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For solving discrete optimization problem using DE,based on the idea of mathematic transform,the concepts of adjuvant search space and individual hybrid encoding are advanced.

接着，给出了HBDE的依概率收敛和完全收敛的定义，并利用离散Markov随机理论证明了HBDE是完全收敛的。

It introduces a mathematic model on the scheduling problem for discrete manufacturing system.

首先介绍了离散制造业中生产调度的最大加工时间最短的数学模型。

The mathematic model of equipment is nonlinear system of distributed parameter, which is influenced by test component, thus it is difficult to carry out effective control.

由于该设备的数学模型是一个分布参数的非线性系统，且受到试验件的影响，较难有效的实施快速控制。

It researches on the approach to achieve continuous connections of container multimodal transport logistics system. Based on the idea of continuous connections the paper discusses the container transport choosing route problem. It combines the appropriate adimensionalize method in the appraisement method and mathematic model and resolves the problem that the unit of time and cost disunite and sets up the time-cost transportation route optimizing model which is an innovation on the basis of previous studies and gives an example to validate the model using the LINDO software.

在"无缝衔接"的思想下研究集装箱运输路径选择问题，在前人的研究上进行了创新，将评价方法中的合适的无量纲化方法与数学模型结合，解决了时间和成本单位不统一的问题，建立了时间—成本运输径路优化模型，并举例验证应用LINDO软件进行求解，说明了此模型的正确性。

A mathematic model of foam fractionation was set up based on the following assumptions: adsorption equilibrium,same bubble size and regular dodecahedron model of real bubbles.

假设吸附过程始终处于平衡态、气泡大小均一以及每一个气泡均为正十二面体，构建了泡沫分离过程的数学模型。

Mathematic model of double four-bar mechanism is very complex,so its speed and acceleration is always the difficult points of the research.

双四杆机构因其数学模型复杂，其速度和加速度曲线一直是研究的难点。

Because of using double Fourier Series, the development of equations isvery simple, and the answer has the advantages of uniform mathematic expression and easily drawing-up calculating program.

由于重三角级数的利用，使方程的推导变得简洁，所得的结果数学形式统一，便于计算机编程计算。

In this paper we will generally discuss the WEMVA method by Double Square Root for the convenience of mathematic expression, and demonstrate how it works in numerical model.

在叠前偏移算子中，因为双平方根算子的数学表达式更为简洁，所以本文基于对波动方程偏移速度分析初步讨论，并通过模型验证其原理。

In this paper, we focus on such aspect as mathematic expression in DNA and protein sequences, similarity analysis and phylogenetic tree structure. Mainly include:After summarization mathematical methods of DNA and protein sequences in detail, the paper presents a 2D graphical representation of DNA sequences based on dual nucleotide, and graphical representation of the distribution curve of sequences with nucleotide sequences of the classification.

论文在DNA和蛋白质序列的数学表示、相似性分析和进化树的构造等方面进行研究，主要工作包括：在对DNA和蛋白质序列的数学表示方法进行较为详细的综述后，提出了一种基于双核苷酸的DNA序列2D图形表示方法，利用核苷酸的分类给出了序列的分布曲线图形表示。

The mathematic theory is the foundation of ECC, which will help to understand the whole article better to start with.

数学理论是椭圆曲线密码体制的基础，从此着手开始论文有助于对后文更好的理解。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。