群定律与群簇

Letω1 and ω2 be two homogeneous words and suppose that they respectively define the varieties Vω1 and Vω2 of groups.Denote by θωi the standard exponent of ωi for i = 1,2,which was introduced in Ref.[1].We obtain that if Vω1 (∈) Vω2,then θω1|θω2.     

Discreteness of Flux Groups

Let （M, ω） be a closed symplectic 2n-dimensional manifold. Donaldson in his paper showed that there exist 2m-dimensional symplectie submanifolds （V^2m,ω） of （M,ω）, 1 ≤m ≤ n - 1, with （m - 1）-equivalent inclusions. On the basis of this fact we obtain isomorphic relations between kernel of Lefschetz map of M and kernels of Lefschetz maps of Donaldson submanifolds V^2m, 2 ≤ m ≤ n - 1. Then, using this relation, we show that the flux group of M is discrete if the action of π1 （M） on π2（M） is trivial and there exists a retraction r ： M→ V, where V is a 4-dimensional Donaldson submanifold. And, in the symplectically aspherical case, we investigate the flux groups of the manifolds.     

The SL(V)-ample Cone of Product of Flag Varieties

Let k be an algebraically closed field, and V be a vector space of dimension n over k. For a set ω =(d(1),...,d(m)) of sequences of positive integers, denote by Lω the ample line bundle corresponding to the polarization on the product X =∏m i=1Flag(V, n(i)) of flag varieties of type n(i)determined by ω. We study the SL(V)-linearization of the diagonal action of SL(V) on X with respect to Lω. We give a sufficient and necessary condition on ω such that Xss(Lω) ≠φ(resp., Xs(Lω) ≠φ).As a consequence, we characterize the SL(V)-ample cone(for the diagonal action of SL(V) on X),which turns out to be a polyhedral convex cone.     

Symplectic Diffeomorphisms with Infinitely Many Elliptic Periodic Points

§ 1.Introduction and Statement of Main Results　 Let M be2 n-dimensional compactmanifold with a symplectic structureω.Recall thata symplectic structureω is a non-degenerate differential2 -form on M.A diffeomorphismf that preserves symplectic formω,i.e.,f* ω=ω,is called a symplectic diffeomor-phism.Symplectic diffeomorphism arises naturally as time-one map and the Poincarémap of Hamiltonian systems.　Let Diffrω(M) denote the set of Cr diffeomorphisms on M that preserveω,with uni-f…     

Problems of Lifts in Symplectic Geometry

Let(M,ω)be a symplectic manifold.In this paper,the authors consider the notions of musical(bemolle and diesis)isomorphisms ω~b:T M→T~*M and ω~?:T~*M→TM between tangent and cotangent bundles.The authors prove that the complete lifts of symplectic vector field to tangent and cotangent bundles is ω~b-related.As consequence of analyze of connections between the complete lift ~cω_(T M )of symplectic 2-form ω to tangent bundle and the natural symplectic 2-form dp on cotangent bundle,the authors proved that dp is a pullback o f~cω_(TM)by ω~?.Also,the authors investigate the complete lift ~cφ_T~*_M )of almost complex structure φ to cotangent bundle and prove that it is a transform by ω~?of complete lift~cφ_(T M )to tangent bundle if the triple(M,ω,φ)is an almost holomorphic A-manifold.The transform of complete lifts of vector-valued 2-form is also studied.     

KERNEL WORDS AND GAP SEQUENCE OF THE TRIBONACCI SEQUENCE

In this paper, we investigate the factor properties and gap sequence of the Tribonacci sequence, the fixed point of the substitution σ(a, b, c) =(ab, ac, a). Let ωpbe the p-th occurrence of ω and Gp(ω) be the gap between ωpand ω_(p+1). We introduce a notion of kernel for each factor ω, and then give the decomposition of the factor ω with respect to its kernel. Using the kernel and the decomposition, we prove the main result of this paper:for each factor ω, the gap sequence {Gp(ω)}p≥1is the Tribonacci sequence over the alphabet{G_1(ω), G_2(ω), G_4(ω)}, and the expressions of gaps are determined completely. As an application, for each factor ω and p ∈ N, we determine the position of ωp. Finally we introduce a notion of spectrum for studying some typical combinatorial properties, such as power, overlap and separate of factors.     

Note on the Concept of Microscopic Measure in R

As is known [1], N= {v|1≤v<(ω)} is the non-Cantorian model of natural numbers in which (ω) denotes the galaxy of the infinite integer ω, and v<(ω) means that v<ω±n n∈N (set of ordinary natural numbers). All the infinite integers contained in N constitute the flying segment and may be denoted by N.It may be viewed that N is the telescopic contents of N when N is embedded and     

On the Approximation of Continuous Function by Harmonic Means

Let f(x) be a continuous and periodic function with period 2π and [f]=a_o/2+sum from n=1 to ∞(a_ncos nx+b_nsin nx) be its Fourier series. Denote by s_n(f,x) the n-th partial sums of [f] and by ω(f,δ) the moduls of continuity of f(x). When ω(δ) is a modul of continuity, we denote by H[ω]。the class of all functions for which ω(f,t)≤ω(t). It is well known that the n-th harmonic means and the n-th Cesro means of f∈C_2, are defined as##属性不符     

POWERS OF AN INVERTIBLE （s,p） - ω-HYPONORMAL OPERATOR

It is known that the square of a ω-hyponormal operator is also ω-hyponormal. For any 0〈 p 〈 1, there exists a special invertible operator such that all of its integer powers are all p - ω-hyponormal. In this article, the author introduces the class of （s, p） -ω-hyponormal operators on the basis of the class of p- ω-hyponormal operators. For s 〉0, 0 〈 p 〈 1, the author gives a characterization of （s,p） -ω-hyponormal operatots; the author shows that all integer powers of special （s, p） -ω-hyponormal operators are （s,p） -ω-hyzponormal.     

Quasi-periodic solutions of a semilinear Li(?)nard equation at resonance

We are concerned with the existence of quasi-periodic solutions for the follow- ing equation x″ F_x(x,t)x′ ω~2x φ(x,t)=0, where F and φare smooth functions and 2π-periodic in t,ω>0 is a constant.Under some assumptions on the parities of F and φ,we show that the Dancer's function,which is used to study the existence of periodic solutions,also plays a role for the existence of quasi-periodic solutions and the Lagrangian stability (i.e.all solutions are bounded).     

一类二元相关威布尔分布及其参数估计

考虑生存函数为的二元威布尔分布,提出θ1,θ2,α,δ的估计并讨论了它们的渐近性,最后作模拟计算,得出了参数估计的渐近效．     

广义超特殊p-群的自同构群Ⅲ

确定了广义超特殊p-群G的自同构群的结构.设|G|=p~(2n+m),|■G|=p~m,其中n≥1,m≥2,Aut_fG是AutG中平凡地作用在Frat G上的元素形成的正规子群,则(1)当G的幂指数是p~m时,(i)如果p是奇素数,那么AutG/AutfG≌Z_((p-1)p~(m-2)),并且AutfG/InnG≌Sp(2n,p)×Zp.(ii)如果p=2,那么AutG=Aut_fG(若m=2)或者AutG/AutfG≌Z_(2~(m-3))×Z_2(若m≥3),并且AutfG/InnG≌Sp(2n,2)×Z_2.(2)当G的幂指数是p~(m+1)时,(i)如果p是奇素数,那么AutG=〈θ〉■Aut_fG,其中θ的阶是(p-1)p~(m-1),且Aut_f G/Inn G≌K■Sp(2n-2,p),其中K是p~(2n-1)阶超特殊p-群.(ii)如果p=2,那么AutG=〈θ_1,θ_2〉■Aut_fG,其中〈θ_1,θ_2〉=〈θ_1〉×〈θ_2〉≌Z_(2~(m-2))×Z_2,并且Aut_fG/Inn G≌K×Sp(2n-2,2),其中K是2~(2n-1)阶初等Abel 2-群.特别地,当n=1时...     

{C}^n$中单位球上Bergman型空间的一种积分算子

设$\omega_1,\omega_2$为正规函数, $\varphi$是$B_n$ 上的全纯自映射,$ g\in H(B_n)$ 满足 $g(0)=0$. 对所有的$0相似文献   

最大度与最小度相差不超过2的图的平衡judicious划分

图G的顶点集V(G)的一个二部划分V_1和V_2叫做平衡二部划分,如果||V_1|-|V_2||≤1成立.Bollobas和Scott猜想:每一个有m条边且最小度不小于2的图,都存在一个平衡二部划分V_1,V_2,使得max{e(V_1),e(V_2)}≤m/3,此处e(V_i)表示两顶点都在V_i(i=1,2)中的边的条数.他们证明了这个猜想对正则图(即△(G)=δ(G))成立.颜娟和许宝刚证明了每个(k,k-1)-双正则图(即△(G)-δ(G)≤1)存在一个平衡二部划分V_1,V_2,使得每一顶点集的导出子图包含大约m/4条边.这里把该结论推广到最大度和最小度相差不超过2的图G.     

Asymptotics of Analytic Semigroups,II

Let $T(\cdot)$ be an analytic $C_0$-semigroup of operators in a sector $S_{\theta}$, such that $||T(\cdot)||$ is bounded in each proper subsector $S_{\theta_0}$. Let $A$ be its generator, and let $D^{\infty}(A)$ be its set of $C^{\infty}$-vectors. It is observed that the (general) Cauchy integral formula implies the following extension of Theorem 5.3 in [1] and Theorem 1 in [4]: for each proper subsector $S_{\theta_0}$, there exist positive constants $M,\,\delta$ depending only on $\theta_0$, such that $(\delta^n/n!)||z^nA^nT(z)x||\leq M\,||x||$ for all $n\in\Bbb N,\, z\in S_{\theta_0}$, and $x\in D^{\infty}(A)$. It follows in particular that the vectors $T(z)x$ (with $z\in S_{\theta}$ and $x\in D^{\infty}(A)$) are analytic vectors for $A$ (hence $A$ has a dense set of analytic vectors).     

E1 ο Ed型距离正则图及 Q -多项式的性质

设$\Gamma$ 是一个直径$d\geq 3$的非二部距离正则图，其特征值 $\theta_{0}>\theta_{1}>\cdots>\theta_{d}.$ 设$\theta_{1'}\in\{ \theta_{1},\theta_{d}\}, $\theta_{d'}$ 是$\theta_{1'}$ 在 $\{\theta_{1},\theta_{d}\}$中的余. 又设 $\Gamma$ 是具有性质$E_{1}\circ E_{d}=|X|^{-1}(q^{d-1}_{1d}E_{d-1}+q^{d}_{1d}E_{d})$的$E_{1}\circ E_{d}$型距离正则图,$\sigma_{0},\sigma_{1},\cdots,\sigma_{d}$,$\rho_{0},\rho_{1},\cdots,\rho_{d}$和$\beta_{0},\beta_{1},\cdots,\beta_{d}$ 分别是关于$\theta_{1'}$,$\theta_{d'}$ 和 $\theta_{d-1}$的余弦序列.利用上述余弦序列,给出了 $\Gamma$关于 $\theta_{1}$ 或$\theta_{d}$是$Q$ -多项式的充要条件.     

The stable equivalence and cancellation problems

Let K be an arbitrary fieldof characteristic 0, and $\mathbf{A}^n$ then-dimensional affine spaceover K.A well-known cancellation problem asks, given twoalgebraic varieties $V_1, V_2 \subseteq \mathbf{A}^n$ with isomorphiccylinders $V_1 \times \mathbf{A}^1$ and $V_2 \times \mathbf{A}^1$, whether$V_1$ and $V_2$ themselves are isomorphic.In this paper, we focus on a related problem: given twovarieties with equivalent (under an automorphism of $\mathbf{A}^{n+1}$)cylinders $V_1 \times \mathbf{A}^1$ and $V_2 \times \mathbf{A}^1$, are$V_1$ and $V_2$ equivalent under an automorphism of $\mathbf{A}^n$?We call this stable equivalence problem.We show that the answer is positivefor any two curves $V_1, V_2 \subseteq \mathbf{A}^2$.For an arbitrary $n \ge 2$, we consider a special, arguably themost important, case of both problems, where one of the varieties isa hyperplane. We show that a positive solution of the stableequivalence problem in this case implies a positive solution ofthe cancellation problem.     

Lightface -indescribable cardinals

-absoluteness for forcing means that for any forcing , . `` inaccessible to reals' means that for any real , . To measure the exact consistency strength of `` -absoluteness for forcing and is inaccessible to reals', we introduce a weak version of a weakly compact cardinal, namely, a (lightface) -indescribable cardinal; has this property exactly if it is inaccessible and .

     

Some remarks on spreading models and mixed Tsirelson spaces

We prove that if a Banach space with a bimonotone shrinking basis does not contain spreading models but every block sequence of the basis contains a further block sequence which is a spreading model for every , then every subspace has a further subspace which is arbitrarily distortable. We also prove that a mixed Tsirelson space , such that , does not contain spreading models.

     

Besov空间中双参数Volterra型重分数过程的弱逼近

In this paper, we prove that two-parameter Volterra multifractional process can be approximated in law in the topology of the anisotropic Besov spaces by the family of processes{B_n(s,t)},n∈N defined by B_n(s,t)=∫_0~s ∫_0~tk_(a(s))(s,u)K_(β(t))(t,u)θ_(n(u,v))dudv,here {θ_n(u, v)}n∈N is a family of processes, converging in law to a Brownian sheet as n→∞,based on the well known Donsker's theorem.