| 1. | Some new regular estimations for the exact solution are obtained
首先给出关于真解的一些新的正则性估计。 |
| 2. | The comparison those estimated from numerical simulation with real data shows the agreement largely in wind direction and in the true wind speed
通过数值模拟和实际算例计算表明反演结果在风向、风速上都与真解是吻合的。 |
| 3. | For a convection - dominated diffusion - convection - reaction equation , some new higher order regular estimates about its true solution are derived firstly
摘要针对对流占优的扩散对流反应方程，首先得到关于真解的一些新的高阶正则性估计。 |
| 4. | The adaptive homotopy method uses the homotopy with parameter to get a enough good approximation xn of the genuine solution x , and then use the newton iteration to attain a more precise one
自适应延拓算法用含参同伦迭代求出一个真解x ~ *的较好近似x ~ n ，再用newton迭代精确化。 |
| 5. | By detailed theoretical analyses , optimal order in h ^ 1 - error estimates is obtained between the exact solution of original problem and the solution of these fully discrete schemes
给出了全离散特征有限体积元格式，并通过详细的理论分析，得到了近似解与原问题真解的最优h ^ 1模误差估计。 |
| 6. | We then prove that the em algorithm becomes a compact map in certain neighborhood of a consistent solution when a measure of the average overlap of gaussians in the mixtures is small enough and the sample size is large enough
我们证明了高斯混合体em算法在混合密度的重叠度很小时在其样本真解相一致的解的一个邻域内是一个压缩映射。 |
| 7. | In the third part , for a class of parabolic integro - differential equations we obtained ultra - approximation between u and its ritz - volterra projection which leads to a ultraconvergence alternating theorem
最后，我们对一类抛物型积分-微分方程获得了真解与ritz - volterra投影之间的强超逼近估计，并在此基础上得到了一个强超收敛二择一定理。 |
| 8. | In chapter three , we consider the finite volume element mstheods for nonlinear hyperbolic problems on the basic of the chapter three , optimal order error estimates in the h1 , l2norms and w1 , almost optimal error estimates in l are also demonstrated
在第二章的基础上也得到了h ~ 1 ， l _ 2和w ~ ( 1 , )误差估计以及l _最优误差估计和近似解和真解的广义椭圆投影间的超收敛估计。 |
| 9. | The traditional methods are to solve the linear algebra equations directly , based on matrix factorization such as lu decomposition . with this kind of methods , the " true " solution can be derived if there is no consideration of the round error
解线性代数方程组的传统方法是利用lu分解等直接求解，虽然传统方法具有理论上直接得到真解的优点，但当系数矩阵条件数很大时，存在严重的稳定性问题。 |
| 10. | In the fields of fluid dynamics , entropy inequality reflects the second law of thermodynamics . i . e . . entropy must increase across shock waves ( a kind of discontinuity ) . all kind of approximate schemes should reflect the fact that it must satisfies some kind of discrete entropy inequality ) . from the view of practical computation , stability and theo - retical error of any kind discrete schemes all dependend of the smoothness of the solution of ( 0 . 2 . 1 ) . generally , the approximate solution have good stability and theoretial error in the area where the solutions have more regularity and poor stability and theoretial error in other area
从流体力学来看，它事实上是热力学第二定理的反映，即熵越过激波(一种间断)要增加。各种估计格式构造的估计解应反映这一事实，即满足熵不等式。从实际计算来看，总是通过离散化求解，不考虑计算的积累误差，它的稳定性与计算精度都依赖与真解的光滑性，一般说，在解较光滑的区域有较好的稳定性与计算精度，而在较粗糙的区域则相反。 |
