发现数学

数学，是一门规律性极强的学科，在学习过程中，虽然，我们不一定会得到重大的数学成果．但我们可以在不断的总结和思索中发现规律，得到乐趣． 下面，给大家介绍我由平常习题得到的两个结论：     

混凝土骨料对高速侵彻弹体质量侵蚀的影响分析

高速侵彻时，弹靶之间发生强烈的局部作用，引起弹体头部发生质量侵蚀，从而影响弹体的侵彻性能。在弹体侵彻过程中，混凝土中的骨料对弹体的质量侵蚀有显著影响。本文通过对高速侵彻混凝土弹体的质量侵蚀实验数据进行分析，进一步分析讨论了混凝土骨料对弹体质量侵蚀的影响。将混凝土靶体视为骨料和砂浆基质混合的二相复合材料，引入混凝土骨料的体积分数χ和骨料的剪切强度τ₁代替骨料的莫氏硬度H，给出无量纲骨料修正因子β，建立了修正的弹体质量损失工程模型。模型预测结果与现有的实验数据符合得很好，更准确地表征了混凝土骨料对弹体质量损失的影响。     

Soliton mode-locked fiber laser with high-quality MBE-grown Bi_2Se_3 film

In this work, a soliton mode-locked erbium-doped fiber laser(EDFL) with a high-quality molecular beam epitaxy(MBE)-grown topological insulator(TI) Bi_2Se_3 saturable absorber(SA) is reported. To fabricate the SA device, a 16-layer Bi_2Se_3 film was grown successfully on a 100 μm thick SiO_2 substrate and sandwiched directly between two fiber ferrules. The TI-SA had a saturable absorption of 1.12% and a saturable influence of 160 MW/cm~2.After inserting the TI-SA into the unidirectional ring-cavity EDFL, self-starting mode-locked soliton pulse trains were obtained at a fundamental repetition rate of 19.352 MHz. The output central wavelength, pulse energy,pulse duration, and signal to noise ratio of the radio frequency spectrum were 1530 nm,18.5 p J, 1.08 ps, and 60d Bm, respectively. These results demonstrate that the MBE technique could provide a controllable and repeatable method for the fabrication of identical high-quality TI-SAs, which is critically important for ultra-fast pulse generation.     

发现数学

数学,是一门规律性极强的学科,在学习过程中,虽然,我们不一定会得到重大的数学成果.但我们可以在不断的总结和思索中发现规律,得到乐趣.下面,给大家介绍我由平常习题得到的两个结论:习题1求Cnm 3Cnm 1 3Cnm 2 Cnm 3的值.Cnm 3Cnm 1 2Cnm 2 Cnm 3=(Cnm Cnm 1) 2(Cnm 1 Cnm 2) (C