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    Order Expansion Algorithm based on the Earthquake Body Tracing
    基于地震体追踪的有序扩展算法
    The Moment Estimates Order Promotion of the Financial Asset Returns ″Fat Tail″ Distribution Shape Parameter Based on Second Order Expansion Form
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    Characteristics of picosecond pulses generated from synchronously pumped dye laser system——The third order expansion of gain of mode-locked equation and its solution
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    A Cubical Order Expansion Algorithm for Finding Irredundant Covering of Combinational Circuits
    求组合电路无冗余覆盖的立方有序扩展法
    TIME-DOMAIN AVERAGING OF PRECISE INTEGRATION AND STOCHASTIC SYSTEM ORDER-EXPANSION METHOD
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    Credit is not only the lube for the operation of a society and an economy, but also the key source of the cooperation order' expansion and the economy development.
    信用不仪是一个社会经济运作的润滑剂,也是保证合作秩序拓展、经济增长与繁荣的重要来源。
    The human civilization is founded on the basis of “extended order of human cooperation”, and the market order came from the order expansion, it has an inconceivable creativity.
    人类文明是建立在“人类合作的扩展秩序”的基础上的,这一自生自发的秩序是人之活动的结果而非人之设计的结果。 市场秩序是这一秩序扩展过程中慢慢才发展出来的,然而它所具有的创造力是人们无法想象的,现在世界上存在的人口规模和结构都要归功于它。
    2. In chaper 2, we recall the basic theroy of UV-decomposition. Some basic propertiesof the U-Lagrangian are presented. These results can help us to deeply understand the first and second-order expansion of f on the U -space.
    2.第二章介绍UV-分解理论的基本思想,借助于中间函数-U-Lagrange函数,得到这一函数的一些基本性质及它的高阶性质,由此得到函数的二阶展式。
    In nonsmooth optimization, second-order expansion theory is significant both for deriving optimalty optimality conditions and developing algorithms . Therefore, the study concerning the theory of the second-order properties of nonsmooth functions have been paid much attention.
    在非光滑优化中,非光滑函数的二阶展开对于最优性条件的研究以及设计具有高阶收敛性的算法都是不可缺少的工具,因此,对非光滑函数的二阶性质与展开的理论研究一直倍受关注。
    the existence of optimal solution set W(u) of the U—Lagrangian and the characterization of the associated smooth trajectary x + u + W(u) tangential to U, so that the second order expansion of f can be develped.
    +u(?) W(u)的刻画,进而得出f在其上的二阶展开,
    3. In chapter 3, we apply uv-theory to semismoothness, obtain the properties of u-Lagrangian, the set of minimizers and the second-order expansion in u-space.
    3.第3章,首先对半光滑函数进行了UV-分解,得出了U-Lagrangian和最优解集W(u)的相关性质,以及二阶近似展开。
 

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