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It is proved by using the function approximation theory and martrix theory that for a degenerate elliptic equation of the first class, if the third boundary value condition is satisfied at its nondegenerate boundary and the given derivative values are satisfied at its degenerate boundary, then its solution is existent and unique.

摘 要 运用逼近理论及矩阵理论证明：如果一类退化椭圆型方程在非退化边界上满足第三边界条件，在退化边界上满足给定微商值，那么它的解是存在且唯一的。

Maritime Boundary Agreement in the Bering Sea still awaits Russian Duma ratification; managed maritime boundary disputes with Canada at Dixon Entrance, Beaufort Sea, Strait of Juan de Fuca, and around the disputed Machias Seal Island and North Rock; The Bahamas and US have not been able to agree on a maritime boundary; US Naval Base at Guantanamo Bay is leased from Cuba and only mutual agreement or US abandonment of the area can terminate the lease; Haiti claims US-administered Navassa Island; US has made no territorial claim in Antarctica (but has reserved the right to do so) and does not recognize the claims of any other states; Marshall Islands claims Wake Island; Tokelau included American Samoa's Swains Island among the islands listed in its 2006 draft constitution

1990白令海沿海边界协议仍然在等候俄国杜马批准；被处理的沿海边界争执涉及到加拿大狄克逊入口， Beaufort 海，胡安 de Fuca 海峡， Machias 封印海岛和 North Rock；巴哈马和美国未能对一个沿海边界达成协议；关塔那摩海湾的美国海军基地被古巴租用，并且仅相互协议或美国自动放弃的情况下才能终止租约；海地要求纳瓦萨岛主权；美国在南极州未做领土要求和不认可南极洲的任何其领土要求；马歇尔群岛要求威克岛主权；托克拉奥在它的2006宪法草案中包括了美洲萨摩亚的 Swains 海岛。

Shen prove a short time existence theorem for manifolds with umbilical boundary. He also derived the Simons' identity for the boundary under the Ricci flow. And as a corollary, Shen show that any three-manifolds with totally geodesic boundary which admits positive Ricci curvature can be deformed to a space form with totally geodesic

而带边流形上的Ricci流的研究始于Shen，在1996年，Shen在中考虑带边三维流形上的黎曼度量的Ricci形变，证明了如果初始三维流形的黎曼度量具有正Ricci曲率和全测地边界，则此三维黎曼流形上存在着常正曲率的黎曼度量。

The CNE-AR model coefficients are invariant to translation, rotation, scale and choice of the starting point in tracing a boundary, in which both linear and nonlinear features of the shape boundary are taken into account, and the intrinsic characteristics of the shape boundary are further depicted.

CNE-AR模型系数具有平移、旋转、比例和轮廓跟踪起始点选择不变性，兼顾了图形轮廓中的线性与非线性特征，深刻反映了图形轮廓的本质特性。

So, in this paper, a circular cavity witha large radius is used to replace the straight boundary of thehalf space, then the half space problem can be changed tothe scattering problem of two circular cavities to the steadyincident P-wave . Having the aid of the mature cylinderfunction theory, the general solutions of the wave functionscan be given, and an infinite linear algebraic equations ofthe unknown coefficients in the wave functions can be gottenwith the boundary conditions and the Fourier complex seriesexpansion technology, the infinite linear algebraic equationscan be approximately solved by the finite trunction withsatisfying some definite precision, at the basis of thissolution of the equation, the variations and the lay-outs ofthe DSCF at the circular cavity boundary vs. the differentincident angles, the different embedded depths of thecircular cavity as well as the different dimensionless wavenumber of the incident P-wave.

为此，本文采用一个半径很大的圆孔来代替半空间的直边界，将该半空间问题转化为一无限大空间中两个圆孔对稳态P波的共同散射问题，借助于成熟的柱函数理论，通过写出问题波函数的一般形式解，利用问题的边界条件，并采用复数傅立叶级数展开技术将其化为一个仅包含问题波函数中未知系数的一无穷线性代数方程组，在满足一定计算精度的前提下，通过有限项截断进行近似求解，进而讨论了圆孔边界处的动应力集中系数随不同入射角、不同的圆孔掩埋深度、入射波的不同无量纲波数以及介质的泊松比变化和分布情况。

Vector to raster: Inside point diffuse method, diffuse from internal seeds within polygon to neighbor points, as far as to the boundary of polygon; Pluralism integral arithmetic, according to the close boundary of polygon, makes uncertain point calculate pluralism integral; Radial and scanning arithmetic, from a uncertain point which located outside of the figure to draw radial, according to the junction of radial and polygon to judge the internal and outside relationship; Boundary algebra filling, a vector convert to raster arithmetic which based on integral thought, suit for polygon vector convert which recorded topological relationship.

矢量转栅格：内部点扩散法，即由多边形内部种子点向周围邻点扩散，直至到达各边界为止；复数积分算法，即由待判别点对多边形的封闭边界计算复数积分，来判断两者关系；射线算法和扫描算法，即由图外某点向待判点引射线，通过射线与多边形边界交点数来判断内外关系；边界代数算法，是一种基于积分思想的矢量转栅格算法，适合于记

In this project, we study the theory of higher order differential equations in Banach spaces and related topics. We solve an open problem put forward by two American Mathematicians and two Italian Mathematicians concerning wave equations with generalized Weztzell boundary conditions, introduce an existence family of operators from a Banach space $Y$ to $X$ for the Cauchy problem for higher order differential equations in a Banach space $X$, establish a sufficient and necessary condition ensuring $ACP_n$ possesses an exponentially bounded existence family, as well as some basic results in a quite general setting about the existence and continuous dependence on initial data of the solutions of $ACP_n$ and $IACP_n$. We set up quite a few multiplicative and additive perturbation theorems for existence families governing a wide class of higher order differential equations, regularized cosine operator families, regularized semigroups, and solution operators of Volterra integral equations, obtain classical and strict solutions having optimal regularity for the inhomogeneous nonautonomous heat equations with generalized Wentzell boundary conditions, gain novel existence and uniqueness theorems,which extend essentially the existing results, for mild and classical solutions of nonlocal Cauchy problems for semilinear evolution equations, present a new theorem with regard to the boundary feedback stabilization of a hybrid system composed of a viscoelastic thin plate with one part of its edge clamped and the rest-free part attached to a visocelastic rigid body. Also we obtain many other research results.

在本研究中，我们对Banach空间中的高阶算子微分方程的理论以及相关理论进行了深入研究，解决了由美国和意大利的四位数学家联合提出的一个关于广义Wentzell边界条件下的波动方程适定性的公开问题，恰当地定义了Banach空间中的高阶算子微分方程Cauchy问题的算子存在族及唯一族，建立了齐次和非齐次高阶算子微分方程Cauchy问题适定性的判别定理，获得了关于高阶退化算子微分方程的算子存在族、正则余弦算子族、正则算子半群、Volterra积分方程解算子族的乘积扰动和混合扰动定理，得到了关于以依赖于时间的二阶微分算子为系数的一大类非自治热方程非齐次情形下的时变广义Wentzell动力边值问题的古典解、严格解的最大正则性结果，获得了半线性发展方程非局部Cauchy问题广义解和经典解存在唯一的判别条件，从实质上推广了现有的相关结果；得到了一部分边缘固定而另一部分附在一粘弹性刚体上的薄板构成的混合粘弹性系统的边界反馈稳定化的新稳定化定理，还建立了一系列其他研究结果。

In the initial stage, the convergence of the low layer was stronger than that of the upper layer of the boundary layer, and the rotation of the boundary layer flow was weak, so a convergence line of the boundary layer was one of important factors to trigger convection.

MCS初期边界层低层的辐合强于边界层高层辐合，边界层气流旋转作用较弱，边界层辐合线是对流触发的重要因素之一。

Based on the classical Ekman theory, a series of intermediate Ekman boundary layer models, which retain the nonlinear advective process while discard embellishments, have been developed with the intention to understand the complex nonlinear features of the Ekman boundary layer and its interaction with the free atmosphere. In this paper, the recent advances in the intermediate boundary-layer theoretical models are reviewed.

摘要大气边界层及其与自由大气之间的相互作用具有明显的非线性特征，而这些特征是经典Ekman理论所不能描述的，因此，发展中等复杂程度（介于完全模式与经典Ekman模型之间）的大气边界层动力学模式，简称中间模式，对人们从理论上认识大气边界层动力学过程的非线性特征具有重要意义。

This paper addresses a new boundary detection algorithm called BORAL (Boundary Points Detector Based on Angle),according to the problem of low efficient boundary detection and that it is uneasy to determine the scope of the parameter pruning in data mining.

针对目前数据挖掘中边界点检测效率低、参数阈值范围不容易确定的问题，提出一种新的边界点检测算法BORAL。

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。