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This course offers an introduction to primary convex analysis, linear programming, non-linear programming, dynamic programming, multi-objective programming, multi-level programming, calculus of variations, and optimal control, which are the optimization methods commonly used in economics and finance.

课程内容简介：本课程介绍凸分析基础、线性规划、非线性规划、动态规划、多目标规划、多层规划、变分法、最优控制，这些都是西方经济学、金融学中常用的最优化方法。

The corresponding relations between the multi-variable canonical difference equation and the extended-state multi-variable equation are also reviewed.

文中还展示了多变量典范差分方程与多变量扩展状态方程之间的对应关系。

The large game collection, of course, allows for multi hand and multi player table and card games.

游戏大集合，当然，允许球员多手，多表和纸牌游戏。

Using the characteristics of multi-resolution of wavelet packet we carry multi-scale decomposition on voice signal.

2为了模拟Mel倒谱滤波的过程，利用小波包多分解的特性，对语音信号进行多尺度的分解。

Two-axis" refers to the central axis and an extension of Chang'an Avenue;"two-zone" refers to the "eastern development belt" and "western ecological belt";"multi-center refers to the construction of urban areas in different functional areas , respectively, to assume different functions of cities in order to improve the efficiency of city services and decentralized traffic pressure, such as the CBD, Olympic Park, the Zhongguancun area, and many other multi-service settings.

两轴"是指中轴线和长安街延长；"两区"指的是"东部发展带"和"西部生态带"，"多中心是指城市建设地区不同功能区，分别承担不同的城市功能，以提高城市的服务效率和分散交通压力，如生物多样性，奥林匹克公园，中关村地区，和许多其他多种服务的设置。

And give the manifest multi-complex features of TJSS, like the syncretizing of multi-structure systems, with weaken administrative levels hiberarchy and the whole structure; dynamic changefully system; TJSS is on the unsteadiness of the total transportation systems.

给出了交通运输结合部具有多重复杂性的表现特征：①系统的多结构融合、具有层次性和整体结构弱化。②系统的动态多变性。③结合部往往处于运输大系统运行的不稳定区域。

Second, On the basis of analysis of density distribution of sequence points on the chaotic orbit of one-dimension chaotic mapping, a mutative interval chaotic optimization algorithm is presented in search for the solution optimums of the non-linear constrained problems with multi-variables and multi-peak values. With the objective function probability measurement approaching a limit 1, the convergence of the algorithm on the global optimal solution is proofed by aid of Chebyshev inequality.

二、基于一维混沌映射混沌点集的概率测度分析，提出了一种适于解决多变量多峰值非线性约束问题的新的混沌优化算法——变区间混沌优化算法，并应用切比雪夫不等式论证了算法依概率收敛于全局最优解。

It was considered that the multi-functional catalysts,in which the active sites were combined in nano/micro scale,was one of the promising methods for the integration of multi-step chemical reactions.

认为催化剂活性相以纳微尺度复合的多功能催化剂是实现多步反应一步化的有效方法之一。

In his speech at Lianhe Zaobao's 75th anniversary gala dinner on September 6, Prime Minister Goh Chok Tong said: In Singapore, we have evolved our own unique formula of a multi-racial, multi-cultural society.

9月6日晚，在《联合早报》75周年报庆晚宴上，吴作栋总理在致词里提及：在新加坡，我们已经为多元种族、多元文化的社会发展出自己的一套独特的方程式。

It is well known that the multi-value CDMA spreading codes can be designed by means of a pair of mirror multi-rate filter-banks based on some optimizing criteria. The dissertation indicates that there exists a theoretical bound in the performance of its circular correlation property, which can be described by an explicit expression.

研究了基于两带镜像多速率滤波器组来设计的多值CDMA扩展码的方法，并推导出了基于这种方法设计的码序列在循环相关特性方面所能达到的极限，以及达到此理论极限时应满足的条件；在此基础上，提出了一种基于熵最大化准则来产生CDMA扩展码的设计方法。

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐