查询词典 infinitesimal operators

For an abitrary set X, appropriate order relations on WCL (the set of all weak closure operators), WIN (the set of all weak interior operators), WOU (the set of all weak exterior operators), WB (the set of all weak boundary operators), WD (the set of all weak derived operators), WD*(the set of all weak difference derived operators), WR (the set of all weak remote neighborhood system operators) and WN (the set of all weak neighborhood system operators) can be defined respectively, which make WCL, WIN, WOU, WB, WD, WD*, WR and WN to be complete lattices that are ismorphic to CS(X,CS is the set of all closure systems on X.

证明了可以在WCL(X上的弱闭包算子的全体)、 WIN(X上的弱内部算子的全体)、 WOU (X上的弱外部算子的全体)、 WB (X上的弱边界算子的全体)、WD、 WD*(X上的弱差导算子的全体)、 WR(X上的弱远域系算子的全体)和WN(X上的弱邻域系算子的全体)上定义适当的序关系，使它们成为与CS(X，〖JX-*5[JX*5]同构的完备格其中CS(X是给定集合X上的闭包系统的全体。

Although many results have been obtained, there are still a number of very interesting questions about composition operators unsolved. There is much more to be learned about the collective compactness and convergence of composition operator sequences, compactness of various product of composition operators, cyclicity, closed range and spectra of composition operators in various settings. Commutants of composition operators seem to be very difficult to characterize. Only a little is known about their reducing invariant subspaces. There has been no work on C〓 algebras generated by composition operators.

尽管已取得如此丰富的结果，但是关于复合算子仍然有大量非常有意义的问题值得研究，例如：复合算子序列的总体紧性及收敛性、复合算子的各种乘积的紧性、复合算子的闭值域问题、复合算子在各种解析函数空间上的谱的描述、换位复合算子的刻画、复合算子诱导的不变子空间问题、循环复合算子的研究、由复合算子生成的C〓-代数的研究、不同解析函数空间之间的加权复合算子及复合算子半群等等问题。

Firstly,by using the estimating methodfor the compact embedding operators(from weighted Sobolev space to the weighted〓space),we obtain a necessary and sufficient condition for the discreteness of thespectrum of certain differential operators.Secondly,based on the property of thespectrum of difinitizable operators on the Krein space,we consider the left definitedifferential equations with middle deficiency indices,and give a completecharacterization for self-adjoint(J-self-adjoint)differential operators in theindefinite inner product space 〓.Especially,we prove that all the J-self-adjoint differential operators are definitizable.

我们首先运用加权Sobolev空间到加权〓空间嵌入算子紧性的判别方法，证明一类加权自伴微分算子具有离散谱的充要条件；然后，基于Krein空间上可定化算子谱的性质，对于具中间亏指数的左定型微分方程，建立其相应的微分算式在不定度规空间〓上所生成自伴算子的完备性刻画（特别证明了J-自伴微分算子具有可定化性）。

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。

This paper discusses such problems which are easily solved incorrectly in limitedteaching as, segment function is uncertain not to be elementary function, elementary function is un-certain to be continuous in its field of definition, unlimited variable is uncertain to be infinity, theinfinitely many infinitesimal is uncertain to be infinitesimal, the multiplication of two non- infinitesi-mal is uncertain not to be infinitesimal.

1分段函数不一定不是初等函数我们知道初等函数的定义是：常数和基本初等函数经过有限次的四则运算或复合，用一个解析式表示的函数叫初等函数。教材中的定义强调的"有限次"和"一个解析式"，使很多同学产生"非有限次"和"非一个解析式"的函数就不是初等函数的误解。例1f=ceox，s xx！0为分段函数，但也可以表示为f=e12(x-x2")+cos12(x+x2#"$)-1，故为初等函数。

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。

The core designs of genetic algorithm are design of parameter coding, initial group, adaptitude function, controlling parameter and genetic operators. On other words, they are designs of choose operators, exchange operators and aberrance operators.

遗传算法的核心是参数编码、初始群体的设定、适应度函数的设计、控制参数设定、遗传算子的设计即选择算子、交换算子和变异算子的设计。

The bung uses the stainless steel plate to make the ledger wall, the built-in aluminum silicate heat preservation, the fire door size extends 350mm, high 580mm, in spandrel wall body whole upward promotion type electrically operated heat preservation fire door, when fire doorclosure the entire fire door is a circular whole, the fire door sealing property strengthens, the turntable uses the stainless steel to make the 1600m/m turntable, with take load bearing work piece, the entire turntable does not divide the location as the plane, the operators may pile up the workpiecewillfully, because turntable every 40 minutes turn on lathe biography one week, when work the operators did not look nearly the turntable in the rotation, the fire door starts in addition in a big way, the operators may pass in and out the work piece willfully, but is not limited the time the turntableto be possible in 20-60The minute revolves one week-long time to modulate velocity willfully, no matter the fire door opens shuts, the turntable from the start work on uninterrupted revolving, not any necessity and the fire door open shut carry on the interconnection, needs to stop when revolves, onlyneed press down on the control electricity tank's pause button then, the fire door opens shuts, grasps voluntarily by the operators, presses installs nearby the fire door opens shuts button then. Transfers the bottom type resistance furnace's temperature control part to use the microcomputer automatic

炉盖采用不锈钢板做底板，内置硅酸铝保温，炉门尺寸宽350mm，高580mm，侧墙体中整体向上提升式电动保温炉门，炉门关闭时整个炉门为一个圆形整体，炉门密封性能增强，转盘采用不绣钢制成1600m/m转盘，用以承载工件之用，整个转盘为平面不分工位，操作人员可以任意堆放工件，由于转盘每40分钟旋传一周，工作时操作人员几乎看不到转盘在转动，加上炉门开的较大，操作人员可以任意进出工件，而不受时间限转盘可以在20—60分钟旋转一周的时间任意调速，不论炉门启闭、转盘从启动工作就不间断的旋转，没有任何必要与炉门启闭进行联锁，需要停止旋转时，只需按下控制电柜上的停止按钮即可，炉门的启闭，由操作人员自行掌握，按动安装在炉门边的启闭钮即可。

The bung uses the stainless steel plate to make the ledger wall, the built-in aluminum silicate heat preservation, the fire door size extends 350mm, high 580mm, in spandrel wall body whole upward promotion type electrically operated heat preservation fire door, when fire door closure the entire fire door is a circular whole, the fire door sealing property strengthens, the turntable uses the stainless steel to make the 1600m/m turntable, with take load bearing work piece, the entire turntable does not divide the location as the plane, the operators may pile up the work piece willfully, because turntable every 40 minutes turn on lathe biography one week, when work the operators did not look nearly the turntable in the rotation, the fire door starts in addition in a big way, the operators may pass in and out the work piece willfully, but is not limited the time the turntable to be possible in 20-60The minute revolves one week-long time to modulate velocity willfully, no matter the fire door opens shuts, the turntable from the start work on uninterrupted revolving, not any necessity and the fire door open shut carry on the interconnection, needs to stop when revolves, only need press down on the control electricity cabinet's pause button then, the fire door opens shuts, grasps voluntarily by the operators, presses installs nearby the fire door opens shuts Niu then.

炉盖采用不锈钢板做底板，内置硅酸铝保温，炉门尺寸宽350mm，高580mm，侧墙体中整体向上提升式电动保温炉门，炉门关闭时整个炉门为一个圆形整体，炉门密封性能增强，转盘采用不绣钢制成1600m/m转盘，用以承载工件之用，整个转盘为平面不分工位，操作人员可以任意堆放工件，由于转盘每40分钟旋传一周，工作时操作人员几乎看不到转盘在转动，加上炉门开的较大，操作人员可以任意进出工件，而不受时间限转盘可以在20—60分钟旋转一周的时间任意调速，不论炉门启闭、转盘从启动工作就不间断的旋转，没有任何必要与炉门启闭进行联锁，需要停止旋转时，只需按下控制电柜上的停止按钮即可，炉门的启闭，由操作人员自行掌握，按动安装在炉门边的启闭钮即可。

Theorem 2 The product of a bounded function and an infinitesimal is an infinitesimal.

定理 2 有界函数与无穷小的乘积是无穷小。

Although translator has turned from being a crystal ball by which the original culture can unrestrainedly penetrate to another crystal ball by which the target culture can freely traverse, the translator's personal embodiment, in the process of cognitive act, are still absent in translation studies. Translators are still subjects without body or simply disembodied subjects.

译者虽然由原语文化可以自由穿透的玻璃球变成了译语文化可以自由穿越的玻璃球，但译者认知过程中的个体体验在翻译研究中依然缺席，译者依然仅仅是一个没有躯体体验的主体。

Chillingly, he claimed our technology is 'not nearly as sophisticated' as theirs and "had they been hostile", he warned 'we would be been gone by now'.

令人毛骨悚然的，他声称我们的技术是'并不那么复杂，像他们一样，和"如果他们敌意"，他警告说，'我们将现在已经过去了。