中国股票市场风险的实证分析研究

本文从实证角度说明了上证指数和深证成份指数存在着GARCH现象 ,并建立了沪、深两市股指波动率的IGARCH(1,1) M模型与EGARCH(1,1) M模型。将估计的IGARCH(1,1) M模型与EGARCH(1,1) M模型比较得出 ,对上证指数的波动率 ,IGARCH(1,1) M模型与EGARCH(1,1) M模型的模拟效果基本相同 ,而对深证成份指数的波动率 ,IGARCH M模型要略优于EGARCH M模型。同时还对两市的股指收益的波动率进行了预测分析     

A Note on Heegaard Splittings of Amalgamated 3-Manifolds

Let M be a compact orientable irreducible 3-manifold, and F be an essential connected closed surface in M which cuts M into two manifolds M1 and M2. If Mi has a minimal Heegaard splitting Mi = Vi ∪Hi Wi with d(H1) + d(H2) ≥ 2(g(M1) + g(M2) -g(F)) + 1, then g(M) = g(M1) + g(M2) - g(F).     

Sn+1中具有调和M(o)bius曲率张量的超曲面

设x:Mn→Sn 1是(n 1)维单位球面Sn 1中的无脐点的超曲面.Sn 1中超曲面x有两个基本的共形不变量:M(o)bius度量g和M(o)bius第二基本形式B.当超曲面维数大于3时,在相差一个M(o)bius变换下这两个不变量完全决定了超曲面.另外M(o)bius形式Ф也是一个重要的不变量,在一些分类定理中Ф=0条件的假定是必要的.本文考虑了Sn 1(n≥3)中具有消失M(o)bius形式Ф的超曲面:对具有调和曲率张量的超曲面进行分类,进而,在M(o)bius度量的意义下,对Einstein超曲面和具有常截面曲率的超曲面也进行了分类.     

Minimal coverings of manifolds with balls

For a closed manifold M, denote by C(M) the minimal number of balls which suffice to cover M. It is shown that C(M) coincides with the Ljusternik-Schnirelmann category cat M if the latter is not too low compared with the dimension of M. In this case it follows in particular that C(M) is an invariant of the homotopy type of M. One of the applications of this result is the following: Let M be a closed manifold of sufficiently high category. Then cat(M×S¹)=cat M+1. This is a partial affirmative answer to a long-standing conjecture.     

关于一类极大子群的θ-偶

对于有限群G的极大子群M，令β（G：M）表示整除│G：M│的素因子个数，β（G）表示所有β（G；M）中的最大数．令μ（G）为使得β（G：M）=β（G）的极大子群的集合．通过对这一类极大子群的θ-偶赋予一定条件，得到了判断群G可解、超可解的新结果．     

On Hilbert Coefficients of Filtrations

Let F be a Hilbert filtration with respect to a Cohen-Macaulay module M. When G(F,M)and F_K(F,M)have almost maximal depths,the Hilbert coefficients g_i(F,M)is calculated.In the general case,an upper bound for g_2(F,M)is also given.     

图M(P_m)和M(C_m)的点可区别边色数

本文研究了圈Cm和路Pm的Mycielski图的点可区别边染色问题.利用构造法给出了M(Cm)图的点可区别边染色法,得到了它的点可区别边色数,进而从图的结构关系,有效获得了M(Pm)图的相应点可区别边染色法和其边色数.该方法对研究存在结构关系的图染色问题具有重要的借鉴意义.     

Hutchison度量完备的充要条件

距离空间Ｘ上，以Ｍ（Ｘ）记定义在Ｘ的Ｂｏｒｅｌ域上的具有有界支撑的概度测度全体，Ｒ（Ｘ）记Ｍ（Ｘ）中所有Ｒａｄｏｎ测度，Ｍ（Ｘ），Ｒ（Ｘ）均赋予Ｈｕｔｃｈｉｓｏｎ度量，本文得到：Ｒ（Ｘ）完备当且仅当Ｘ完备且有界，若Ｘ可分，则：Ｍ（Ｘ）完备当且仅当Ｘ完备且有界。     

New dected CO(1-0) emission from planetary nebulae

We report the results of CO(1-0) (J=1-0) observations for 20 selected planetary nebulae (PNe), using the 13.7 m radio telescope of Purple Mountain Observatory at the Qinghai Station. Due to weak CO(1-0) emission, long integrated time observations have been carried out for most of sampled PNe. Among these PNe, nine are first detections in CO(1-0) named NGC6445, M1-59, M4-9, M2-51, M4-18, He2-459, Sh2-71, K3-31, M2-52, and one is the first possible detection named V-V1-8, a probably misclassified PN. NGC 6445, M1-59, M4-9 and M2-51 have been detected in CO(2-1) (J=2-1). Although having been observed in previous CO surveys, Sh2-71 and M4-18 were not detected in CO; M2-52, K3-31, He2-459 are the first detected PNe in CO emission and V-V1-8 is given with a first completed spectrum detected in CO(1-0). Comparing these data with other previous observational ones, we discuss the relationships between CO(1-0) emission and evolution of PNe: While the nebular radii increase, the CO(1-0) line integrated intensities multiplied by distances have a decreasing trend. Also the masses of molecular envelopes (from 0.001 to 1 M⊙) for PNe are decreased with increasing nebular radii. All the results mean the CO(1-0) emission decreases dramatically with the nebular evolution. The detectability of CO restricted by different PNe which have different dust properties and different evolutionary stages is also analyzed.     

Characterizations of Centralizable Mappings on Algebras of Locally Measurable Operators

A linear mapping φ from an algebra A into its bimodule M is called a centralizable mapping at G ∈ A if φ(AB)=φ(A)B=Aφ(B) for each A and B in A with AB=G. In this paper, we prove that if M is a von Neumann algebra without direct summands of type I₁ and type II, A is a *-subalgebra with M ⊆ A ⊆ LS(M) and G is a fixed element in A, then every continuous (with respect to the local measure topology t(M)) centralizable mapping at G from A into M is a centralizer.     

Trivial and simple spectrum for SL(d, ℝ) cocycles with free base and fiber dynamics

Let AC_D(M,SL(d,R)) denote the pairs (f,A) so that f ∈ A ⊂ Diff¹(M) is a C¹-Anosov transitive diffeomorphisms and A is an SL(d,R) cocycle dominated with respect to f. We prove that open and densely in AC_D(M,SL(d,R)), in appropriate topologies, the pair (f,A) has simple spectrum with respect to the unique maximal entropy measure μ_f. Then, we prove prevalence of trivial spectrum near the dynamical cocycle of an area-preserving map and also for generic cocycles in AutLeb(M) × L^p(M,SL(d,R)).     

Antisymmetry and analytic structure in the spectrum of a uniform Fréchet algebra

Let M be a C-smooth submanifold of a domain GCⁿ. Denote by 0(M) the algebra of germs of holomorphic functions on M, that is, each f0(M) is holomorphic in some neighbourhood of M, the neighbourhood dependent of f. Now define A(M) as the closure of 0(M) with respect to the topology of compact convergence on M.If M coincides with A(M), the spectrum of A(M), we give a necessary and sufficient condition for A(M) such that M is a complex manifold.     

因子von Neumann代数上的非线性Lie导子

设M是作用在维数大于2的复可分Hilbert空间,■上的因子von Neumann代数.证明了因子von Neumann代数M上的每一个非线性Lie导子具有形式A→ψ(A)+h(A)I,其中:.M→M是可加的导子,h:M→C是非线性映射且对所有A,B∈M,有h(AB-BA)=0.     

关于Malcev代数的幂零性

We investigate the nilpotence of a Malcev algebra M and of its standard enveloping Lie algebra L(M)=M D(M, M). The main result shows that an ideal A of M is nilpotent in M if and only if the corresponding ideal Ⅰ(A) = A D(A, M)is nilpotent in L(M).     

On Separation Index of Heegaard Splittings

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｃｏｎｃｅｐｔｏｆｒｅｄｕｃｉｂｌｅＨｅｅｇａａｒｄｓｐｌｉｔｉｎｇｓｗａｓｆｉｒｓｔｄｅｖｅｌｏｐｅｄｂｙＨａｋｅｎ［１］．Ｉｔｓｒｅｌａ－ｔｉｏｎｔｏｔｈｅｃｏｒｒｅｓｐｏｎｄｉｎｇ３－ｍａｎｉｆｏｌｄｓｃｏｎ...     

WHITEHEAD GROUPS OF MODULE EXTENSIONS

When R satisfies (strong unit) 1-stable range and M is a R-R-bimodule, theauthors calculate that K1(R ∞ M) ≌ U(R ∞ M)/L(R ∞ M). As applications, the authors also calculate some Whitehead groups for exchange rings with artinian primitive factors.Key words Whitehead group, module extension, (strong unit) 1-stable range     

匹配多面体的一个性质

证明了若M（G）为图G的匹配多面体,M1,M2为M（G）的两个距离为d的顶点,则M1,M2间有d条内部不相交的最短路．     

Hypersurface with Constant Main Curvature Symmetric Functions

ＨｙｐｅｒｓｕｒｆａｃｅｗｉｔｈＣｏｎｓｔａｎｔＭａｉｎＣｕｒｖａｔｕｒｅＳｙｍｍｅｔｒｉｃＦｕｎｃｔｉｏｎｓ￥ＷｕＢａｏｑｉａｎｇ；ＳｏｎｇＨｏｎｇｚａｏ（ＸｕｚｈｏｕＴｅａｃｈｅｒｓＣｏｌｌｅｇｅ，２２１００９）（ＨｅｎａｎＵｎｉｖｅｒｓｉｔｙ，...     

Nielsen theory on 3-manifolds covered by S 2 × ℝ

Let f: M → M be a self-map of a closed manifold M of dimension dim M ≥ 3. The Nielsen number N(f) of f is equal to the minimal number of fixed points of f among all self-maps f in the homotopy class of f. In this paper, we determine N(f) for all self-maps f when M is a closed 3-manifold with S²×R geometry. The calculation of N(f) relies on the induced homomorphisms of f on the fundamental group and on the second homotopy group of M.     

Mycielski图的BBC染色

基于图G的Mycielski图M（G）,研究xb（G,TG）与xb（M（G）,T’）之间的关系以及xb（G,TG）与xb（M（G）,T＂）之间的关系,其中Tc为G的生成树,T’,T＂分别为M（G）的两类特殊生成树．并给出当G为二部图,完全图以及Halin图时,Xb（M（G）,T＂）的值．