The finite dimension approximating solution for initial-boundary value problem of coupling nonlinear system of hyperbolic equation is constructed by orthogonal basis of characteristic value sequence of the Laplace operator in the Dirichlet boundary conditions.
以Laplace算子在Dirichlet条件下的特徵值序列为正交基底构造耦合非线性双曲型方程组初边值问题的有限维近似逼近解，证明该逼近解的一致收敛性。
Basing on the Dirichlet tessellation and Voronoi diagram theory, the Voronoi cells were defined by thier tessellated points and the peculiar arithmetic mapping particles to cells satisfied the statistical requirements of DSMC method.
基于Dirichlet镶嵌与Voronoi图理论，Voronoi网格利用特征点表征网格单元，具有建立粒子与网格单元之间映射关系的独特算法，适合于DSMC方法的统计特点。
We will use the method provided by Cai to deal with it. Also, we will discuss the Lagrange multipliers method to conquer it. Based on the analysis for the combination of non-overlapping DDM and RBF meshless method, we find that the convergent rate of meshless Dirichlet-Neumann iteration dramatically depend on the density h, while the Robin iteration is lack of information about the convergent rate.
通过对无网格Dirichlet-Neumann区域分解方法和Robin方法的分析，我们发现在径向基无网格方法下，Dirichlet-Neumann迭代的收敛阶依赖于密度h，并且每一步所求解的线性方程组的条件数都很大，这些都会影响加速参数的选取。
In this paper, we study the convergences and the growth of bi-random Dirichlet series by the strong law of large number s for independent and non-equally distributed random variables, and obtain some new result.
利用独立不同分布的随机变量序列的强大数定律研究了双随机狄里克莱级数的收敛性和增长性，得到了一些新的结果。
To this end, we generalize the results and get the sufficient and necessary conditions for the sum of two or countably many Dirichlet forms to be regular or quasi-regular.
为此，我们得到至多可数个Dirichlet型之和的正则性与拟正则性的判别准则。
In the 19th century, Dirichlet is a German mathematician, Who built the number theory of rational number by Drawer principle firstly. then, his theory spread extensively in the corners of the world.
中文摘要：十九世纪德国数学家狄里克雷首先利用抽屉原理来建立有理数的理论，随后在世界各地广泛流传。
The numerical results indicate that the generalized Dirichlet distribution should be a reasonable prior, and the computation in forecasting coproduct output is relatively straightforward with respect to the approximation approach.
本研究所採用的贝氏统计分析方式，对於预测生產量的计算，比求近似解的方法简单，可计算变数二阶以上的动率，而且在使用的时机上较不受限制。
The linear sampling method for the inverse scattering problem of acoustic waves is based on the fact that: a linear integral equation of first kind-far field equation including a parameter has an unbounded solution as the parameter approaches the scattering boundary from inside.
本文在此基础上就Dirichlet边界条件的声波反散射问题，利用积分方程理论严格证明了线性抽样方法对其的可用性，具体数值例子表明该方法是有效的。
Within this context, four specific areas are addressed:(1) By means of finite integration technique, a new kind of the first order partial difference equation is derived from the original disperse transmission line equation of the uniform waveguide's. As it is the kind of one dimension Dirichlet's boundary problem, it is convenient for us to solve this equation from the leapfrog scheme. Because computation is carried out in one dimension, both high calculation efficiency and precision have been obtained in this method. Meanwhile, this method provide us a different selection to simulate the transient response of waveguide with non-simplical, for examples cylinder and elliptic waveguide, and avoid solving the second order equation, or using finite difference time domain to simulate a three dimension problem, sometimes the latter precision is not satisfied with the need, or low efficiency.
在这一研究内容下，主要研究四个方面的问题：(1)在完成金属波导传输线方程时域形式的基础之上，应用有限积分技术，把波导特征模式的色散传输线方程，化简为一组新的一阶偏微分方程组，该边值问题属一维Dirichlet边值问题，从而便于用蛙跳格式求解，由于是在一维中计算，该方法具有很高计算效率和精度，从而避免了以往为得到金属波导中特征模的时域响应特性，须要求解二阶方程，或用时域有限差分方法求解三维问题的方法，对于后者来说，计算有时是不准确的，或是很耗时的例如计算诸如圆波导、椭圆波导等其它复杂形状的波导。
This article discusses the analyzing nature of Dirichlet function and Riemann function.
本文讨论了狄利克雷函数、黎曼函数的分析性质。
In this paper, firstly, by using the supersolution and subsolution principle. we prove the existence of the solutions of the equation, we also prove that the solutions have good smoothness, we prove that the solutions are radially symmetric mature by using the Gidas-Ni-Nirenberg theorem, that is to say, no matter which direction, the solutions will have the same value if they have the same distance from the center, in this way, we are able to invert PDE into Lane-Emden equation, we give a form of expression.
本文首先利用上下解原理，证明了目标方程的解是存在的，并且其解拥有较好的光滑性，然后用反证法证明了其解有且只有一个；其次，本文用Gidas-Ni-Nirenberg定理证明了方程的解具有径向对称的性质，即不管在哪个方向上，只要离中心的距离是相同的，那么其解的值就是相同的；从而可以把偏微分方程转化为Lane-Emden形式的常微分方程，我们给出了其表达形式；最后，我们证明了我们的Dirichlet问题对应的常微分方程求解是稳定的，并给出了几个数值算例。
In this paper we mainly utilize super and sub solution techniques, use comparision principle and construct appropriate supersolution and subsolution by eigenfunctions to discuss two kinds of nonlocal nolinear parabolic systems with homogeneous Dirichlet boundary condition.
两类非线性抛物方程解的整体存在与爆破性质本文主要利用上下解方法，运用比较原理，通过特征函数等构造适当的上下解讨论了两类抛物型方程组解的整体存在与爆破。
In part one, we dissuss the Galerkin method and error estimate for first-kind boundary integeral equation derived by forrowing exterior Dirichlet problems Then result in superconvergent results by Least-squares processing.
首先，第一部分讨论了由Dirichlet外问题：导出的一型边界积分方程的解法及其误差，然后进行最小二乘处理后得到超收敛结果。
In the view of pragmatic implement, the theoretical framework of our proposed condition for spatial boundaries indeed can be reduced to the hybrid formulation of nudging filter, radiation condition taking account of ambient forcing, together with Dirichlet kind of compatible boundary condition to the observations prescribed in data assimilation procedure.
我们提出的空间边界条件的算法构架事实上是在数据同化过程中综合运用了张弛滤波、考虑外部强迫的辐射边界条件以及与观测相容的狄里希利边界条件。
In this dissertation, we compute and visualize multiple solutions of the boundary valueproblem of the Henon equation on the disk of planewhereΩis a unit circle, ?
中文摘要：本文讨论平面单位圆上Henon方程的齐次Dirichlet边界条件的边值问题的多解计算，这里Ω为单位圆，？
By using the spatial finite sine and cosine transform, and the temporal Laplace transform, the existence of the analytic solutions of its initial-boundary problems in a boundedspace domain with Dirichlet and Neumann boundary conditions is derived.
利用空间有限的sine或cosine变换及时间Laplace变换，给出了该方程有限区间上带Dirichlet和Neumann边界条件的两类初边值问题的解析解。
It is proved that transient and recurrent are invariant under h-trasformation of symmetric Dirichlet forms.
通过对称保正型h-变换的暂留性、常返性和不可约性的讨论，证明了对称保正型的暂留性、常返性和不可约性在h-变换下是不变的，由此得到h-结合的m-胎紧m-特殊标准马氏过程的相应性质。
This method allows for a more accurate processing of boundary condition on the semiconductor layer in XLPE cable of stator winding than the standard finite element, so that the interlaminated issue of boundary condition on interface can be avoided. A general algorithm is applied to deal with both the Dirichlet and the periodic boundary condition in 2D or 3D magnetic field problem.
提出了用有限元法计算磁场问题时周期性边界条件和第一类边界条件的统一处理方法，利用该方法在不改变代数方程组阶数、保持系数矩阵性质不变和带宽基本不变的条件下，使两种强加边界条件能同时处理，简化了程序编制，并与寻址方法相结合，提高了计算速度。
, for the Random Dirichlet series with order ρ(0 < ρ < ∞), there is at least a Borel line of order ρ without finite exceptional value in every horizontal strip of width $ πρ $ a. s..
在任何宽为πρ的水平带形内，至少有一条ρ级没有有穷例外值的Borel线。
Linear Sampling Method for Reconstructing the Acoustic Scattering Region with Dirichlet Boundary
利用线性抽样方法重建Dirichlet边界条件声波散射区域