“原子结构”教学中引入哲学理念

The structural discovery and understanding of atoms are a microcosm of the process of human cognition and a concrete practice of materialistic dialectics and methodology, which contains a wealth of dialectical thought. The "atomic structure" chapter (section) in inorganic chemistry course is a difficult part for the first-year undergraduates to understand. The introduction of philosophical idea into the teaching process of this chapter (section) will not only help them learn and master chemistry, but also help them establish a correct world view and methodology.     

On lower iteration complexity bounds for the convex concave saddle point problems

Mathematical Programming - In this paper, we study the lower iteration complexity bounds for finding the saddle point of a strongly convex and strongly concave saddle point problem: $$\min _x\max...     

On Cones of Nonnegative Quartic Forms

Historically, much of the theory and practice in nonlinear optimization has revolved around the quadratic models. Though quadratic functions are nonlinear polynomials, they are well structured and many of them are found easy to deal with. Limitations of the quadratics, however, become increasingly binding as higher-degree nonlinearity is imperative in modern applications of optimization. In recent years, one observes a surge of research activities in polynomial optimization, and modeling with quartic or higher-degree polynomial functions has been more commonly accepted. On the theoretical side, there are also major recent progresses on polynomial functions and optimization. For instance, Ahmadi et al. (Math Program Ser A 137:453–476, 2013) proved that checking the convexity of a quartic polynomial is strongly NP-hard in general, which settles a long-standing open question. In this paper, we proceed to study six fundamentally important convex cones of quartic forms in the space of super-symmetric tensors, including the cone of nonnegative quartic forms, the sums of squared forms, the convex quartic forms, and the sums of fourth-power forms. It turns out that these convex cones coagulate into a chain in a decreasing order with varying complexity status. Potential applications of these results to solve highly nonlinear and/or combinatorial optimization problems are discussed.     

An Extragradient-Based Alternating Direction Method for Convex Minimization

In this paper, we consider the problem of minimizing the sum of two convex functions subject to linear linking constraints. The classical alternating direction type methods usually assume that the two convex functions have relatively easy proximal mappings. However, many problems arising from statistics, image processing and other fields have the structure that while one of the two functions has an easy proximal mapping, the other function is smoothly convex but does not have an easy proximal mapping. Therefore, the classical alternating direction methods cannot be applied. To deal with the difficulty, we propose in this paper an alternating direction method based on extragradients. Under the assumption that the smooth function has a Lipschitz continuous gradient, we prove that the proposed method returns an \(\epsilon \)-optimal solution within \(O(1/\epsilon )\) iterations. We apply the proposed method to solve a new statistical model called fused logistic regression. Our numerical experiments show that the proposed method performs very well when solving the test problems. We also test the performance of the proposed method through solving the lasso problem arising from statistics and compare the result with several existing efficient solvers for this problem; the results are very encouraging.     

Ku波段扩展互作用速调管设计

 微波电真空器件随着频率的升高,不但聚焦系统难以实现,而且其输出增益和带宽都受到很大的限制,要解决该问题,建议采用扩展互作用速调管,采用分布作用谐振腔技术来扩展其工作带宽和提高增益。利用CST和粒子模拟(PIC)3维软件对其工作在Ku波段扩展互作用速调管进行了设计和仿真,在工作电压30 kV、束流8.5 A的条件下,聚焦系统采用幅值为0.48 T的周期反转永磁聚焦,在输入功率为5.1 W时,得到效率为23%,3 dB带宽为306 MHz,频带内最大增益为39 dB,其峰值功率为58 kW的微波输出。     

云爆药剂爆炸超压测试及威力评价

借助压力测试系统,在自由场及地面布置压力传感器,分别测量了熔铸TNT、一次云爆药剂和二次云爆药剂在自由场和地面的爆炸场冲击波超压,经分析处理后拟合得到适用于3种炸药的自由场和空中爆炸超压发展公式,并计算云爆药剂的TNT当量。实验结果表明:实验选用的二次云爆药剂的自由场和地面平均TNT当量相比一次云爆药剂分别提高了60%和69%,说明二次云爆药剂比一次云爆药剂具有更大的超压作用效果;3种药剂的自由场超压峰值都比地面小10%左右,说明地面的反射效应依旧存在,在实际超压威力评估时应采用一定的修正系数。实验结果可丰富云爆药剂和传统炸药的小当量实验对比数据,为云爆药剂爆炸场参数的研究和威力评估提供参考。     

恒电流库仑分析法测定硫酸亚铁铵等基准试剂的纯度

在1．8mol／L硫酸介质中,以恒电流通过含有Mn^2＋的电解质溶液,使工作电极铂阳极上电生出Mn^3＋,Mn^3＋与溶液中待测基准试剂硫酸亚铁铵、草酸钠或草酸定量反应,以永停终点法确定库仑滴定终点,通过测量电解电流及电解时间,利用法拉弟电解定律计算基准试剂的纯度。该方法的相对误差为0．32％～0．36％,测量结果的相对标准偏差为0．045％-0．050％（n=11）。     

Gain-clamped dual-stage L-band EDFA by using backward C-band ASE

A dual-stage L-band gain-clamped erbium-doped fiber amplifier (GC-EDFA) by using backward C-band amplified spontaneous emission (ASE) is proposed. Compared with other similar GC-EDFAs, the proposed structure has higher and flatter clamped gain in L-band because of its optimal pump power and EDF length. The flatness from 1570 nm to 1600 nm arrives 0.77 dB, the bandwidth of 3 dB is more than 35 nm and the maximal input signal power arrives −15 dBm.