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.     

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.     

有界平均振幅空间上的乘法算子

有界平均振幅空间的研究在算子理论及全纯空间的研究中具有重要的作用.主要研究了有界平均振幅空间上乘法算子的性质,并且得到了托普里兹算子有界性及紧性的条件.     

多重调和Bergman空间上径向Toeplitz算子的交换性

In this paper, we study the commutativity of Toeplitz operators with radial symbols on the pluriharmonic Bergman space. We obtain the necessary and sufficient conditions for the commutativity of bounded Toeplitz operator and Toeplitz operator with radial symbol on the pluriharmonic Bergman space.     

Solvent-Free Mechanochemical Synthesis of Aryl Glycosides[ 1 ]

Aryl glycosides have been prepared from a range of readily available glycosyl halides by a solvent-free mechanochemical procedure employing a planetary ball mill in excellent yields. Besides being a solvent-free reaction, the procedure has been successful in eliminating the need for employing any phase-transfer catalyst in the reaction.     

Effects of ball-to-powder diameter ratio and powder particle shape on EDEM simulation in a planetary ball mill

The effects of the ball-to-powder diameter ratio (BPDR) and the shape of the powder particles on EDEM simulation results and time in the planetary ball mill was investigated. BPDR was varied from 1 to 40/3 by changing the powder particle diameter from 8 to 0.6 ?mm. The size and shape of the powder particles do not give a significant change in both the ball motion pattern and simulation results when BPDR is over 20/3. It can be assumed that the kinetic energy of the ball has nothing to do with the size and shape of the powder particle. The simulation time and data size increase exponentially as BPDR increases. The effect of change of the powder particle shape on the calculated data size is not significant, but the more complicated its shape, the longer the simulation time, which is linearly related to the number of spheres composing a particle.     

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。     

Inverse Hall–Petch like behaviour in a mechanically milled nanocrystalline Al5Fe2 intermetallic phase

In the present investigation, the indentation study on the high-energy ball-milled nanocrystalline Al₅Fe₂ intermetallic compound has established the inverse Hall–Petch (IHP) behaviour. The structural characterisation of the milled powder particles by X-ray diffraction (XRD) and transmission electron microscopy has shown the evolution of nanocrystalline phase. Micro-indentation measurements have revealed the increase in hardness with decreasing grain size, reaching to a maximum of 9.0 ± 0.3 GPa up to a grain size of 32 ± 4 nm, followed by a decrease. The decrease in hardness with further refinement, an indication of grain size softening, demonstrates the IHP-like behaviour. The deviation from the Hall–Petch behaviour has been discussed using various models based on the dislocations and grain boundary-mediated processes. From the analysis, it appears that the model based on mesocopic grain boundary sliding phenomena is more appropriate to account for the observed grain size softening.     

Low temperature synthesis and luminescence investigations of YAG:Ce,Eu nanocomposite powder for warm white light-emitting diode

The preparation of the cerium and europium co-doped YAG materials as well as the study for their synthesis and emitting mechanism of the energy transfer between Ce³⁺ and Eu³⁺ were investigated in the present study. YAG:Ce³⁺, Eu³⁺ powders were synthesized using a high-energy ball milling method in different sintering temperature and atmosphere: air and H₂/N₂. The effects of the synthesis procedure on the crystallinity, morphology, structure, and luminescence spectra were examined by X-ray diffraction, field emission-scanning electron microscopy, and photoluminescence spectroscopy. The europium co-doped YAG:Ce³⁺ phosphors is improved the chromaticity coordinates.