Density Functional Theory as a Data Science

The development of density functional theory (DFT) functionals and physical corrections are reviewed focusing on the physical meanings and the semiempirical parameters from the viewpoint of data science. This review shows that DFT exchange‐correlation functionals have been developed under many strict physical conditions with minimizing the number of the semiempirical parameters, except for some recent functionals. Major physical corrections for exchange‐correlation function‐ als are also shown to have clear physical meanings independent of the functionals, though they inevitably require minimum semiempirical parameters dependent on the functionals combined. We, therefore, interpret that DFT functionals with physical corrections are the most sophisticated target functions that are physically legitimated, even from the viewpoint of data science.     

Slodkowski定理的Chirka证明的一些注解(英文)

通过在一个积分算子上运用Schauder不动点定理,Chirka对Slokowski的全纯运动扩张定理提供了一个优美的简单证明.本文中,作者对构造此证明的启发提供一个参考同时用此方法通过不同方式来构造全纯扩张.一个自然的问题是研究这些用不同方式得到的全纯扩张是否相同.因此对全纯扩张唯一性已有的判断法提供一个简单的综述.最后介绍在全纯扩张唯一性存在时的一个应用.     

A Normal Criterion Concerning Omitted Holomorphic Function

In this paper, we continue to discuss the normality concerning omitted holomorphic function and get the following result. Let F be a family of meromorphic functions on a domain D, k ≥ 4 be a positive integer, and let a(z) and b(z) be two holomorphic functions on D, where a(z) 0 and f(z) ≠ ∞ whenever a(z)=0. If for any f ∈ F, f'(z) -a(z)f^k(z) ≠ b(z), then F is normal on D.     

采用(meta)-GGA泛函对Ag(111)、Rh(111)和Ir(111)上乙烯吸附的理论研究

本文针对在多种催化反应的重要中间体乙烯,使用(meta)-GGA等级的包含PBE,BEEF-vdW,SCAN以及SCAN+rVV10在内的多种交换关联泛函,系统研究了在过渡金属表面(Ag,Rh和Ir)上乙烯吸附势能面对泛函的依赖关系. 研究发现,对于乙烯在贵金属Ag(111)上的吸附,除了PBE外,BEEF-vdW,SCAN以及SCAN+rVV10均能预测出物理吸附态的存在. 对于乙烯在Rh(111)面的吸附,SCAN和SCAN+rVV10预测在化学吸附位之前存在有物理吸附前驱态,而基于PBE和BEEF-vdW的势能面并没有发现前驱态的存在. 而对于乙烯在Ir(111)上的吸附,BEEF-vdW也能微弱地预测出化学吸附前驱态的存在. 研究结果表明,无论在哪一种金属表面上,四种泛函中SCAN+rVV10给出的吸附能最强,其次是SCAN,最后是PBE或者BEEF-vdW.     

Determining the role of the underlying orbital‐dependence of PBE0‐DH and PBE‐QIDH double‐hybrid density functionals

We study the orbital‐dependence of three (parameter‐free) double‐hybrid density functionals, namely the PBE0‐DH, the PBE‐QIDH models, and the SOS1‐PBE‐QIDH spin‐opposite‐scaled variant of the latter. To do it, we feed all their energy terms with different sets of orbitals obtained previously from self‐consistent density functional theory calculations using several exchange‐correlation functionals (e.g., PBE, PBE0, PBEH&H), or directly with HF‐PBE orbitals, to see their effect on selected datasets for atomization and reaction energies, the latter proned to marked self‐interaction errors. We find that the PBE‐QIDH double‐hybrid model shows a great consistency, as the best results are always obtained for the set of orbitals corresponding to its hybrid scheme, which prompts us to recommend this model without any other fitting or reparameterization. © 2017 Wiley Periodicals, Inc.     

Non-commutative complex differential geometry

This paper defines and examines the basic properties of non-commutative analogues of almost complex structures, integrable almost complex structures, holomorphic curvature, cohomology, and holomorphic sheaves. The starting point is a differential structure on a non-commutative algebra defined in terms of a differential graded algebra. This is compared to current ideas on non-commutative algebraic geometry.     

Banach空间中全纯映射的若干性质

本文将全纯映射的若干性质推广到Ｂａｎａｃｈ空间，并应用这些性质研究有界域中的凸映射与星形映射．     

Locally Asplund Preduals of Spaces of Holomorphic Functions

Defant [5] introduced the local Radon–Nikodym property for duals of locally convex spaces. This is a generalization of Asplund spaces as defined in Banach space theory. In this paper we generalise Dunford"s Theorem [7] to Banach spaces with Schauder decompositions and apply this result to spaces of holomorphic functions on balanced domains in a Banach space. This revised version was published online in June 2006 with corrections to the Cover Date.