以0为飞射壁的生灭过程爆发前的若干性质

该文首次研究以0为飞射壁的生灭过程爆发前的若干性质, 通过引入线性方程组和推移算子,得到了多种情况下此类过程在爆发前从状态 i 出发运动到状态 n(i ≤ n ≤∞ 或 n≤ i)的概率和平均时间的精确表达式.同时,我们还定义了m_i,e_i,N_i,R 等一系列特征数, 并表明了这些特征数的概率意义.     

以O为吸引壁的生灭过程爆发前后的若干性质

研究以 0为吸引壁的生灭过程爆发后的若干性质     

由随机过程序列产生的滑动平均过程部分和的弱收敛

本文讨论了由ρ-混合随机过程序列产生的形如Xk(t)=∑j=0∞ajεk-j(t),0≤t≤1,其中{aj;j≥0)为一实数序列,满足∑j=0∞|aj|<∞的滑动平均过程部分和的弱收敛性;同时也讨论了由此滑动平均过程产生的形如Yn(s,t)=1/n~(1/2)∑k=1[n,s]Xk(t),0≤s,t ≤ 1的随机过程的弱收敛性,以及随机足标和SNn(t)=∑k=1NnXk(t)的弱收敛性.     

长程相依过程关于矩完全收敛的精确渐近性质

令X_t=∑_k=0^∞a_kε_t-k为一滑动平均过程,其中ε_k为均值为零的独立同分布随机变量序列,{a_k,k≥0}为满足条件a_k～k^-αl（k）的实数序列,其中l（k）为缓变函数.当1/2<α<1时,X_t为一长程相依过程,如分数积分过程等.该文得到了长程相依过程X_t关于一类矩完全收敛的精确渐近性质,此结果可直接得到X_t完全收敛的精确渐近性质.     

由φ-混合序列产生的长程相依过程的广义强逼近定理

设{X_k;k≥1}是由X_k=∑_(i=0)~βα_iε_(k-i)所定义的滑动平均过程,其中{ε_i;-∞i∞}是一同分布的φ-混合相依变量序列,{α_i;i≥0}为满足条件α_i~i~(-α)l(i)的实数序列,l(i)为一缓变函数.当1/2α1时,{X_k;k≥1}为一长程相依过程.在Eε_0~2可能为无穷的条件下,对长程相依过程{X_k;k≥1}的部分和建立了一个更为一般性的强逼近定理.     

BMAP的轨道分析和Q过程的伴随MAP

本文用轨道分析方法研究批量Markov到达过程(BMAP),有别于研究BMAP常用的矩阵解析方法.通过BMAP的表现(D_k,k=0,1,2,…),得到BMAP的跳跃概率,证明了BMAP的相过程是时间齐次Markov链,求出了相过程的转移概率和密度矩阵.此外,给定一个带有限状态空间的Q过程J,其跳跃点的计数过程记为N,证明了Q过程J的伴随过程X*=(N,J)是一个MAP,求出了该MAP的转移概率和表现(D_0,D_1),它们是通过密度矩阵Q来表述的.     

一类Gauss序列极值的极限律

本文讨论一类非平稳Gauss序列的极值．利用点过程收敛定理得到多水平超过的点过程的收敛性,同时得到在不相交区间上最大值的联合渐近分布,第k个最大值的渐近分布以及前r个极值的联合渐近状态．     

长程相依过程精确渐近性的一般规律

X_t=∑_(k=0)~∞a_kε_(t-k)为长程相依滑动平均过程,得到了X_t关于精确渐近性质的一般规律,它能够在研究完全收敛性中精确描述边界函数,权重函数,收敛率和极限值之间的关系.     

Weibull过程将来第k次失效时间的Bayes预测区间

具Weibull强度函数的非齐次Poisson过程经常被用来分析可修系统的失效模式.基于极大似然估计,Engelhardt ＆ Bain(1978)导出了Weibull过程将来第k次失效时间的经典预测区间.在本文中,我们用无信息联合验前分布,根据Weibull过程的前n次失效时间,给出了建立将来第k次失效时间的Bayes预测区间的方法,并说明了如何应用这些方法。     

网络概率模型的建立与特征量概率公式的推证

基于网络系统状态的设置,建立起该系统网络可靠性概率模型.按再生过程给出可靠性特征量tw的初步估计式,通过定理进一步推证出tw的概率估计与极限分布公式.并在两种条件下论证故障概率θ(1θ和θ2)的估计公式,又以两种极限监理情况为例分别对θ进行双侧估计,给出该估计的上下限.同时在两种条件下分别提出可靠性特征量twk(tw′k,t″wk)概率估计的极限定理.最后评价了网络系统概率估算的主要结果.     

Affine-inscribed and affine-circumscribed polygons and polytopes

Five theorems on polygons and polytopes inscribed in (or circumscribed about) a convex compact set in the plane or space are proved by topological methods. In particular, it is proved that for every interior point O of a convex compact set in ℝ³, there exists a two-dimensional section through O circumscribed about an affine image of a regular octagon. It is also proved that every compact convex set in ℝ³ (except the cases listed below) is circumscribed about an affine image of a cube-octahedron (the convex hull of the midpoints of the edges of a cube). Possible exceptions are provided by the bodies containing a parallelogram P and contained in a cylinder with directrix P. Bibliography: 29 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 231, 1995, pp. 286–298. Translated by B. M. Bekker.     

Partitions and pairwise sums and products

A seven cell partition of N is constructed with the property that no infinite set has all of its pairwise sums and products in any one cell. A related Ramsey Theory question is shown to have different answers for two and three cell partitions.     

Linear birth and death models and associated Laguerre and Meixner polynomials

We study birth and death processes with linear rates λ_n = n + α + c + 1, μ_{n + 1} = n + c, n 0 and μ₀ is either zero or c. The spectral measures of both processes are found using generating functions and the integral transforms of Laplace and Stieltjes. The corresponding orthogonal polynomials generalize Laguerre polynomials and the choice μ₀ = c generates the associated Laguerre polynomials of Askey and Wimp. We investigate the orthogonal polynomials in both cases and give alternate proofs of some of the results of Askey and Wimp on the associated Laguerre polynomials. We also identify the spectra of the associated Charlier and Meixner polynomials as zeros of certain transcendental equations.     

Distributive and Multiplication Modules and Rings

We study rings in which every ideal is a finitely generated multiplication right ideal.     

Beliefs and beyond: affect and the teaching and learning of mathematics

The importance of beliefs for the teaching and learning of mathematics is widely recognized among mathematics educators. In this special issue, we explicitly address what we call “beliefs and beyond” to indicate the larger field surrounding beliefs in mathematics education. This is done to broaden the discussion to related concepts (which may not originate in mathematics education) and to consider the interconnectedness of concepts. In particular, we present some new developments at the conceptual level, address different approaches to investigate beliefs, highlight the role of student beliefs in problem-solving activities, and discuss teacher beliefs and their significance for professional development. One specific intention is to consider expertise from colleagues in the fields of educational research and psychology, side by side with perspectives provided by researchers from mathematics education.