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.     

函数空间Cp(X)与有限乘积空间的弱Lindelof性

给出了空间 Ｘ 与 Ｘ 的有限乘积空间的两种弱 Ｌｉｎｄｅｌｏｆ 对偶性并证明了当 Ｘ是 Ｐ 空间时，对于 每个 ｎ ∈ ω， Ｘｎ 为拟 Ｌｉｎｄｅｌｏｆ空间当且仅当ｔ（ Ｃｐ （ Ｘ）） ＝ ω     

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…     

多元Cp值

本文给出了多元工序能力指数C_p的定义,有关分布,置信下限和判断工序是否有能力的临界值,可用来对多质量特性工序能力作统计推断。     

弱闭T(N)-模中Cp空间的等距映射

刻划了弱闭T(N)-模中Schatten类之间的等距线性满映射.设U、W分别为由左连续序同态N→和N→所确定的弱闭T(N)-模.Φ为U∩Cp到W∩Cp(1≤p<∞,p≠2)上的等距线性映射.若(0)+=(0),H-=H且min{dim(0),dim(0)#,dim(HH～),dim(HH∧)}≥2,则存在到的等距Ui(i=1,2)及酉算子Vi(i=1,2),使得Φ(A)=U1AV1或Φ(A)=V2AU2.     

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.     

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.     

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.     

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．     

l_p(Γ,X)的λ性质(英文)

本文讨论lp（Γ．X）和（ΓXt）lp的λ性质和λ-函数，从而回答了[1]的一个公开问题．     

SOME PROPERTIES OF (A)ρω(X,μ)

In this paper, we shall give a necessary and sufficient condition for which the dual of (A)pω(X, M,μ)(0 ＜ p ＜∞) is zero , and a necessary and sufficient condition for which (A)pω(X,M,μ) (0 ＜ p ＜1) is normable.     

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).     

Existence of finitely dominatedCW-complexes withG 1(X) = π1(X) and non-vanishing finiteness obstruction

We show for a finite abelian groupG and any element in the image of the Swan homomorphism sw: that it can be realized as the finiteness obstruction of a finitely dominated connectedCW-complexX with fundamental group π₁(X) =G such that π₁(X) is equal to the subgroupG ₁(X) defined by Gottlieb. This is motivated by the observation that anyH-spaceX satisfies π₁(X) =G ₁(X) and still the problem is open whether any finitely dominatedH-space is up to homotopy finite.     

LP(X)中MP归结推理

首先讨论格值命题逻辑系统LP(X)中子句的规则型范式以及极简规则型子句集的形式,然后定义MP归结式以及(A,α)-归结演绎、α-逻辑推理以及α-不可满足,讨论了它们的一系列逻辑性质,最后证明了MP归结推理的可靠性以及弱完备性.     

范畴X(R)与X-群

构造了一类新群:X-群.在环的刻划上,它反映了比Grothendieck群更为广泛的性质且更易于计算。作为应用,研究了具有无挠K₀群环的特征,得到了两个简洁的Gauss猜测的新形式。     

Dual spaces of C∞ (X)

ForX a locally compact Stonian Space, letC _∞ (X) denote the universally complete Riesz space of all extended-real-valued continuous functionsf onX for which {x∈X| |f (x)|=∞} is nowhere dense. In this paper the dual spaces ofC _∞ (X) (i.e. the spaces of order bounded; of σ-order continuous; of order continuous linear forms onC _∞ (X), and the extended order dual ofC _∞ (X) denote here byC _∞ (X)^ρ (introduced by W.A.J. Luxemburg and J.J. Masterson)) are characterized. It is shown thatC _∞ (X)^ρ can be identified in a canonical way with the inductive limitM _q (X) of the Riesz spaces of all normal Radon measures defined on the dense open subsets ofX. More generally, ifY is a locally compact space thenM _q (Y) is the extended order dual of the inductive limit of the Riesz spaces of all real-valued continuous functions defined on the dense open subsets ofY. IfX is locally compact and hyperstonian, then it is proved thatC _∞ (X) andC _∞ (X)^ρ are isomorphic, and a criterion forC _∞ (X)^ρ to be the universal completion of the space of order continuous linear forms onC _∞ (X) is given.     

相对于g(X)的导出范畴

设A是有足够投射对象的Abel范畴,(x,y)是A中的完备遗传余挠对.本文引入Gorenstein x-导出范畴,记作Dg(x)(A),并且从不同的角度研究D_g(x)(A).当(x,y)取作特殊的余挠对时,得到一些已知的导出范畴,如Gorenstein导出范畴和Gorenstein平坦导出范畴等.通过与g(X)有关的同伦范畴K~(-,gxb)(g(x))描述有界Gorenstein x-导出范畴D~b_(g(x))(A)和有界导出范畴D~b(A),并给出一些三角等价.     

Fuzzy-valued Propositional Logic FP~* (X)

Ｆｕｚｚｙ－ｖａｌｕｅｄＰｒｏｐｏｓｉｔｉｏｎａｌＬｏｇｉｃＦＰ~＊（Ｘ）￥ＱｉｎＫｅｙｕｎ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈ．，ＨｅｎａｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，４５３００２）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒ，ｗｅｔａｋｅ［０，１?..     

Units of ℤ(Cp × C2) and ℤ(Cp × C2 × C2)

The goal of this article is to describe a multiplicatively independent set, which generates the group of units of the integral group ring ?G, where G is either the cyclic group of order 2p or C₂ × C₂ × C_p, for a prime number p that satisfies some suitable conditions that will be specified later.