Eigenvalues of the k‐th power of a graph

The k‐th power of a graph G, denoted by , is a graph with the same set of vertices as G such that two vertices are adjacent in if and only if their distance in G is at most k. In this paper, we give the bounds on the spectral radius of and . The Nordhaus–Gaddum‐type inequality for the spectral radius of the graph is also presented. Moreover, we obtain an upper bound on the energy of the second power of graphs.     

Stability analysis of the Pareto optimal solutions for some vector boolean optimization problem

In this article we consider the boolean optimization problem of finding the set of Pareto optimal solutions. The vector objectives are the positive cuts of linear functions to the non-negative semi-axis. Initial data are subject to perturbations, measured by the l ₁-norm in the parameter space of the problem. We present the formula expressing the extreme level (stability radius) of such perturbations, for which a particular solution remains Pareto optimal.     

Extremal graph characterization from the bounds of the spectral radius of weighted graphs

We consider weighted graphs, where the edge weights are positive definite matrices. The eigenvalues of a graph are the eigenvalues of its adjacency matrix. We obtain a lower bound and an upper bound on the spectral radius of the adjacency matrix of weighted graphs and characterize graphs for which the bounds are attained.     

Improved Bohr’s inequality for locally univalent harmonic mappings

We prove several improved versions of Bohr’s inequality for the harmonic mappings of the form $f=h+\overline{g}$, where $h$ is bounded by 1 and $\left|g^{\prime }\left(z\right)\right|\le \left|h^{\prime }\left(z\right)\right|$. The improvements are obtained along the lines of an earlier work of Kayumov and Ponnusamy, i.e. (Kayumov and Ponnusamy, 2018) for example a term related to the area of the image of the disk $D(0,r)$ under the mapping $f$ is considered. Our results are sharp. In addition, further improvements of the main results for certain special classes of harmonic mappings are provided.     

一般矩阵函数的不等式

本文研究一般矩阵函数不等式.运用一般矩阵函数的两个公式和lp-范数的性质,结出了两个矩阵运算的一般矩阵函数不等式.     

高能机械球磨法制备V-Ti-O超细微粒催化剂

负载型V2O5/TiO2氧化物催化剂因具有优良的催化性能而广泛地用于烃类选择性氧化[1,2]和氮氧化物选择性催化还原(SCR)[3]. 迄今,所研究的负载型V2O5/TiO2氧化物催化剂大多是采用浸渍法制备的[2,4～6],通过调整催化剂的组成[2,5]、引入适当的助剂组分[2,6]和选择适宜的反应操作条件[2,5]可进一步优化其催化性能.     

Factors affecting the nodule size of asymmetric PMMA membranes

Several factors that may affect the surface nodule size of a polymeric membrane were under investigation. The increase of polymer concentration and molecular weight were found to increase the surface nodule size. The increase of casting temperature also resulted in an increase in nodule size. These results supported that the radius of gyration and the collision frequency between polymer chains were the key factors affecting the nodule size. However, when the radius of gyration was reduced by the use of a poor solvent or by pre-adding nonsolvent in the casting solution, the surface nodule size increased. It suggested that there existed other factors affecting the nodule size on membrane surface besides the gyration radius and the collision frequency of polymer chains. In this study, we found in most cases that the surface nodule size decreased along with the surface tension difference between the casting solution and the coagulant. To demonstrate the effect of surface tension, we examined the nodule size inside the membranes where the nodule formation was not significantly affected by the interfacial tension. Opposite to what was observed on the surface, the nodule size increased with the solvation power of the solvent. This result suggested that it was the interfacial tension that overpowered the gyration radius in affecting the surface nodule size.     

A kind of carbon whiskers in new structure and morphology

Carbon whiskers with new structure and morphology were observed when heating the milled graphite. Transmission electron microscopy (TEM) and high resolution electron microscopy (HREM) show that carbon layers are almost perpendicular to the growth axes of carbon whiskers. Field emission scanning electron microscopy (FESEM) indicates that there are spirals appearing on the surface of the whiskers. The structure analysis shows that the growth mechanism of carbon whiskers is related to the trace amount of ZrC in the heated samples.     

Synergetic catalytic effect of rGO,Pd, Fe3O4 and PPy as a magnetically separable and recyclable nanocomposite for coupling reactions in green media

In this paper, rGO/Pd–Fe₃O₄@PPy as an efficient stable nanocomposite was synthesized. To understand the synergetic effects of rGO, Pd, Fe₃O₄ and PolyPyrrole, the performance of rGO/Pd–Fe₃O₄@PPy as a heterogeneous recyclable nanocatalyst in the green synthesis of C‐C and C‐O coupling products, as well as different conditions are studied. Synthesized rGO/Pd–Fe₃O₄@PPy was characterized by FT‐IR, XRD, FE‐SEM, EDS, TGA and AFM analysis. Best results are obtained under sonication in H₂O for C‐C coupling and by ball‐milling for C‐O coupling. The benefits of this method include: green solvents and conditions, absence of external base, low reaction times with high yield and easy work‐up method.     

黑磷的制备及表征研究

黑磷是一种具有高的载流子迁移率、高的通断比,带隙为0.3~2 eV的二维材料,对中红外、近红外新型光电器件的开发具有十分重要的意义.本文利用高能球磨法和化学气相转移法成功将红磷转化为黑磷,并进行液相剥离,得到了一层或两层的磷烯.利用X射线衍射仪、透射电子显微镜、差示扫描量热仪对其微观结构和稳定性进行了研究,并表征了化学气相转移法制备黑磷的电学性能.结果表明：高能球磨法制备的黑磷尺寸小、结晶度低,样品中有红磷存在,稳定性差.化学气相转移法制备的黑磷尺寸大、结晶度好、纯度高,且较为稳定.此方法制备的黑磷可成为剥离磷烯的优异原料,进而应用于先进微电子器件.