边界条件

Self-adjoint Sturm-Liouville problems, separated and coupled boundary conditions, inequalities among eigenvalues, equalities.

| 自伴Sturm-Liouville问题；分离与偶合边界条件；特征值间的不等式

In the light of the phenomenon such as flowing sand ,and sand boil subjected from the flowing sand stratum,in the construction of artificial digging piles,the advanced support with rein- foreement and the chemical churning pile technology can be used to form the watertight curtain,thereby preventing successfully the loss of san.

文章针对挖孔桩施工中遇到流砂层，出现的流砂、涌砂现象，采用钢筋超前支护及旋喷桩技术形成隔水帷幕，成功地阻止了砂层的流失，解决了施工进度慢、不安全的难题，改善了桩周的边界条件，提高了抗滑桩的承载能力。

In order to verify the accuracy of heat transfer coefficient,2D nonlinear finite element axisymmetric model is established by the means of finite element software MSC.Marc, which is utilized to simulate the transient temperature field coupled with phase transformation process and nonlinear synthetic surface heat transfer coefficient of several typical steels in the different quenchants.

Marc作为模拟平台，建立了淬火过程二维非线性有限元模型，模拟淬火过程中的瞬态温度场，在模拟过程中以多种常用钢在不同淬火介质中的非线性表面综合换热系数为边界条件，同时耦合了相变过程的影响。

During the calculation of the early age temperature field, the early age physical and mechanical performance of concrete varies with its age, therefore in the second chapter we discuss the early age physical and mechanical performance of concrete and its development regulation with time, we emphasize elastic module and the development about the early age strength of concrete varying with time, at the same time consider the effect of shrink and creep upon the early age of concrete, in succession discuss how to confirm the physical parameter of thermodynamics of concrete.

之后讨论了混凝土的热物理参数的确定。为了能够正确合理的应用有限元方法求解早期混凝土温度场问题，第三章论述了求解温度场的有限元方法。第三章首先对热传导的微分方程作了阐述。之后确定温度场的边界条件。本章采用变分原理推导有限单元法计算温度场的公式。因此在第二小节叙述了变分原理，然后阐明了不稳定温度场的计算的三种方法，确定第四章分析中将采用向后差分法求解0#箱梁早期的温度场。

In order to be fit for the calculation of wave transformation in harbor basin with irregular solid boundary, the governing equations and the boundary conditions of the present model are transformed by a non--orthogonal coordinate. Comparisons with the theoretical solutions indicate that the transformation is correct.

其次对上述完全型波浪绕射折射控制方程及边界条件进行非正交坐标变换，以适应存在固体边壁的港内水域波浪传播变形计算，经与理论解的验证比较，本文采用的坐标变换算法是正确的。

Systematically, hydrothermal circulations with different strata permeability structures and under different boundary conditions are analyzed for the first time.

首次系统地分析了不同地层渗透率结构及不同边界条件下热液循环的特征。

The dynamic response of the large crosssection shallow tunnels in new sand loess under viscouselastic boundary is calculated by means of transient dynamic FEM so as to find out the weak points of the lining and the stress, deformation and safety of the tunnel structure.

对大断面浅埋砂质新黄土隧道，利用瞬态动力学有限元方法，计算了粘弹性边界条件下，隧道在Ⅷ度地震荷载作用下的动力响应，找出衬砌的薄弱部位和结构的受力、变形及安全性，为设计提供指导和参考作用。

1Finding out the principles of the two-dimensional finite element method for temperature field simulation of high power laserThe profile and boundary conditions of the chip and submount of the high power laser is simply, we adopt the right-angled triangle cell to divide the submount and chip of the laser into triangular elements.

1找到了适用于大功率半导体激光器温度场模拟的二维有限元规则大功率半导体激光器芯片与载体具有规整的外形和多个边界条件，所以我们对激光器载体和芯片都采用了直角三角形单元进行有限单元剖分。

In the VR interactive interface provided by the software, a GTAW arc geometrical 'model has been constructed in two-dimensional (2D) axisymmetry through main menu. Using PHOENICS code and developing it secondly, a series of subroutines has been programmed in the Ql file and GROUND file. Boundary conditions and special sources about temperature profile .velocity and potential profile have been loaded by these subroutines.

在软件所提供的交互界面VR(Visual Reality虚拟现实)里，通过主界面菜单操作实现了在二维柱坐标下对电弧几何模型的建立，对软件进行了二次开发，在Q1和GROUND文件中编译了子程序，处理了温度场、速度场和电势场的边界条件和源项。

We investigate the contact force distributions inside the static granular systems under the conditions of stochastic packing and confining pressure constraint. The influences of particle size distribution, packing fraction and constraint condition are also considered.

根据微观尺度下粒子的排列及接触特征，研究了静态堆积颗粒系统和围压约束下静态颗粒系统中接触力网的分布特征，同时分析了粒径分布、体积分数、边界条件等对接触力分布特征的影响。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。