圆锥曲线切线的一个统一性质

性质1 如图1,已知P是过抛物线y^2=2px（p〉0）的准线与x轴的交点M的弦AB在两端点处的切线的交点,线段AB的中点为C,F为抛物线的焦点,则（1）PF⊥x轴;（2）PC⊥PF． 证明 （1）设A（x1,y1）,B（x2,y2）,直线AB的方程为x=ty-p/2,联立直线AB的方程和抛物线方程消x整理得y^2-2pry＋p^2=0,所以由韦达定理有y1＋y2=2pt,y1y2=p^2     

Θ-type Calderón-Zygmund operators with non-doubling measures

Let µ be a Radon measure on ? ^d which may be non-doubling. The only condition that µ must satisfy is µ(B(x, r)) ≤ Cr ⁿ for all x∈? ^d , r > 0 and for some fixed 0 < n ≤ d. In this paper, under this assumption, we prove that θ-type Calderón-Zygmund operator which is bounded on L ²(µ) is also bounded from L ^∞(µ) into RBMO(µ) and from H _atb ^1,∞ (µ) into L ¹(µ). According to the interpolation theorem introduced by Tolsa, the L ^p (µ)-boundedness (1 < p < ∞) is established for θ-type Calderón-Zygmund operators. Via a sharp maximal operator, it is shown that commutators and multilinear commutators of θ-type Calderón-Zygmund operator with RBMO(µ) function are bounded on L ^p (µ) (1 < p < ∞).     

SOME NEW EXTENSIONS OF EDELSTEIN-SUZUKI-TYPE FIXED POINT THEOREM TO G-METRIC AND G-CONE METRIC SPACES

In this paper, we prove some fixed point theorems for generalized contractions in the setting of G-metric spaces. Our results extend a result of Edelstein [M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc., 37 （1962）, 74-79] and a result of Suzuki [T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 （2009）, 5313-5317]. We prove, also, a fixed point theorem in the setting of G-cone metric spaces.     

随机环境中分枝随机游动的极限定理

假定环境平稳遍历, 考虑随机环境中的分枝随机游动. 在此模型中, 粒子以上临界的Galton-Watson 过程分枝产生后代, 而以一维紧邻随机环境中的随机游动进行运动. 令~$Z_{n}(B)$ 表示时间~$n$ 落于~$B$ 中的粒子数, 其中~$B$ 为~$\mathbb{R}$ 中任一子集. 得到了计数测度~$Z_{n}(\cdot)$ 经过适当的规范化之后, 在~``annealed" 情形下的中心极限定理.     

HOMOCLINIC SOLUTIONS FOR A CLASS OF SECOND ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL SYSTEMS

By means of an extension of Mawhin’s continuation theorem and some analysis methods, the existence of a set with 2kT-periodic solutions for a class of second order neutral functional differential syste...     

ROBUST WEAK ERGODICITY AND STABLE ERGODICITY

In this paper, we define robust weak ergodicity and study the relation between robust weak ergodicity and stable ergodicity for conservative partially hyperbolic systems. We prove that a Cr(r > 1) cons...     

具有n个小时滞脉冲系统的周期解

本文考虑有n个小时滞的脉冲系统,利用隐函数存在性定理证明了该系统时滞 充分小时,系统的周期解存在性,推广了已有的相关结论.     

具S-型分布时滞的细胞神经网络的概周期解

该文研究一类具S-型分布时滞的细胞神经网络(CNNs)的概周期解及全局指数型稳定性问题.利用指数型二分性和Schauder不动点定理以及构造Lyapunov函数,得到了细胞神经网络模型概周期解和指数稳定性的一些充分条件.此外,给出一个实例说明结果是可行的.