Every Large Point Set contains Many Collinear Points or an Empty Pentagon

We prove the following generalised empty pentagon theorem for every integer ℓ ≥ 2, every sufficiently large set of points in the plane contains ℓ collinear points or an empty pentagon. As an application, we settle the next open case of the “big line or big clique” conjecture of Kára, Pór, and Wood [Discrete Comput. Geom. 34(3):497–506, 2005].     

Absolutely continuous spectrum for random Schrödinger operators on the Bethe strip

The Bethe strip of width m is the cartesian product $\mathbb {B}\times \lbrace 1,\ldots ,m\rbrace$, where $\mathbb {B}$ is the Bethe lattice (Cayley tree). We prove that Anderson models on the Bethe strip have “extended states” for small disorder. More precisely, we consider Anderson‐like Hamiltonians $H_\lambda =\frac{1}{2} \Delta \otimes 1 + 1 \otimes A\,+\,\lambda \mathcal {V}$ on a Bethe strip with connectivity K ≥ 2, where A is an m × m symmetric matrix, $\mathcal {V}$ is a random matrix potential, and λ is the disorder parameter. Given any closed interval $I\subset \big (\!-\!\sqrt{K}+a_{{\rm max}},\sqrt{K}+a_{\rm {min}}\big )$, where a_min and a_max are the smallest and largest eigenvalues of the matrix A, we prove that for λ small the random Schrödinger operator H_λ has purely absolutely continuous spectrum in I with probability one and its integrated density of states is continuously differentiable on the interval I.     

Zur Kinetik der salpetrigen Säure als Oxydans

Zusammenfassung Es wird die Annahme zur Diskussion gestellt, daß salpetrige Säure auch im Sinne von {ie388-1} zu reagieren vermag. Ein allgemeines Reaktionsschema für die Wirkungsweise von salpetriger Säure als Oxydans wird entwickelt. Einige Oxydationsreaktionen der salpetrigen Säure werden in diesem Sinne diskutiert. Im besonderen wird versucht, diesem Reaktionsschema den Mechanismus der dem Bleikammerverfahren zugrunde liegenden Oxydation von schwefliger Säure durch salpetrige Säure an Hand seinerzeitiger experimenteller Befunde einzuordnen. Der viel diskutierte Oxydationsvorgang bei Bildung von Schwefelsäure im Bleikammerverfahren innerhalb der flüssigen Phase scheint in seinen wesentlichen Hauptzügen aufgeklärt zu sein.     

Synthesis and crystal structure of [Re2Cl2(CO)6(S e)]

The dinuclear complex [Re₂Cl₂(CO)₆S e] has been prepared and characterized in the solid state by X-ray crystallography. Proton NMR spectroscopy has shown the structure to be stereochemically rigid in solution.     

Sortin1-hypersensitive mutants link vacuolar-trafficking defects and flavonoid metabolism in Arabidopsis vegetative tissues

Sortin1 is a chemical genetic-hit molecule that causes specific mislocalization of plant and yeast-soluble and membrane vacuolar markers. To better understand its mode of action, we designed a Sortin1-hypersensitive screen and identified several Sortin1-hypersensitive and flavonoid-defective mutants. Mechanistically, Sortin1 mimics the effect of the glutathione inhibitor buthionine sulfoximine and alters the vacuolar accumulation of flavonoids, likely blocking their transport through vacuole-localized ABC transporters. Structure-activity relationship studies conducted in Arabidopsis revealed the structural requirements for Sortin1 bioactivity and demonstrated that overlapping Sortin1 substructures can be used to discriminate between vacuolar-flavonoid accumulations and vacuolar-biogenesis defects. We conclude that Sortin1 is a valuable probe for dissecting novel links among flavonoid transport, vacuolar integrity, and the trafficking of vacuolar targeted cargoes in Arabidopsis.     

Hydrogen oxidation reaction on platinum nanoparticles: Transition between mechanistic routes

The present work reports for the first time results which demonstrate that the hydrogen oxidation reaction on platinum nanoparticles supported on gold and glassy carbon substrates displays a transition between the Tafel–Volmer route, which dominates at low overpotentials, and the Heyrovsky–Volmer route, predominant at high overpotentials.     

Determination of caffeoylquinic acids and flavonoids inCynara scolymus L. by high performance liquid chromatography

Summary The main phenolic compounds in dried extracts fromCynara scolymus (artichoke)—monocaffeoylquinic acids, dicaffeoylquinic acid, and flavonoids–have been separated by high-performance liquid chromatography. By use of a narrow bore C₁₈ column and an acidic mobile phase this HPLC method enabled improved separation within 31 min with significantly reduced solvent consumption compared with other methods. The method was validated to demonstrate its linearity, precision, accuracy, and robustness. Twelve commercial samples were analyzed. Monocaffeoylquinic acids were the most abundant phenolic compounds; the amounts present ranged from 0.48 to 4.24%. The amounts of dicaffeoylquinic acids and flavonoids were smaller—from 0.03 to 0.52%. The method is a good combination of efficiency and economy and should be especially useful for commercial applications.     

Nature of Alkali- and Coinage-Metal Bonds versus Hydrogen Bonds

We have quantum chemically studied the structure and nature of alkali- and coinage-metal bonds (M-bonds) versus that of hydrogen bonds between A−M and B⁻ in archetypal [A−M⋅⋅⋅B]⁻ model systems (A, B=F, Cl and M=H, Li, Na, Cu, Ag, Au), using relativistic density functional theory at ZORA-BP86-D3/TZ2P. We find that coinage-metal bonds are stronger than alkali-metal bonds which are stronger than the corresponding hydrogen bonds. Our main purpose is to understand how and why the structure, stability and nature of such bonds are affected if the monovalent central atom H of hydrogen bonds is replaced by an isoelectronic alkali- or coinage-metal atom. To this end, we have analyzed the bonds between A−M and B⁻ using the activation strain model, quantitative Kohn-Sham molecular orbital (MO) theory, energy decomposition analysis (EDA), and Voronoi deformation density (VDD) analysis of the charge distribution.