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Thermodynamic process of direct aluminium extraction from aluminium sub-sulphide, which is unstable and easily decomposed into Al and Al2O3 at a low temperature, was analytically studied. The temperature, at which alumina, FeS and carbon react to form aluminium sub-sulphide in different pressure, was evaluated with "Substance Gibbs' Free Energy Functional Determinant" method.

本文利用铝的低价硫化物在高温下存在，低温下不稳定容易分解得到金属铝的特性，从热力学角度引入"物质吉布斯自由能函数法"讨论在不同压力下，氧化铝、硫化亚铁与还原剂碳的反应生成低价硫化物的条件。

In general, this equation can not be solved analytically, so we need deal with it numerically.

该方程一般情况下不适合于解析求解，通常需做数值处理。

The stress intensity factors and the size of saturation strips were derived analytically and their dependencies on the ratio of the periodicity to half-length of the crack h/l were analyzed in detail.

对应力强度因子和饱和条带尺寸进行了理论推导，详细分析了它们与周期长和半裂纹长的比值h/l之间的关系。

The DFP method is proved a officient one in processing unconstrainted optimization problem, so in this thesis, used the idea of mechanical structural optimization for reference analytically and extended modified formula of DFP—matrix to shape optimiation the DFP—Hamilton function method is put forward.

由于变尺度方法是有效的无约束优化方法，本文在分析的基础上借鉴了机械结构参数优化的思想，并将变尺度矩阵的修正公式扩展至形状优化中去，进而提出了变尺度—H函数极值法，并用其解决了梁、柱和复杂曲面的形状优化设计问题，取得了较好的效果。

From the start [50] I can apprehend the concept of body analytically through the characters of extension, impenetrability, figure, etc.

从一开始，我就可以分析性的理解物体的概念(空间性，密性，形状等等)，这些都是包含在物体概念之内的。

The error of quadratic interpolation method on sine wave signal was analytically studied and numerical evaluated in this paper.

该文从理论分析和数值仿真两个方面，对二次插值算法在正弦信号分析中存在的误差进行了详细的研究，得到了误差范围的解析表达式。

For example, a floor joist may be subjected to loads that cause bending moment and shear as well as torsion.in these situations ,measurement of the inherent strength becomes analytically and experimentally complex,and in many situations cannot be done .

例如，地板龙骨可能受到荷载引起的弯矩和剪力以及torsion.in这种情况下，测量的固有实力和实验解析变得复杂，在许多情况下不能做。

Basing on the law of conservation and conversion of energy, we can obtain analytically Newton\\\\\\\s three laws of motion and the law of conservation of momentum.

文章深入讨论了能量与力之间的内在联系，根据能量守恒和转换定律，直接获得牛顿三大运动定律和动量守恒定律。

Recurrent formulas for calculating the coefficients of the Legendre polynomial and the expressions for calculating the sedimentation coefficient are deduced analytically.

为了研究多分散低Péclet数沉降问题，我们先以Legendre多项式展开法得到了计算对分布函数的普遍递推式，以及由Legendre多项式的系数表示的沉降积分。

Finally, the contribution of the boundary fields to both the magnetic susceptibility and specific heat are obtained, and their exact expressions are analytically derived.

最后，得到了边界场对于磁化率和比热的贡献，并给出了确切的表达式。

When this condition occurs, inbound replication with the source partner is stopped on the destination domain controller and event ID 2042 is logged in the Directory Services event log.

计算机密码学是研究计算机信息加密、解密及其变换的科学，是数学和计算机的交义学科，也是一门新兴的学科。

Instructions: click on the thumbnails to see a larger image, then use the left-right arrow keys to scroll through the slideshow.

使用说明：滑鼠点在小图上即可放大观赏。开启后键盘左右键可用来换照片。