Description of Continuous Isometry Covariant Valuations on Convex Sets

We present a characterization of continuous isometry covariant valuations on convex sets. The main result generalizes previous results of Hadwiger and Hadwiger and Schneider.     

Density functional theory for molecular and periodic systems using density fitting and continuous fast multipole method: Stress tensor

A full implementation of the analytical stress tensor for periodic systems is reported in the TURBOMOLE program package within the framework of Kohn–Sham density functional theory using Gaussian-type orbitals as basis functions. It is the extension of the implementation of analytical energy gradients (Lazarski et al., Journal of Computational Chemistry 2016, 37, 2518–2526) to the stress tensor for the purpose of optimization of lattice vectors. Its key component is the efficient calculation of the Coulomb contribution by combining density fitting approximation and continuous fast multipole method. For the exchange-correlation (XC) part the hierarchical numerical integration scheme (Burow and Sierka, Journal of Chemical Theory and Computation 2011, 7, 3097–3104) is extended to XC weight derivatives and stress tensor. The computational efficiency and favorable scaling behavior of the stress tensor implementation are demonstrated for various model systems. The overall computational effort for energy gradient and stress tensor for the largest systems investigated is shown to be at most two and a half times the computational effort for the Kohn–Sham matrix formation. © 2019 Wiley Periodicals, Inc.     

Divagations about the periodic table: Boolean hypercube and quantum similarity connections

In this study, several simple aspects associated with the periodic table (PT) of the elements are commented. First, the connection of the PT with the structure of a seven-dimensional Boolean hypercube leads afterward to discuss the nature of those PT elements bearing prime atomic numbers. Second, the use of quantum similarity (QS) to obtain an alternative insight on the PT element relations will be also developed. The foundation of the second part starts admitting that any element of the PT can be attached to a schematic electronic density function, constructed with a single Gaussian function: a Gaussian atomic density function, allowing to consider the PT elements as a set of quantum objects, and permits a straightforward construction of a QS matrix. Such QS scheme can be applied to the whole PT or to any subset of it. Manipulation of the QS matrices attached to any quantum object set allows the evaluation of statistical-like values, acting as coordinates to numerically or graphically represent the chosen PT atomic element sets. © 2019 Wiley Periodicals, Inc.     

BSSE-correction scheme for consistent gaussian basis sets of double- and triple-zeta valence with polarization quality for solid-state calculations

Revised versions of our published pob-TZVP [Peintinger, M. F.; Oliveira, D. V. and Bredow, T., J. Comput. Chem., 2013, 34 (6), 451–459.] and unpublished pob-DZVP basis sets, denoted as pob-TZVP-rev2 and pob-DZVP-rev2, have been derived for the elements H Br. It was observed that the pob basis sets suffer from the basis set superposition error (BSSE). In order to reduce this effect, we took into account the counterpoise energy of hydride dimers as an additional parameter in the basis set optimization. The overall performance, portability, and SCF stability of the resulting rev2 basis sets are significantly improved compared to the original pob basis sets. © 2019 Wiley Periodicals, Inc.     

约束含参分岔问题的分类

约束边界与分岔参数有关的约束分岔问题,称为约束含参分岔问题．通过引入适当的变换,将约束含参分岔问题转化为新变量的非约束分岔问题,推导出了约束含参分岔问题转迁集的一般形式,结果表明只有约束分岔集受约束含参的影响,其它转迁集与不含参约束分岔的转迁集相同．以含参约束树枝分岔为例分析了此类问题的分岔分类,讨论了约束含参对分岔分类的影响．     

Existence of solutions for fourth-order boundary value problem with parameter

This paper is a sequel to a previous paper (Yang,Y.and Zhang,J.H.Existence of solutions for some fourth-order boundary value problems with parameters.Nonlinear Anal.69(2),1364–1375 (2008)) in which the nontrivial solutions to the fourthorder boundary value problems were studied.In the current work with the same conditions near infinity but different near zero,the positive,negative,and sign-changing solutions are obtained by the critical point theory,retracting property,and invariant sets.     

基于二元语义的犹豫模糊语言决策方法

当决策者在给出语言评价信息而表示出犹豫时,决策信息更适合用犹豫模糊语言术语集表达。为了减少语言决策过程中信息的丢失,得到较精准的评价结果,本文提出基于二元语义的犹豫模糊语言决策方法。首先定义了犹豫模糊二元语义集、犹豫模糊二元语义集的均值函数、方差函数及其集结算子,然后用集结算子求出各方案的综合评价值,通过犹豫模糊二元语义的均值函数和方差函数确定方案排序。最后通过实例说明了该方法的实用性和有效性。     

基于证据推理的直觉模糊多属性群决策方法

针对属性值为直觉模糊数的多属性群决策问题,提出了一种证据推理的扩展方法。首先,在考虑主观因素与客观因素的基础上运用直觉模糊熵法计算出属性及专家的综合权重。其次,提出一种基于证据推理的直觉模糊信息融合方法,该方法可以避免由于评价值的隶属度为0而导致的信息丢失现象,弥补了现有直觉模糊信息融合方法存在的不足。在此基础上,集结评价信息并按照备选方案与理想方案的相对贴近度对备选方案进行比选。最后,运用实例验证了所提方法的有效性。     

基于群体一致性的犹豫模糊多属性决策方法

犹豫模糊集允许一个元素属于一个集合的隶属度可以是多个不同的值,是表达决策者之间偏好不一致性的有力工具。针对决策者评价偏差不宜过大的问题,提出了一种基于群体一致性的犹豫模糊多属性决策方法。首先, 我们定义了犹豫模糊元的犹豫度函数,进而定义了犹豫模糊元的一致性指数;在此基础上,构建了基于群体一致性指数最大化的权重优化模型,通过求解优化模型可以得到属性的权重向量。然后,运用灰色关联分析法实现对方案的排序和择优。最后,通过实例分析说明了该方法的可行性和有效性。     

基于MC-ZF-HD-DS的高端装备制造企业持续创新能力评价研究

为客观和准确地评价高端装备制造企业的持续创新能力,建立了高端装备制造企业持续创新能力评价指标体系,采用MC-ZF-HD-DS对具体的高端装备制造企业持续创新能力进行评价。通过模糊粗糙集法对高频海选评价指标进行筛选,采用极差最大化组合赋权法对已筛选出的指标体系进行赋权,运用灰色定权聚类对评价对象进行聚类,在此基础上,运用证据理论对聚类结果进行合成,形成最终评价结果,最后通过实证分析验证了该方法的可行性和有效性。