时间序列与时空序列的建模

本文介绍了作者和他的博士研究生于近五年内,在时间序列与时空序列的统计建模方面所完成的研究工作。文章包含两个部分:第一部分将给出平稳与非平稳的ARMA模型(包括平稳ARMA,ARUMA与一般ARMA模型)的阶与参数估计的新结果,我们假设模型的噪声项满足鞅差条件,这比要求它们是i.i.d要弱,而且合理。第二部分给出了二维ARMA模型的谱鉴别,对于一类特殊的二维AR模型(即所谓的象限马氏模型,它们恰好就是熟知的一维马氏AR模型在二维情形的相配模型。)给出了它的阶与参数的强相合估计与重对数收敛速度。     

统计序列空间及统计序列商映射

统计收敛性是收敛性的重要推广,讨论了统计序列空间的性质,引入了统计序列连续映射、统计序列覆盖映射与统计序列商映射,探讨了这些映射与非统计意义下相应映射的关系及他们在统计序列空间中的作用,否定地回答了关于统计序列空间乘积性的一个问题.     

MO序列分析与ME序列分析

本文从复合顺序滤波出发,建立一类非线性随机数学模型——顺序模型,导出MO序列与ME序列。这不仅在理论上为时间序列提供了新方法,而且为应用开辟了极为广阔的前景。本文致力于考察MO序列与ME序列的统计特性。通过一系列的递归方程,证明其分布定理并确定其数值算法。分析MO序列的相关性质,研究ME序列的三类极限分布,给出高维ME序列的分布定理。同时还简介这些序列及其相应的滤波模型在图片处理等方面的应用。     

前馈序列与反馈序列的关系

本文引入移位寄存器序列的向量值表示讨论了线性移位寄存器的前馈序列与反馈序列同时为ｍ序列时的关系,得到了它们在向量值表示下的一个关系式。     

Orlicz序列空间的弱收敛序列系数

本文给出了Orlicz序列空间的弱收敛序列系数的表达式.     

序列连通空间

序列连通性具有许多相似于连通的性质．本文讨论了拓扑空间的序列连通性，并给出了序列连通空间的刻面及其性质．     

关于算子序列

本文主要引入了Fredholm算子序列概念,而且讨论了它们的性质,得到了一些类似单个Fredholm算子的结果。     

鞅型序列

引言 自经典鞅论建立以来,鞅型序列的研究得到了发展,其中最重要的是渐近鞅(Amart),它保持了鞅的一些最基本的性质,并且鞅的推广不能超过渐近鞅而仍保持有可选采样定理和Riesz分解的很弱的形式,但是鞅的收敛性可以推广到更广泛的一些鞅型序列,若只要求依概率收敛,则鞅型序列的范围可以更宽。本文引入了渐近上(下)鞅等一些新的鞅型序列,并对鞅型序列作了较全面的综合,得到了一些新的结果并改进了一些已知结果。     

序列的作用

《高等数学研究》即将迎来她的50周年刊庆,这无疑是广大数学教师的盛事。应主编张肇炽教授之邀,我想撰此短文以示祝贺。     

New β-delayed proton decays in the rare-earth region near the proton drip line

The β-delayed proton precursors 125Nd, 128Pm, 129Sm, 137Gd and 139Dy near the proton drip line were produced by the irradiation of 92Mo, 96Ru and 106Cd with an 36Ar beam, and conclusively identified for the first time by using proton-gamma coincidence in combination with a He-jet tape transport system. Their half-lives were determined to be 0.60(15)s,1.0(3)s,0.55(10)s,2.2(2)s and 0.6(2)s, respectively. The measured energy spectra of β-delayed protons and estimated proton branching ratios to the final states in "daughter" nuclei for the precursors 125Nd, 129Sm, 137Gd and 139Dy, as well as the previously reported ones for the precursors 135Gd and 121Ce, were fitted by a statistical model calculation. The ground-state spins and parities of 121Ce, 125Nd, 129Sm, 135Gd, 137Gd and 139Dy were then assigned as 5/2±,5/2±,1/2±(or 3/2+),5/2+,7/2± and 7/2, respectively. The consistency between the experimental spin-parity assignment and the predicted Nilsson diagrams indirectly indicates that the ground states of 121Ce, 125Nd, 129Sm, 135Gd, 137Gd and 139Dy are highly deformed with β2～0.3.     

Complex Jordan operators

We prove that an operator J is of the form J = M + N where M is normal, N² = 0, and M commutes with N if and only if J satisfies the three equations J^*nJ³-3JJ^*nJ²+3J²J^*nJ-J³J^*n = 0, n = 1, 2, and 3.     

子流形的测地曲率

该文研究了黎曼齐次空间G/H中子流形M~p和子流形N~q的交M~p∩gN~q的测地曲率,其中g∈G为等距群,并把M~p∩gN~q的第二基本形式表示成M~p和N~q的测地曲率以及它们之间的夹角的组合.     

关于复射影空间的三维全实极小子流形

本文给出复射影空间中三维紧致全实极小子流形的Ricci曲率和数量曲率的鞭些拼挤定理.特别是证得:若M³是CP³的紧致全实极小子流形且它的Ricci曲率大于1/6,则M³是全测地的.     

Separability and entanglement in tripartite states

While classical correlations can be freely distributed among many systems, this is not true for entanglement and quantum correlations. If a quantum system S^a is entangled with another quantum system S^b, then its entanglement with any third quantum system S^c cannot be arbitrary. This is the celebrated monogamy of entanglement. Implicit in this general statement is the plausible belief that only entanglement between the systems S^a and S^b constrains the entanglement between S^a and the third system S^c. We demonstrate that even classical correlations between S^a and S^b may impose surprisingly stringent restrictions on the possible entanglement between S^a and S^c. In particular, perfect bipartite classical correlations and full entanglement cannot coexist in any tripartite state. An intuitive explanation of this monogamy of hybrid classical and quantum correlations might be that the system S^a has a correlating capability, which cannot be used to establish any entanglement with a third system (but can still be used to establish classical correlations) if it is exhausted when correlated with S^b (in either a classical or quantum fashion). This may be interpreted as an alternate version of monogamy.     

A new upper bound on the cyclic chromatic number

A cyclic coloring of a plane graph is a vertex coloring such that vertices incident with the same face have distinct colors. The minimum number of colors in a cyclic coloring of a graph is its cyclic chromatic number χ^c. Let Δ^* be the maximum face degree of a graph. There exist plane graphs with χ^c = ?3/2 Δ^*?. Ore and Plummer [ 5 ] proved that χ^c ≤ 2, Δ^*, which bound was improved to ?9/5, Δ^*? by Borodin, Sanders, and Zhao [ 1 ], and to ?5/3,Δ^*? by Sanders and Zhao [ 7 ]. We introduce a new parameter k^*, which is the maximum number of vertices that two faces of a graph can have in common, and prove that χ^c ≤ max {Δ^* + 3,k^* + 2, Δ^* + 14, 3, k^* + 6, 18}, and if Δ^* ≥ 4 and k^* ≥ 4, then χ^c ≤ Δ^* + 3,k^* + 2. © 2006 Wiley Periodicals, Inc. J Graph Theory     

Partition relations for uncountable ordinals

Partition relations of the form α→(α,m)², where α is an ordinal andm is a positive integer, are considered. Let κ be a cardinal. The following are proved: If κ is singular and 2^K=K ⁺ then (K⁺)²?((K⁺)²,3)². If κ is a strong limit cardinal, then², iff ((cfκ)²→((cfκ)²,m)². If κ is regular and K²→(K²,3)², then the κ-Souslin hypothesis holds. If K^ω<α+ and cfα=cfκ>ω, then α?(α,3)².     

一类堆垒数论问题(Ⅰ)

§1 引言 堆垒数论中有一个著名的猜测: 设k_1,…,k_s是s个大于1的整数,且k_1≤k_2≤…≤k_s及sum from j=1 to s (k_j~(-1)>1)。又对每个素数p,对大的k,同余方程 X_1~(k_1)+X_2~(k_2)+…+X_s~(k_s)≡n(modp~k) 对某些j,P|x_j都有解,那末当n充分大时,方程     

LEGENDRE TRANSFORMATIONS AND CARTAN FORMS IN THE CALCULUS OF VARIATIONS OF MULTIPLE INTEGRALS

ABSTRACT

(PART II): In terms of a given Hamiltonian function the 1-form w = dH + ?_j|dπ^j is defined, where {?_j:j = 1,…, n} denotes an invariant basis of the planes of the distribution D_n. The latter is said to be canonical if w = 0 (which is analogous to the definition of Hamiltonian vector fields in symplectic geometry). This condition is equivalent to two sets of canonical equations that are expressed explicitly in term of the derivatives of H with respect to its positional arguments. The distribution D_n is said to be pseudo-Lagrangian if dπ^j(?_j,V_h) = 0; if D_n, is both canonical and pseudo-Lagrangian it is integrable and such that H = const. on each leaf of the resulting foliation. The Cartan form associated with this construction [9] is defined a II = π² ? ? πⁿ. If π is closed, the distribution D_N is integrable, and the exterior system {π^j} admits the representation ψ^j = dS^j in terms of a set of 0-forms S^j on M. If, in addition, the distribution D_N is canonical, these functions satisfy a single first order Hamilton-Jacobi equation, and conversely. Finally, a complete figure is constructed on the basis of the assumptions that (i) the Cartan form be closed, and (ii) that the distribution D_n, be both canonical and integrable. The last of these requirements implies the existence of N functions ψ^A that depend on x^h and N parameters w^B, whose derivatives are given by ?ψ^A (x^h, w^B)/?x^j = B^A _j (x^h, ψ^B (x^h,w^B)). The complete figure then consists of two complementary foliations: the leaves of the first are described by the functions ψ^A and satisfy the standard Euler-Lagrange equations, while the second, that is, the transversal foliation, is represented by the aforementioned solution of the Hamilton-Jacobi equation. The entire configuration then gives rise in a natural manner to a generalized Hilbert independent integral and consequently also to a generalized Weierstrass excess function.     

More Epsilonized Bounds of the Boas-Kac-Lukosz Type

In this paper we give a further investigation of the method introduced by the author in [1, Frequency-domain bounds for nonnegative unsharply band-limited functions] for proving bounds for functions with nonnegative Fourier transforms. We also dealt with the question of how large the supremum K^S of all numbers |f(u)| is with f the Fourier transform of a nonnegative integrable function F and f(0) = 1, |f(ku)| ≤ ε for k ∈ S. Here u > 0 and S ⊂ {2, 3, . . .}. This problem was related in [1] to finding the infimum M^S of all numbers M_h = max_ϑ [(1−h(ϑ))/(1− cos ϑ)] over all 2π-periodic even, smooth functions h whose Fourier cosine coefficients a_k vanish for k ∉ S, and it was proved and announced for several cases that M^S (1−K^S ) = 1. In this paper we prove the results announced in [1]. To that end we generalize the method given in [1] to include Fourier transforms f of probability measures on R and a certain generalized function h, and we show that the numbers K^S, M^S are assumed as |f(u)|, M_h for certain allowed f,h. Moreover, we establish a fundamental relation between finding the numbers K^S, M^S and the numbers K^T, M^T where T = {2, 3, . . .}\S. In particular, we show that M^T = 2K^S (2K^S − 1)−1,K^T = 1/2 M^S(M^S − 1)−1 and that M^T (1 − K^T) = 1,K^SK^T = 1/2 , whenever M^S (1 − K^S) = 1.