查询词典 mathematical notation

Use appendices for mathematical derivations and supporting material too detailed to include in the body of the paper.

使用附录的数学推导和辅助材料过于详细，包括正文中的文件。

At that time, we studied applied mechanics and used mathematical calculations to resolve complicated engineering problems.

那时，我们这些搞应用力学的，就是用数学计算来解决工程上的复杂问题。

Based on force characters of the model, authors put forward the mathematical expression of approximate deformation curves and compared calculation curves with measured curves.

基于模型的受力特点，提出了近似变形曲线的数学表达式，并将计算曲线与试验观测曲线进行了比较。

To resolve thismodel,one approximate liner first derivative equation is used.An simple caculatemodel is setted up for caculating the motive adjust,and a mathematical equation incaculating the range of pressure motion in the system.Experiment data showe thatthese models have high accurecy.

在此基础上，对分析模型采用一阶微分近似线性化处理，建立了计算动态调节过程的简化计算模型，并以此建立了计算系统压力动态变幅的计算式，试验表明简化模型具有较高的精度。

Combining the definition of CWT and the derivative property of convolution, we constructed a general method to calculate the approximate derivative of signal through CWT by using the first and second derivative of Gaussian function, Haar, and the first derivative of three-order-Spline function as wavelets. As compared with the other approaches of calculating derivative, which include the numerical differentiation, polynomial filters, Fourier transform, and the recently proposed DWT method, fast calculation and simple mathematical operation were remarkable advantages of CWT method. For the signal corrupted by severe noise (Signal-toNoise Ratio=5), the satisfactory results could also obtained via CWT method through appropriately adiusting the dilations.

在此基础上，(1)结合连续小波变换的特点和卷积的微分性质，提出了使用Gaussian函数的一阶和二阶导数，Haar和三次样条函数的一阶导数作为小波函数的连续小波变换计算信号近似导数的一般性方法，与其他导数计算方法(包括数字微分法，多项式滤波法，Fourier变换法和离散小波变换法)相比，本法简单便捷，计算速度快，对于噪声含量较高的信号(S/N为5)，只要适当调节尺度即可获得比较满意的结果。

In this paper, they have not only illustrated the practical approaches and methods of modern mathematical analysis used in anode baking and thermotechnical procedure, but also provided computational techniques for the approximate solution to thermotechnical differential equations.

它的创新之处在于借助Mathematica系统的强大的符号运算功能与该系统提供的控制语句，能实现系统有效渐近解的自动求解，到目前为止，还很少见到用计算机实现其自动求解过程。

With the advancement of science and technology, some new theories and new ways emerged gradually, some of them merged with specific theoretical tools, this specific theoretical tools include mathematical morphology, fuzzy techniques, neural networks, wavelet and so on. Secondly, in this paper, it described and analyzed the segmentation method based on the edge in the domain of image segmentation in detail. It did experiments on several edge detection operators using MATLAB, it summarized the advantage and the shortcoming of traditional edge detection operators, and the operating environment. On the basis of the experimental analysis, it implemented an edge location more precise, more efficient operating speed edge extraction method——Template Vector. In this method, it optimized differential approximate calculation of first differential operators the paper mentioned. After experimented on this edge extraction method, contracted with the traditional methods, the edge outline is extracted more accurately and more exquisitely, furthermore, it retained the object outline furthest, and achieved more satisfied edge extraction result.

其次，对图像分割领域中常用的基于边缘的分割方法进行了详细的研究与分析，对各种边缘检测算子进行了MATLAB环境下的实验，分析总结了各种传统边缘检测算子的优缺点和适应环境，并针对传统边缘检测算子在处理显微图像时的缺陷，在实验分析的基础上研究并实现了一种边缘定位更加精确、运算速度更加快捷的边缘提取方法——模板向量算法，在该算法中，对文章提到的一阶微分算子中微分的近似计算作进一步优化，经过对该边缘提取方法进行实验，其结果与传统方法相比，轮廓提取更为精确细腻，且最大程度的保留了图像中物体(目标个体或者明显噪声点)的轮廓，得到了比较理想的边缘提取效果。

An example is demonstrated for comparing between the mathematical model and the approximate method.

结果表明，本文提出的动防洪库容计算方法与采用数学模型的计算结果基本吻合。

Taylor Formula is a very important content of mathematical analysis, it can intensively embody the soul of "approximation" of calculus, and it is extensively applied in the theoretical analysis and practical application.

泰勒公式是数学分析中的重要内容，集中体现了微积分中"逼近法"的思想，在理论分析和实际应用中经常涉及。

It is the aim of this book to present various basic and important results of vector optimization in an abstract mathematical setting and to demonstrate its usefulness in vector approximation and cooperative differential game theory.

本书的目的是在抽象数学柜架下给出向量优化的各种基本和重要结果并阐述它们在向量逼近和合作微分对策理论中的应用。

"Second Life is remarkably easy to work with, and is very popular,"

"第二次生命是显着容易的工作，并且很受欢迎，"

For example, we usually assume that materials are homogeneous and isotropic and free of internal defects or flaws.

为了得到适合有限元分析的模型，我们必须经过如图2所示的简化步骤。