查询词典 boundary condition

Firstly, the existence and uniqueness of the solution for neutral stochastic functional differential equations with infinite delay under the uniformly Lipschitz condition, linear grown condition and contractive condition can be directly derived; And the moment estimate of the solution and the estimate for error between the approximate solution and the accurate solution can be both given; If the uniformly Lipschitz condition is replaced by the local Lipschitz condition, the existence and uniqueness theorem can be gained; Meanwhile, the existence and uniqueness of the global solution in the interval 0,+∞ can also be obtained; Secondly, L~p-exponential estimate of the solution for neutral stochastic functional differential equations with infinite delay can be studied; At length, the theorem of the local solution about neutral stochastic functional differential equations with infinite delay only under the local Lipschitz condition and the contractive condition can be established.

首先，在一致Lipschitz条件，线性增长条件和压缩性条件下，直接得到了具无限时滞中立型随机泛函微分方程解的存在惟一性，并给出了解的矩估计，近似解与精确解之间的误差估计；将一致Lipschitz条件替换为局部Lipschitz条件，也得到了具无限时滞中立型随机泛函微分方程解的存在惟—性，同时，也给出了在整个区间0，+∞上具无限时滞中立型随机泛函微分方程解的存在惟一性定理；其次，也讨论了具无限时滞中立型随机泛函微分方程解的L~p指数估计；最后，在局部Lipschitz条件和压缩性条件下，建立了具无限时滞中立型随机泛函微分方程局部解的存在惟一性定理。

Take the method of "subarea" and "conjunction" to segment the whole request model to three parts. Making use of boundary continuousness between medium and lining structure at stress and displacement, construct a wave function that can satisfy the stress boundary condition at horizontal surface by the scattering of SH-waves in circular part. And then, availing of the wave function, conjoin the circular part into the semi-circular hollow space at common boundary. The problem can be reduced to solve the question that can only meet the condition of "conjunction". Finally, the solution of the problem can be summarized to a series of algebraic equations and solved numerically by truncating the finite terms of the infinite algebraic equations.

采用"分区"与"契合"的方法，将整个求解区域分割成三部分，利用介质与衬砌结构在边界上的应力、位移的连续性，构造一个可以自动满足水平界面上应力边界条件的圆域对SH波散射的波函数；再利用这一波函数将圆域与半圆形凹陷半空间的"公共边界"进行"契合"，将问题简化成对一个只需满足'契合'边界条件的散射问题的求解；最终归结为对一组无穷代数方程组的求解问题，利用截断有限项的方法对其进行计算。

Under the condition that the flux function has one inflection point, by the structure of weak entropy solution of the corresponding initial value problem and the boundary entropy condition developed by Bardos-Leroux-Nedelec, we give a construction method for the global weak entropy solution of the initial-boundary value problem arid clarify the solution structure nearby the boundary.

在流函数具有一个拐点的条件下，由相应的初始值问题弱熵解的结构和Bardos-Leroux-Nedelec提出的边界熵条件，给出初边值问题整体弱熵解的一个构造方法，澄清弱熵解在边界附近的结构。

Taking electrostatic field as an example problem, based on the general analytical series solution of electrostatic field,(1) the zero, first and second order asymptotic boundary conditions on circular truncation boundary; and (2) the zero and first order asymptotic boundary conditions on arbitrary polygonal truncation boundary are derived.

有限元法计算无界电磁场问题是电磁场数值分析中的一个重要课题，在这里计算精度与计算量之间的矛盾尤为突出。

Based on the boundary integral formula and natural boundary integral equation for the boundary value problems of biharmonic equation , the non-symmetrical banding solutions to the circular plate under thermal boundary conditions are gained by the Fourier series and convolution formulae.

根据双调和方程边值问题的边界积分公式和自然边界积分方程，利用傅立叶级数及卷积的几个公式，求得了相应变温边界条件下非对称载荷圆板的弯曲解，从实践上证明了此方法的可行性。

In view of geological records preserved from different regions of the world are not identical, it's suggested that, when correlating the Ordovician-Silurian boundary, at the global boundary stratotype section, the FAD of N. persculptus be selected as the biomark, the transgression event identical to the FAD of N. persculptus as the auxiliary physical mark and the mass extinction and chemical anomaly events respectively as the auxiliary biomark and chemomark. In some regions with few graptolite, the Ordovician-Silurian boundary should be indicated by the auxiliary marks, such as the transgression event, mass extinction or chemical anomaly event, with the other fossil such as conodont nearest to other geological events as the provincial biomark for correlation. In other regions with much stratigraphic hiatus originated from the regression, the Ordovician-Silurian boundary should be marked by the regression-transgression event nearly relevant to the N. persculptus Zone.

鉴于不同地区留下的地质记录不完全相同，奥陶/志留系界线对比方法不同：在界线层型剖面上，以N.persculptus的首现为生物标志，以与之基本一致的海侵事件为辅助的物理标志，以生物集群绝灭事件和化学异常事件为辅助的生物和化学标志；在笔石极不发育的地区，则以海侵事件、生物绝灭事件或化学异常事件为辅助标志，以与其相距最近、并且具有区域对比性的其它门类化石作为界线对比的生物标志；对于由于海退事件所造成地层缺失很多的地区，则以海退/海侵事件作为划分界线的物理标志，并以相映的海侵事件的开始作为奥陶/志留系的分界。

Chapter 1 gives the background,current research process of relatedproblems and summarizes this thesis\'s work.In chapter 2,we study the Brownian motion with holding and jumping on the boundary.We use the resolvent method to obtain the infinitesimal generator because the domain of the infinitesimal generator is essentially the same as the range of the resolvent.Knowledge of this range and of the differential operator determines uniquely the infinitesimal generator.Since the semigroup generated by the DHJ is not strongly continuous,to use the nice property of strongly continuous semigroup in analytic theory,in chapter 3 we show that the dual is strongly continuous and derive ergodicity through spectral radius formulas and finally obtain the ergodic theorem by duality. In chapter 4,we discuss a class of a more general process---one dimensional Feller diffusion proposed by W.Feller in 1954.The Feller diffusion allows the possibility of jumps from boundary to boundary,not only from boundary to the interior.We give the stationary distribution of this process.

具体地，本文的结构如下：第一章给出了问题产生的背景，研究现状及本文的主要工作；第二章研究了在边界上逗留后随机跳的布朗运动，我(来源：3dABC论文网www.abclunwen.com)们用预解算子的方法得到其无穷小生成元，因为无穷小生成元的定义域本质上就是预解算子的值域，知道这个值域和微分算子形式就能唯一地决定无穷小生成元；由于DHJ过程产生的半群不是强连续的，为利用强连续半群的一些漂亮性质，在第三章中我们证明其对偶半群是强连续的，然后由谱半径公式得到遍历性并且最后由对偶得到遍历定理；第四章讨论了Feller在1954年引入的更广的一类过程----一维Feller扩散过程，Feller扩散过程允许有从边界到边界的跳发生，即不仅仅局限于从边界到内部的跳，在这一章中，我们给出了一维Feller扩散过程的平稳分布；在第五章，我们讨论了一些相关的问题，给出了DHJ过程对应的PDE问题及特征值与收敛速度的关系。

In the last chap-ter,the natural integral equation and natural boundary element method forharmonic problem on exterior elliptic domain are introduced.Then,based onthis,the natural boundary reduction method for a kind of exterior problem ofanisotropic constant coefficients elliptic equation is discussed, the natural inte-gral equation and its solving method on circular boundary and elliptic bound-ary are obtained.These results can be directly applied in coupled methodand DDM for exterior boundary value problem.

最后，讨论了椭圆外区域调和问题的自然积分算子即D-N算子及自然边界元方法，并基于此研究了一类各向异性常系数椭圆型方程外问题的自然边界归化方法，首次得到其在圆周边界及椭圆边界上的自然积分方程及其求解方法，并将这些结果直接应用于外边值问题的耦合算法。

In viewof geological records preserved from different regions of the world are not identical, its suggested that, whencorrelating the Ordovician-Silurian boundary, at the global boundary stratotype section, the FAD of N.persculptus be selected as the biomark, the transgression event identical to the FAD of N. persculptus as theauxiliary physical mark and the mass extinction and chemical anomaly events respectively as the auxiliarybiomark and chemomark. In some regions with few graptolite, the Ordovician-Silurian boundary should beindicated by the auxiliary marks, such as the transgression event, mass extinction or chemical anomaly event,with the other fossil such as conodont nearest to other geological events as the provincial biomark forcorrelation. In other regions with much stratigraphic hiatus originated from the regression, theOrdovician-Silurian boundary should he marked by the regression-transgression event nearly relevant to the N.persculptus Zone.

鉴于不同地区留下的地质记录不完全相同，奥陶／志留系界线对比方法不同：在界线层型剖面上，以N.persculptus的首现为生物标志，以与之基本一致的海侵事件为辅助的物理标志，以生物集群绝灭事件和化学异常事件为辅助的生物和化学标志；在笔石极不发育的地区，则以海侵事件、生物绝灭事件或化学异常事件为辅助标志，以与其相距最近、并且具有区域对比性的其它门类化石作为界线对比的生物标志；对于由于海退事件所造成地层缺失很多的地区，则以海退／海侵事件作为划分界线的物理标志，并以相映的海侵事件的开始作为奥陶／志留系的分界。

Boundary polynomial point interpolation mesh-free method and boundary radial point interpolation mesh-free method were presented, based on polynomial basis and radial basis respectively for transient eddy current analysis, and their interpolation shape functions satisfy the Kronecker delta function and the essential boundary conditions can be directly imposed on the boundary nodes. An example on analyzing transient eddy current of a square metal column was set to prove the validity of the proposed methods, and a comparison on accuracy between BPPIM and BRPIM was analyzed as well.

运用多项式点插值法和径向基点插值法构造形函数，推导了适合于工程电磁场瞬态涡流问题的多项式基点插值边界无单元方法和径向基点播值边界无单元方法，这两种方法的空间插值形函数满足Kronecker delta条件，从而强加边界条件可以直接施加在边界点上，以金属长方柱的瞬态涡流分析作为数值算例，证实了两种方法的正确性和有效性，并对两种基类的点插值法进行了精度分析和比较。

"Bird Man's Diary, Butting on the Love Island", Changsha, China

2008年"鸟人日记，顶在爱情岛"，中国长沙

As long as they were in the service of a family of wizards, their magic would remain dormant.

只要他们一天为家庭服务，他们的法力就潜藏不动。