查询词典 theorem of alternative

Theorem Let be a function of period . If satisfies the convergent theorem, the Fourier series of is

定理 设周期为的周期函数满足收敛定理的条件，则它的傅立叶级数展开式为

The Lyapunov theorem and its converse theorem of globally exponential stability for the discrete-time systems family in which the sampling period is a parameter are proved.

对以采样周期为参数的离散时间系统族，证明了全局指数稳定的Lyapunov定理和逆定理。

In Chapter 3,we discuss theconvergence of Newton's method for nonlinear inclusion problems with values in aclosed convex cone,using the new theory developed by Wang Xinghua,we generalizeRobinson's Kantorovich theorem for this problem to a more widely function classes,inthe same time our results take Smale theorem as a special case.

在第三章，我们利用王兴华最近提出的理论框架研究在闭凸锥中取值的非线性包含问题的Newton方法，将Robinson在特殊Lipshitz条件下建立的Kantorovich型收敛性定理推广至满足中心Lipshitz条件的函数类，我们建立的一般的收敛性定理同时将Smale型收敛性定理包容其中。

Tan and Xu [1] had proved the theorem on convergence of Ishikawa iteration processes of asymptotically nonexpansive mapping on a compact convex subset of a uniform convex Banach space , Then Liu Qihou [3] presents the necessary and sufficient conditions for the Ishikawa iteration of asymptotically quasi-nonexpansive mapping with an error member on a Banach space convergent to a fixed point . Xu and Noor [5] had proved the theorem on convergence of three-step iterations of asymptotically nonexpansive mapping on nonempty closed, bounded and convex subset of uniformly convex Banach space.

Tan和Xu已经证明了建立在一致凸Banach空间紧凸子集上的渐进非扩张映射的Ishikawa迭代序列的收敛原理，随之，刘齐侯又阐述了Banach空间上渐进准非扩张映射T的具误差的Ishikawa迭代序列收敛于T的不动点的充分必要条件；之后，Xu和Noor也证明了定义在一致凸Banach空间某非空有界闭凸子集上的渐进非扩张映射的三步迭代序列的收敛原理。

Then is the property of fourier transform detally,it contains linar, symmetry,uncover,switch,time-move,frequency-move,time-differentialcoefficient,frequency-differential coefficient,time-intergrate, frequency-intergrate,odd even, theorem of Parseval ,and theorem of convolution,and make testify to some property,some have the example.

接着详细概括了傅立叶变换的性质，即线性、对称性、折叠性、尺度变换性、时移性、频移性、时域微分性、频域微分性、时域积分性、频域积分性、帕塞瓦尔定理、奇偶性及卷积定理等，对某些性质相应的做了推导，并附有适当事例。

Stationary process: spectral decomposition of covariance function, spectral decomposition of stationary process, linear time invariant system, ergodic theorem, sampling theorem.

平稳过程：协方差函数的谱分解，平稳过程的谱分解，线性时不变系统，遍历定理，采样定理。

Because the kinematically-admissble cyclic strain rate field required in kninematical-type theorem of shakedown analysis is rather difficult to be constructed, shakedown analysis based on kinematcal theorem cannot be directly applied.

在竖向载荷与水平载荷共同作用下，研究了地基土体的强度特性与土层分布特征对地基承载力的彤响，对地基的极限载荷与安定戳荷进行了比较分析，为全面、综合地评价非均质地基的稳定性提供了有益的参考。

Aiming at bottom roof caving and support impact problems induced with abrupt large scale caving upper roof in face 21303 of Daliuta mine, this paper put forward the motion parameter at roof caving and calculation formula of roof shear breaking force with the help of theorem of momentum, theorem of moment of momentum and D' Alembert principle. Roof caving process was simulated by Ansys Ls-DYNA program, and maxim impact force was got. The theoretical research outcomes in the paper were applied in face 21303 of Daliuta mine, and were accordant with actual observing status of roof caving process.

针对神东煤炭公司大柳塔煤矿活井21303综采工作面，上层采空区顶板突然大规模垮落对下层顶板及支架的突然冲击问题，文章采用动量定理、动量矩定理、达朗伯原理推出了顶板垮落瞬间的运动量及顶板切顶垮落所需要的剪力值计算公式，用ANSYS LS-DYNA程序对顶板垮落过程进行了数值计算，得到了最大冲击力，在大柳塔煤矿活井21303综采工作面对顶板垮落特征进行了实际观测和理论成果验证。

In this paper we introduce some new definitions, they are the generalizations of those concepts in Lie theory, and we discuss initially the elementary properties of operator Lie algebras. Finally, the famous Jordan-Holder theorem and the uniqueness of decomposition theorem of operator Lie algebras are proved.

在这篇文章里，我们将李代数理论中的诸多概念加以推广，并初步地探讨了算子李代数的性质，最后还给出了算子李代数的一个分解定理，其唯一性也得到了证明。

Properties of cut sets, decomposition theorem, representation theorem of intuitionistic fuzzy sets are discussed.

在此基础上，给出了直觉模糊集的分解定理和表现定理。

The shaping method of noncircular part and the tool holder's radial motion characters in noncircular turning process are discussed in detail in the thesis.

论文详细研究了非圆零件的成型方法和加工过程中刀架的径向运动规律。

I have not really liked him,I do not like his this kind of disposition.

我没有真的喜欢他，我不喜欢他的这种性格。