四边形的内接三角形的一个性质

图1我们先了解关于圆内接三角形的一个性质.如图1,△x1y1z1为⊙O的内接三角形,P为圆内一点,x1P、y1P、z1P与圆分别交于x2、y2、z2.则△x1y1z1△x2y2z2=Px1·Py1·Pz1Px2·Py2·Pz2.注本文等式中的“△xyz”均表示△xyz的面积.简证设⊙O的半径为R,连z1O并延长交圆于y1′,连x1y1′,则∠x1y1z1=∠x1y1′z1.于是△x1y1z1=12x1y1·y1z1·sin∠x1y1z1=12x1y1·y1z1·sin∠x1y1′z1=12x1y1·y1z1·x1z12R=14Rx1y1·y1z1·x1z1.同理△x2y2z2=14Rx2y2·y2z2·x2z2.故△x1y1z1△x2y2z2=x1y1·y1z1·x1z1x2y2·y2z2·x2z2=     

收益管理中非正态无约束估计的PD方法

PD方法在收益管理无约束估计应用中较EM算法更加具有灵活性。无约束需求数据的非正态化假设更加符合收益管理实践中产品各"预售提前期间隔"的需求数据特征,包括对数正态、伽玛、指数和泊松分布。本文分别建立了上述非正态假设下的PD方法;并针对计算过程中可能出现的样本数据均受到截尾的情况,对所提方法的应用进行了改进;数值算例说明了所提方法迭代过程简单,且易收敛;通过与EM算法进行比较,验证了所提各PD方法的有效性,并就参数Υ对无约束估计效果的影响进行了分析和总结。     

Hilbert空间中非扩张余弦族的显式、隐式和黏性迭代

研究了Hilbert空间中一些逼近单参数非扩张余弦族公共不动点的迭代格式.借助余弦族理论,在较弱的条件下分别对显式、隐式和黏性的迭代过程建立了一系列的收敛定理.结果表明上述三种迭代过程适用于非扩张余弦族;并且隐式和黏性迭代格式在收敛性上优越于显式迭代格式.     

一类具有局部弱稳定退化解的奇摄动Robin问题

研究一类一般的二阶非线性方程的奇摄动Robin问题的边界层现象.在退化解是局部弱稳定的主要假设下,利用界定函数法和微分不等式理论证明了呈边界层性态的解的存在性,并给出解的渐近估计.     

非奇异H-矩阵新的含参数细分迭代判别法

结合矩阵自身的元素,构造了含参数的迭代公式,进而细分了矩阵非对角占优行指标集.利用广义严格α-对角占优矩阵与非奇异H-矩阵的关系,给出了非奇异H-矩阵一组新的细分迭代判定准则,推广和改进了已有的结果,通过数值算例说明了结果的优越性.     

一类中立型泛函微分方程的周期解

利用K-集压缩算子拓扑度抽象连续定理,得到一类带分布时滞的中立型泛函微分方程存在周期解的充分条件.     

种群细胞增生中一类Rotenberg模型研究

本文在Lp（1（≤）p＜＋∞）空间上,研究了种群细胞增生中一类具非光滑边界条件的Rotenberg模型,讨论了这类模型相应的迁移算子的谱分析,证明了该迁移算子的本征值的存在性,得到了该迁移算子的谱在某半平面上仅由有限个具有限代数重数的离散本征值组成等结果.     

Riemann problem for a geometrical optics system

The paper solves analytically the Riemann problem for a nonstrictly hyperbolic system of conservation laws arising in geometrical optics,in which the flux contains the nonconvex function possessing an infinite number of inflection points.Firstly,the generalized Rankine–Hugoniot relations and entropy condition of delta shock waves and left(right)-contact delta shock waves are proposed and clarified.Secondly,with the help of the convex hull,seven kinds of structures of Riemann solutions are obtained.The solutions fall into three broad categories with a series of geometric structures involving simultaneously contact discontinuities,vacuums and delta shock waves.Finally,numerical experiments confirm the theoretical analysis.     

Uniform exponential attractor for nonautonomous partly dissipative lattice dynamical system

In this paper,we consider the existence of a uniform exponential attractor for the nonautonomous partly dissipative lattice dynamical system with quasiperiodic external forces.     

Efficient statistical inference for partially nonlinear errors-in-variables models

In this paper, we consider the partially nonlinear errors-in-variables models when the non- parametric component is measured with additive error. The profile nonlinear least squares estimator of unknown parameter and the estimator of nonparametric component are constructed, and their asymptotic properties are derived under general assumptions. Finite sample performances of the proposed statistical inference procedures are illustrated by Monte Carlo simulation studies.