关于树T的的界

控制数γ和连通控制数γc是图的两个重要的控制参数.本文通过对树中的点进行恰当分类,给出了树中的γ/γc值的最好界,为刻画单圈图和双圈图中γ/γc值的界打下良好的基础.     

正规弱空间的无限Tychonoff积

本文证明(1)如果X=∏σ∈∑Xσ是|Σ|-仿紧空间,则X是正规弱(-θ)-可加空间当且仅当 F∈[∑]＜ω,∏σ∈FXσ是正规弱(-θ)-可加空间.(2)设X=∏i∈ωXi是可数仿紧的,则下列三条等价X是正规弱(-θ)-可加的; F∈[ω]＜ω,∏i∈FXi是正规弱(-θ)-可加的; n∈ω,∏i≤nXi是正规弱(-θ)-可加的.     

Cn单位球上的向量值D函数

讨论了Cn单位球上的向量值Dpμ,q函数, 利用Banach空间几何学的方法,推广了标量值Dpμ,q函数的结果.     

不同分布混合序列的强收敛速度

讨论了(～ρ)混合序列的强收敛性,获得了与独立情形几乎一致的结果,推广了著名的Marcinkiewicz-Zygmund强大数律.     

函数F(α)=的最优单调区间

设p≥0且A,B是Hilbert空间上两个正算子,Furuta给出若A≥B＞0,那么对任意r≥0,F(α)=(ArBαAr)p+2r/α+2r是关于α≥p单调递减的,但是他指出这个结果在0≤α≤p和r≥0的条件下并不一定成立.本文给出(1)如果-1/2＜r＜0且p＜-2r,那么F(α)在[-p-4r,+∞)及(-∞,p]上单调递减,并且这两个区间不能扩大;(2)如果-1/2＜r＜0且p＞-2r,那么F(α)在(-∞,-p-4r]及[p,+∞)上单调递增,并且这两个区间不能扩大;(3)如果r＞0,p＞0,那么[p,+∞)也是F(α)的最佳单调区间.     

Vasiek利率模型下的亚式期权的定价问题和数值分析

本文研究了随机利率满足Vasiccek模型时带有浮动的敲定价格的欧式看涨亚式期权的定价问题.通过对所涉及的退化的抛物型方程的Cauchy问题进行变量代换,我们把状态空间的维数降低了一维.为克服其中的奇异性问题,本文对方程进行了分解,第一部分的方程虽然保持奇性,但是其解具有一个精确表达式;而残差部分满足系数和初始条件都充分光滑的Cauchy问题,我们运用一般的差分方法对该部分进行了有效的数值计算.     

广义Mbius变换和算术Fourier变换

离散Fourier变换(DFT)在数字信号处理等许多领域中占有重要地位.近年来,出现一种优于FFT的算术Fourier变换来计算DFT.在广义M     

乘积的平方性

本文证明了乘积 (f(x)=ax²+bx+c∈Z[x]是二次不可约多项式)在n充分大时不是平方数.       

A new family of Padé-type approximants in

This paper gives the definition and some properties of a new family of Padé-type approximants (PTA) for k-variate formal power series (FPS). These PTA have the form P(t)/Q(t) where Q(t) = Π^r_{i = 0}(1 ? x(i)·t), {x(i), 0 ? i ? r} being a given set of points in

, and x·t is the scalar product of x and t in

. Some results about the approximation order, the unicity and some invariance properties of these PTA are proved together with a convergence result when the FPS is defined by a Stieltjes integral.     

中约化子空间上的仿射与伪仿射对偶小波标架

本文讨论中约化子空间上的仿射(伪仿射)对偶小波标架.我们建立了仿射系与伪仿射系之间的一个标架 和对偶标架保持定理,并且在没有任何衰减性假设的条件下获得了仿射(伪仿射)对偶小波标架在傅立叶域上的一个刻画.进一步, 我们也给出了仿射Parseval标架在傅立叶域上的刻画.       

Hadamard foliations of

We introduce the notion of an Hadamard foliation as a foliation of Hadamard manifold which all leaves are Hadamard.We prove that a foliation of an Hadamard manifold M of curvature −a² with a norm of the second fundamental form is Hadamard. For we construct a canonical embedding of the union of leaf boundaries into the boundary of . This embedding is continuous and it is homeomorphism on any fixed leaf boundary.Some methods of hyperbolic geometry are developed. It is shown that a ray in with the bounded by κ<1 curvature has a limit on the boundary.     

Shadow Codes over 4

The notion of a shadow of a self-dual binary code is generalized to self-dual codes over ₄. A Gleason formula for the symmetrized weight enumerator of the shadow of a Type I code is derived. Congruence properties of the weights follow; this yields constructions of self-dual codes of larger lengths. Weight enumerators and the highest minimum Lee, Hamming, and Euclidean weights of Type I codes of length up to 24 are studied.     

Complexity of Weighted Approximation over

We study approximation of univariate functions defined over the reals. We assume that the rth derivative of a function is bounded in a weighted L_p norm with a weight ψ. Approximation algorithms use the values of a function and its derivatives up to order r−1. The worst case error of an algorithm is defined in a weighted L_q norm with a weight ρ. We study the worst case (information) complexity of the weighted approximation problem, which is equal to the minimal number of function and derivative evaluations needed to obtain error . We provide necessary and sufficient conditions in terms of the weights ψ and ρ, as well as the parameters r, p, and q for the weighted approximation problem to have finite complexity. We also provide conditions which guarantee that the complexity of weighted approximation is of the same order as the complexity of the classical approximation problem over a finite interval. Such necessary and sufficient conditions are also provided for a weighted integration problem since its complexity is equivalent to the complexity of the weighted approximation problem for q=1.     

-Modules on Smooth Toric Varieties

Let X be a smooth toric variety. Cox introduced the homogeneous coordinate ring S of X and its irrelevant ideal . Let A denote the ring of differential operators on Spec(S). We show that the category of -modules on X is equivalent to a subcategory of graded A-modules modulo -torsion. Additionally, we prove that the characteristic variety of a -module is a geometric quotient of an open subset of the characteristic variety of the associated A-module and that holonomic -modules correspond to holonomic A-modules.     

Finite Interpolation with Minimum Uniform Norm in

Given a finite sequence a{a₁, …, a_N} in a domain Ω ⁿ, and complex scalars v{v₁, …, v_N}, consider the classical extremal problem of finding the smallest uniform norm of a holomorphic function verifying f(a_j)=v_j for all j. We show that the modulus of the solutions to this problem must approach its least upper bound along a subset of the boundary of the domain large enough so that its A(Ω)-hull contains a subset of the original a large enough to force the same minimum norm. Furthermore, all the solutions must agree on a variety which contains the hull (in an appropriate, weaker, sense) of a measure supported on the maximum modulus set. An example is given to show that the inclusions can be strict.