Accurate Kohn–Sham ionization potentials from scaled‐opposite‐spin second‐order optimized effective potential methods

One important property of Kohn–Sham (KS) density functional theory is the exact equality of the energy of the highest occupied KS orbital (HOMO) with the negative ionization potential of the system. This exact feature is out of reach for standard density‐dependent semilocal functionals. Conversely, accurate results can be obtained using orbital‐dependent functionals in the optimized effective potential (OEP) approach. In this article, we investigate the performance, in this context, of some advanced OEP methods, with special emphasis on the recently proposed scaled‐opposite‐spin OEP functional. Moreover, we analyze the impact of the so‐called HOMO condition on the final quality of the HOMO energy. Results are compared to reference data obtained at the CCSD(T) level of theory. © 2016 Wiley Periodicals, Inc.     

On regularization of plurisubharmonic functions near boundary points

We prove in an elementary way that for a Lipschitz domain \(D\subset \mathbb {C}^n\), all plurisubharmonic functions on D can be regularized near any boundary point.     

Support-type properties of convex functions of higher order and Hadamard-type inequalities

It is well known that every convex function (where I⊂R is an interval) admits an affine support at every interior point of I (i.e. for any x₀∈IntI there exists an affine function such that a(x₀)=f(x₀) and a?f on I). Convex functions of higher order (precisely of an odd order) have a similar property: they are supported by the polynomials of degree no greater than the order of convexity. In this paper the attaching method is developed. It is applied to obtain the general result—Theorem 2, from which the mentioned above support theorem and some related properties of convex functions of higher (both odd and even) order are derived. They are applied to obtain some known and new Hadamard-type inequalities between the quadrature operators and the integral approximated by them. It is also shown that the error bounds of quadrature rules follow by inequalities of this kind.     

Real-World Data Difficulty Estimation with the Use of Entropy

In the era of the Internet of Things and big data, we are faced with the management of a flood of information. The complexity and amount of data presented to the decision-maker are enormous, and existing methods often fail to derive nonredundant information quickly. Thus, the selection of the most satisfactory set of solutions is often a struggle. This article investigates the possibilities of using the entropy measure as an indicator of data difficulty. To do so, we focus on real-world data covering various fields related to markets (the real estate market and financial markets), sports data, fake news data, and more. The problem is twofold: First, since we deal with unprocessed, inconsistent data, it is necessary to perform additional preprocessing. Therefore, the second step of our research is using the entropy-based measure to capture the nonredundant, noncorrelated core information from the data. Research is conducted using well-known algorithms from the classification domain to investigate the quality of solutions derived based on initial preprocessing and the information indicated by the entropy measure. Eventually, the best 25% (in the sense of entropy measure) attributes are selected to perform the whole classification procedure once again, and the results are compared.     

Copper Oxide-Based Photocatalysts and Photocathodes: Fundamentals and Recent Advances

This work aims at reviewing the most impactful results obtained on the development of Cu-based photocathodes. The need of a sustainable exploitation of renewable energy sources and the parallel request of reducing pollutant emissions in airborne streams and in waters call for new technologies based on the use of efficient, abundant, low-toxicity and low-cost materials. Photoelectrochemical devices that adopts abundant element-based photoelectrodes might respond to these requests being an enabling technology for the direct use of sunlight to the production of energy fuels form water electrolysis (H₂) and CO₂ reduction (to alcohols, light hydrocarbons), as well as for the degradation of pollutants. This review analyses the physical chemical properties of Cu₂O (and CuO) and the possible strategies to tune them (doping, lattice strain). Combining Cu with other elements in multinary oxides or in composite photoelectrodes is also discussed in detail. Finally, a short overview on the possible applications of these materials is presented.     

On numerical realizability of thermal convection

Astounded at the regularity of convective structures observed in simulations of mesoscale flow past realistic topography, we investigate the computational aspects of a classical problem of flow over a heated plane. We find that the numerical solutions are sensitive to viscosity, either incorporated a priori or effectively realized in computational models. In particular, anisotropic viscosity can lead to regular convective structures that mimic naturally realizable Rayleigh–Bénard cells, which are unphysical for the specified external parameter range. Details of the viscosity appear to play a secondary role; that is, similar structures can occur for prescribed constant viscosities, explicit subgrid-scale turbulence models, ad-hoc numerical filters, or implicit dissipation of numerical schemes. This implies the need for a careful selection of numerical tools suitable for convection-resolving simulations of atmospheric circulations. The implicit large-eddy-simulation (ILES) approach using non-oscillatory schemes is especially attractive, as for under-resolved calculations it reproduces well the coarsened results of finely-resolved boundary layer convection.     

Application of d-SPE before SPE and HPLC-FLD to Analyze Bisphenols in Human Breast Milk Samples

In this study, we propose a simple, cost-effective, and sensitive high-performance liquid chromatography with fluorescence detection (HPLC-FLD) for the simultaneous determination of seven bisphenols (bisphenol F (BPF), bisphenol E (BPE), bisphenol B (BPB), BADGE (bisphenol A diglycidyl ether), BADGE∙2H₂O, BADGE∙H₂O, BADGE∙2HCl) in human breast milk samples. The dispersive solid phase extraction (d-SPE) coupled with solid phase extraction (SPE) procedure performed well for the majority of the analytes with recoveries in the range 57–88% and relative standard deviations (RSD%) of less than 9.4%. During the d-SPE stage, no significant matrix effect was observed thanks to the application of different pairs of salts such as zirconium-dioxide-based sorbents (Z-Sep or Z-Sep +) and primary secondary amine (PSA) or QuEChERS Enhanced Matrix Removal-Lipid (EMR-Lipid) and PSA. The method limits of quantification (mLOQs) for all investigated analytes were set at satisfactory low values in the range 171.89–235.11 ng mL⁻¹. Analyte concentrations were determined as the average value from human breast milk matrix samples. The results show that the d-SPE/SPE procedure, especially with the application of EMR-Lipid and PSA, could be used for further bisphenol analyses in human breast milk samples.     

Synthesis of siloxy-modified second generation Hoveyda-Grubbs catalysts and their catalytic activity

Efficient syntheses of the first ruthenium alkylidene complexes bearing siloxide ligands are described. Second generation Hoveyda-Grubbs catalyst is shown to undergo efficient functionalization with a number of potassium silanolates to give disiloxy derivatives. The complexes obtained are found catalytically active in selected metathesis transformations.     

Internal Architecture and Adsorption Sites of Violet Lander Molecules Assembled on Native and KBr‐Passivated InSb(001) Surfaces

The adsorption of individual Violet Lander molecules self‐assembled on the c(8×2) reconstructed InSb(001) surface in its native form and on the surface passivated with one to three monolayers of KBr is investigated by means of low‐temperature scanning tunneling microscopy (STM). Preferred adsorption sites of the molecules are found on flat terraces as well as at atomic step edges. For molecules immobilized on flat terraces, several different conformations are identified from STM images acquired with submolecular resolution and are explained by the rotation of the 3,5‐di‐tert‐butylphenyl groups around σ bonds, which allows adjustment of the molecular geometry to the anisotropic substrate structure. Formation of ordered molecular chains is found at steps running along substrate reconstruction rows, whereas at the steps oriented perpendicularly no intermolecular ordering is recorded. It is also shown that the molecules deposited at two or more monolayers of the epitaxial KBr spacer do not have any stable adsorption sites recorded with STM. Prospects for the manipulation of single molecules by using the STM tip on highly anisotropic substrates are also explored, and demonstrate the feasibility of controlled lateral displacement in all directions.     

Average-optimal string matching

The exact string matching problem is to find the occurrences of a pattern of length m from a text of length n symbols. We develop a novel and unorthodox filtering technique for this problem. Our method is based on transforming the problem into multiple matching of carefully chosen pattern subsequences. While this is seemingly more difficult than the original problem, we show that the idea leads to very simple algorithms that are optimal on average. We then show how our basic method can be used to solve multiple string matching as well as several approximate matching problems in average optimal time. The general method can be applied to many existing string matching algorithms. Our experimental results show that the algorithms perform very well in practice.