查询词典 mapping theorem

Nonuniform sampling can acquire signal of which the frequency exceeds the threshold in Nyquist theorem when the sample rate of analogue-to-digital device is lower than usual.

非均匀采样可以在对模数转化器件的采样频率要求较低的情况下，提取超出Nyquist采样定理限制的频率。

It investigates mainly infinite matrix conver-gence、infinite matrix transformations、the automatic continuity and boundedness of infinitematrix operators、infinite matrix topological algebras、invariant theory、infinite matrix meth-ods、compact operators series and Eberlein-Smulian theorem,etc.

主要研究了无穷矩阵收敛、无穷矩阵变换、无穷矩阵算子的自连续性和自有界性、无穷矩阵拓扑代数、不变性理论、无穷矩阵方法、紧算子级数与Eberlein-Smulian定理等。

This paper introduced the appliance of probability and statistics in reality,including classical model,formula of total probability, normal distribute,mathematics expectation and the central limit theorem.While it also discusses the widely uses of probability and statistics and the close relationship with the real life.Therefore,it lays the theoretical foundation for the practical uses with probability and statistics,and the basis of mathematics model.

本文介绍了概率统计的某些知识在实际问题中的应用，主要围绕古典概型，全概率公式，正态分布，数学期望，极限定理等有关知识，探讨概率统计知识在实际生活中的广泛应用，进一步揭示概率统计与实际生活的密切联系，为应用概率知识解决实际问题，数学模型的建立，学科知识的迁移奠定一定的理论基础。

First, a large class of ideal Einstein and conformally flat immersions are proved to be totally geodesic, which generalizes a theorem of Dillen on the simplest ideal immersion.

首先证明了实空间形式中一大类理想的爱因斯坦和共形平坦浸入均为全测地浸入，所得结果大大推广了Dillen等人关于欧氏空间中最简单的理想浸入定理。

Shen prove a short time existence theorem for manifolds with umbilical boundary. He also derived the Simons' identity for the boundary under the Ricci flow. And as a corollary, Shen show that any three-manifolds with totally geodesic boundary which admits positive Ricci curvature can be deformed to a space form with totally geodesic

而带边流形上的Ricci流的研究始于Shen，在1996年，Shen在中考虑带边三维流形上的黎曼度量的Ricci形变，证明了如果初始三维流形的黎曼度量具有正Ricci曲率和全测地边界，则此三维黎曼流形上存在着常正曲率的黎曼度量。

We introduce a set of real functions H, and use to it to give a fixed point theorem of tother type for complex mappings on complete metric spaces, which improves and generalizes the corresponding results on compact metric spaces or under the condition of weakening compactness obtained by Fisher, Telci and Xu Xiao-li, respectively.

利用引入的实函数类H，在完备度量空间上给出了复合映射的另一种类型的不动点定理，改进并推广了Fisher、Telci和徐晓立等在紧致度量空间上或在弱化紧性条件下得到的相应结果。

Because the governing equations have the relationship of translation symmetry, the displacement fields and the electrical potential fields can be represented by Bloch theorem to get the periodical structural governing equations.

将应力和电位移场以位移和电位场表示，即可利用层与层间的位移、应力、电位和电位移必须连续等条件求得转换矩阵，再满足上下表面的边界条件即能求得出压电周期叠层板波传频谱。

In this paper transversality idea from singularity theory is applied to set up the universal unfolding theorem of bifurcation problem s with multiparameter.

利用奇点理论中的横切性思想建立了多参数分支问题的方有开折定理。

The existence of solutions for two-point boundary value problem subject to nonlinear second order differential equation with mixed boundary conditions is studied by using topological transversality theorem, and some known results are improved.

现利用拓扑横截定理，考虑了二阶常微分方程两点边值问题在组合边界条件下的解的存在性，对二阶常微分方程两点边值问题所对应的辅助问题作先验界估计，并利用拓扑横截定理，得到了边值问题解的存在性，推广了一些已有结果。

The frequency range and distortion model affected by Faraday rotation were analyzed. A kind of calibration algorithm was introduced, in which trihedral corner reflectors were used to calibrate POLSAR image subject to channel imbalance, Faraday rotation and RCS distortion. [2]Three kinds of target decomposition theorems used to extract polarimetric features of SAR image were studied in detail. A kind of POLSAR MLC image data decomposition method based on classical coherent decomposition theorem of POLSAR SLC image was introduced, which was used to extract polarimetric features of POLSAR MLC image.

当工作频率小于1GHz时，法拉第旋转是影响低频星载极化SAR图像定标的一个重要因素，论文分析了受法拉第旋转影响的波段范围和误差模型，提出了一种校正通道不平衡度、法拉第旋转和绝对幅度增益的极化定标算法，仅使用一种点目标——三角反射器作为定标体，应用于受法拉第旋转影响的极化SAR图像定标； [2]深入研究了三类用于SAR图像极化特征提取的目标分解理论。

He paid $5,000 for this cupcake.

他我这个纸杯蛋糕花了5000美元。

I mean, if you want to, that is

我的意思是，如果你们想吃的话。