数值不等式

Chapter 1 we introduce the risk process with positive and negative risk sums,show the background of the risk process. Chapter 2 we show the integral and differential equation of birth probability,give the Lundberg inequation that the ruin probability satisfies with martingale approach,then discuss then ruin probability of the risk process with two dependent positive and negative risk sums,study how the dependence impacts on the ruin probability. Chapter 3 we compare the concrete examples by numbers,and makes further comparison between the two results coming out of independency and dependency,with the purpose of narrating their respective impacts on the probability of ruin probability.

本文第一章引入含正、负风险和的风险模型，介绍风险过程的实际背景；第二章给出生存概率Φ所满足的积分-微分方程，利用典型鞅方法给出破产概率Ψ满足的Lundberg不等式，并且讨论两个相关正、负风险和模型的破产概率，研究相关性对破产概率的影响；第三章对具体实例给出数值比较，进一步把相关性和独立性两种情形的结果进行比较，说明对破产概率的影响。

In modeling heavy tails,we focus on multivariate t distributions and derive the moment generating function of the quadratic approximation.Then we use Fourier transform,Chebychev's Inequality and numerical technique inversion to approximate VaR value of portfolio,compared with Cornish-Fisher Expansions normal model and Delta-Normal model.

在推导出多个外汇期权的投资组合的二次近拟的矩母函数表达式基础上，本文使用傅里叶变换、切比雪夫不等式、数值转换计算求出投资组合的VaR的值，并和基于多元正态分布Cornish-Fisher模型以及基于Delta-正态模型计算所得的VaR值了进行比较。

By means of Floquet theory,Lyalpunov function, Hurwitz criterion, linearization, Lasalle invariable set principle,, characteristic line, coincidence degree, estimation of inequality ,numerical simulation and so on, we study two kinds of models with impulsive vaccination.

其中综合运用Floquet 原理、Lyapunov函数、 Hurwitz判据、线性化、 Lasalle不变集、数值模拟、射频映射、分支理论、不等式估计、重合度理论等方法和知识，系统地研究了两类实施脉冲疫苗策略的非线性模型。

The results show that the effective methods to deal with the LMIs are the matrix transformation, similarity transformation and Schur's Complement Lemma.

线性矩阵不等式可以有效地用内点法进行数值求解，目前已成为研究控制问题的一种重要工具。

The result shows that the transformation from linear system of strict inequalities to minimax problem avoids the shortage of getting a boundary point solution and is satisfying.

最后在Matlab环境下给出了数值实验，实验结果表明，将严格线性不等式组问题转化为Minimax问题来求解，避免了得到边界点解的情形，得到的结果比较令人满意

Poincaré inequalities play an important role in the research of many fields such as in harmonic analysis and in theory and numerical method of differential equations.

Poincar 不等式在调和分析、微分方程理论及其数值方法等领域的研究中具有极其重要的作用。

The long-term seepage control effects of the surrounding rocks of the underground powerhouse are performed by a stationary seepage analysis method combining the variational inequality formulation of Signorini's type with an adaptive penalty Heaviside function to guarantee the numerical stability and convergence. Meanwhile, the difficulty in finite element mesh generation is reduced and the calculation time and modeling accuracy are balanced with a global model of equivalent modeling and a submodel of accurate modeling for drainage hole array.

为确保数值计算的稳定性和收敛性，采用Signorini型变分不等式和自适应罚函数相结合的稳定渗流分析方法，对厂房围岩的长期渗控效应进行计算分析；同时，采用基于等效模拟的整体模型分析和基于精细模拟的子模型分析相结合的方法，以减小有限元建模难度并协调计算量和计算精度之间的矛盾。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。