15 September 1987, Volume 3 Issue 3

    

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  Selection in Factorial Experiments with Interaction, Especially the 2×2 Case

  Baldeo K. Taneja, Edward J. Dudewicz

  Acta Mathematica Sinica. 1987, 3(3): 191-203. https://doi.org/10.1007/BF02560033

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  In this pioneering 1954 paper on selection, Bechhofer recognized the importance of considering experiments carried out in some design other than the completely randomized design. However, over the years, little has been done along these lines. This paper's goal is to extend selection procedures to other designs. We first briefly review the existing state of knowledge of selection in designed experiments, and then proceed to new results on complete factorial experiments. In particular, we formulate and study a selection procedure which is valid in the presence of unbounded interaction, yet adapts to the presence/absence of interaction.
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  Eigenvalues of Certain Differential Operators Related to Automorphic Forms

  Pei Dingyi

  Acta Mathematica Sinica. 1987, 3(3): 204-214. https://doi.org/10.1007/BF02560034

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  G.Shimura introduced a certain kind of differential operators when he studied the arithmetic properties of Eisenstein series of several variables. The invariable differential operators of the classical domain of types Ⅰ and Ⅱ are included in it as its special cases. In this paper the eigenvalues of this kind of differential operators with respect to the eigenfunction (det i((^tZ-Z))² are calculated.
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  On the Representation of the Joint Spectrum for a Commuting n-tuple of Non-normal Operators

  Chen Xiaoman, Huang Chaocheng

  Acta Mathematica Sinica. 1987, 3(3): 215-226. https://doi.org/10.1007/BF02560035

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  The main purpose of the present paper is to describe the Taylor joint spectra for n-tuples of double commuting hyponormal operators, and to study the representation of the joint spectra in terms of that of n-tuples of commuting normal operators.
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  On Chern Numbers of Algebraic Varieties with Arbitrary Singularities

  Wu Wentsün

  Acta Mathematica Sinica. 1987, 3(3): 227-236. https://doi.org/10.1007/BF02560036

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  In 1965 the author introduced the notion of Chern classes for an algebraic variety with arbitrary singularities. Based on this definition the well-known Miyaoka-Yao inequalities have been proved and extended by quite simple direct computations.
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  Global Solutions to The Second Initial Boundary Value Problem for Fully Nonlinear Parabolic Equations

  Zheng Songmu

  Acta Mathematica Sinica. 1987, 3(3): 237-246. https://doi.org/10.1007/BF02560037

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  This paper is concerned with the global existence of the second initial boundary value problem for fully nonlinear parabolic equations. It is proved that when the initial data is sufficiently small, the problem admits a unique global solution. Moreover, as t goes to +∞, the solution exponentially decays to zero.
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  The Structure of Symplectic Groups over Arbitrary Commutative Rings

  Li Fuan

  Acta Mathematica Sinica. 1987, 3(3): 247-255. https://doi.org/10.1007/BF02560038

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  Let R be an arbitrary commutative ring, and n be an integer ≥3. It is proved for any ideal J of R that
  ESp_2n(R,J)=[ESp_2n(R), ESp_2n(J)]=[ESp_2n(R), ESp_2n(R,J)] =[ESp_2n(R), GSp_2n(R,J)]=[Sp_2n(R), ESp_2n(R,J)].
  Furthermore, the problem of normal subgroups of Sp_2n(R) has an affirmative solution if and only if aR=a²R+2aR for each a in R. This covers the relevant results of [4], [8], [10], [12] and [13].
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  On Ricci Flat 3-Fold

  Roan Shishyr, Yau Shingtung

  Acta Mathematica Sinica. 1987, 3(3): 256-288. https://doi.org/10.1007/BF02560039

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  In this paper we study a sub-class of compact Ricci flat manifolds from certain standard constructions.