Joint distributions of random sets and their relation to copulas

Random sets are set-valued random variables. They have been applied in various fields like stochastic geometry, statistics, economics, engineering or computer science, and are often used for modeling uncertainty. In an earlier paper the author has defined joint capacity and joint containment functionals which are multivariate set functions describing the joint distribution of random sets. This paper is concerned with the question how copulas can be used to describe or model the dependence of random sets. It is demonstrated that a joint containment functional can be related to its margins by a family of copulas. Furthermore, the paper provides a first insight how copulas can be used to define joint containment functionals.     

On the Nano/Micro-Mechanics of Metallic Glass

Metallic glass (MG) is amorphous and has some outstanding properties such as ultrahigh strength, superior elasticity, and excellent thermo-plasticity. However, as MG is relatively new to the metal family, the relationship between its physical properties and amorphous structure is still unclear. This article aims to provide an insightful discussion through a comprehensive review about the investigations in the past few decades on the scientific mechanisms of this class of material. The discussion of the paper will include the following key aspects: (1) the formation mechanism of an amorphous structure through glass transition, (2) the structural characterization and models, (3) the micromechanics of plastic event and shear band, and (4) the correlation between the amorphous structure and its mechanical properties.     

Gold‐Catalyzed 1,2‐Acyloxy Migration/Intramolecular [3+2] 1,3‐Dipolar Cycloaddtion Cascade Reaction: An Efficient Strategy for Syntheses of Medium‐Sized‐Ring Ethers and Amines

A highly efficient strategy for the formation of medium‐sized‐ring ethers and amines based on a gold‐catalyzed cascade reaction, involving enynyl ester isomerization and intramolecular [3+2] cyclization, has been developed. Various multisubstituted medium‐sized‐ring unsaturated ethers and amines were obtained through this transformation. This method represents one of the relatively few transition metal catalyzed intramolecular cycloaddition reactions for medium‐sized ring synthesis.     

Theoretical investigation on submicron particle penetration through circular tubes inside a porous medium

The analytical infinite series solution of submicron particle transport in a circular tube bounded by a porous wall, such as a pinhole, is determined under the slip velocity boundary condition, and the solution is verified by using the experimental data in the previous studies for the specific cases. The results show that particle penetration rate increases with the increase of the porous parameter, the axial pressure drop, and the pinhole radius, whereas it decreases with increasing the pinhole length. The penetration rate of nano-particles are more sensitive to the variation of these parameters. However, the differences between the penetrations of particles ranging from 0.3 μm to 1 μm are not evident because the diffusion becomes weak gradually in this size range. In addition, a further comparison is performed between the analytical solution and the existing studies, and approximate expressions are presented for accurate calculation of particle penetration rate through pinholes appearing in porous materials including filter devices and masks.     

虚拟原子探针随机采样法用于氨基酸结构描述及其构效关系研究

考虑药物与蛋白质受体的3类非键作用模式, 利用8类虚拟原子探针和Monte Carlo随机采样技术, 得到了一套新的氨基酸侧链表面静电、立体及疏水势能场(ASSPF)参数. 在此基础上对苦味二肽和血管舒缓激五肽进行了结构表征和QSAR研究, 所建模型复相关系数R2和留一法交互检验复相关系数QLOOCV2分别为0.8457, 0.851和0.7688, 0.7952, 同时分析了肽链不同位置上氨基酸侧链对活性的影响, 取得较好的结果.     

与色散介质毗邻的一维半无限光子晶体表面态

运用Bloch定理和传输矩阵方法,研究了与色散介质毗邻的由两种材料组成的半无限一维光子晶体局域表面态的电场和色散关系.和以空气为背景的一维光子晶体相比,毗邻色散介质的光子晶体表面模色散曲线在一定堆积次序下会在较低的带隙中发生断开,较高带隙中的表面模群速度在不同堆积次序下会有很大差异.当与色散介质毗邻的物质折射率较大时,较高带隙中的表面模群速度较小;与色散介质毗邻的物质折射率较小时,较高带隙中表面模的群速度较大.     

求解一阶隐微分方程的微分法与参数法及奇解注记

主要指出了微分法与参数法的实质及二者的本质区别,以及求奇解的一个注意事项.     

一种可能的简并谱NNS分布

To expose the statistical properties of the degenerated spectrum, with the aid of the random matrix theory,a possible form of the NNS distribution function of the degenerate spectrum was proposed by providing a solution in terms of the same-degeneracy case. The results indicate that the target spectrum is transformed into two sub-spectra: a random one and a regular one, and that the repulsion level of the regular spectrum is also decreased.     

三元层状MAX相固溶体研究进展

MAX相是一类具有层状结构的三元碳化物或(和)氮化物,M是过渡金属元素,A主要是ⅢA~ⅤA族元素,X是C或N元素。这类化合物兼具陶瓷材料和金属材料的特点,具有优异的导电、导热、耐腐蚀以及抗氧化等性能,在诸多领域具有潜在应用价值。近年来,新元素、新结构和固溶体MAX相的不断出现,进一步扩展了MAX相家族。固溶体MAX相是将合适的元素固溶到已知MAX相中而得到的新MAX相。本文分四类总结了127种MAX相固溶体,对其结构改变和性能调控进行了概括,并指出目前研究存在的理论问题和亟须解决的关键技术,最后对MAX相固溶体的发展进行了预测和展望。