A branch-and-bound method for the minimum k−enclosing ball problem

The minimum k-enclosing ball problem seeks the ball with smallest radius that contains at least k of m given points. This problem is NP-hard. We present a branch-and-bound algorithm on the tree of the subsets of k points to solve this problem. Our method is able to solve the problem exactly in a short amount of time for small and medium sized datasets.     

氧化铝/氮化硅双层膜晶硅钝化的开尔文探针力显微镜研究

对晶体硅(c-Si)太阳能电池而言, 氧化铝(AlOx)是一种广泛使用的钝化材料, 因为它具有优异的沉积保形性和良好的钝化质量. 为了确保AlOx发挥其良好的钝化效果, 在沉积后退火并氢化处理是必不可少的. 通过在AlOx薄膜上沉积氢化氮化硅(SiNx:H)来实现氢化, 利用开尔文探针力显微镜研究了在不同热处理和氢化作用下, AlOx/SiNx:H双层薄膜功函数的变化, 并基于沉积薄膜所含氢与固定电荷展开了讨论. 发现钝化质量和功函数之间有相关性, 影响因素包括薄膜厚度、氢化与热处理顺序.     

Wave packet dynamics of nonlinear Gazeau–Klauder coherent states of a position-dependent mass system in a Coulomb-like potential

AD = 1 position-dependent mass approach to constructing nonlinear quantum states for a modified Coulomb potential is used to generate Gazeau–Klauder coherent states. It appears that their energy eigenvalues are scaled down by the quantum number and the nonlinearity coefficient. We study the basic properties of these states, which are found to be undefined on the whole complex plane, and some details of their revival structure are discussed.     

Addendum to “On the Riesz potential operator of variable order from variable exponent Morrey space to variable exponent Campanato space”, Math Meth Appl Sci. 2020; 1–8

In the paper mentioned in the title, it is proved the boundedness of the Riesz potential operator of variable order α(x) from variable exponent Morrey space to variable exponent Campanato space, under certain assumptions on the variable exponents p(x) and λ(x) of the Morrey space. Assumptions on the exponents were different depending on whether $\frac{\alpha (x)p(x)?n+\lambda (x)}{p(x)}$ takes or not the critical values 0 or 1. In this note, we improve those results by unifying all the cases and covering the whole range $0?\frac{\alpha (x)p(x)?n+\lambda (x)}{p(x)}?1$. We also provide a correction to some minor technicality in the proof of Theorem 2 in the aforementioned paper.     

Additive Hermitian idempotent preservers between operator algebras

Let L be an additive map between (real or complex) matrix algebras sending $n\times n$ Hermitian idempotent matrices to $m\times m$ Hermitian idempotent matrices. We show that there are nonnegative integers $p,q$ with $n(p+q)=r\le m$ and an $m\times m$ unitary matrix U such that$L(A)=U[(I_p?A)\oplus (I_q?A^t)\oplus 0_{m?r}]U^{?},\text{for any}n\times n\text{Hermitian}A\text{with rational trace}.$ We also extend this result to the (complex) von Neumann algebra setting, and provide a supplement to the Dye-Bunce-Wright Theorem asserting that every additive map of Hermitian idempotents extends to a Jordan ?-homomorphism.     

A−H…σ Hydrogen Bonds: Dihydrogen and Cycloalkanes as Proton Acceptors

ωB97XD/aug-cc-pVTZ calculations were performed for complexes of dihydrogen, cyclopropane, cyclobutane and cyclopentane, with simple proton donating species such as hydrogen fluoride, hydrogen chloride, water, hydrogen cyanide and acetylene. Numerous dependencies between geometrical, energetic and topological parameters of complexes considered were found, since various theoretical approaches were applied: Quantum Theory of ‘Atoms in Molecules’ (QTAIM), Natural Bond Orbital (NBO) method and energy decomposition analysis (EDA). It was confirmed that complexes of dihydrogen and cyclopropane are linked through the A−H…σ interactions that may be classified as hydrogen bonds. In the case of complexes of cyclobutane such hydrogen bonds are rather weak. Other type and also weak A−H…C hydrogen bonds are formed for complexes with cyclopentane.     

Mechanism and rate constants of the CH2 + CH2CO reactions in triplet and singlet states: A theoretical study

Ab initio and density functional CCSD(T)-F12/cc-pVQZ-f12//B2PLYPD3/6-311G** calculations have been performed to unravel the reaction mechanism of triplet and singlet methylene CH₂ with ketene CH₂CO. The computed potential energy diagrams and molecular properties have been then utilized in Rice–Ramsperger–Kassel–Marcus-Master Equation (RRKM-ME) calculations of the reaction rate constants and product branching ratios combined with the use of nonadiabatic transition state theory for spin-forbidden triplet-singlet isomerization. The results indicate that the most important channels of the reaction of ketene with triplet methylene lead to the formation of the HCCO + CH₃ and C₂H₄ + CO products, where the former channel is preferable at higher temperatures from 1000 K and above. In the C₂H₄ + CO product pair, the ethylene molecule can be formed either adiabatically in the triplet electronic state or via triplet-singlet intersystem crossing in the singlet electronic state occurring in the vicinity of the CH₂COCH₂ intermediate or along the pathway of CO elimination from the initial CH₂CH₂CO complex. The predominant products of the reaction of ketene with singlet methylene have been shown to be C₂H₄ + CO. The formation of these products mostly proceeds via a well-skipping mechanism but at high pressures may to some extent involve collisional stabilization of the CH₃CHCO and cyclic CH₂COCH₂ intermediates followed by their thermal unimolecular decomposition. The calculated rate constants at different pressures from 0.01 to 100 atm have been fitted by the modified Arrhenius expressions in the temperature range of 300–3000 K, which are proposed for kinetic modeling of ketene reactions in combustion. © 2018 Wiley Periodicals, Inc.