查询词典 galerkin equations

Carleman不等式及其在最优控制问题中的应用.Optimal control theory of distributed parameter systems mainly includes: Pontryagin's maximum principle; controllability; Hamilton-Jacobi equation (i.e., dynamic programming equation); time optimal control, etc.In this dissertation, we establish Pontryagin's maximum principle of optimal control problems governed by some nonlinear differential equations (parabolic differential equations, elliptic differential equations and 3-dimensional Navier-Stokes equations), which in particular could have local solut...

在这篇博士论文中，我们建立了非线性微分方程(包括抛物型微分方程，椭圆型微分方程以及3维Navier-Stokes方程)最优控制问题的庞特里雅金最大值原理，特别地，这些方程可能只有局部解或存在多解(我们称这样的系统为非适定系统，相应的最优控制问题为非适定最优控制问题)，以及适定的非线性发展方程最优控制问题的庞特里雅金最大值原理；我们研究了phase-field系统的时间最优控制问题以及Boussinesq系统的局部内可控性。

The calculation of the rotordynamic coefficients of a multistepped annular seal in hydraulic turbines is discussed in this paper. Based on the Hirs' turbulence lubrication theory and the bulk flow model, the governing equations for the flow in the seal are developed by using the Moody's friction equations. The governing equations are perturbed when the rotor and the stator are coaxial. The Runge Kutta integration method and the Newton Raphson iteration method are used to solve the perturbation equations....

本文首先在Hirs紊流润滑理论的基础上，采用体积流动模型及Moody摩擦方程建立起阶梯口环水封中流体流动的控制方程，将各个方程在转子与定子同心处进行摄动，采用Runge－Kuta积分法及迭代过程求解摄动方程，建立起水轮机阶梯式口环水封的转子动力特性系数的计算方法，为水轮发电机组轴系的动力学分析提供了必要的理论基础。

The viscoelastic modeling in 2-D SEG/EAGE salt dome model is carried out by using the simplified viscoelastic equations. A comparison of the viscoelastic single-shot records derived from acoustic equations, Carcione's equations and the simplified viscoelastic equations is made.

并利用该简化方程对SEG/EAGE二维盐丘模型进行了正演数值模拟，将模拟得到的单炮记录和声波、Carcione黏弹性波方程模拟得到的单炮记录进行了对比分析。

The numerical calculation commonly used for the Delphi process more than 100, including solutions of linear algebraic equations, interpolation, numerical integration, special, function approximation, eigenvalue problems, data fitting equation Root and solve nonlinear equations, functions and the extreme optimization, statistical data description, Fourier transform spectra, solution of ordinary differential equations reconciliation partial differential equations.

本书共有数值计算中常用的Delphi子过程100多个，内容包括解线性代数方程组、插值、数值积分、特殊函数、函数逼近、特征值问题、数据拟合、方程求根和非线性方程组求解、函数的极值和最优化、数据的统计描述、傅里叶变换谱方法、解常微分方程组和解偏微分方程组。

Neutral differential equations with variable sign coefficients are separated into neutral differential equations with positive and negative coefficients by transformation. According to the characteristic of these equations, a real number set with supremum is constructed, and sufficient conditions for oscillation of all solutions to neutral equations with variable sign coefficients are obtained.

通过变换将具有变号系数的中立型微分方程分解为具有正负系数的中立型微分方程；分析具有正负系数中立型微分方程的特征，构造存在上确界的实数集；并对中立型微分方程的解作细致分析，得到了具有变号系数中立型微分方程所有解振动的充分条件。

Neutral differential equations with variable sign coefficients are separatedinto neutral differential equations with positive and negative coefficients bytransformation.According to the characteristic of these equations,a real number setwith supremum is constructed,and sufficient conditions for oscillation of all solutionsto neutral equations with variable sign coefficients are obtained.

通过变换将具有变号系数的中立型微分方程分解为具有正负系数的中立型微分方程；分析具有正负系数中立型微分方程的特征，构造存在上确界的实数集；并对中立型微分方程的解作细致分析，得到了具有变号系数中立型微分方程所有解振动的充分条件。

Based on orthogonal function unfolding theory, the transverse fields can be represented as a superposition of waveguide modes. And according to coupled-wave theory, the time-dependent multi-mode coupling-wave equations (or the generalized telegrapher's equations) and the coupling coefficients among the different modes were deduced. The generalized telegrapher's equations are a set of coupled one-dimensional partial differential equations for the amplitudes of the modes.

应用正交函数的展开理论，将变截面波导中的电磁场表示为横电波和横磁波本征模式的级数；然后根据耦合波理论，推导了考虑波导金属壁有限电导率的变截面波导时域多模耦合波方程组及各模式间耦合系数的表达式。

For obtaining the numeral solutions of round elastic plates in axisymmetrical deformation with varying-thickness in nonlinear deformation in the unsteady electromagnetic field and mechanical field,by establishing the equations of motion,the equations of distortion,the equations of Lorentz force,the equations of electronic dynamic mechenical,and adopting iterative method,we gained the nonlinear magneto-elastic calculation method and outcome of current-carrying shell,and gained the influencing degree toward mechanical parameter of varying thickness round ferreous plates in the electromagnetic field and mechanical field.

为了获得内边界固定的环形导电薄板在均布力与横向磁场作用下的变形问题的数值解，通过建立运动方程、变形方程、电动力学方程和洛仑兹力方程，运用迭代法得出了载流板壳的非线性磁弹性的计算方法和结果，以及机械场、电磁场对铁质变厚度圆板各力学参量的影响程度。

The results calculated by the Elovich rate equation showed that K release rates from 1 mol.L-1 HNO3 extraction ＞those from 2 mol.L-1 HNO3 extraction ＞those from H-resin extraction. Elovich equations combining with the data of H-resin and 2 mol.L-1 HNO3 successive extraction could well described the release characteristics of soil K. The correlation coefficients of the equations reached most significant levels (r＝0.956**—0.999**), and standard errors of specific K release capacities between the vaules calculated by the equations and those measured by both successive extractions were smaller(s=1.61 and 3.52). The specific release rates of soil K calculated by the Elovich rate equations were significantly correlated with the indices of soil K availability (the amounts of easily available K, nonexchangeable K, total available K in soils and K absorbed by ryegrass).

研究结果表明：1 mol.L-1 HNO3提取法的释K速率＞2 mol.L-1 HNO3提取法的释K速率＞氢饱和交换树脂提取法的释K速率；氢质交换树脂和2 mol.L-1 HNO3提取法结合Elovich模型较理想地描述了土壤K素的释放特性，拟合方程的相关系数均达极显著水平(r＝0.956**-0.999**)，土壤特征累积释K量的计算值与实测值的标准差较小(s=1.61和3.52)，且通过速率方程计算的土壤特征释K速率与K素有效性指标(速效K、缓效 K、有效K及黑麦草总吸K量)的相关性也较为密切。

The main creating aspects are finding and clarify such a fundamental physical process that the grain boundaries emit vacancies under compressive stress to induce solute non-equilibrium grain boundary dilution and absorb vacancies under tensile stress to induce non-equilibrium grain boundary segregation, formulizing the structural equations and the composition equations in force equilibrium in grain bounary region to describe this physical processes and the kinetic equations for non-equilibrium grain boundary segregation under tensile stress, calculating the modulus in grain boundary region from the expermental data of grain bounday segregation using the structure and coposition equations and calculating the diffusion coefficients of vacancy-solute atom complexes using the kinetic equation simulating the experimental results of grain boundary segregation.

本项目的主要创新点是，发现并阐明了弹性应力场作用下空位与晶界交互作用的基本物理过程：在张应力作用下，晶界会吸收空位，引起溶质非平衡晶界偏聚；压应力作用下，晶界会发射空位，引起非平衡晶界贫化。建立了描述此物理过程的晶界区力学平衡的结构方程和成分方程；？建立了张应力引起的非平衡晶界偏聚动力学方程？；用晶界区力学平衡的结构方程和成分方程？，首次通过实验测量计算出多晶材料晶界区的弹性模量；通过建立的动力学方程模拟实验结果，首次获得溶质原子－空位形成的复合体的扩散系数。

"Please accept this talisman as a token of our thanks."

请收下这个护身符以表达我们的感谢。

If I have that magic, I will be more acceptable in the society.

如果我拥有那种魔法，我将更加被这个社会所容纳。