函数

Firstly, we get the necessary and sufficient conditions for Toeplitz operators that commutes with another such operator whose symbol is a monomial, meanwhile, we completely characterize when the mellin transform of the bounded function on the interval 0,1 is a rational function.

首先得到了以有界函数为符号的Toeplitz算子和以单项式函数为符号的Toeplitz算子可交换的充要条件，同时给出了0，1区间上的有界函数的Mellin变换为有理函数的充要条件。

Monotone functions; functions of bounded variation and Borel measures; absolute continuity; differentiation and integration; convex functions; semicontinuity; Borel sets; properties of the Cantor set.

单调函数；囿变函数；绝对连续性；微分和积分；凸函数；半连续性；博雷尔集类；康托集的性质

Calculus of variations is a field of mathematics that deals with functionals , as opposed to ordinary calculus which deals with functions .

变分法是处理函数的函数的数学领域，和处理数的函数的普通微积分相对。

As functions of the function of mathematics, the Key theorem of calculus of variations is Euler LaGrange, it can be used to the pan-seeking function of the maximum and minimum of mathematical.

变分法是处理函数的函数的数学领域，关键定理是欧拉－拉格朗日方程，用来求的泛函数的极大值和极小值的数学方法。

In the spatial domain,canonical projection of the Wigner distribution function of the associated pupil function to show the insensitivity of the point spread function to the defocus-related aberrations is mainly used,and in the frequency domain,it is shown that the optical transfer function of such a system is also insens.

空域中，主要利用维格纳分布函数的正则投影来分析系统的点扩展函数对离焦像差的变化不敏感特性；频域中，则利用考纽螺线的图解方法来分析系统的光学传递函数对离焦像差的变化不敏感特性。

In the spatial domain, canonical projection of the Wigner distribution function of the associated pupil function to show the insensitivity of the system's point spread function to the defocus-related aberrations is mainly used, and in the frequency domain, it is shown that the optical transfer function of such a system is also insensitive to misfocus through a geometrical description of the so-called Cornu spiral.

空域中，主要利用维格纳分布函数的正则投影来分析系统的点扩展函数对离焦像差的变化不敏感特性；频域中，则利用考纽螺线的图解方法来分析系统的光学传递函数对离焦像差的变化不敏感特性。

By discussing the position hypothesis of fractional-dimension derivative about general function and the formula form the hypothesis of fractional-dimension derivative about power function, the concrete equation formulas of fractional-dimension derivative, differential and integral are described distinctly further, and the difference between the fractional-dimension derivative and the fractional-order derivative are given too. Subsequently, the concrete forms of measure calculation equations of self-similar fractal obtaining by based on the definition of form in fractional-dimension calculus about general fractal measure are discussed again, and the differences with Hausdorff measure method or the covering method at present are given. By applying the measure calculation equations, the measure of self-similar fractals which include middle-third Cantor set, Koch curve, Sierpinski gasket and orthogonal cross star are calculated and analyzed.

通过讨论一般函数的分维导数的位置假设及幂函数的分维导数的形式假设，进一步明晰了幂函数的分维导数、分维微分及分维积分的具体方程形式，给出分维导数与分数阶导数的区别，随后讨论了基于一般分形测度的分维微积分形式定义导出的自相似分形的测度计算方程具体形式，给出了其与目前 Hausdorff 测度方法的区别，并对包括三分 Cantor 集合、 Koch 曲线、 Sierpinski 垫片及正交十字星形等自相似分形在内的测度进行了计算分析。

This passeage discusses the sequence of cauchy criterion function limit, the convergence of cauchy criterion, the convergence of the series, the function of cauchy criterion listed uniform convergence of cauchy criterion function series, uniform convergence of cauchy criterion, plane of cauchy criterion, some abnormal integral parameter uniform convergence of cauchy criterion and summarized and proof, and through a lot of sample reflected their status and role.

马上要交论文了，摘要不晓得如何翻译，现在请诸位高人帮助翻译1下，不能在线翻译哦，高悬赏~~~~~~感谢本文主要论述了数列地柯西收敛准则，函数极限存在的柯西准则，级数收敛的柯西准则，函数列一致收敛的柯西准则，函数项级数一致收敛的柯西准则，平面点列的柯西准则，含参量非正常积分一致收敛的柯西准则的应用并进行了总结和证明，并通过大量的例题体现了它们的地位和作用。

Secondly,we firstly study the properties of functions with values in a uni-versal Clifford algebra 〓,and we obtain the following very important basictheorems in universal Clifford analysis:Cauchy's integral formula,Cauchy's inte-gral theorem,the mean value theorem,the three versions of the maximum mod-ulus theorem,the Taylor's expansion,the Laurent's expansion and the residuetheorem etc..All of these results generalized the classical results.

第二，本文所讨论的各种函数性质以及所得的结果都在泛Clifford代数〓上所做的工作，它一方面包含了从前在泛Clifford代数〓上所做的工作，所得到的结果更广泛、更漂亮、更自然，另一方面，本文也是迄今为止第一次建立起来了在泛Clifford分析中与经典函数论相对照处基础地位的LR正则函数在特异边界上的Cauchy积分公式、Cauchy积分定理、平均值定理、极大模原理的三种表达形式、Taylor展式、Laurent展式留数定理等深刻的结果。

By combining the theory of sectionally holomorphic function, the analytical extending method, Cauchy model integral, the analysis of the singularity of complex functions and Riemann boundary problem, analytic relations between the complex potentials were obtained.

研究压电材料在均匀热流作用下螺型位错与圆弧裂纹的相互作用，综合运用复变函数分区全纯理论、解析函数奇性主部分析方法、解析延拓原理、Cauchy型积分以及Riemann边值问题求解方法，获得各复势函数之间的解析关系，进一步得到了特殊情况下所讨论问题的封闭解，并求解出像力随温度梯度和位错位置变化的表达式。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。