具有性质$b_1$空间的乘积性

In this note,we present that:(1)Let X=σ{Xα:α∈A} be|A|-paracompact (resp.,hereditarily |A|-paracompact).If every finite subproduct of {Xα:α∈A} has property b1 (resp.,hereditarily property b1),then so is X.(2) Let X be a P-space and Y a metric space.Then,X×Y has property b1 iff X has property b1.(3) Let X be a strongly zero-dimensional and compact space.Then,X×Y has property b1 iff Y has property b1.     

On the Howson Property of HNN-Extensions with Nilpotent Base Group and Amalgamated Free Products of Nilpotent Groups

We give necessary and sufficient conditions under which an amalgamated free product of finitely generated nilpotent groups is a Howson group (that is the intersection of any two finitely generated subgroups is finitely generated). Also we prove that if G = ? t, K | t ^?1 At = B ?, where K is a finitely generated and infinite nilpotent group and A, B non-trivial infinite proper subgroups of K, then G is not a Howson group. The problem of deciding when an ascending HNN-extension of a finitely generated nilpotent group is a Howson group is still open.     

On Countable Products of Finite Hausdorff Spaces

We investigate in ZF (i.e., Zermelo‐Fraenke set theory without the axiom of choice) conditions that are necessary and sufficient for countable products ∏_m∈ℕX_m of (a) finite Hausdorff spaces X_m resp. (b) Hausdorff spaces X_m with at most n points to be compact resp. Baire. Typica results: (i) Countable products of finite Hausdorff spaces are compact (resp. Baire) if and only if countable products of non‐empty finite sets are non‐empty. (ii) Countable products of discrete spaces with at most n + 1 points are compact (resp. Baire) if and only if countable products of non‐empty sets with at most n points are non‐empty.     

知识产权保护、模仿威胁、研发能力与高技术产品出口

基于我国2004-2013年对30个主要贸易伙伴国的高技术产品出口的面板数据,采用扩展的贸易引力模型,依次从总体样本、模仿威胁和研发能力三个层面,实证检验了进口国知识产权保护水平对我国高技术产品出口贸易的影响效应.研究表明:从总体看,进口国知识产权保护水平的提升对我国高技术产品的出口具有明显的促进作用;考虑模仿威胁,发现模仿威胁程度不同的进口国,加强知识产权保护都会增加我国高技术产品的出口;考虑研发能力,发现知识产权保护的促进作用依然显著.     

$(\omega_1)$性质与单值延拓性质

In this note we study the property（ω1）,a variant of Weyl＇s theorem by means of the single valued extension property,and establish for a bounded linear operator defined on a Banach space the necessary and sufficient condition for which property（ω1） holds.As a consequence of the main result,the stability of property（ω1） is discussed.     

On strongly α-preinvex functions

In this paper, by means of a series of counterexamples, we study in a systematic way the relationships among (pseudo, quasi) α-preinvexity, (strict, strong, pseudo, quasi) α-invexity and (strict, strong, pseudo, quasi) αη-monotonicity. Results obtained in this paper can be viewed as a refinement and improvement of the results of Noor and Noor [M.A. Noor, K.I. Noor, Some characterizations of strongly preinvex functions, J. Math. Anal. Appl. 316 (2006) 697–706].     

Clone Segments of the Tychonoff Modification of Space

For every natural number n > 1, we construct a topological space X such that the clone segments of its Tychonoff modification T M X verify Clo _k (X) = Clo _k (T M X) if k < n and Clo _n (X) is not isomorphic to Clo _n (T M X).     

On Products of Shifted Primes

Any rational representable as a product of shifted primes p+1 or their reciprocals, has a representation with exactly 19 terms.     

关于相对紧性质的研究

利用有限交性质的集族及网的性质描述了相对紧性质,给出了相对紧性质的两个等价结果.     

一类积分函数的SC1性质

研究一类积分函数的半光滑性和SC1性质,所得结果在求解随机线性互补问题的Newton算法的收敛性分析中起关键作用.     

一类积分函数的SC^1性质

研究一类积分函数的半光滑性和SC^1性质,所得结果在求解随机线性互补问题的Newton算法的收敛性分析中起关键作用.     

关于正规δθ-可加空间的逆极限

This paper proves the following results: Let X = lim← { Xσ,π^σρ，∧ },| ∧ | =λ, and every pro-jection πσ : X → Xσ be an open and onto mapping. (A) If X is λ-paracompact and every Xσ is normal and δθ-refinable, then X is normal and δθ-refinable; (B) If X is hereditarily λ-pamcompact and every Xσ is hereditarily normal and hereditarily δθ-refinable, then X is hereditarily normal and hereditarily δθ-refiable.     

Super-Relational Fixed Point Property and Products in Ordered Sets

Super-relational fixed point property for ordered sets is formulated. It is weaker than the strengthened fixed point property and stronger than the product property. Presented at the Summer School on General Algebra and Ordered Sets, Radějov, 3–9 September 2006.     

一类第一 Betti数为奇数的曲面上的向量丛

本文得到一些有关一类第一Betti数为奇数的曲面上的全纯向量丛的结果,以及例外Hopf曲面上的集合IS2(X,0)的描述．     

𝒱-Nilpotent Groups and 5-Term Exact Sequence

In this paper, we prove that any nontrivial normal subgroup N of 𝒱-nilpotent group G, intersects nontrivially with the marginal subgroup of G with respect to the variety 𝒱. This is a generalization of a well-known theorem by Philip Hall which refers to the case where 𝒱 is the variety of abelian groups. Moreover, we give a generalized version of a 5-term exact sequence of homology groups and establish some isomorphisms of the factors of the lower marginal series.     

On the Density Property of P𝒮C Fields

Let 𝒮 be a finite set of finite and real local primes of a field K. We prove two results. First, a PAC field over K is already PAC over each nonempty 𝒮‐open subset of K; if K is global, this implies that it is also PAC over each separable Hilbert subset of K. Second, each P𝒮C field inside K_tot,𝒮 has the 𝒮‐density property.     

Exactly -to-1 maps and hereditarily indecomposable tree-like continua

In 1947, W.H. Gottschalk proved that no dendrite is the continuous, exactly -to-1 image of any continuum if . Since that time, no other class of continua has been shown to have this same property. It is shown that no hereditarily indecomposable tree-like continuum is the continuous, exactly -to-1 image of any continuum if .