A metrizable X with Cp(X) not homeomorphic to Cp(X) × Cp(X)

We give an example of an infinite metrizable space X such that the space C_p(X), of continuous real-valued functions on X endowed with the pointwise topology, is not homeomorphic to its own square C_p(X) × C_p(X). The space X is a zero-dimensional subspace of the real line. Our result answers a long-standing open question in the theory of function spaces posed by A. V. Arhangel’skii.     

统计学入门(X)

二十、两个正态总体方差的比较20-1.两个正态总体样本方差比的分布,F分布 为对两个正态总体的方差进行比较和检验,我们首先讨论来自两个正态分布的独立样本的样本方差比的分布。这个分布称为F分布。 设 , 是相互独立的两个随机变量,的分布称为自由度为f1,f2的 F分布,记为F(f1,f2).其中f1和f2分别称为第一(分子)自由度与第二(分母)自由度,其顺序不能颠倒。显然F只能取正值,它的分布曲线的形状见图20—1. 与x2分布类似,我们可以定义F分布的上侧分位数。对任意概率p,可确定一个正数Fp(f1,f2),使得则Fp(f1,f2)称为自由度为f1,f2的F分布的上…     

J值法(一种新的X射线衍射物相定量法)中配比的最优化

在综合利用钢渣中,遇到准确测定钢渣中游离氧化钙含量的问题,上钢一厂开展了对该问题的研究,提出一种新的X射线衍射物相定量法——J值法。本文由J值法的要求,建立J值法中配比优化的数学模型,提出其求解方法,并用计算机进行计算。该法经实际使用,适用性强,计算迅速,结果准确,为在定量分析中采用数学方法及计算机技术作了新的探索,经过专家鉴定,认为值得推广应用。     

向量值鞅空间_pH_T~S(X)与_pH_r~σ(X)的共轭

证明了B值鞅空间,pHSr(X)和pHσr(X)的共轭分别是qKSr′(X*)与qKσr′(X*),此外还讨论了pKSr(X)和pKr(X),pKσr(X)和pK+r(X)的相互嵌入关系与Banach空间的p一致光滑性和q一致凸性之间的密切联系.     

透镜空间L~n(4)的J群

<正> 设L~n(4)为透镜空间.在[6]中计算了K_∧(L~n(4)).在本文中计算了J(L~N(4)),所用的符号完全和[6]中相同.为了方便,叙述KO(L~n(4))的结果如下: 设CP~n是n维复射影空间,以及     

The cardinality of β A (S J )

Let J be an infinite set and let $I=\mathcal{P}_{f}( J)$ . For i??I, define $\mathcal{B}_{J}( i) =\{ f\mid f:\mathcal{P}( i) \rightarrow \mathcal{P}( i) \} $ and let $$S_{J}=\{ ( i,f) \mid i\in I\text{ and } f\in \mathcal{B}_{J}( i) \}.$$ For (i,f), (k,g)??S _J , define $f\ast g:\mathcal{P}( i\cup k) \rightarrow \mathcal{P}( i\cup k) $ as follows. For $x\in \mathcal{P}( i\cup k) $ , let $$( f\ast g) ( x) =\left\{\begin{array}{l@{\quad }l}g( x) , & \text{if\ }x=\emptyset, \\g( x\cap k) , & \text{if\ }x\cap k\neq \emptyset, \\f( x) , & \text{if\ }x\in \mathcal{P}( i\backslash k)\text{ and }x\neq \emptyset.\end{array}\right.$$ Define (i,f)?(k,g)=(i??k,f?g). It is shown that (S _J ,?) is a semigroup. Let ??S _J denote the collection of all ultrafilters on the set S _J . We consider (??S _J ,?), the compact (Hausdorff) right topological semigroup that is the Stone?C?ech Compactification of the semigroup (S _J ,?) equipped with the discrete topology. Similar to the construction in Grainger (Semigroup Forum 73:234?C242, 2006), it is shown that there is an injective map A???? _A (S _J ) of $\mathcal{P}( J) $ into $\mathcal{P}( \beta S_{J}) $ such that each ?? _A (S _J ) is a closed subsemigroup of (??S _J ,?), the set ?? _J (S _J ) is the smallest ideal of (??S _J ,?) and the collection $\{ \beta_{A}( S_{J}) \mid A\in \mathcal{P}( J) \} $ is a partition of???S _J . The main result is establishing that the cardinality of??? _A (S _J ) is $2^{2^{\vert J\vert }}$ for any?A?J.     

Continuous Selections in C(X)

Suppose C(X)is a Banack space of real-valued continuous functions on X.For a finite-dimensional subapace G C(X),define d(f; G)=inf{||f-g||:g∈G}; P_G(f)={g∈G: ||f-g||=d(f;G)}. If there exists a continuous mapping S from C(X)to G such that S(f)∈P_G(f)for every f∈C(X),then we say P_G has a continuous selection. In this paper,we give several characterizations of P_G with a continuous sele-ction.     

Lindelöf σ-property in Cp(X) and p(Cp(X)) = ω do not imply countable network weight in X

We prove that there are Tychonoff spaces X for which p(C_p(X)) =? and C_p(X) is a Lindelöf Σ-space while the network weight of X is uncountable. This answers Problem 75 from [4]. An example of a space Y is given such that p(Y)=? and C_p(Y) is a Lindelöf Σ-space, while the network weight of Y is uncountable. This gives a negative answer to Problem 73 from [4]. For a space X with one non-isolated point a necessary and sufficient condition in terms of the topology on X is given for C_p(X) to have countable point-finite cellularity.     

向量值鞅空间pHST(X)与pHσr(X)的共轭

证明了B值鞅空间,pH^Sr(X)和pH^σr(X)的共轭分别是qK^Sr′(X^*)与qK^σr′(X^*)，此外还讨论了pK^Sr(X)和pKr(X)，pK^σr(X)和pK^ r(X)的相互嵌入关系与Banach空间的P一致光滑性和q一致凸性之间的密切联系．     

On Banach spaces X for which Π2 (X,L 1) = N1(X,L 1)

We prove that every 2-summing operator from a Banach space X into an L ₁-space is nuclear if and only if X is isomorphic to a Hilbert space. Then we study the class of Banach spaces X for which Π₂(l ₂, X) = N ₁(l ₂, X).     

J(o)rgens结果的一个新证明

文章研究有界线性算子半群的扰动问题.在一定条件下,我们表明:设算子B生成最终依范连续半群S(t)(t≥τ),K是有界线性算子.如果‖ KR(σ+iτ,B)K ‖→0,τ→∞,那么算子A=B+K生成的半群T(t),t＞2τ是依范连续的.我们将此结果应用于迁移箅子,给出Jorgens结果的一个新证明.     

Ein Wohlordnungsbeweis für das OrdinalzahlensystemT(J)

Summary A recursive notation system of a strong segment of ordinals was developped by Jäger [3]. An unessential modified versionT(J) of this notation system was described in [4]. In the following, the well-ordering ofT(J) is proved in a formal system of second order arithmetic with the axiom schema of ₂ ¹ -comprehension. It follows, that the proof theoretical ordinal of ₂ ¹ -analysis is greater than the order type ofT(J).     

J—J方程组的渐近惯性流形

本文构造了Ｌｉａｐｕｎｏｖ泛函，得出了Ｊｏｓｅｐｈｓｏｎ结中的ｓｉｎｅ－Ｇｏｒｄｏｎ方程组的高模态的衰减性质，从而给出了渐近惯性流形。     

刚性方程组M(X)(t)+C(X)(t)+KX(t)=F(t)解的探讨

讨论了刚性常微分方程组(1)的解析解和数值解,给出了解的一般形式和应用该算法的数值例子.     

CP(2n)∧L_p(p 为素数)的 J 群

<正> 设 CP(2n) 为复2n 维射影空间.L_p 是 co-moore 空间 S~1∪_fe~2,f:S~1→S~1为保持基点、度数为 p 的映射([9,631页]).本文的目的是计算了(?)(CP(2n)∧L_p),这里出现的p 都是素数.     

On Polarized Surfaces (X, L) with h0(L) > 0, κ(X) ≥ 0 and g(L) = q(X) + 1

Let (X,L) be a polarized surface. If h⁰(L)>0, then g(L) q(X). In our previous papers, we classified polarized surfaces (X,L) with g(L)=q(X) and h⁰(L)>0. In this paper, we classify polarized surfaces (X,L) with g(L)=q(X)+1, h⁰(L)>0, and (X) 0.     

Some Conditions for K_0(B(X))=0

Let A be an unital Banach algebra with the unital element I. We denote the set of (n×n)-matrices over A by Mn(A). The set of idempotent elements of A is denoted by P1(A):={P∈A: P2=P}, and accordingly the set of idempotent elements of Mn(A) is denoted by Pn(A):=P1(Mn(A)). We define P∞(A) :=∪n∈N Pn(A). In the set of P∞(A), for P,Q ∈ Pn(A), we say that P is (algebraic) equivalent to Q, if there exist A,B∈ Mn(A) such that