A Fine Structure in the Theory of Isols

In this paper we introduce a collection of isols having some interesting properties. Imagine a collection W of regressive isols with the following features: (1) u, v ? W implies that u ? v or v ? u, (2) u ? v and v ? W imply u ? W, (3) W contains ? = {0,1,2,…} and some infinite isols, and (4) u e? W, u infinite, and u + v regressive imply u + v ? W. That such a collection W exists is proved in our paper. It has many nice features. It also satisfies (5) u, v ? W, u ? v and u infinite imply v ? g(u) for some recursive combinatorial function g, and (6) each u ? W is hereditarily odd-even and is hereditarily recursively strongly torre. The collection W that we obtain may be characterized in terms of a semiring of isols D(c) introduced by J. C. E. Dekker in [5]. We will show that W = D(c), where c is an infinite regressive isol that is called completely torre.     

偏最小二乘回归分析在均匀设计试验建模分析中的应用

本文分析了目前应用一般的最小二乘法建立均匀试验数据的二次多项式回归模型时存在的局限性,提出了应用偏最小二乘法(Partial least-square,PLS)建立二次多项式回归模型的技术,并且进一步介绍了偏最小二乘回归(PLS回归)在均匀设计中的应用。作者认为,PLS回归分析建模技术将为均匀设计的更广泛应用提供有力的技术支持。     

On a Theorem of V. Dlab

A new proof is given of Dlab's theorem asserting that the left regular representation of an algebra is filtered by the standard modules if and only if the right regular representation of it is filtered by the proper standard modules.     

关于J.Hersch的一个定理

我们证明在与典型n维球面（S^n,g0)共形的n维球面上,成立不等式λ≤n(VOL(S^n,g0)VOL(S^n,g)2/n,这推广了Hersch关于拉普拉斯算子第一特征值λ1的一个定理。     

On a Theorem of F. Riesz

We prove a theorem of Riesz characterizing the convergence in spaces of functions N_? generated by concave functions ?.     

On a result of R. R. Hall

An upper bound for the mean value of a non-negative submultiplicative function by R. R. Hall [3] is sharpened and generalised. Hall's inequality implies a certain rather accurate upper sieve estimate, and this aspect of Hall's result is exploited in deriving good lower bounds for π(x) via the sieve.     

关于H．Yao－D．Knuth定理

本文研究一类有限连分数展开的部分商数之平均和。所得结果改进了这方面已有的最好工作。     

改进的R.Nevanlinna第二基本定理

设ｆ（ｚ）是超越亚纯函数，ｎ为任一非负整数，ε为任意正数，ａ＾（ｉ）ｒ＝（ｖ＝１，２，…，ｑｉ，ｉ＝０，１，…，ｎ）均为有穷非零复数，满足ｍｉｎ／１≤ｖ１＜ｖ２≤ｑｉ｜ａ＾（ｉ）ｖ１－ａ＾（ｉ）ｖ２｜≥δ＞０，ｉ＝０，１，…，ｎ。若ｆ（０）≠０，∞，П＾ｎｉ＝１ｆ（ｉ）（０）≠０，则对０＜ｒ＜＋∞有ｍ（ｒ，ｆ）＋ｍ（ｒ，１／ｆ）＋Σ＾ｕｉ＝０Σ＾ｑｉｒ＝１ｍ（ｒ，ａ＾（ｉ）ｖ，ｆ＾（ｉ）≤（２＋ε     

On a Theorem of Ossa

If is an elementary abelian -group, Ossa proved that the connective -theory of splits into copies of and of the connective -theory of the infinite real projective space. We give a brief proof of Ossa's theorem.

     

关于一个次可乘定理

本文证明了次可乘定理：设A是一个*代数,A上范数||.||使得（A,||.||）成为完备的赋范线性空间,而且,（I）对于X∈A,||x*x||||x||2;（II）对于正规元x∈A,||x*x||=||x||2,则（A,||.||）是C*-代数．同时,也给出了其对应的C*-等价定理．     

On a Theorem of Matiyasevich

Mathematical Notes - Using the restatement of the Riemann hypothesis proposed in a recent paper of Matiyasevich, we explicitly write out the system of Diophantine equations whose unsolvability is...     

On a Theorem of Mislin

An alternative proof is given of a result, originally due toGuido Mislin, giving necessary and sufficient conditions forthe inclusion of a subgroup to induce an isomorphism in modp cohomology.     

On a Theorem of Strobel

Received April 17, 2000 / Accepted May 9, 2000 / Published online September 14, 2000     

On a Theorem of Grothendieck

A smooth projective morphism p : T S to a smooth variety S is considered. In particular, the following result is proved. The total direct image Rp _*(/n) of the constant étale sheaf /n is locally (in Zariski topology) quasiisomorphic to a bounded complex on S that consists of locally constant, constructible étale sheaves of /n-modules. Bibliography: 2 titles.     

On a Theorem of Dubins and Freedman

Under a notion of splitting the existence of a unique invariant probability, and a geometric rate of convergence to it in an appropriate metric, are established for Markov processes on a general state space S generated by iterations of i.i.d. maps on S. As corollaries we derive extensions of earlier results of Dubins and Freedman;⁽¹⁷⁾ Yahav;⁽³⁰⁾ and Bhattacharya and Lee⁽⁶⁾ for monotone maps. The general theorem applies in other contexts as well. It is also shown that the Dubins–Freedman result on the necessity of splitting in the case of increasing maps does not hold for decreasing maps, although the sufficiency part holds for both. In addition, the asymptotic stationarity of the process generated by i.i.d. nondecreasing maps is established without the requirement of continuity. Finally, the theory is applied to the random iteration of two (nonmonotone) quadratic maps each with two repelling fixed points and an attractive period-two orbit.     

On a Theorem of Godefroy and Shapiro

G. Godefroy and J. H. Shapiro have shown that every operator on , that commutes with all translation operators , and that is not a scalar multiple of the identity is hypercyclic. We show that they are even frequently hypercyclic. In addition, we obtain growth conditions that may be satisfied by corresponding frequently hypercyclic entire functions.