上微分

This paper considers the estimate of the upper bound of second eigenvalue for the differential operator with any order.

考虑了任意阶微分算子第二特征值的上界估计，获得了用第一特征值来估计第二特征值的上界的不等式，其估计系数与区间的度量无关。

Chapter 1 gives the background,current research process of relatedproblems and summarizes this thesis\'s work.In chapter 2,we study the Brownian motion with holding and jumping on the boundary.We use the resolvent method to obtain the infinitesimal generator because the domain of the infinitesimal generator is essentially the same as the range of the resolvent.Knowledge of this range and of the differential operator determines uniquely the infinitesimal generator.Since the semigroup generated by the DHJ is not strongly continuous,to use the nice property of strongly continuous semigroup in analytic theory,in chapter 3 we show that the dual is strongly continuous and derive ergodicity through spectral radius formulas and finally obtain the ergodic theorem by duality. In chapter 4,we discuss a class of a more general process---one dimensional Feller diffusion proposed by W.Feller in 1954.The Feller diffusion allows the possibility of jumps from boundary to boundary,not only from boundary to the interior.We give the stationary distribution of this process.

具体地，本文的结构如下：第一章给出了问题产生的背景，研究现状及本文的主要工作；第二章研究了在边界上逗留后随机跳的布朗运动，我(来源：3dABC论文网www.abclunwen.com)们用预解算子的方法得到其无穷小生成元，因为无穷小生成元的定义域本质上就是预解算子的值域，知道这个值域和微分算子形式就能唯一地决定无穷小生成元；由于DHJ过程产生的半群不是强连续的，为利用强连续半群的一些漂亮性质，在第三章中我们证明其对偶半群是强连续的，然后由谱半径公式得到遍历性并且最后由对偶得到遍历定理；第四章讨论了Feller在1954年引入的更广的一类过程----一维Feller扩散过程，Feller扩散过程允许有从边界到边界的跳发生，即不仅仅局限于从边界到内部的跳，在这一章中，我们给出了一维Feller扩散过程的平稳分布；在第五章，我们讨论了一些相关的问题，给出了DHJ过程对应的PDE问题及特征值与收敛速度的关系。

In this paper, a mathematical model of differential-type electrified reset circuit of single chip computer had been established.

建立了微分型单片机上电复位电路的数学模型，并在此基础上对其性能进行了分析。

The life-cycle of C.baileyi in Beijing duck and in the CAM of chicken embryowas studied with both the light-microscope and the Nomarski interference-contrastmicroscopy.The results indicated that the life-cycle within duck was simillar tothat of CAM.It included excystation, merogony,gamogonyand sporogony.The thin-walled oocyst was first observed and described in China.

借助普通光学显微镜和微分干涉显微镜对C.baileyi在北京鸭体内的生活史和在鸡胚绒毛尿囊膜上的生活史进行了较详细的研究，结果表明：C.baileyi在北京鸭体内和在CAM上的生活史相同，主要包括"脱囊—裂殖生殖—配子生殖—孢子生殖"四个阶段。

It is impossible to logically infer the classically expressed geodesic differential equation from the ontology differential geometry. Besides, the initial proposition how to construct a functional extreme value problem for the shortest curve on a surface, which was supposed first by Gauss, would be an improper formal expression with a wrong premise.

不仅仅无法由"实体论"微分几何逻辑地推导出经典的测地线方程，而且Gauss曾经为"曲面上最短线"问题所构造的泛函极值命题，实质上属于一个"前提认定"完全错误的不当表述。

Using the method of approximating the Lipschitz functions by the convex functions, we give a sufficient condition for the set where Lipschitz functions on a Hilbert space are Frechet differentiable is a residual set.

我们利用Lipschitz函数空间中凸函数的逼近性质来分析Lipschitz函数的微分性质，得到Hilbert空间上Lipschitz函数的Frechet可微点集是剩余集的一个充分条件，以标题"Lipschitz函数与凸函数之间的一些联系"在中国科学杂志上发表。

The main results are as follows: the relations between local fractional integrated semigroups and the corresponding Cauchy problem, global fractional integrated semigroups and regularized semigroups are given; introduction of the notion of regularized resolvent families, and the generation theorem and analyticity criterions for regularized resolvent families are obtained; the spectral inclusions between fractional resolvent family and its generator, and the approximation for fractional resolvent families in the cases of generators approximation and fractional orders approximation; elliptic operators with variable coefficients generating fractional resolvent family on L^2 by using numerical range techniques; and the L^p theory for elliptic operators with real coefficients highest order are obtained by Sobolev''s inequalities and the a priori estimates for elliptic operators; and a kind of coercive differential operators generates fractional regularized resolvent family by applying the Fourier multiplier method, functional calculus and some basic properties of Mittag-Leffler functions.

主要结论是：给出了局部分数次积分半群和相应的Cauchy问题的关系以及分数次积分半群和正则半群的关系；引入了正则预解族的概念，并给出了其生成定理和解析生成法则；给出了分数次预解族与其生成元的谱包含关系，并研究了在生成元逼近和分数阶逼近两种情况下相应的预解族的逼近问题；利用数值域方法证明了具变系数的椭圆算子在L^2上生成分数次预解族；利用Sobolev不等式和椭圆算子的先验估计证明了具变系数的椭圆算子在其最高项系数为实数时在L^p上生成分数次预解族；运用Fourier乘子理论、泛函演算和Mittag-Leffler函数证明了一类强制微分算子可以生成分数次正则预解族，并给出了该预解族的范数估计。

An integral operator I(subscript n+p) defined by Hadamard product is introduced. Making use of this operator, the subclass S(superscript * subscript n+p) of p(superscript -) valent analytic function is defined in the open unit disk, the inclusion relation of S(superscript * subscript n+p+1)S(superscript * subscript n+p) and the best dominant function of differential subordination q1 are obtained. Furthermore, some conclusions are made according to the special parameters A and B.

用Hadamard卷积定义线性算子I，并利用算子I定义在单位圆内的解析的p叶函数类S(上标*下标 n+p)，给出了此函数类的包含关系S(上标*下标 n+p+1)S和微分从属的最佳控制函数q1，并根据参数A，B取不同的特殊值得出了相应的推论。

By extending the concepts of supremum and infimum in real space to the casein any finite-dimensional Euclidean space a weak supremum set and infimumset theory with respect to cones for the set in finite-dimensional Euclideanspace is developed,and several similar properties to the set in real space are ob-tained,with the concepts of this weak supremumset,w-D-conjugate maps and w-D-subdifferentials theory for the point-to-setmap are developed,and its several properties and its relationships with weakefficient solutions of the multiobjective programming are studied.

推广实空间中上、下确界的概念至任意有限维欧氏空间，建立了有限维欧氏空间中集合的锥弱上、下确界集理论，得到了与实空间中十分相似的性质。借助于这一理论，应用上、下确界的概念，给出了点集映象的w-D-共轭映象及w-D-次微分理论，并研究了它们的若干特性及其与弱有效解之间的关系，此外还讨论了弱鞍点问题。

Ablish two decision theorems of relative compactness for unbounded function groups in an infinite interval.

sect；2.3我们建立了判定无穷区间上抽象无界连续函数组和抽象无界可微函数组相对紧性的充分必要条件，并对无穷区间上抽象二阶微分方程两点边值问题无界解的存在性做了研究。

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。