查询词典 ordered set bounded below

In Chapter 2, we use Zorn lemma and generalized order set general principle [47] to generalize classical Caristi fixed point theorem, respectively, which weaken the condition that the functional is bounded from below.

在第二章中，我们首先分别利用Zorn引理和推广的序集一般原理[47]推广了古典的Caristi不动点定理，削弱了泛函下方有界这个条件。

FR conjugate gradient methods with perturbations are proposed. The global convergence property of the first method is proved under the condition of main directions' sufficient descent. Whereas, in the proof of the convergence for the other two methods, we only need main directions' descent. Importantly and quite interesting, boundedness conditions such as objective function being bounded below, boundedness of level set are not needed. Chapter 5 presents a version of Dai-Yuan conjugate gradient method with perturbations.

在主方向充分下降的条件下证明了第一个方法的全局收敛性，而后两个方法的收敛性是在主方向下降的条件下证明的，这些收敛性证明的一个共同特征就是不需要目标函数有下界或水平集有界等有界性条件，第5章采用Wolfe或Armijo步长规则提出了带扰动项的Dai-Yuanabbr。

The existence of the minimal and maximal fixed points for order preserving set-valued operators on semi-ordered sets and semi-ordered topological spaces was analyzed.

讨论了半序集和半序拓扑空间中保序集值算子的最小与最大不动点的存在性。

We prove the fuzzy set-valued characteristicfunction of a compact Baire fuzzy set can be approached by fuzzy set-valuedcontinuous functions with fuzzy compact support sets,the integral of integrablesimple Baire fuzzy set-valued function can be approached not only by the integralsof integral simple fuzzy set-valued functions,but also by the integrals of fuzzy set-valued continuous function with fuzzy compact support sets.

定义了诱导空间上具有模糊紧支集的模糊集值连续函数，说明了它与分明的具有紧支集的连续函数的关系，证明了紧贝尔模糊集的模糊集值特征函数可以用具有模糊紧支集的连续函数列来逼近，可积简单贝尔模糊集值函数的积分可以用可积简单模糊集值函数的积分来逼近，还可以用具有模糊紧支集的模糊集值连续函数的积分来逼近。

Direct Correspondence of Display Data RAM to LCD Pixel Display Data RAM2,500 bits LCD Drivers25-common and 100-segment Selectable Duty and Bias Ratio ; 1/25 Duty 1/6 Bias or 1/15 Duty 1/5 Bias Direct connection to 8-bit Microprocessor interface for both of 68 and 80 type MPU Serial Interface (SI, SCL, A0, CS) Useful instruction set Display ON/OFF, Display Start Line Set, Page Address Set, Column Address Set, Status Read, Write Display Data, Read Display Data, Normal or Inverse ON/OFF Set, Static Drive ON/Normal Display, EVR Register Set, Read Modify Write, End, Reset, Internal Power Supply ON/OFF, Driver Output ON/OFF, Power Save and ADC select.

直接显示数据RAM的对应像素液晶显示数据RAM2，500位液晶Drivers25，共同和100段可选择的职务和偏差率； 1 / 25的责任1 / 6的偏见或1 / 15的责任1 / 5偏见的直接连接至8位微处理器的接口为68和80型微控制器的串行接口（司，沙田至中环线时，A0，CS）的相关指令集显示开/关，显示开始行设置，页面地址设置，列地址设置，状态读取，写入显示数据，读取数据显示，正常或逆开/关设置，静态驱动器/正常显示，腔内注册设置，读取修改写入，完，复位，内部电源开/关，开/关，节能和ADC选择驱动器输出。

The invention discloses a double-temperature double-chamber light wave sterilizing cabinet, which comprises the following parts: box, low-temperature chamber and high-temperature chamber in the box and control device, wherein the upper baffle rack is set in the low-temperature chamber, one lower baffle rack is set in the high-temperature chamber, the screen and keyboard are set on the box, the low-temperature chamber possesses first door with drawer switch and the high-temperature chamber possesses second door with drawer switch, the knife and fork rack is set on the bottom of first door, whose extending direction is vertical the door, the rotary lamp rack of ultraviolet tube is set in the low-temperature chamber, the light wave generating device is set in the high-temperature to emit light wave.

一种双温双室光波消毒柜，包括一箱体、设置在箱体内的低温室和高温室、控制装置，该低温室中设有一上隔物架，该高温室中设有一下隔物架，在箱体的上部依次设有显示屏、按键；该低温室具有抽屉式开关的第一门体，该高温室具有抽屉式开关的第二门体；在第一门体的底部设有一拉伸方向与门体拉伸方向垂直的、可以从左右两侧拉出的刀叉架；在该低温室内设有一设置有紫外线灯管的旋转灯架，在该高温室内设有一用于发射光波的光波发生装置。本发明消毒柜，使用范围广泛，功能齐全，消毒效果好。

It is shown that the return time set of strong scattering is Poincaré set, the return time set of scattering is recurrent set and the return time set of weak scattering is recurrent set for group rotation.

特别地，我们得到了强扩散系统的回复时间集为Poincaré序列，扩散系统的回复时间集为回复序列以及弱扩散系统的回复时间集为相对于群旋转的回复序列。

Some new basic concepts are proposed in this paper, including the approximation space of generalization, rough approximation axiom, disturbance set axiom, classification principle of rough set, principle of nondeterministic even set, principle classification, bit quantum symmetric classification, of concentration, game classification, quantum logic incomparable set, bit space set, protocol relation, rough set function of protocol relation, rough classification algebra, rough simple algebra, etc., and a guess is also proposed.

提出了广义近似空间、粗近似公理、干扰集公理、粗糙集的分类原则、粗选原则、不确定偶集原则、精选原则、对策分类、量子逻辑分类、bit量子对称分类、不可比集、bit空间集、协议关系、粗糙集函数、粗糙分类代数和粗糙单代数等基本概念，并提出了一个猜想；展示了一些新观点；基于协议关系构造了粗糙商代数和粗糙子代数，给出了回避-归并算法及算例。

Upward dual pairs, dual theorem, positive extension, L-topology, semi-bounded, ordered locally convex spaces.

上偶对，对偶定理，正延拓，L-拓扑，半有界，半序局部凸空间，局部体空间

In Chapter 2, we use the generating function to count the number of ordered shapes and the number of bounded-shape partitions.

在第二章，我们使用生成函数去计算对於有序及无序的有界形分割各有多少形及分法。

Chinese traditional virtue is humility and wariness,the compliment and praise to the others should be declination

中国人的传统美德是谦虚谨慎，对别人的恭维和夸奖应是推辞。如

We bought this house on the never-never.

我们以分期付款的方式买下这座房子。