable conditions, where 0<λ<2,and s>2 is a given natural number. Finally, some examples about the result of the convergence rates are given.