椭机幂级数的亏函数

研究了十分一般的随机幂级数,并证明了有限级的随机幂级数几乎必然没有亏函数。     

多复变数随机幂级数

本文讨论了多复变数的随机幂级数,得到了若干与单复变数随机幂级数类似的结果,但证明方法与单复变数的情形是完全不同的.     

系数的模为两两NQD序列的随机幂级数的增长性

本文研究了系数的模为两两NQD序列的B-值随机幂级数的增长性.利用两两NQD列推广的Borel-Cantelli引理及其它极限定理，在给定条件下得出其增长级和非随机幂级数的增长级有类似的性质.     

随机α-Bloch函数(英文)

本文给出了随机幂级数 fw(z) =∑∞n=0αneiwnzn(其中wn 是随机的 )属于α_Bloch空间和小α_Bloch空间的条件 ,推广了Anderson ,Clunie和Pommerenke的结果。     

随机a—Bloch函数

本文给出了随机幂级数fw(z)∑n=0^∞ane^iwnz^n(其中wn是随机的）属于a-Bloch空间和小a-Bloch空间的条件，推广了Anderson,Clunie和Pommerenke的结果。     

求幂级数和函数的微分方程方法

按照通常求幂级数和函数的思路．对一些幂级数并不能奏效．在某些情况下．可以引入求幂级数和函数的微分方程方法．其主要思路是通过建立和函数的微分方程。将幂级数求和函数问题化为微分方程初值问题来求解．     

例谈函数幂级数展开方法与系数相等的证明

函数展开为幂级数的过程中由于采用的方法不同有时会出现不同的系数表达形式,这与幂级数展开式的唯一性并不矛盾．本文通过几例揭示了幂级数展开式中系数表达形式不同的现象．分析了幂级数展开方法之间的差异．介绍了证明系数相等的一些方法．     

模糊D0L幂级数

将Lindenmayer代数系统推广到模糊半环上,引入模糊L代数系统及模糊L代数幂级数的概念。定义由模糊代数系统生成的模糊D0L幂级数,并研究模糊D0L幂级数的性质。模糊D0L幂级数的重数序列具有很好的性质,且两个模糊D0L幂级数的等价性是可判定的。此外,模糊D0L幂级数的F-代数性、F-上下文无关性及F-有理性也是可判定的。     

关于幂级数收敛域的几点注记

<正> 对幂级数进行代数运算后所得到的仍然是幂级数,这些运算在幂级数的研究及应用中经常碰到。而每给出一个幂级数都应同时指出它的收敛域,因此,正确地确定经代数运算后     

线性微分方程解的存在唯一性在幂级数中的应用

在幂级数的学习中,如何将函数展开成幂级数和求幂级数的和函数这两类问题是学习的重点和难点.利用线性微分方程解的存在唯一性,分别给出了求函数的麦克劳林展开式和计算幂级数和函数的一般步骤.     

Random Hermite differential equations: Mean square power series solutions and statistical properties

This paper deals with the construction of random power series solution of second order linear differential equations of Hermite containing uncertainty through its coefficients and initial conditions. Under appropriate hypotheses on the data, we establish that the constructed random power series solution is mean square convergent. We provide conditions in order to obtain random polynomial solutions and, as a consequence, random Hermite polynomial are introduced. Also, the main statistical functions of the approximate stochastic process solution generated by truncation of the exact power series solution are given. Finally, we apply the proposed technique to several illustrative examples comparing the numerical results with respect to those provided by other available approaches including Monte Carlo simulation.     

VECTOR-VALUED RANDOM POWER SERIES ON THE UNIT BALL OF C^n

In this article, the authors study the vector-valued random power series on the unit ball of Cn and get vector-valued Salem-Zygmund theorem for them by using martingale technique. Further, the relationships between vector-valued random power series and several function spaces are also studied.     

Randomization of Q_p spaces on the unit ball of C~n

In this paper, we study the random power series of several complex variables, and give some sufficient conditions for random power series to belong to Qp and Qp,0 spaces by means of their characterizations of Carleson measure. Moreover, we show that such conditions are best possible in some sense.     

Randomization of Q<Subscript>p</Subscript> spaces on the unit ball of ℂ<Superscript>n</Superscript>

In this paper, we study the random power series of several complex variables, and give some sufficient conditions for random power series to belong to Q_p and Q_p,0 spaces by means of their characterizations of Carleson measure. Moreover, we show that such conditions are best possible in some sense.     

Randomization of Qp spaces on the unit ball of ℂn

In this paper, we study the random power series of several complex variables, and give some sufficient conditions for random power series to belong to Q_p and Q_p,0 spaces by means of their characterizations of Carleson measure. Moreover, we show that such conditions are best possible in some sense.

     

Natural boundaries and spectral theory

We present and exploit an analogy between lack of absolutely continuous spectrum for Schrödinger operators and natural boundaries for power series. Among our new results are generalizations of Hecke's example and natural boundary examples for random power series where independence is not assumed.     

Asymptotic behavior of roots of random polynomial equations

We derive several new results on the asymptotic behavior of the roots of random polynomial equations, including conditions under which the distributions of the zeros of certain random polynomials tend to the uniform distribution on the circumference of a circle centered at the origin. We also derive a probabilistic analog of the Cauchy-Hadamand theorem that enables us to obtain the radius of convergence of a random power series.     

Schur-Weyl duality and the heat kernel measure on the unitary group

We investigate a relation between the Brownian motion on the unitary group and the most natural random walk on the symmetric group, based on Schur-Weyl duality. We use this relation to establish a convergent power series expansion for the expectation of a product of traces of powers of a random unitary matrix under the heat kernel measure. This expectation turns out to be the generating series of certain paths in the Cayley graph of the symmetric group. Using our expansion, we recover asymptotic results of Xu, Biane and Voiculescu. We give an interpretation of our main expansion in terms of random ramified coverings of a disk.     

风电场可靠性模型及其应用

考虑了风速分布的季节性差异和风速的随机变化的影响、风电机组的实际功率特性、风电场尾流效应以及风电机组故障状况,建立了风电场可靠性模型.根据某海上风电场实测数据进行数值仿真实验,结果验证了模型的正确性和有效性.模型为进一步研究大规模风电并网以及风电场功率预测等问题打下了基础.