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分维反映了复杂形体占有空间的有效性，它是复杂形体不规则性的量度。它与动力系统的混沌理论交叉结合，相辅相成。它承认世界的局部可能在一定条件下或过程中，在某一方面（形态，结构，信息，功能，时间，能量等）表现出与整体的相似性，它承认空间维数的变化既可以是离散的也可以是连续的，进而拓展了视野。(Fractal dimension reflects the validity of space occupied by complex bodies, which is a measure of irregularity of complex bodies. It combines with chaos theory of dynamic system and complements each other. It recognizes that the part of the world may be similar to the whole in certain conditions or processes (form, structure, information, function, time, energy, etc.). It recognizes that the change of spatial dimension can be discrete or continuous, thus expanding the horizon.)

通过对钢轨和车轮的ansys有限元建模，分析在钢轨的接头处的动力学特性。(Rail and wheel ansys finite element modeling, analysis of the dynamics of the rail joints.)

牛顿插值法进行多项式逼近，matlab编译成功，直接可用(Newton interpolation polynomial approximation method, matlab compiled successfully, directly available)

说明：  基于MATLAB蚁群算法LF解决聚类问题源程序代码，包括文档与论文(MATLAB-based ant colony algorithm to solve clustering problem LF source code, including documents and papers)

二层地质模型波场模拟,用有限差分进行波场的模拟,充分利用多波多分量地震记录，以及各向异性方面的独特信息，可有效地减少 纵波勘探的多解性，定量地描述裂缝储层，改善某些纵波资料成像不好地区的构造 成像。这样可获得比纵波分辨率高的多波剖面，从而有利于研究小幅度构造、断层、 裂缝裂隙等复杂地质现象，对油气勘探与开发具有现实意义和实用价值(Two-layer geological model wave field simulation, using finite difference wave field simulation to make full use of multi-wave multi-component seismic records, and the anisotropy of the unique information can be effective in reducing the P-wave exploration, multi-solution and quantitatively describe the crack reservoir to improve the poor image of some P-wave data area structure imaging. This availability of higher resolution than the longitudinal wave of multi-wave profile, thus contributing to the small amplitude structures, faults, cracks, fissures and other complex geological phenomena, for oil and gas exploration and development of practical significance and practical value)

通过建立截面为多边形的水平柱体模型，运用c语言程序进行编程，得出该地质体的重磁异常特点(By establishing a horizontal cylinder model with polygon cross section and programming with C language, the characteristics of gravity and magnetic anomalies of the geological body are obtained.)

说明：  二阶曲线拟合，最小二乘法，此程序是在c++ builder6.0环境下开发的(second curve fitting, least squares method, this procedure is in c builder6.0 development of the environment)

文章简述了一位大牛研究深度学习（Deep Learning）后的心得及见解(Article outlines a large cattle study deep learning (Deep Learning) after experiences and insights)

C 语言，模拟流体相平衡过程，得到混合气体平衡态以后的工况参数(C language to simulate fluid phase equilibrium process, to obtain a mixed gas equilibrium after working parameters)

计算方法中的复数运算(calculation method in the plural Operational)