A tight Hermite–Hadamard inequality and a generic method for comparison between residuals of inequalities with convex functions

Periodica Mathematica Hungarica - We present a tight parametrical Hermite–Hadamard type inequality with probability measure, which yields a considerably closer upper bound for the mean value...     

Crystal Growth and Crystal Structures of Gold(V) Compounds: Cu(AuF6)2, Ag(AuF6)2, and O2(CuF)3(AuF6)4 ⋅ HF

Crystal growth from anhydrous hydrogen fluoride solutions of M²⁺ (M=Cu, Ag) and [AuF₆]⁻ gave M(AuF₆)₂ salts (M=Cu, Ag). Similar attempts to prepare single crystals of the corresponding nickel, zinc and magnesium salts failed. The crystal structure of Cu(AuF₆)₂ consists of layers of Cu²⁺ cations connected by [AuF₆]⁻ anions, thus forming slabs. Only van der Waals interactions exist between adjacent slabs. The crystal structure of Ag(AuF₆)₂ consists of a three-dimensional framework in which Ag⁺ cations are linked by [AuF₆]⁻ anions. Both structures are members of the M^II(X^VF₆)₂ family, in which seven different structure types have been observed to date. In the crystal structure of O₂(CuF)₃(AuF₆)₄ ⋅ HF, the bridging AuF₆ units connect [−Cu−F−Cu−F−]_∞ chains to form stacks between which O₂⁺ cations and HF molecules are located.     

High‐Resolution Single‐Molecule Fluorescence Imaging of Zeolite Aggregates within Real‐Life Fluid Catalytic Cracking Particles

Fluid catalytic cracking (FCC) is a major process in oil refineries to produce gasoline and base chemicals from crude oil fractions. The spatial distribution and acidity of zeolite aggregates embedded within the 50–150 μm‐sized FCC spheres heavily influence their catalytic performance. Single‐molecule fluorescence‐based imaging methods, namely nanometer accuracy by stochastic chemical reactions (NASCA) and super‐resolution optical fluctuation imaging (SOFI) were used to study the catalytic activity of sub‐micrometer zeolite ZSM‐5 domains within real‐life FCC catalyst particles. The formation of fluorescent product molecules taking place at Brønsted acid sites was monitored with single turnover sensitivity and high spatiotemporal resolution, providing detailed insight in dispersion and catalytic activity of zeolite ZSM‐5 aggregates. The results point towards substantial differences in turnover frequencies between the zeolite aggregates, revealing significant intraparticle heterogeneities in Brønsted reactivity.     

Crystal Structures of Hydrazinium(II) Salts of [SbF6]– and [Sb2F11]–

N₂H₆(Sb₂F₁₁)₂ was synthesized by the reaction of N₂H₆F₂ with excess of SbF₅ in anhydrous hydrogen fluoride (aHF). It crystallizes in the triclinic space group P$\bar{1}$ (No. 2) with a = 6.6467(3) Å, b = 8.3039(4) Å, c = 8.3600(5) Å, α = 76.394(5) ^o, β = 70.161(5) ^o, γ = 70.797(5) ^o, V = 405.90(4) ų at 150 K, Z = 2. When it is redissolved in aHF, it solvolysis with the release of SbF₅ yielding N₂H₆(SbF₆)₂ which crystallizes in the monoclinic C2/c space group (No. 15) with a = 7.3805(3) Å, b = 12.3248(5) Å, c = 10.4992(4) Å, β = 92.218(4) ^o, V = 954.33(7) ų at 150 K, and Z = 8. No other phases were observed in crystallization products when different molar ratios of N₂H₆F₂/SbF₅ (1:1,2:3,1:3) in aHF were used as starting materials.     

$$\mathcal {H}^+$$-multivalued contractions and their application to homotopy theory

Kikkawa and Suzuki (Nonlinear Anal 69:2942–2949, 2008) and Kikkawa and Suzuki (Fixed Point Theory Appl, 2008, Art. ID 649749) proved some fixed point results that are generalizations of Kannan’s, Nadler’s and Suzuki’s fixed point theorems. Here, we present fixed point results of this kind for multivalued mappings in the setting of \(\mathcal {H}^+\)-metric spaces. The theorems provided allow upgrading of some known results which is shown by examples. Moreover, we give a homotopy result as an application of our main theorem.     

Tailoring the electrochemical charge storage properties of carbonaceous support by redox properties of heteropoly acids: where does the synergy come from?

Journal of Solid State Electrochemistry - The synergistic effects between two Keggin-type heteropoly acids (HPAs) and carbon surface were examined and elucidated. An improved high rate capability...     

Normal art galleries: Wall in – all in

We introduce the notion of a normal gallery, a gallery in which any configuration of guards that visually covers the walls necessarily covers the entire gallery. We show that any star gallery is normal and any gallery with at most two reflex corners is normal. A polynomial time algorithm is provided deciding if, for a given gallery and a finite set of positions within the gallery, there exists a configuration of guards in some of these positions that visually covers the walls, but not the entire gallery.     

Synergy between thermal analysis and simulation

Available databases presently used by commercial simulation software packages for the aluminum casting industry are usually armed with material properties for only a few selected standard alloys. In the case of other alloys with different chemical compositions and refinement or modification treatment, thermal analysis could be an invaluable tool to gain necessary properties. The aim of this article is to demonstrate the potential application of the cooling curve analysis in the existing simulation software by improving its accuracy.     

Advances in positron and electron scattering*

The topical issue on Advances in Positron and Electron Scattering” combines contributionsfrom POSMOL 2015 together with others devoted to celebrate the unprecedented scientificcareers of our loyal colleagues and trusted friends Steve Buckman (Australian NationalUniversity, Australia) and Michael Allan (University of Fribourg, Switzerland) on theoccasion of their retirements. POSMOL 2015, the XVIII International Workshop on Low-EnergyPositron and Positronium Physics and the XIX International Symposium on Electron-MoleculeCollisions and Swarms, was held at Universidade NOVA de Lisboa, Lisboa, Portugal, from17–20 July 2015. The international workshop and symposium allowed to achieve a veryprivileged forum of sharing and developing our scientific expertise on current aspects ofpositron, positronium and antiproton interactions with electrons, atoms, molecules andsolid surfaces, and related topics, as well as electron interactions with molecules inboth gaseous and condensed phases. Particular topics include studies of electroninteractions with biomolecules, electron induced surface chemistry and the study of plasmaprocesses. Recent developments in the study of swarms are also fully addressed.