多元线性模型中条件最优预测的稳健性

研究了多元线性模型中条件最优线性无偏预测的稳健性问题,得到了条件线性可预测变量的这种预测关于协方差矩阵具有稳健性的充要条件.     

一般生长曲线模型中最优预测的稳健性

研究了一般生长曲线模型中最优线性无偏预测的稳健性,得到了线性可预测变量的这种预测关于协方差阵具有稳健性的充要条件.     

Single‐cell fourth‐order difference approximations for $${\font\twelvesl=cmsl10\partial {\sl\bf u}\over\partial {\sl\bf x}},{\partial \sl\bf u\over\partial\sl\bf y}$$ , and $${\font\twelvesl=cmsl10\partial {\sl\bf u}\over\partial{\sl\bf z}}$$ of the three‐dimensional quasi‐linear elliptic equation

Finite difference methods of O(h⁴) are proposed for obtaining estimates of first‐order partial derivatives of the solution of three‐dimensional quasi‐linear elliptic equation with mixed derivative terms subject to Dirichlet boundary conditions on a uniform cubic grid. In all the cases, we use a single computational cell and the methods are applicable to the problems both in cartesian and polar coordinates. The utility of the new methods is shown by testing the methods on three‐dimensional poisson solvers in polar coordinates. Some numerical examples are provided to demonstrate the accuracy and efficiency of the methods discussed. © 2000 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 16: 417–425, 2000     

有限群的$\Phi$-$\tau$-可补子群

假设$\tau$是一个子群算子, $H$是有限群$G$的一个$p$-子群. 令 $\bar{G}=G/H_{G}$且$\bar{H}=H/H_{G}$, 如果$\bar{G}$有一个次正规子群$\bar{T}$ 和一个包含于$\bar{H}$ 的$\tau$-子群$\bar{S}$满足$\bar{G}=\bar{H}\bar{T}$且$\bar{H}\cap\bar{T}\leq \bar{S}\Phi(\bar{H})$, 就称$H$是$G$的一个$\Phi$-$\tau$- 可补子群. 文章通过讨论群$G$的准素数子群的$\Phi$-$\tau$-可补性给出了超循环嵌入和$p$-幂零性的一些新的特征.     

Outer-\Sigma Groups of Finite Order

Suppose that \Sigma is a group-theoretic property. A group whose every proper subgroup but itself is a \Sigma group is called an outer-\Sigma group. The paper gives a series of results to groups which possess trivial Frattini subgroup and only one solvable minimal normal subgroup. The outer groups are such groups when the classe of \Sigma groups is a saturated formation. By use of aforementioned results, the c(k) groups (group with classes less than k),Г_k-pn groups (groups whose k-th term of lower central series are p-nilpotenit) and p-supersolvable groups are discussed.     

Subgroups of free profinite groups and large subfields of\mathop Q\limits^ \sim

We prove that many subgroups of free profinite groups are free, and use this to give new examples of pseudo-algebraically closed subfields of satisfying Hilbert’s Irreducibility Theorem, and to solve problems posed by M. Jarden and A. Macintyre. We also find a subfield of which does not satisfy Hilbert’s Irreducibility Theorem, but all of whose proper finite extensions do. The first author was supported by NSF grant MCS76-11625.     

Lipschitzian Properties of Integral Functionals on Lebesgue Spaces $\bf{L_p, 1 \leqslant {p} < \infty}$

We give complete characterizations of integral functionals which are Lipschitzian on a Lebesgue space L _p with p ≠ ∞. When the measure is atomless, we characterize the integral functionals which are locally Lipschitzian on such Lebesgue spaces. In every cases, the Lipchitzian properties of the integral functional can be described by growth conditions on the subdifferentials of the integrand which are equivalent to Lipschitzian properties of the integrand.     

On $\mathfrak{F}_\tau$-$s$-Supplemented Subgroups of Finite Groups

Let $\mathfrak{F}$ be a non-empty formation of groups, $\tau$ a subgroup functor and $H$ a $p$-subgroup of a finite group $G.$ Let $\overline{G}=G/H_G$ and $\overline{H} =H/H_G.$ We say that $H$ is $\mathfrak{F}_\tau$-$s$-supplemented in $G$ if for some subgroup $\overline{T}$ and some $\tau$-subgroup $\overline{S}$ of $\overline{G}$ contained in $\overline{H},$ $\overline{H}\overline{T}$ is subnormal in $\overline{G}$ and $\overline{H} ∩ \overline{T} ≤ \overline{S}Z_{\mathfrak{F}}(\overline{G}).$ In this paper, we investigate the influence of $\mathfrak{F}_\tau$-$s$-supplemented subgroups on the structure of finite groups. Some new characterizations about solubility of finite groups are obtained.     

On the Dynamics of x_{\bf{n} + \bf{1}} = {{ \mgreek{a} + \mgreek{g} x_{n-1} + \mgreek{d} x_{n-2}} \over {A + x_{n-2}}}

We investigate the global stability, the periodic character and the boundedness nature of solutions of the equation in the title for all admissible nonnegative values of the parameters and the initial conditions. We show that the solutions exhibit a trichotomy character depending on how the parameter γ compares to the sum of the parameters δ and A.