伸张函数增长阶的估计

本文建立了Beurling-Ahlfors扩张的伸张函数的一个新的估计式,并对当ρ-函数在递减函数控制下伸张函数的增长阶进行了估计,改进了已有的结果,得到估计式: 当ρ(y/2)≥2时,D(x,y)≤2ρ(y/2); 当1≤ρ(y/2)<2时,D(x,y)2≤ρ(y/2)+1/2.     

带有Hecke-Maass形式傅里叶系数的指数和估计

设g(z)是拉普拉斯特征值为1/4+t²的Hecke-Maass尖形式,λ_g(n)是g的第n个正规化傅里叶系数.本文研究与λ_g(n)相关的指数和,并给出估计式■,其中■.通过λ_g(n)的高次均值估计,改进了前人的结果.     

一种对称损失函数下一类指数分布族刻度参数的估计

在p,q对称熵损失函数L(θ,δ)=θp/δp+δq/θq-2(p,q0)下,研究了一类指数分布族c(x,n)θ-ve-T(x)/θ的刻度参数θ的Bayes估计与可容许估计,并应用积分变换定理证明了这两个估计具有不变性.     

相依样本的经验过程振动模的收敛性

文中研究了两类重要相依样本(即φ-混合和α-混合样本)的经验过程振动模强一致收敛速度,证明了该速度与独立样本下的经验过程振动模的最优收敛速度相同.利用这些结果建立了密度函数核估计和直方图核估计的强相合性,并证明了这些强相合收敛速度达到最好速度O(n~(-1/3) log~(1/3)n)以及建立分位估计Bahadur类型的表示定理.     

某些抛物型算子在加权L~p空间和Morrey空间上的估计

考虑了一致抛物型算子■=_t-∑_(i,j)ⁿ=_1_i(a_(i,j)(x)_j)+V(x),其中势函数V(x)是Rn=_1_i(a_(i,j)(x)_j)+V(x),其中势函数V(x)是Rⁿ(n≥3)上的非负函数,并且属于反霍尔德类.得到了算子(?)的基本解的梯度估计,以及算子V■n(n≥3)上的非负函数,并且属于反霍尔德类.得到了算子(?)的基本解的梯度估计,以及算子V■^(-1),V(-1),V^(1/2)▽■(1/2)▽■^(-1)和V(-1)和V^(1/2)(1/2)^(-1/2)在加权L(-1/2)在加权L^p(Rp(R⁽ⁿ⁺¹⁾)空间和Morrey空间上的估计.     

定时截尾场合指数分布表决系统产品的统计分析

本文针对指数分布2/3(G)表决系统产品,在截尾样本场合下给出了参数的拟矩估计、极大似然估计和近似区间估计,并通过大量的Monte-Carlo模拟分别考察了点估计和区间估计的精度。     

多线性向量值奇异积分极大算子的加权不等式

本文研究向量值奇异积分极大多线性交换子的性质,得到该算子的加权估计及加权弱型估计,作为该估计的推论可知算子T_(q,(?))~*在L~p(ω)上有界,其中ω∈A_p。当ω∈A_1时,满足加权L(logL)~(1/r)型估计。     

七阶非线性色散方程初值问题解的局部和整体存在性

该文研究七阶非线性弱色散方程:∂u/∂t + au(∂u/∂x) +β(∂^3 u/∂x^3) +γ(∂^5 u/∂x^5) + μ(∂^7 u/∂x^7)=0, (x,t)∈R^2的初值问题,通过运用震荡积分衰减估计的最近结果, 首先对相应线性方程的基本解建立了几类Strichartz型估计. 其次, 应用这些估计证明了七阶非线性弱色散方程初值问题解的局部与整体存在性和唯一性. 结果表明, 当初值u_0(x)∈H^s(R), s≥2/13 时, 存在局部解; 当s≥1时, 存在整体解.     

众数的核估计问题

设 X_1,…X_n,为 iid 样本,其总体的分布函数、密度函数、众数分别记为 F(x)、f(x)、θ,即有 f(θ)=supf(x)。我们来考虑θ的估计问题。Parzen[1]在研究密度 f 的核估计问题时首先提出了 θ 的核估计方法,并在一定假设条件下证明了这种估计具有弱相合性。陈桂景在[7]中进一步证明了众数 θ 的核估计还具有强相合性,而且当 f 的二阶导函数连续有界时,这种估计的强收敛速度可达到 O((1nn/n)~(2/7))。那么,一个自然的问题是,     

加权平方损失下伽玛分布族Γ(θ,1/2)参数θ的EB估计

在加权平方损失函数下讨论了伽玛分布族T(θ,1/2)参数θ的经验Bayes(EB)估计,并讨论了EB估计的收敛速度问题,在一定条件下,收敛速度可充分接近于1.     

An edge version of the matrix-tree theorem and the wiener index

Let T be a tree on n vertices. The Laplacian matrix is L(T)=D(T)-A(T), where D(T) is the diagonal matrix of vertex degrees and A(T) is the adjacency matrix. A special case of the Matrix-Tree Theorem is that the adjugate of L(T) is the n-by-n matrix of l's. The (n-l)-square "edge version" of L(T)is K(T). The main result is a graph-theoretic interpretation of the entries of the adjugate of K(T). As an application, it is shown that the Wiener Index from chemistry is the trace of this adjugate.     

Markoff数性质的研究

1913年,Frobenius对Markoff方程a~2+b~2+c~2=3abc提了一个著名猜想:若abc是Markoff方程的正整数解,则a,b的值由最大的数c唯一确定.此猜想仍未得到解决.本文证明了:任给定正整数s_i,t_i,w,u,v=1,2),若(a_i,b_i,c)是Markoff方程的两组不同的正整数解,且a_ib_ic(i=1,2),则gcd(s_1a_1+s_2a_2+t_1b_1+t_2b_2+w,uc+v)≤K(uc+v)~(13/14),其中K是仅与s_i,t_i,w,u,v(i=1,2)有关的正数.     

Bandwidth of the composition of two graphs

The bandwidth B(G) of a graph G is the minimum of the quantity max{|f(x)−f(y)| : xyE(G)} taken over all proper numberings f of G. The composition of two graphs G and H, written as G[H], is the graph with vertex set V(G)×V(H) and with (u₁,v₁) is adjacent to (u₂,v₂) if either u₁ is adjacent to u₂ in G or u₁=u₂ and v₁ is adjacent to v₂ in H. In this paper, we investigate the bandwidth of the composition of two graphs. Let G be a connected graph. We denote the diameter of G by D(G). For two distinct vertices x,yV(G), we define w_G(x,y) as the maximum number of internally vertex-disjoint (x,y)-paths whose lengths are the distance between x and y. We define w(G) as the minimum of w_G(x,y) over all pairs of vertices x,y of G with the distance between x and y is equal to D(G). Let G be a non-complete connected graph and let H be any graph. Among other results, we prove that if |V(G)|=B(G)D(G)−w(G)+2, then B(G[H])=(B(G)+1)|V(H)|−1. Moreover, we show that this result determines the bandwidth of the composition of some classes of graphs composed with any graph.     

Cases of equality for the spectral norm submultiplicativity of the hadamard product

In this note, we characterize those pairs of nonzero r-by-d complex matrices that satisfy N₂(A ∘ B) = N₂(A)N₂(B), in which N₂(·) is the spectral norm and · is the Hadamard product.     

On the planarity of jump graphs

For a graph G of size m1 and edge-induced subgraphs F and H of size k (1km), the subgraph H is said to be obtained from F by an edge jump if there exist four distinct vertices u,v,w, and x in G such that uvE(F), wxE(G)−E(F), and H=F−uv+wx. The minimum number of edge jumps required to transform F into H is the k-jump distance from F to H. For a graph G of size m1 and an integer k with 1km, the k-jump graph J_k(G) is that graph whose vertices correspond to the edge-induced subgraphs of size k of G and where two vertices of J_k(G) are adjacent if and only if the k-jump distance between the corresponding subgraphs is 1. All connected graphs G for which J₂(G) is planar are determined.     

On the degree of the inverse of an automorphism of the affine space

We study the degree of the inverse of an automorphism f of the affine n-space over a -algebra k, in terms of the degree d of f and of other data. For n = 1, we obtain a sharp upper bound for deg (f^{− 1}) in terms of d and of the nilpotency index of the ideal generated by the coefficients of f^′'. For n = 2 and arbitrary d≥ 3, we construct a (triangular) automorphism f of Jacobian one such that deg(f^{− 1}) > d. This answers a question of A. van den Essen (see [3]) and enables us to deduce that some schemes introduced by authors to study the Jacobian conjecture are not reduced. Still for n = 2, we give an upper bound for deg (f^{− 1}) when f is triangular. Finally, in the case d = 2 and any n, we complete a result of G. Meisters and C. Olech and use it to give the sharp bound for the degree of the inverse of a quadratic automorphism, with Jacobian one, of the affine 3-space.     

On the structure of the group of equivariant diffeomorphisms of G-manifolds with codimension one orbit

It is known that the equivariant diffeomorphism group Diff_G^∞(M)₀ of a principal G-manifold M is perfect. If M has at least two orbit types, then it is not true. The purpose of this paper is to determine the first homology group of Diff_G^∞(M)₀ when M is a G-manifold with codimension one orbit.     

Spectral analysis of the covariance of the almost periodically correlated processes

This paper deals with the spectrum of the almost periodically correlated (APC) processes defined on . It is established that the covariance kernel of such a process admits a Fourier series decomposition, K(s+t, s) , whose coefficient functions b are the Fourier transforms of complex measures m, , which are absolutely continuous with respect to the measure m_o. Considering the APC strongly harmonizable processes, the spectral covariance of the process can be expressed in terms of these complex measures m.

The usual estimators for the second order situation can be modified to provide consistent estimators of the coefficient functions b from a sample of the process. Whenever the measures m are absolutely continuous with respect to the Lebesgue measure, so m(dλ)=f(λ) dλ, the estimation of the corresponding density functions f is considered. Under hypotheses on the covariance kernel K and on the coefficient functions b, we establish rates of convergence in quadratic mean and almost everywhere of these estimators.     

The existence of moments of the conditioned limit of the subcritical Crump-Mode-Jagers branching process

If Z (t) is the sum of the characteristics at time t of the population in a Crump-Mode-Jagers branching process, and T is the time to extinction, it is known that under certain conditions, the distribution of Z (t) conditioned on {T > t} converges to a proper distribution as t→∞. We derive necessary and sufficient conditions in terms of the offspring process, for the existence of integral moments of this limit distribution.     

On an explicit formula for the distribution of the supremum

Let M_∞ be the supremum of a random walk drifting to -∞ which is generated by the partial sums of a sequence of independent identically distributed random variables with a common distribution F. We prove that the moment generating function E exp(sM_∞) is a rational function if and only if the function ∫₀^∞ exp(sx)F(dx) is rational.