关于单位圆内解析系数的二阶线性微分方程的复振荡

对二阶线性微分方程f″ A_1(z)f′ A_0(z)f=F(z)的复振荡进行了研究,其中系数A_i(z)(i=0,1)和F(z)是单位圆△={z:|z|<1}内的解析函数,获得解的超级和超零点收敛指数的估计,也得到了一些关于解的不动点的结果.     

关于丛属函数的几个不等式

<正> 1.引言.设(?)是单位圆中的正则函数,函数w=F(z)将|z|<1映照成黎曼面S_F.设函数(?)在单位圆中是正则的.假如w=f(z)的一切函数值都落在 S_F,上,那末说 f(z)丛属于 F(z),记此关系为 f(z)(?)F(z).我们知道 f(z)(?)F(z)的充要条件是存在|z|<1上的正则函数ω(z),适合|ω(z)|<1,ω(0)=0,和 f(z)≡F(ω(z)).     

Some properties for certain classes of univalent functions defined by differential inequalities

Let A be the space of functions analytic in the unit disk D = {z:|z| 1}.Let U denote the set of all functions f ∈ A satisfying the conditions f(0) = f'(0)-1 = 0 and|f'(z)(z/f(z))~2-1|1(|z|1).Also,let Ω denote the set of all functions f ∈ A satisfying the conditions f(0) = f'(0)-1 = 0and|zf'(z)-f(z)|1/2(|z|1).In this article,we discuss the properties of U and Ω.     

二阶齐次与非齐次线性微分方程亚纯解的零点与增长性质估计(英文)

本文研究了方程f′′+A(z)f′+B(z)f=0与f′′+A(z)f′+B(z)f=F亚纯解的零点与增长性,其中A(z),B(z)(■0),F(z)(■0)为亚纯函数,得到了方程亚纯解的增长级、下级、超级、二级不同零点收敛指数等的精确估计,改进了KwonKi-Ho、陈宗煊与杨重骏、Benharrat Beladi等的结果.     

关于方程f″+Af=F(z)的复振荡

本文讨论了当A(z)为多项式,F(z)为具有无穷多个零点的整函数时,微分方程 f″+A(z)f=F(z)的解f(z)的复振荡的性质.     

关于具有有界边界旋转的函数族

一、引言及表示公式设△={z:|z|<1},A表示△中解析函数的全体。F?A,HF表示F的闭凸包。EHF表示HF的极值点的全体。用f(z)〈g(z)表示f(z)从属于g(z)。用f(z)<相似文献   

单位圆中线性微分方程的解

本文研究了线性微分方程$f^{(k)}+A(z)f=0$ 和 $f^{(k)}+A(z)f=F(z)$解的性质,推广了原有的一些结果.     

微分方程f″ e~(az)f′ Q(z)f=F(z)的复振荡

该文研究了线性微分方程f″ eazf′ Q( z) f=F( z)的复振荡问题,其中Q( z)、F( z) ( 0 )是整函数,且σ( Q) =1 ,σ( F) < ∞,Q( z) =h( z) ebz,h( z)是多项式,b≠- 1是复常数,那么上述线性微分方程的所有解f( z)满足λ( f) =λ( f) =σ( f) =∞,　λ2 ( f) =λ2 ( f) =σ2 ( f) =1 .至多除去两个例外复数a及一个可能的有穷级例外解f0 ( z) .     

新题征展(20)

A　题组新编1 .已知 z∈ C,解下列方程 :( 1 ) z2 - 5| z| 6 =0( 2 ) z| z| - 5z 6 =0( 3) z| z| - 5| z| 6 =0( 4 ) | z2 | - 5| z| 6 =02 .已知棱长为 a的正方体 ABCD -A1B1C1D1,则( 1 )各棱在平面 AB1D1上的射影长之和为 ;( 2 )各棱与平面 AB1D1所成角之和为;( 3)各面在平面 AB1D1上的射影的面积之和为 ;( 4 )各面与平面 AB1D1所成角之和为.3.( 1 )在实数集 R上定义的函数 f( x) ,对任意α,β有f (α) f (β) =f ( α β2 ) f ( α -β2 ) ,且　 f ( 1 ) =2 ,f ( x) 2 ,则满足条件的一个函数是 .( 2 )已知 f ( x)…     

关于单叶从属函数的一个系数不等式

<正> §1.引言 记■={z||z|<1}.设F(z)■是■上的解析函数.函数w=F(z)将映成区域S_F.设f(z)在中解析,如果w=f(z)的一切值都落在S_F上,那么说f(z)从属于F(z).记为f(z)相似文献   

On the distributions of the ratios of the extreme roots to the trace of the Wishart matrix

In this paper, the authors cosider the derivation of the exact distributions of the ratios of the extreme roots to the trace of the Wishart matrix. Also, exact percentage points of these distributions are given and their applications are discussed.     

On the comparison between the APV and the NPV computed via the WACC

The valuation of levered investment in the practice is made with the WACC approach, even if the superior technique of the APV is available. The paper shows that the APV can be interpreted as the arbitrage free value of the portfolio made by an investment and a supporting loan. Therefore the WACC evaluation, generally different from the APV, allows for arbitrage. We provide various conditions which completely characterize the sign of the error as a functions of all the variables entering the model.     

用常微分方程模型分析预防和隔离措施对SARS发病率的影响

通过建立常微分方程模型 ,分析了预防和隔离措施对 SARS发病率的影响 ,并把计算结果与实际统计数据进行了比较 ,结果表明 ,及时高效的预防和隔离措施能够有效地控制 SARS的传播 .     

From the neutrino to the edge of the universe

Two recent findings necessitate a closer look at the existing standard models of particle physics and cosmology. These are the discovery of neutrino oscillation, and hence a non-zero mass on the one hand and, on the other, observations of distant supernovae which indicate that contrary to popular belief, the universe would continue to expand for ever, possibly accelerating in the process. In this paper it is pointed out that relatively recent studies which indicate a stochastic, quantum vacuum underpinning and a fractal structure for space time, reconcile both of the recent observations, harmoniously.     

On the Gap in the Spectrum of the Translations

The spectrum of the translations in local quantum field theory will be analyzed in order to show that in a positive energy representation without vacuum vector and with lowest mass m₁ there is no gap in the spectrum which is larger than 2m₁. In particular in a zero mass representation there is no hole at all. These results are obtained with methods of analytic functions of several complex variables.     

From the subalgebras of the square to the discriminator

Presented by A. F. Pixley.     

On the Decomposition of the Riesz Operator and the Expansion of the Riesz Semigroup

For a Riesz operator T on a reflexive Banach space X with nonzero eigenvalues denote by E(λ_i; T) the eigen-projection corresponding to an eigenvalue λ_i. In this paper we will show that if the operator sequence is uniformly bounded, then the Riesz operator T can be decomposed into the sum of two operators T_p and T_r: T = T_p + T_r, where T_p is the weak limit of T_n and T_r is quasi-nilpotent. The result is used to obtain an expansion of a Riesz semigroup T(t) for t ≥ τ. As an application, we consider the solution of transport equation on a bounded convex body.     

On the dependence of the growth rate on the length of the defining relator

Let { } be a sequence of finitely presented groups with generating setA={a1, …, am}, and letRk be the symmetrized set of words over the alphabetA∪A−1 obtained from the defining words and their inverses by all cyclic shifts. We shall assume that the words inRk are cyclically irreducible, and their lengths tend to ∞ ask increases. In the paper, it is proved that ifRk satisfies the small cancellation conditionC'(1/6) and the number of relators increases not very rapidly with increasingk, then the growth rate ψ(Gk) tends to 2m−1 ask→∞. Translated fromMatematicheskie Zametki, Vol. 65, No. 4, pp. 611–617, April, 1999.