一类解析函数族的极值点与支撑点

设Ｇ＝｛ｆ（ｚ）：ｆ（ｚ）在│ｚ│〈１上解析，ｆ（ｚ）＝ｚ－Σｎ＝２→∞ ａｎｚ＾ｎ，ａｎ≥０，Σｎ＝２→∞ ｎａｎ≤１，Σｎ＝３→∞ｎ（ｎ－１）ａｎ≤２ａ２｝。本文找出了函数族Ｇ的极值点与支撑点。     

关于一类p叶解析函数

本文考虑了函数类Tσ（p,a)闭凸包极值点,并用它确定系数估计。对函数类Tσ（p,a)的其它一些有趣性质也进行也研究。     

关于ff＇的辐角分布

设f为一整函数,下级为μ,级为λ,若ff′-1的零点均聚集于q(<∞)条射线上,则λ必为有穷,并且
(i) 当q=1时,λ≤1/2;
(ii)当q=2与μ≥1时,这两条射线之夹角必等于π/λ;
(iii)当q≥2时,至少存在两条射线,其夹角不超过π/λ。     

关于从属的若干注记

关于从属的若干注记杨定恭（苏州大学数学系，２１５００６）设Ｈ表示单位圆盘内解析函数的全体；Ａ＿ｎ是Ｈ中形如的ｆ（Ｚ）组成的类，这里ｎ是正整数。设ｆ（Ｚ）和ｇ（Ｚ）在Ｈ中，（ｆ＊ｇ）（Ｚ）表示ｆ（Ｚ）与ｇ（Ｚ）的Ｈａｄａｍａｒｄ乘积或卷积；表示ｆ（Ｚ）...     

关于复函数微分中值公式的一个注记

本文给出并论证了复函数微分中值公式的“中值点”的渐近性的一些结果     

关于解析凸性的注记

本文研究了解析一致凸性Ｂａｎａｃｈ空间,证明了重赋范定理并且给出了具有解析一致凸性的一些具体空间。     

关于微分多项式零点的注记

The value distribution of differential polynomials is studied.The re- suits in this paper improve and generalize some previous theorems given by Yang Chungchun(On deficiencies of differential polynomials,Math.Z.,116(1970),197- 204),H.S.Gopalakrishna and S.S.Bhoosnurmath(On distribution of values of differential polynomials,Indian J.Pure Appl.Math.,17(1986),367-372),I.Lahiri (A note on distribution of nonhomogeneous differential polynomials,Hokkaido Math. J.,31(2002),453-458)and Yi Hongxun(On zeros of differential polynomials,Adv. in Math.,18(1989),335-351)et al.Examples show that the results in this paper are sharp.     

单叶解析函数族修正卷积及极值点应用

用线性乘数算子定义了单叶负系数解析函数族J_(λ,μ)~L(α,β),讨论得到其极值点和修正卷积的参变量值,并利用极值点理论对J_(λ,μ)~L(α,β)中有限阶导函数模的界作了精确估计,主要结论可以自然覆盖相关的子类.     

Transformation of equations with retarded argument to equations with the best argument

The problem of choosing the best argument in the Cauchy problem for a system of ordinary differential equations with retarded argument is studied from the viewpoint of the method of continuation of the solution with respect to a parameter. It is proved that the arc length counted along the integral curve of the problem is the best argument for the system of continuation equations to be well-posed in the best possible way. A transformation of the Cauchy problem to the best argument is obtained. Translated fromMatematicheskie Zametki, Vol. 63, No. 1, pp. 62–68, January, 1998.     

Regularity of solutions of evolution integrodifferential equations with deviating argument

In this paper we prove the existence of mild and classical solutions of delay integrodifferential equation and delay integrodifferential evolution equations with nonlocal condition in Banach spaces. The regularity solutions of integrodifferential evolution equations interconnected with viscoelastic material is derived to guarantee the stabilization. The results are established by using the resolvent operators and the fixed point principles. Finally, an example is given to show the potential of the proposed techniques.     

Solvability of a neutral differential equation with deviated argument

The paper contains theorem on the existence and asymptotic characterization of solutions of a differential equation of neutral type with deviated argument. The mentioned differential equation admits both delayed and advanced arguments. In our considerations we use the technique linking measures of noncompactness with the classical Schauder fixed point principle.     

The efficient evaluation of the hypergeometric function of a matrix argument

We present new algorithms that efficiently approximate the hypergeometric function of a matrix argument through its expansion as a series of Jack functions. Our algorithms exploit the combinatorial properties of the Jack function, and have complexity that is only linear in the size of the matrix.

     

On solutions of a neutral differential equation with deviating argument

We prove a theorem on the existence and asymptotic behaviour of solutions of a differential equation with a deviating argument of neutral type. The considered equation contains both delayed and advanced arguments. The method used in the proof of our main result depends on conjunction of the classical Schauder fixed point theorem with the technique of measures of noncompactness.     

一类带导数项的非线性特征值问题正解的存在性

应用 Schauder不动点定理 ,证明了带导数项的非线性特征值问题 :　　 u″+λa( t) f ( u,u′) =0 ,0 0充分小 ,f :[0 ,∞ )× R→ R连续且 f( 0 ,0 ) >0 .     

Precise and fast computation of a general incomplete elliptic integral of third kind by half and double argument transformations

This is a continuation of our works to compute the incomplete elliptic integrals of the first and second kind (Fukushima (2010, 2011) [21] and [23]). We developed a method to compute an associate incomplete elliptic integral of the third kind, J(φ,n|m)≡[Π(φ,n|m)−F(φ|m)]/n, by the half argument formulas of the sine and cosine amplitude functions and the double argument transformation of the integral. The relative errors of J(φ,n|m) computed by the new method are sufficiently small as less than 20 machine epsilons. Meanwhile, the simplicity of the adopted algorithm makes the new method run 1.5 to 3.7 times faster than Carlson’s duplication method. The combination of the new method and that to compute simultaneously two other associate incomplete elliptic integrals of the second kind, B(φ|m)≡[E(φ|m)−(1−m)F(φ|m)]/m and D(φ|m)≡[F(φ|m)−E(φ|m)]/m, which we established recently [23], enables a precise and fast computation of arbitrary linear combination of Legendre’s incomplete elliptic integrals of all three kinds, F(φ|m), E(φ|m), and Π(φ,n|m). These new procedures share the same device, the half argument transformations, while the double argument transformation of J(φ,n|m) includes those of B(φ|m) and D(φ|m) as its sub component. As a result, the simultaneous computation of the three associate integrals is significantly faster than computing them separately. In fact, our combined procedure is 2.7 to 5.9 times faster than the combination of Carlson’s duplication method to compute R_D and R_J.     

P叶近于凸函数类的一个扩展

给出了P叶近于凸函数类的一个扩展.得到包含关系,结合算子理论导出类中函数的积分表达式,端点性质,推出偏差定理,证明积分平均不等式.