高阶上同调运算与 π~n(K~(n+3))

<正> 在[1]里面,张素诚从同伦边界的观念入手,系统地介绍了同调运算和精密的问调运算.我们现在从上同伦的情形出发,所获得的运算是上同调运算.在用这个办法所得到的上同调运算中,包括有熟知的 Steenrod 平方、J.Adem 二阶运算 Φ.就象通常所知道的那样,Steenrod 平方可以用来解决映(n+1)维多面体入 n 维球的映射的分类间     

Multi-step hybrid methods for special second-order differential equations y″(t) = f(t,y(t))

In this paper, multi-step hybrid methods for solving special second-order differential equations y^″(t) = f(t,y(t)) are presented and studied. The new methods inherit the frameworks of RKN methods and linear multi-step methods and include two-step hybrid methods proposed by Coleman (IMA J. Numer. Anal. 23, 197–220, 8) as special cases. The order conditions of the methods were derived by using the SN-series defined on the set SNT of SN-trees. Based on the order conditions, we construct two explicit four-step hybrid methods, which are convergent of order six and seven, respectively. Numerical results show that our new methods are more efficient in comparison with the well-known high quality methods proposed in the scientific literature.     

Computation of K0(RMNS_(θ,h))

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｐｕｒｐｏｓｅｏｆｔｈｉｓｐａｐｅｒｉｓｔｏｃｏｍｐｕｔｅｔｈｅＧｒｏｔｈｅｎｄｉｅｃｋｇｒｏｕｐｏｆＴ＝ＲＭＮＳ（θ，φ）．ＴｉｓｃａｌｌｅｄｔｈｅｒｉｎｇｏｆＭｏｒｉｔａＣｏｎｔｅｘｔｉｎｓｏｍｅｌｉｔｅｒａｔｕｒｅ（ｓｅｅ［１］）．Ｉｎ１９７４，ＱｕｉｌｌｅｎａｎｎｏｕｃｅｄｔｈａｔＫ０（ＲＭＯＳ）Ｋ０（Ｒ）Ｋ０（Ｓ）．ＵｐｔｏｔｈｅｐｒｅｓｅｎｔｍｏｍｅｎｔｔｈｅｒｅｓｔｉｌｌｅｘｉｓｔｓｎｏｉｎｆｏｒｍａｔｉｏｎｃｏｎｃｅｒｎｉｎｇＫ０（Ｔ）ｆ…     

Transformations z(t) = L(t)y(ϕ(t)) of ordinary differential equations

The paper describes the general form of an ordinary differential equation of an order n + 1 (n ≥ 1) which allows a nontrivial global transformation consisting of the change of the independent variable and of a nonvanishing factor. A result given by J. Aczél is generalized. A functional equation of the form $f\left( {s,w_{00} \upsilon _0 ,...,\sum\limits_{j = 0}^n {w_{nj\upsilon _j } } } \right) = \sum\limits_{j = 0}^n {w_{n + 1j\upsilon j} + w_{n + 1n + 1} f\left( {x,\upsilon ,\upsilon _1 ,...,\upsilon _n } \right),}$ where $w_{n + 10} = h\left( {s,x,x_1 ,u,u_1 ,...,u_n } \right),w_{n + 11} = g\left( {s,x,x_1 ,...,x_n ,u,u_1 ,...,u_n } \right){\text{ and }}w_{ij} = a_{ij} \left( {x_i ,...,x_{i - j + 1} ,u,u_1 ,...,u_{i - j} } \right)$ for the given functions a _ij is solved on $\mathbb{R},u \ne {\text{0}}$ .     

On conditional expectations in $$L^p(\mu ;L^q(\nu ;X))$$ L p ( μ ; L q ( ν ; X ) )

Positivity - Let $$(A,{\mathscr {A}},\mu )$$ and $$(B,{\mathscr {B}},\nu )$$ be probability spaces, let $${\mathscr {F}}$$ be a sub- $$\sigma $$ -algebra of the product $$\sigma $$ -algebra...     

On solvability of f(p(x)) = q(f(x)) for given real functions p,q

We investigate the solvability of functional equations f(p(x)) =  q(f(x)) for given functions p and q which are partially or completely defined on the set of all real numbers. For these investigations, we use methods for constructions of homomorphisms of mono-unary algebras. We can present a simple characterisation of solvability of the above equation in the case that p, q are strictly increasing and continuous functions. It gives, on the one hand, a practical use for a class of functional equations. On the other hand, it is a contribution to questions on topological conjugacy of monotonous real functions.     

Gal(E/F)与Gal(L(E)/L(F))的同构

Let E be a field of finite extension of a perfect field F. We show that Gal(E/F) is isomorphic to Gal(L(E)/L(F)).     

内-(π,π′)-闭群与Isaacs定理

一群G叫做内-Σ群,若G不为Σ群但其每真子群为Σ群。群G叫做(π,π′)-闭,若G为π-闭或π′-闭,其中π′是π对素数全集的余集。G叫做π-闭,若其有正规π-Hall子群。本文给出了内-(π,π′)-闭群的结构并得到了下述结果。 设群G的p-Sylow子群循环。如果1)每p′-子群幂零;2)对每q|p-1,G的q-Sylow子群为准正则;3)当p=3时,G与S_4无关,则G为(p,p′)-闭群。     

A cosine operator approach to modelingL 2(0,T; L 2 (Γ))—Boundary input hyperbolic equations

This paper investigates the regularity properties of the solution of a second-order hyperbolic equation defined over a bounded domain with boundary , under the action of a boundary forcing term inL ₂(0,T; L ₂()). Both Dirichlet and Neumann nonhomogeneous cases are considered. A functional analytic model based on cosine operator functions is presented, which provides an input-solution formula to be interpreted in appropriate topologies. With the help of this model, it is shown, for example, that the solution of the nonhomogeneous Dirichlet problem is inL ₂(0,T; L ₂()), when is either a parallelepiped or a sphere, while the solution of the nonhomogeneous Neumann problem is inL ₂(0,T; H ^3/4-e()) when is a parallelepiped and inL ₂(0,T; H ^2/3() when is a sphere. The Dirichlet case for general domains is studied by means of pseudodifferential operator techniques.This research was supported in part by the Air Force Office of Scientific Research under Grant AFOSR-78-3350 (1st author) and Grant AFOSR-77-3338 (2nd author).This research was performed while the author was visiting the Department of System Science, University of California, Los Angeles.     

三角形与0,π/3的缘份

请看下面一些重要事实:△ABC中,有关等差、等比数列与范围0,π/3结下不解之缘.亲爱的读者将会疑云顿消,晴空万里.     

函数π(x;α,β)的单调性

在文章中，我们对Gerber(1992)所提出的与函数π（x;α,β)相关的单调性问题给出了一个分析的证明。     

L2(B2, d(z))正交分解及 Hankel型算子

令B2是2维复平面C2上的单位球,d(z)=((+1)(+2))/(2)(1-|z|2)dm(z) ( > - 1)是它上的加权测度.由Cauchy-Riemann算子观点和［1］中给出的三角域上的正交多项式, 我们得到了正交分解L2(B2,d(z)) = n = 0(An(+,+) An(+,-) An(-,+) An(-,-))和正交基,其中A0(+,+)和A0(-,-)分别是Bergman空间和共轭Bergman空间.利用单纯形上的正交多项式,可以将这种分解推广到L2(Bn, d(z))上去.另外,我们还得到了Hankel型算子的一些结果.     

The existence spectrum of Meta(K 4 (3) >K 4 (3) − e)

Let H and J1 be both t-uniform hypergraphs. Let J2 be a sub-hypergraph of J1. In this paper, the metamorphosis of a hypergraph decomposition is introduced, denoted by (H, J1 J2)-design, which is a generalization of the concept of metamorphosis of a graph decomposition. Let Meta(J1J2) denote the set of all integers v such that there exists a (Kv((3)), J1J2)-design. We completely determine the set Meta(K4((3))K4((3))-e).     

实(四元)Stiefel流形V_(n,2)(X_(n,2))的KO-群和J-群

<正> 命V_(n,2),X_(n,2)为实、四元Stiefel流形(实、四元n维欧氏空间中的所有二维正交标架)。本文在§1中计算了KO~(-i)(V_(n,2)以及J(V_(n,2)):在§2中计算了KO~(-i)(X_(n,2)以及J(X_(n,2)).映射c,r分别表示为复化和实化,定义可见[1,610页].     

SL(n,K)在 GL(n,F)(KF)中的扩群

设 F 是任意域.当 K 是 F 的子域且[F:K]<(?)时,或当 K 是 F 的极大子环但不是域时,本文定出了 SL(n,K)在 GL(n,F)中的全部扩群,从而得出了 SL(n,F)的一类极大子群.     

SL(n,K)在 GL(n,F)(KF)中的扩群

设 F 是任意域.当 K 是 F 的子域且[F:K]<(?)时,或当 K 是 F 的极大子环但不是域时,本文定出了 SL(n,K)在 GL(n,F)中的全部扩群,从而得出了 SL(n,F)的一类极大子群.     

方程(dx-dt=(ψ)(y)-F(x),dy-dt=h(x,y)-g(x))的极限环存在定理

在不同的区域上构造适当的比较函数,将Filippov定理推广到更一般的非线性系统(dx-dx==(ψ)(y)-F(x),dy-dt=h(x,y)-g(x)).     

一类裂变图的L(_(d,d,1)~(0,1,2))-标号数上界

将图的标号问题由每个顶点需要一个标号的情况推广到每个顶点需要多个标号的情况,给出裂变图的概念以及赋权图的L(_(d,d,1)~(0,1,2))-标号的概念,给出R-单位球图对应裂变图的L(_(d,d,1)~(0,1,2))-标号数的一个上界。     

Discrete Morse theory and a reformulation of the K(π,1)-conjecture

A recent theorem of Dobrinskaya [20 Dobrinskaya, N.È. (2006). Configuration spaces of labeled particles and finite Eilenberg-MacLane complexes. Proc. Steklov Inst. Math. 252(1):30–46.[Crossref] , [Google Scholar]] states that the K(π,1)-conjecture holds for an Artin group G if and only if the canonical map BM→BG is a homotopy equivalence, where M denotes the Artin monoid associated to G. The aim of this paper is to give an alternative proof by means of discrete Morse theory and abstract homotopy theory. Moreover, we exhibit a new model for the classifying space of an Artin monoid, in the spirit of [13 Charney, R., Meier, J., Whittlesey, K. (2004). Bestvina’s normal form complex and the homology of Garside groups. Geom. Dedicata 105:171–188.[Crossref], [Web of Science ®] , [Google Scholar]], and a small chain complex for computing its monoid homology, similar to the one of [44 Squier, C. C. (1994). The homological algebra of Artin groups. Math. Scand. 75(1):5–43.[Crossref], [Web of Science ®] , [Google Scholar]].