查询词典 exterior boundary problem

Two problems were solved in numerical calculation, one was that a term of 1/r in Maxwell was divergence in cylindrical center where r=0, another was that the value of optical field at cylindrical center was difficult to decided when the cylindrical center set as a boundary condition in Maxwell equation, So the values of optical field need just calculate from cylindrical center to cylindrical boundary, comparing from cylindrical boundary to cylindrical boundary, near upon half CPU time and RAM saved.

计算中解决了在圆柱中心线上Maxwell方程存在发散项1/r以及用圆柱中心线作为边界条件时，中心线上光场值难确定的问题，因而光场只需从圆柱中心计算到圆柱边界，和以圆柱的两条边做为边界条件比较，节省了将近一半的计算时间和计算机存储空间。

The author compares the effects of Dirichlet boundary condition and attenuation one on artificial boundary with that on transmitting boundary, so does the absorption effects, the author also demonstrates the advantage of transmitting boundary.

文中还就刚性边界条件、衰减边界条件对人工边界的影响及吸收效果与透射边界作了对比，验证了透射边界的优越性。

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 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。

The establishment principles of traditional and improved PML absorbing boundary condition were described. Through numerical simulation, the absorbing effect of improved and traditional PML absorbing boundary and low-order Higdon absorbing boundary on boundary reflection was discussed.

阐述了传统和改进的PML吸收边界条件的构建原理，通过数值模拟讨论了改进和传统的PML吸收边界以及低阶Higdon吸收边界对边界反射的吸收效果。

Sometimes the boundary and the boundary approximately equate, sometimes the boundary contains the ideal condition, but the boundary and the ideal condition not are a chapter of matter.

境与境界有时大致等同，境有时包含意境在内，但境界与意境并不就是一回事情。

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。

For a given Sturm-Liouville equation with positive leading coefficient function, by use of the monotonicity results of its natural loops, limit of boundary conditions and eigenvalues in the space of self-adjoint boundary conditions, a proof of the equalities among eigenvalues for coupled boundary conditions and those for separated boundary conditions is made.

内蒙古工业大学理学院副教授 2。对于给定的首相系数函数为正的 Sturm-Liouville方程，利用在自伴边界条件空间上自然圈、边界条件的极限和特征值的单调性的几个结果，给出了在偶合边界条件与分离边界条件下的特征值间的一些等式的证明。

Lakatos'the principle of tolerance led to blurring of boundary line about progressive and deteriorative research program, mistiness of boundary line of reasonable and unreasonable research program. His standard of demarcation led to obscuring the boundary line of science and non science. His principle of theory of error made boundary line of right and wrong theory, ture and false theory blurred.

拉卡托斯的宽容原则导致进步的研究纲领和退步的研究纲领，合理的研究纲领和不合理的研究纲领之间的界线模糊；他的划界标准使科学与非科学之间的界线模糊；他的可错主义原则使正确的理论和错误的理论，真的理论和假的理论之间的界线模糊。

Assign the Boundary conditions 5,设置边界条件 A natural air cooling heat Boundary condition will be applied all around the sand box, a velocity Boundary condition will be applied and a temperature Boundary condition will be imposed to some nodes of the top surface of the down sprue.

砂型周围是一个自然空气冷却的热边界条件。一个速度边界条件和一个温度边界条件将被设置到直浇口的上平面的一些节点上。

In the days of sailing vessels the crew were afraid they would be becalmed on the ocean.

在使用帆船的时代，船员们担心他们会因为无风而无法在海洋上航行。

As long as foreign donors pay the PA's salary bill, few expect a new intifada.

只要外国继续为巴权力机构的薪水买单，希望发动新暴动的人便寥寥无几。