查询词典 numerical inequality

We first got the PML equations by making the radius complex, and then proved that the sesquilinear form in the weak formulation of the PML problem satisfies the Grding inequality under the hypothesis of the absorption factor, and further could prove the existence and uniqueness of the solutions of the PML problem, finally, we gave the numerical experiments which show that this method is feasible to a certain extent.

首先通过复化极径得到PML方程，然后在关于吸收参数的假设下，证明了PML问题变分形式中的半双线性形式满足Grding不等式，进而证明了PML问题解的存在惟一性，并给出了数值实验。实验结果表明，该方法有一定的可行性。

We first got the PML equationsby making the radius complex, and then proved that the sesquilinear form in the weak formulation of the PML problem satisfies the Garding inequality under the hypothesis of the absorption factor, and further could prove the existence and uniqueness of the solutions of the PML problem, finally, we gave the numerical experimentswhich show that this method is feasible to a certain extent.

首先通过复化极径得到PML方程，然后在关于吸收参数的假设下，证明了PML问题变分形式中的半双线性形式满足Garding不等式，进而证明了PML问题解的存在惟一性，并给出了数值实验。实验结果表明，该方法有一定的可行性。

To regard definite integral inequality as numerical value inequality,and use the monotone of function.

我们应当吸取不同时期因脱离群众而导致的曲折和深

The argument about "conceding" numerical inequality was due either to a misunderstanding or to demagoguery.

所谓我们"承认"了数量的不平等，这不是出于误解就是想蛊惑人心。

In order to reasonably depict four basic problems with friction, one Coulomb friction new form in first Kirchhoff stress is proposed to deal with finite deformation problems, other Coulomb friction form in incremental mode to elastoplastic flow theory; Hilbert function spaces concerning elastoplastical problems with friction are established, so it makes all operations and calculations in the treatise standardized within the scope of reasonably topologic structure; In view of functional extremum, the equivalence between generalized variational inequalities principles in elastoplasticity with friction and corresponding basic problems are testified by inducing Lagrangian multipliers, so it provides a rationally theoretical basis for numerical methods in elastoplasticity with friction; From the viewpoint of variational inequality, the theory of generalized variational inequalities in elasticity and elastoplasticity with frictional constraint is studied, and the uniqueness and existence of the solution of FEM is proofed under the proposed conditions of stress compatibility, and them FEM approximation and a discrete solution are discussed; Based on the principles of generalized variational inequalities in elastoplasticity with friction, direct generalized variational inequalities methods is pretended, which is a natural generalization and development of direct variational methods; Using generalized variational inequalities methods, some examples in metal forming including plane deformation, upset and extrusion are analyzed and the results prove that all the theories and methods in the paper are right, feasible, accurate and advanced.

主要内容有：为了合理地描述金属塑性成形中摩擦约束弹性、弹塑性基本问题，提出和研究了有限变形下以Kirchhoff第一应力表示的Coulomb摩擦定律形式和弹塑性流动理论下以增量形式表示的Coulomb摩擦定律表示形式；系统建立了摩擦约束弹塑性问题的Hilbert函数空间，使本文规范在一个具有合理的代数拓扑结构内进行一切操作和运算；利用Lagrange乘子，从泛函极值的角度系统地阐述和论证了一系列摩擦约束弹性、弹塑性广义变分不等原理与相应的实际问题之间的等价性，它为处理摩擦约束的弹塑性力学数值方法提供了合理的理论基础；从变分不等式的角度出发，阐述了对应于摩擦约束弹性、弹塑性问题的广义变分不等式理论，首次提出了在应力相容性条件下，它的有限元解具有存在唯一性，进而讨论了其有限元近似及离散解法；基于摩擦约束弹塑性广义变分不等式原理，首次提出了直接广义变分不等式方法，这一方法是直接变分法的合理推广和发展；利用直接广义变分不等式方法对金属压力加工中的平面变形问题、镦粗、挤压等塑性成形问题进行了分析计算，验证了该理论和数值算法的正确性、实用性、精确性和优越性。

In chapter 4 we proposed a linear inequality constraint optimization question frame about projection of gradient algorithm, and has performed the numerical experimentation, but its convergence also needs further study.

在第四章中我们提出了线性不等式约束最优化问题的一个投影梯度算法框架，做了数值试验，但其收敛性还有待进一步研究。

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。

For the characteristic of the ring permanent magnet torque motor used in direct drive numerical control round table suffering from the effect of load disturbances and parameters variations, a multi-objective mixed H2/H∞ static output feedback controller, which makes all poles of the closed-loop system be located within a prescribed linear matrix inequality region D to achieve pole placement, is designed based on LMI.

针对直接驱动数控转台用环形永磁力矩电机易受负载扰动及自身参数变化影响的特点，文中基于线性矩阵不等式(linear matrix inequality， LMI)，设计了一个多目标混合H2/H￥静态输出反馈控制器，该控制器可使闭环系统的极点均落在预先选定的线性矩阵不等式区域D内来实现极点配置。

By applying the H〓lder inequality, the Gronwall inequality, the Doob's inequality and the properties of the Ito stochastic integral to the integral form of the test equation, several important inequalities related to the analytical solution are proved, and the local order of the numerical solutions in mean square sense is obtained accordingly.

通过对试验方程的积分形式使用Holder不等式、Gronwall不等式、Doob不等式和Ito随机积分的性质，得出了试验方程解析解满足的几个重要不等式，进而得出了数值方法在均方意义下的局部误差阶。

Shule River project area is located in northwest China\'s Gansu province,Hexi Corridor,which is the largest agricultural crop production base of Gansu province and typically arid and semi-arid areas. There are characteristics such as scarce rainfall,the temporal and spatial distribution inequality,strong evaporation,fragile ecological environment,the limited quantity of surface water. Agriculture,the people\'s living and ecological environment are significantly dependent on the groundwater. Based on the collection and processing of regional hydrological and geological data and the groundwater monitoring data,using the numerical simulation,geostatistics theory and multi-objective evolutionary algorithm,this paper studied the monitoring and evaluation of groundwater resources from the three aspects: groundwater numerical simulation and prediction,groundwater spatial variability and distribution and optimization modeling and sloving of groundwater monitoring network. The main work and research lies:(1) Using Yumen-Tashi basin,Anxi-Dunhuang basin and Huahai basin as study area,this paper used modflow model to simulate groundwater flow of three areas.

本文在收集和整理项目区水文地质数据以及地下水监测数据的基础上，基于数值模拟、地统计学理论及多目标进化算法，从地下水数值模拟与预测、地下水空间变异与分布特征分析以及地下水监测网优化建模与求解三个方面展开了对项目区地下水资源监测与评价的研究，主要研究工作如下：(1)以项目区内的玉门-踏实盆地、安西-敦煌盆地和花海盆地为研究区域，在《河西走廊项目中期计划调整报告》规划条件下，基于modflow模型对地下水水流进行数值模拟，计算并生成了三个区域2007-2030年地下水埋深预测数据以及等值图。

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。