唯一解

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。

This scheme, by a rigorous analysis, is proved to be unconditionally stable and convergent, its global error order is also obtained.

经过严格的理论分析，证明了该差分格式是唯一可解的、无条件稳定的和收敛的，并给出了收敛阶。

Since the lengths of the line segments and the angles between line segments are treated as representation parameters, it is convenient to construct energy function and to deal with displacement and length constraints. Based on this advantage, a parametrical model for human body is proposed, which can easily produce human body models with different feature sizes. The above method is just suitable for polylines. Therefore, a generic deformation method for both discrete curves and surfaces is presented. The energy function is constructed by analyzing the relationship of the points before and after deformation. Together with the displacement constraints, the deformation problem is converted to a convex quadratic programming. A necessary condition for constraint points and a sufficient condition for the uniqueness of solution are given. The proposed method can be combined with skeleton-driven animation to control the deformation.

将线段长度与线段之间的角度作为表示参数，既有利于能量函数的构造，又便于处理位移约束和长度内蕴约束条件，利用这一优势，将其应用于三维人体的参数化建模，可以方便地产生具有不同特征尺寸参数的人体模型，由于这种方法只适用于折线变形，具有较大局限性，因此，本文进一步提出一种较通用的离散曲线曲面变形方法，通过分析变形前后的位置关系来构造能量函数，再加上位移约束条件，将变形问题转化为一个凸二次规划问题，并且给出了约束点应满足的必要条件及模型解唯一的充分条件，这种方法还可以与骨架驱动变形的思想相结合，能更好的控制变形。

For the uniqueness problem of generator, by using some new methods (see Theorem 2.2.7), we prove the uniqueness theorem of generator under the assumptions which guarantee that the solution exists and is unique.

对于生成元的唯一性问题，我们采用与已有文献不同的全新的方法(见论文定理2.2.7)，在仅保证方程解存在唯一的假设条件下，证明了生成元的唯一性定理。

In accordance with the vector field existence and uniqueness of the traveling wave solution were proved.

根据相量场说明满足条件的行波解是否唯一存在。

Because the coefficient matrix of system equation with mixed method is indefinitive, an iterative solution method of the system equation is given out.

由于后者系数矩阵非正定，为使方程唯一可解，要求压力插值函数的阶必须低于固体相位移插值函数的阶，对此提出了一种系统方程的迭代求解方法。

At the end, through a mapping and Banach fixed point theory, the existence and uniqueness of the classical solution to this integrodifferential equation is obtained.

最后建立一个映射，利用Banach压缩映射定理证明了这个积分微分方程存在唯一古典解。

Due to anti-solution's non-uniqueness, sometimes there is not only one solution when using different inversive models.

由于反问题解的不唯一性，当采用不同的反演模型有时其解是不唯一的。

The stability and the periodic nature of the positive solutions ofare considered, we will prove that there exist monotonical solutions and converge to the unique positive equilibrium point of the equation ifα≠β.

第四章讨论了方程的全局稳定性，其中F=fx_(n-r1，x_(n-r2)，…，x_，G=gx_(n-m1，x_(n-m2)，…，x_，H=Hx_(n-p1，x_(n-p2)，…，x_，并给出了x=1是方程的唯一正解且全局渐进稳定的充分条件。

From her uniquely qualified perspective, Philippa Gregory explores this most famous unsolved mystery of English history, informed by impeccable research and framed by her inimitable storytelling skills.

从她的唯一有资格的角度来看，菲莉帕格雷戈里探讨这个英国历史上最著名的未解之谜，以及完美的研究提供信息和技能，独特的故事框架。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。