Strongly countable dimensional compacta form the Hurewicz set

The hyperspaces of strongly countable dimensional compacta of positive dimension and of strongly countable dimensional continua of dimension greater than 1 in the Hilbert cube are homeomorphic to the Hurewicz set of all nonempty countable closed subsets of the unit interval [0,1]. These facts hold true, in particular, for covering dimension dim and cohomological dimension dimG, where G is any Abelian group.     

On a theorem of Shchepin and Repovš concerning the smoothness of compacta

We show that a theorem of Shchepin and Repovš concerning the smoothness of compacta follows from the theory of semicontinuous relations.     

嵌套病例对照研究中的两步估计方法（英）

本文讨论嵌套病例对照研究中相对危险率的估计问题，引入了相对危险率的两步估计，并在一般嵌套病例对照抽样的假设下讨论了相对危险率的两步估计的相合性问题，最后给出了几个例子。     

乳腺癌PKCs表达与其分化程度的相关性

为了研究蛋白激酶C（PKC）和乳腺癌分化及转移的相关性，采用免疫组化SABC方法检测48例人乳腺癌的PKC蛋白表达，包括PKCα、βI、η和ξ等蛋白。结果表明，与分化低的乳腺癌对比，分化高的乳腺癌PKC蛋白表达水平提高。在临床I－II和III级的乳腺癌中，PKCη蛋白表达率分别为61．5％和9．1％，具有显著意义（P＜0．05），PKCξ蛋白表达率分别为92．3％和27．3％，具有极显著意义（P＜0．01）。另外，在乳腺癌未转移的病例中，PKCs蛋白表达水平普遍较高，其中PKCξ与肿转移相关性极显著（P＜0．01）。此外，PKCs蛋白表达水平与肿瘤患者年龄无关。以上结果提示，PKCη和PKCξ有可能作为评价临床乳腺癌分化和转移程度的指标之一。     

Bounds for the cup-length of Poincaré spaces and their applications

Our main result offers a new (quite systematic) way of deriving bounds for the cup-length of Poincaré spaces over fields; we outline a general research program based on this result. For the oriented Grassmann manifolds, already a limited realization of the program leads, in many cases, to the exact values of the cup-length and to interesting information on the Lyusternik-Shnirel'man category.     

Limit cycles and Lie symmetries

Given a planar vector field U which generates the Lie symmetry of some other vector field X, we prove a new criterion to control the stability of the periodic orbits of U. The problem is linked to a classical problem proposed by A.T. Winfree in the seventies about the existence of isochrons of limit cycles (the question suggested by the study of biological clocks), already answered by Guckenheimer using a different terminology. We apply our criterion to give upper bounds of the number of limit cycles for some families of vector fields as well as to provide a class of vector fields with a prescribed number of hyperbolic limit cycles. Finally we show how this procedure solves the problem of the hyperbolicity of periodic orbits in problems where other criteria, like the classical one of the divergence, fail.     

There is no upper bound of small transfinite compactness degree in metrizable spaces

In [J.M. Aarts, T. Nishiura, Dimension and Extensions, North-Holland, Amsterdam, 1993], Aarts and Nishiura investigated several types of dimensions modulo a class P of spaces. These dimension functions have natural transfinite extensions. The small transfinite compactness degree trcmp is such transfinite dimension function extending the small compactness degree cmp. We shall prove that there is no upper bound for trcmp in the class of metrizable spaces, i.e. for each ordinal number α there exists a metrizable space Xα such that trcmpXα=α. We also give a characterization of the dimension dim of a separable (compact) metrizable space in terms of the function cmp of the product of this space with a nowhere locally compact zero-dimensional factor.     

Filament sets and homogeneous continua

New tools are introduced for the study of homogeneous continua. The subcontinua of a given continuum are classified into three types: filament, non-filament, and ample, with ample being a subcategory of non-filament. The richness of the collection of ample subcontinua of a homogeneous continuum reflects where the space lies in the gradation from being locally connected at one extreme to indecomposable at another. Applications are given to the general theory of homogeneous continua and their hyperspaces.     

Almost maximal spaces

A topological space X is called almost maximal if it is without isolated points and for every x∈X, there are only finitely many ultrafilters on X converging to x. We associate with every countable regular homogeneous almost maximal space X a finite semigroup Ult(X) so that if X and Y are homeomorphic, Ult(X) and Ult(Y) are isomorphic. Semigroups Ult(X) are projectives in the category F of finite semigroups. These are bands decomposing into a certain chain of rectangular components. Under MA, for each projective S in F, there is a countable almost maximal topological group G with Ult(G) isomorphic to S. The existence of a countable almost maximal topological group cannot be established in ZFC. However, there are in ZFC countable regular homogeneous almost maximal spaces X with Ult(X) being a chain of idempotents.     

化学一级强化+悬浮填料活性污泥处理污水

针对浙江无锡市惠山区新建的惠山污水处理厂设计工艺,采用化学一级强化处理工艺及悬浮填料活性污泥法,并且就这两种工艺结合组成的二级强化处理工艺在工程实践中的应用作了技术可靠性和经济合理性分析.得出化学一级强化及悬浮填料活性污泥法的处理工艺具有工程投资省、适应水质变化操作灵活等优点.但由于没有太多运行经验,所以需要一个逐步摸索的过程.