查询词典 variations equation

By the analysis of Euler\'s three earlier papers on the calculus of variations and that of his mistake on the fundamental principle,and the comparison with Euler\'s and his pioneers\' solutions,the refinement of Euler\'s two core achievements,i.e., fundamental equation and isoperimetric rule,is explained.

通过对欧拉与伯努利兄弟和泰勒等人的解法进行比较和分析，揭示了欧拉对变分法一般性研究的背景、切入点、思想来源和演变；通过对欧拉所犯错误的原因及其影响进行深入分析，指出《技巧》一书并不仅仅是欧拉对早期研究的系统总结和改进，还包含着某种突破和变革。4。

The performance function and constraint equation in calculus of variations were constructed by analyzing input and output equations of the system containing parameters to be estimated. The traditional parameter estimation problem could be transformed to that of least squares estimation.

通过分析包含待估参数的系统输入输出方程，构造变分法中的性能范函和约束方程，将传统的参数估计问题化为带约束条件的最小二乘估计问题；利用拉格朗日乘子法，分析参数估计方程，得到参数的最优估计。

In this thesis, sound wave path equation is derived from Fermat's theorem and the calculus of variations, and then the temperature field is reconstructed by the combination least-square method and the modified sound wave path.

本文通过求解由费马定理和变积分原理确定的声波路径方程，结合最小二乘法实现了声波路径的修正。

Considering the characteristic of dynamic consolidation in soft soil, L'place transformation is carried out on the basis of relaxed resolution problem of dynamic consolidation in saturated soft soil proposed by Zienkiewicz. With calculus of variations as the principal theory, the function of dynamic consolidation equation is constructed, and further, dynamic consolidation equation in matrix forms is deducted.

本文针对软土地基上动力固结法的特点，在Zienkiewicz提出的饱和土体动力固结定解问题的基础上做拉氏变换，以变分原理为基本理论，构造动力固结方程的泛函，进一步推导得到动力固结方程的矩阵形式表达式。

Through establishing the functional of the source pulse which is based on the concept of "usable energy" in the received pulse and then extremizing the functional by means of the calculus of variations, the mathematical models of the optimized source pulse waveforms are shown to be associated with the eigenfunctions of a homogeneous Fredholm linear integral equation of the second kind. An efficient algorithm is developed for numerically solving the integral equation models.

论文研究了基于延迟反射脉冲序列无源标签的UWB RFID系统的基本工作原理并进行了详细的信号描述和分析，通过建立基于接收脉冲"有效能量"概念的源脉冲波形函数的泛函和使用变分计算泛函极值，得到了相关于第二类齐次Fredholm线性积分方程特征函数的源脉冲波形最优解数学公式模型，并开发了一套有效的数值求解算法。

An inhomogeneous Benjamin-Davis-Ono-Burgers equation including topographic forcing and turbulent dissipation is derived in terms of the quasi-geostrophic vorticity equation, an approximate analytic solution of the BDO-Burgers equation with a small dissipation is obtained, the time variations of mass and energy of the algebraic solitary waves are discussed, and finally, the forced BDO-Burgers equation is integrated numerically and the numerical solutions are given for a given basic flow with a weak shear and a localized topographic forcing.

利用包括地形外源和湍流耗散的准地转涡度方程导出了包含强迫项和湍流耗散项的非齐次强迫BDO-Burgers方程，求出了小耗散存在情况下BDO-Burgers方程的近似解析解，讨论了代数孤立波的质量和能量的守恒关系，最后，对给定的弱切变基本气流和局地地形强迫，数值积分强迫BDO-Burgers方程，求得了不同参数下的数值解。

Supposed stochastic variations are perturbed in a small range, we can get a nonlinear equation of these stochastic variations by using a Taylor series or a Neumann series expansion of the system matrix. The application of perturbation techniques translates this nonlinear equation into a pair of constant linear recursive equations. Then we have written a paper "Stochastic Finite Element Method for Interconnect Including Variational Analysis" which has been contributed to 11th Asia and South Pacific Design Automation Conference.

本文所取得的主要成果就是提出了一种新的算法，即用随机有限元来分析变化的互连线，将方程按随机变量泰勒展开或者纽曼展开，从而化无限维为有限维；应用matlab进行了算法仿真，并将结果与传统Monte-Carlo与GETA进行了比较；最后写了一篇文章《Stochastic Finite Element Method for Interconnect Including Variational Analysis》，已投第11届亚洲和南太平洋设计自动化会议。

Considering the spatial correlations of interconnect process variations, we modelprocess variations as continual stochastic processes with correlation. For decoupleing thespatial correlation, we express them as an expanded form of independent random variablesby Karhunen-Loeve expansion. Then we use stochastic Galerkin method to solve thedecoupled telegraph equation in the presence of process variations.

考虑互连线工艺变化的空间相关性，将互连线工艺变化建模为具有相关性的连续随机过程；提出采用Karhunen-Loeve展开将该随机过程表示为一组独立随机变量的展开式，从而进行解耦；对解耦后得到的工艺变化下的电报方程，应用随机迦辽金方法求解。

In chapter3, information is divided into two basic types, the marginal equation of bond price and short-term interest variations is established, thus the security price variations and the price equilibrium of other assets (risk security non-risk security are included) are analyzed by the implement of portfolio Theory.

第三章将债券的价格均衡划分为两大基本类型，建立了债券与短期利率变动的边际方程，运用组合原理分析债券价格变动与其它资产（包括风险证券和无风险证券）的价格均衡关系，通过比较收益原理建立了债券以市场均衡收益为折现参数的价值方程，并通过实证检验了该模型的合理性；第四章，分析了内部信息与价格的传导原理，建立了非完全信息市场条件下价格传递信息的做市商模型和预期模型，并讨论外部信息与内部信息对股票价格影响的非一致性。

In chapter3, information is divided into two basic types, the marginal equation of bond price and short-term interest variations is established, thus the security price variations and the price equilibrium of other assets (risk security non-risk security are included) are analyzed by the implement of portfolio Theory. Finally the bond value equation which takes equilibrium return as its yield Parameter is established through the theory of comparative return. In chapter 4, the intra-information and the transferable system of price is emphasized and the market-maker model and expected model under non-perfect information market conditions are established, and the disaccord of the influence of extra-information and intra-information on the security price is discussed.

第三章将债券的价格均衡划分为两大基本类型，建立了债券与短期利率变动的边际方程，运用组合原理分析债券价格变动与其它资产(包括风险证券和无风险证券)的价格均衡关系，通过比较收益原理建立了债券以市场均衡收益为折现参数的价值方程，并通过实证检验了该模型的合理性；第四章，分析了内部信息与价格的传导原理，建立了非完全信息市场条件下价格传递信息的做市商模型和预期模型，并讨论外部信息与内部信息对股票价格影响的非一致性。

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起初我只晓得布鲁克雷德丝是美国少男少女崇拜的偶像，后来回台湾，甚至去年在北京，居然也四处看见她的海报，才惊讶她的魅力之大。