阶

Though comparing Canny operator and center B spline dyadic wavelet, the following conclusion is proven in this dissertation: a Center B spline function has tight support and Canny operator hasn't. b Center B spline function asymptotic convergence to Gaussian function and the derivative of Center B spline function asymptotic convergence to Canny operator. c The derivative of fourth order center spline B function is more suitable as a optimal edge detector than Canny operator. d Center B spline function can balance the smoothing and approximation of original data, and the fourth center B spline function is the only optimal solution of two order smoothing problem. e The error between the valve of time-frequency uncertainty of the fourth center B spline function and the lower bound of time-frequency uncertainty does not exceed 0.143% of the lower bound. f The derivative of center spline B function can construct a stability dyadic wavelet and can give a fast algorithm for multiscale edge detection, but Canny operator can do neither.

作者给出了Canny算子与中心B样条二进小波严格的比较证明，得出如下结论：a中心B样条函数具有紧支集，Canny算子不具有紧支集。b中心B样条函数的极限收敛于高斯函数，中心B样条函数的导数收敛于Canny算子。c四阶中心B样条函数的导数比Canny算子更接近最佳边缘检测滤波器。d中心B样条函数比高斯函数更能兼顾对原函数平滑和逼近的折中要求，并且四阶中心B样条函数是二阶逼近问题的唯一最优解。e四阶中心B样条函数的时频测不准关系值与时频测不准关系下界的逼近误差不超过0.143％。f中心B样条函数的导数可以构成稳定的二进小波，存在快速的多尺度算法；而Canny算子不构成稳定的二进小波，无法给出快速的多尺度算法。

In order to obtain more general solution of second order linear differential equation with constant coefficients, which is important in theory and practice, on the basis of knowing a special of the second order linear differential equation with constant coefficients and by using the method of variation of constant, the second order linear differential equation with constant coefficients is transferred to the reduced differential equation and a general formula of the second order linear differential equation with constant coefficients is derived.

为了更多地得到理论上和应用上占有重要地位的二阶常系数线性非齐次微分方程的通解，这里使用常数变易法，在先求得二阶常系数线性齐次微分方程一个特解的情况下，将二阶常系数线性非齐次微分方程转化为可降阶的微分方程，从而给出了一种运算量较小的二阶常系数线性非齐次微分方程通解的一般公式，并且将通解公式进行了推广，实例证明该方法是可行的。

In this paper,we present a new class of second order linear differential equation s with meromorphic coefficients and investigate the problems on the fixed points and hyper order of solutions and their 1st,2nd derivatives.

该文提出了一类新型的亚纯函数系数的二阶线性微分方程，研究了其亚纯解及其一阶和二阶导数的不动点及超级问题，得到了有关复域微分方程亚纯解及其一阶和二阶导数的不动点性质。

Because of the condition of 〓 for two neighbour parametricspline surfaces is too strong,here,instead of it,some simple and practicableconditions of 〓 resulted from the general theorem obtained by Prof.LiuDing Yuan in Chapter 1 were proved,and three 〓 triangular splinesurfaces schemes wre presented:one is piecewise cubic spline surface patcheshaving local 〓 and whole 〓 continuity based on the refined HCTtriangulation,another is the same degree spline surface patches but based onthe refined Powell-Sabin triangulation,the third is piecewise quartic splinesurface patches having local 〓 and whole 〓 continuity based on therefined P-S triangulation.

由于对参数曲面，一阶导数连续的要求较强，我们采用第一章从刘鼎元定理导出的简单实用的几何连续条件，讨论了基于HCT加细三角剖分和P-S加细三角剖分上的两种局部达一阶导数连续而整体有一阶几何连续的分片三次样条曲面构造算法，一种局部达二阶导数连续整体有一阶几何连续的分片四次样条曲面构造方法。

In this paper,we present a new class of second order linear differential equations with meromorphic coefficients and investigate the problems on the fixed points and hyper order of solutions and their 1st,2nd derivatives.

该文提出了一类新型的亚纯函数系数的二阶线性微分方程，研究了其亚纯解及其一阶和二阶导数的不动点及超级问题，得到了有关复域微分方程亚纯解及其一阶和二阶导数的不动点性质。

The order of an element is a significant concept in group. There are certain internal connections between the order of an element and the order of a group, the order of an element and the type of group, certain order of an element in groups too.

而元的阶又是群的一个重要概念，元的阶和群的阶有着内在的联系；元的阶和群的类型有着内在的联系；群中某些元的阶也有着内在的联系。

We put it across that the sign of nonlinear refractiveindex changes under certain conditions if the high-order excited state contributessignificantly to the refractive index.The nonlinearity changes from self-defocusing to self-focusing if the refrangibility of the ground state is larger thanthat of the first excited state and smaller than that of the second excited state.

高阶激发态折射度贡献较大时，非线性折射率符号在一定条件下存在转化：如果基态折射度大于低阶激发态的折射度而小于高阶激发态折射度，材料发生自散焦—自聚焦转化；如果基态折射度小于低阶激发态折射度大于高解阶激发态折射度则发生自聚焦—自散焦转化。

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。

There was no significant difference of higher order wavefront aberrations between emmetropic and ametropic eyes. Comparing the age of 40 years or less with the age over 40 years, there were significant differences in RMS3 between the two under 7 mm pupil size, and statistical diffenences in RMS6 and RMSh between the two under 4 mm pupil size.

除第2阶像差均方根(RMS2)以外，正视眼及近视眼各阶像差平均RMS值在7 mm与4 mm瞳孔下，差异均无统计学意义。40岁及以下者与40岁以上者相比，在7 mm瞳孔时，两者第3阶像差均方根(RMS3)差异有统计学意义；而在4 mm瞳孔时，两者第6阶像差均方根(RMS6)及高阶像差均方根差异均有统计学意义。

The horizontal and vertical first derivatives of magnetic anomalies of an infinite cylinder are calculated by the cosine transform method, in which the maximum errors are -0.28 nT/m and 0.47nT/m, respectively and the percent errors are generally within -3.57%~3.27% and -1.94%~1.88%, respectively except several data of the boundary and part are bigger because of remains of Gibbus effect. The calculating curve and theoretical curve are approximately coincident, and there is no influence by effective magnetic dip angle in computing. But the errors with the Fourier transform method are -10.62nT/m and 14.42nT/m, there is large departure between the calculating curve and theoretical curve and evident influence by effective magnetic dip angle in computing.

利用余弦变换法计算的无限长水平圆柱体磁异常水平和垂向一阶导数的最大误差分别为-0.28nT/m、0.47nT/m；水平一阶导数的误差一般在-3.57%~3.27%之间，垂向一阶导数的误差一般在-1.94%~1.88%之间；计算的磁异常一阶导数值与理论值大致重合，而且不受有效磁化倾角的影响而Fourier变换法计算的水平和垂向一阶导数最大误差分别为-10.62nT/m、14.42nT/m，计算曲线与理论曲线偏离大，受磁化倾角的影响也较大。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。