假设

According to the hypothesis of continuum, a tube with the corner strengthened is gained to make an equal of the frame-tube. B3-spline functions and parabola functions are applied to simulate the displacement functions of the frame-tube. The system of equations about the undetermined coefficients of displacement functions is deduced by using energy-variational principle, by solving which the displacement of the frame-tube is gained. Then the internal forces in the columns and beams of the former frame-tube are obtained according to the principles of elasticity mechanics.

根据连续化假设将框筒等效为角部加强筒体，将三次样条函数与抛物线函数结合假定框筒的位移函数，运用能量变分原理推导出了关于位移函数待定系数的方程组，解得位移函数待定系数进而解得框筒的位移，再根据弹性力学原理确定原框筒中梁柱的内力。

Nonstandard analysis ; nlargements of number systems ; transfer principle ; external producing principle ; comparative principle ; potential numbers ; measure ; continuum ; discontinuum ; cardinal number ; continuum hypothesis ; Hilbert's first problem Ner

非标准分析；数系的扩大；转移原则；外的生成原则；比较原则；潜在数；测度；连续统；离散统；基数；连续统假设； Hilbert第一问题；新的数学实体；不可分的连续体； Zeno的总格言； Aristotle的猜想；庄周；无厚不可积；万世不竭；测度论的基础

Paper theoretical starting point and the basic assumption that sustains are: Since modern social transition middle class has broken up, made up and developed that makes itself filling with contradictoriness, different quality and complexity, it is not one for class.

本论文主要理论取向则不同于西方中产阶级理论研究中的"稳定器"、"平衡轮"、"缓冲器"等理论观点，论文理论起点和支撑的基本假设是：自近代社会转型以来，中产阶级的分化、组合和发展变化，使其自身充满着矛盾性、异质性和复杂性，其并非是一个自为的阶级。

The case assumes a different aspect, when wholly external contrary propositions, relating to position in space, are used in reference to the bilocated individual.

如此假设的一个不同方面，当全外部相反的主张，有关立场，在太空中，用得其所在参考了bilocated个人。

Furthermore, without any assumption, the global convegence is proved.

在不需要任何假设的情况下，证明了算法的全局收敛性。

Firstly, the difference of per capita GDP tends to convergence between the Western region and the Eastern region.

文章摘要：本文假设我国西部与东部地区的能源消费强度差异是西部与东部地区人均GDP差异的函数，然后同其他回归变量一起检验这两个变量之间的关系，并通过使用面板数据计量经济学模型进行实证估计。

We prove, under some mild assumptions, the local convergence theorem for this class of dual algorithms and present the error bound for approximate solutions.

在适当的假设条件下，证明了该类算法的局部收敛性质，并给出近似解的误差界。

A word before we move on, I assume that the reader is conversant with VB ActiveX technology

一个字在我们继续之前，我假设读者已经熟悉VB的ActiveX技术

Under some assumption conditions, we also developed trust region and affine scaling algorithm and potential reduction algorithm for convex programming problem with linear constraints.

然后在一定的假设条件下，对线性约束下的凸规划问题我们给出了相应的信赖域仿射尺度算法和势函数下降算法。

Under a convexity assumption, we show that the extended B-well-posedness is closely related to property.

在凸性假设下，我们研究了集值向量优化的广义B-适定性与-性质的紧密关系。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。