变分问题

This article use the improved integral inequalities with the deviate variable and some skills of inequalities as well as related knowledge about second-order differential equation,to obtain the following results: the classification of limit point case or limit circle case and boundedness for second order differential or difference equation with deviative variable,discussed the classification for certain n-order differential equations,Criteria for the classification of second order differential equation with deviative variable.

本文利用推广的具有偏差变元的积分不等式，结合不等式的一些技巧以及常微分方程的相关知识对一类二阶具有偏差变元的微分方程及一类二阶差分方程极限圆型的分类问题作了相关的研究工作，并且讨论了一类n阶具有偏差变元的常微分方程解的平方可积性与有界性和一类二阶非线性具有偏差变元的微分方程解的有界性。

The relation between the parameter of ground motion and time is transformed into a pure random process with the amplitude varying with time. Based on the concept that there is the scaling invariant fractal structure in the transmission of earthquake motion and the self-affinity of the ground motion signal in time domain, an assumption is deduced that the curve of the stationary random noise of the ground motion varying with time is a fractal graph.

将一个运动参数的时间变化过程转化为具有时变振幅的一个纯随机振荡问题，运用地震运动传递具有无特征尺度的分形结构和地运动时域信号具有统计自相似性的概念，提出地面运动随机平稳噪声的时变曲线是一条分形曲线的假设。

In this paper, a series of strong convergence theorems are discussed, which concern with generarized set-valued variational inclusions, a class of strongly accretive operator equation and a class of nonexpansive mappings.

第二章，我们在Hilbert空间中研究-单调算子的概念，以及与此相关的预解式算子R_~，利用预解式算子技巧构造了一类迭代算法，求解变分包含的逼近解问题，并讨论了由此算法产生的迭代序列的收敛性。

Firstly, the lake water quality model is developed under the condition of both internal and external pollution by using the method of microelement analysis, then homogenizes the non-cylindrical boundary condition and utilizes the methods of vector expending and pseudomonotone of the variational operator, and last the existence and uniqueness of the solution for a type free initial-boundary value problem is obtained.

本文首先运用微元分析法导出在外源和内源双重污染下湖泊水质模型，然后对一类自由初边值问题通过对非柱形边界条件的齐次约化，运用变分型算子的向量扩张和拟单调方法获得解的存在性、唯一性。

Interlayer oxidized zone can be divided accurately by Fe_2O_3, Fe_2O_3/FeO and U parameters. We can correct the field macroscopic color zoning by combining the macroscopic zoning and microscopic zoning. Univalent major elements components(Al_2O_3, SiO_2, K_2O, Na_2O) show remarkable activity at the process of interlayer oxidizing, their contents are variable and mingled in different zones and it can't be used in zoning. But we can speculate the developmental degree of interlayer oxidized zone and uranium mineralization according to the concentration trends and variation characteristics of sensitivity group, activity group and their ratios .(3)The comparatively steady elements such as lithiphile elements, sulfophile elements and high field strength elements change regularly at the process of interlayer oxidation except some radioactive elements. Trace elements and rare earth elements commonly enrich in thin rock clast such as mudstone, in which the enriched elements species are more than those in the whole rock, which indicate that the regeneration action in caulking matter are more deep than that in whole rock at the process of interlayer oxidation, and the reallocate intention of trace elements in main minerlized rock in Tuha basin are more intensive than that in Yili basin at the process of deposition ,diagenesis and later changes .

根据化学蚀变参数PC值和分离迁移位等将常量元素组分分为敏感组分组、活动组分组、次活动组分组和惰性组分组，不同组分可分别用于讨论层间氧化带低温地球化学中不同问题；敏感组分(变价元素组分Fe_2O_3、FeO)和U在层间氧化带中迁移富集规律明显，Fe_2O_3／FeOFe~(3+／Fe~(2+)比值具分带判别能力，配合U含量对层间氧化带进行较准确的分带，可克服野外宏观颜色分带偏差：提出Fe~(3+)／Fe~(2+)分带判别值在不同盆地、不同地段不同，除受氧化作用控制外，流体酸碱度不同也是重要因素的观点，对找矿实践有实际指导意义；活动组分(Al_2O_3、SiO_2、K_2O、Na_2O)在层间氧化作用过程中具有较明显的活动性，其含量值变化跳跃，在不同分带相互交织，不具分带指示意义；但利用敏感组分、活动组分及其比值在层间氧化带中的变化特征可推测层间氧化带发育的完善程度及其含矿性；次活动组分组(CaO、MgO、MnO_2)含量低，变化规律性差；惰性组分组(TiO_2、P_2O_5)含量低，活动稳定，可用来反映沉积物源特征。

The weak form of the governing equations of coupled thermo-hydro-mechanical problems in porous media within the element is established on the basis of the Hu-Washizu three-field variational principle.

基于胡海昌-Washizu 三变量广义变分原理给出的多孔介质中热-渗流-力学耦合问题控制方程的单元弱形式，导出了单元公式。

In Chapter 2, an existence theorem is obtained for periodic solutions of non-autonomous second order systems with even-typed potentials. We also investigate solutions of linear bounded positive self-conjugation operators equations in Hilbert Space by variation methods.

第二章主要利用临界点理论中的归药方法、极小作用原理研究具偶型位势的二阶非自治系统周期边值问题，得到了周期解的存在；利用变分方法证明了Hilbert空间中有界线性正自共轭算子方程解的存在性。

Moreover, it indicates that the error is reduced with the increase of the exponent number of the Asymptotic Boundary Conditions. In the third chapter, based on the Laplace equation, the limitation of the variation methods are deduced from the process proving the operator to be self-adjoint and positive definite.

针对二阶渐近边界条件中含有微分项的情况，第三章研究了基于变分的有限元方法对边界条件的限制，提出对所适用的边界条件的要求，从而说明针对二阶渐近边界条件问题可以采用迦辽金有限元方法。

In chapter two ,we consider the Expanded Mixed Finite Method for the following quasilinear parabolic integro-differential equation.

在本章中我们给出了拟线性抛物问题的混合体积元的变分形式，并利用该方法得到了其真解与离散解的最优L~2模误差估计。

And from this variational principle,it can derive the corresponding boundary value problem governing nonlinearly static analysis of Timoshenko beams.

在假定梁不可伸长的基础上，给出了描述几何非线性、物理线性的大挠度Timoshenko梁的变分原理，由此导出了大挠度Timoshenko梁平面静动力学分析的边值问题。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。