On weighted spectral radius of unraveled balls and normalized Laplacian eigenvalues

For a graph G, the unraveled ball of radius r centered at a vertex v is the ball of radius r centered at v in the universal cover of G. We obtain a lower bound on the weighted spectral radius of unraveled balls of fixed radius in a graph with positive weights on edges, which is used to present an upper bound on the $s^{\text{th}}$ (where $s\ge 2$) smallest normalized Laplacian eigenvalue of irregular graphs under minor assumptions. Moreover, when $s=2$, the result may be regarded as an Alon–Boppana type bound for a class of irregular graphs.     

现代分析仪器在高中化学教学中的应用*——以“防晒霜的防晒效果实验探究”为例

从高中化学原子、分子等抽象性的知识教学出发,以防晒霜的防晒效果实验探究为例,探讨了现代分析仪器在高中化学教学中的应用。通过利用现代分析仪器紫外可见分光光度计,结合紫外线变色球实验探究防晒霜的防晒效果,分析并认识防晒霜中化学防晒的机理。结果表明,防晒霜的厚度越大、SPF越高,防晒霜的防晒效果越好,并且防晒霜的防晒效果可以持续一段时间,但是不同类型的防晒产品存在一定差异。在化学教学中渗透现代分析仪器的应用,为学生进一步了解化学学科在改变学习方式、拓宽学科知识领域、推动自身全面与可持续发展方面打下坚实的基础。     

On the complexity of extending the convergence ball of Wang’s method for finding a zero of a derivative

Ball convergence results are very important, since they demonstrate the complexity in choosing initial points for iterative methods. One of the most important problems in the study of iterative methods is to determine the convergence ball. This ball is small in general restricting the choice of initial points. We address this problem in the case of Wang’s method utilized to determine a zero of a derivative. Finding such a zero has many applications in computational fields, especially in function optimization. In particular, we find the convergence ball of Wang’s method using hypotheses up to the second derivative in contrast to earlier studies using hypotheses up to the fourth derivative. This way, we also extend the applicability of Wang’s method. Numerical experiments used to test the convergence criteria complete this study.     

A branch-and-bound method for the minimum k−enclosing ball problem

The minimum k-enclosing ball problem seeks the ball with smallest radius that contains at least k of m given points. This problem is NP-hard. We present a branch-and-bound algorithm on the tree of the subsets of k points to solve this problem. Our method is able to solve the problem exactly in a short amount of time for small and medium sized datasets.     

基于相场描述的拉压不对称强度结构拓扑优化

运用了基于相场描述的拓扑优化方法，来寻找在拉伸和压缩中表现出不对称强度行为的连续体结构的最优布局。依据Drucker-Prager屈服准则和幂率插值方案，优化问题可以描述为在局部应力约束下的最小化结构的体积。用qp放松法来解决应力约束的奇异性，并采用基于P-norm函数的聚合方法对应力约束进行凝聚，该方法实现了约束个数的降低，同时引入了稳定转化法来处理大量的局部应力约束和高度非线性的应力行为，以修正应力，提高优化收敛的稳定性。在优化问题求解时，使用拉格朗日乘子法对目标函数和应力约束进行处理。利用伴随变量法进行灵敏度分析，并通过求解Allen-Cahn方程更新相场函数设计变量。数值算例证明了该优化模型和相应数值技术的有效性，相关算例还揭示了考虑拉压不同强度和考虑同拉压强度约束时得到的结构优化拓扑构型具有显著的差异。     

Conventional vs. Microwave- or Mechanically-Assisted Synthesis of Dihomooxacalix[4]arene Phthalimides: NMR,X-ray and Photophysical Analysis §

Direct O-alkylation of p-tert-butyldihomooxacalix[4]arene (1) with N-(bromopropyl)- or N-(bromoethyl)phthalimides and K₂CO₃ in acetonitrile was conducted under conventional heating (reflux) and using microwave irradiation and ball milling methodologies. The reactions afforded mono- and mainly distal di-substituted derivatives in the cone conformation, in a total of eight compounds. They were isolated by column chromatography, and their conformations and the substitution patterns were established by NMR spectroscopy (¹H, ¹³C, COSY and NOESY experiments). The X-ray structures of four dihomooxacalix[4]arene phthalimide derivatives (2a, 3a, 3b and 5a) are reported, as well as their photophysical properties. The microwave (MW)-assisted alkylations drastically reduced the reaction times (from days to less than 45 min) and produced higher yields of both 1,3-di-substituted phthalimides (3a and 6a) with higher selectivity. Ball milling did not reveal to be a good method for this kind of reaction.     

Comprehensive performance of a ball-milled La0.5Pr0.5Fe11.4Si1.6B0.2Hy/Al magnetocaloric composite

Due to the hydrogen embrittlement effect, La(Fe,Si)₁₃-based hydrides can only exist in powder form, which limits their practical application. In this work, ductile and thermally conductive Al metal was homogeneously mixed with La_0.5Pr_0.5Fe_11.4Si_1.6B_0.2 using the ball milling method. Then hydrogenation and compactness shaping of the magnetocaloric composites were performed in one step via a sintering process under high hydrogen pressure. As the Al content reached 9 wt.%, the La_0.5Pr_0.5Fe_11.4Si_1.6B_0.2H_y/Al composite showed the mechanical behavior of a ductile material with a yield strength of ~44 MPa and an ultimate strength of 269 MPa accompanied by a pronounced improvement in thermal conductivity. Due to the ease of formation of Fe-Al-Si phases and the several micron and submicron sizes of the composite particles caused by ball milling process, the magnetic entropy change of the composites was substantially reduced to ~1.2 J/kg· K-1.5 J/kg· K at 0 T-1.5 T.     

水热法制备锂电池Si@C负极材料的工艺优化研究

水热法是广泛应用于锂离子电池Si@C电极材料的一种制备方法,其反应条件是影响产物最终形貌和性能的重要因素, 采取最佳的反应工艺可以大大提升材料的电化学性能。本研究中, 使用葡萄糖作为碳源, 光伏切割废料硅为硅源, 探究了水热法制备核壳结构Si@C电极材料的最优工艺, 分别研究了温度、 原料浓度、 反应时间和原料比例对产物的形貌、 性能的影响以及相互之间的关系, 并得到最佳反应条件。在该条件下(葡萄糖浓度为0.5 mol·L^-1, 硅与葡萄糖重量比为0.3:1, 反应温度190 ^oC, 反应时间9 h), 得到了包覆完整、 粒径适中的Si@C电极材料(CS190-3), 对以该样品为负极的扣式半电池进行电化学测试, 在655 mA·g^-1的电流密度下, 其首圈放电比容量为3369.5 mAh·g^-1, 经过500次循环剩余容量为1405.0 mAh·g^-1。倍率测试中, 在6550 mA·g^-1的电流密度下,其剩余容量为937.1 mAh·g^-1,当电流密度恢复至655 mA·g^-1时,电池放电比容量仍可恢复至1683.0 mAh·g^-1。