Two NP-Hard Art-Gallery Problems for Ortho-Polygons

D. T. Lee and A. K. Lin [2] proved that VERTEX-GUARDING and POINT-GUARDING are NP-hard for simple polygons. We prove that those problems are NP-hard for ortho-polygons, too.     

Kryoskopische Titrationen zur Bestimmung der bei chemischen Reaktionen auftretenden Teilchenzahl?nderungen

Zusammenfassung Es wird eine neue Arbeitstechnik beschrieben, die es gestattet, kryoskopische Messungen so zu gestalten, daß sich bis zu 150 Meßpunkte fortlaufend innerhalb eines Versuches aufnehmen lassen. Man erhält dadurch direkt die Teilchenzahländerung als Funktion der Zugabe einer Reagenslösung. Die quantitative Auswertung der Titrationskurven für zahlreiche Reaktionen zeigt die Brauchbarkeit dieser Indikationsmethode.

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Cryoscopic titrations for the determination of the change of the number of particles in chemical reactions

A new working technique is described which allows to take cryoscopic measurements in such a way that up to 150 measuring points can be registered continually during one test. In this way one directly obtains the change in the number of particles as a function of adding a dissolved reagent. The quantitative valuation of titration curves for a great number of reactions proves the usefulness of this method of indication.

     

Oxidation with the “O2−H2O2-vanadium complex-pyrazine-2-carboxylic acid” reagent

The oxidation of cyclohexene with hydrogen peroxide catalyzed by a vanadium complex and pyrazine-2-carboxylic acid (PCA) in air results in the formation of cyclohex-2-enyl hydroperoxide as the main product and cyclohex-2-enol, cyclohex-2-enone, cyclohex-3-enyl hydroperoxide, cyclohex-3-enol, cyclohexanol, cyclohexane, and 1,2-epoxycyclohexane in lesser amounts. The composition of the products of oxidation of decalin isomers with the system in question is similar to those obtained in the photochemical oxidation with hydrogen peroxide in air and in the oxidation with air in the presence of anthraquinone. A proposed mechanism for the oxidation includes the initiation by hydroxyl radicals generated from hydrogen peroxide under the action of the V-PCA system. For Part 8, see Ref. 1. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 253–258, February, 1998.     

Basis set exchange: a community database for computational sciences

Basis sets are some of the most important input data for computational models in the chemistry, materials, biology, and other science domains that utilize computational quantum mechanics methods. Providing a shared, Web-accessible environment where researchers can not only download basis sets in their required format but browse the data, contribute new basis sets, and ultimately curate and manage the data as a community will facilitate growth of this resource and encourage sharing both data and knowledge. We describe the Basis Set Exchange (BSE), a Web portal that provides advanced browsing and download capabilities, facilities for contributing basis set data, and an environment that incorporates tools to foster development and interaction of communities. The BSE leverages and enables continued development of the basis set library originally assembled at the Environmental Molecular Sciences Laboratory.     

Beiträge zur chemie des bors LXXX. Pentacarbonylchromkomplexe von diorganylmethylthioboranene und von 2-diäthylboryl-5-methylthiophen

Substitution of THF by diorganylmethylthiboranes in (CO)₅Cr · THF yields the rather unstable complexes (CO)₅Cr · CH₃SBR₂ (R = CH₃, C₆H₅). In contrast to the σ-thiophene complex (CO)₅Cr · SC₄H₄ the pentacarbonylchromium complex of the σ-S-bonded 2-diethylboryl-5-methylthiopene is quite stable due to interaction of the boryl group with CO ligands.     

Reduced titanium dioxide as support for Ziegler–Natta catalysts

Titanium tetrachloride heterogenized on reduced TiO₂ has been studied as a catalyst for ethylene polymerization. The catalyst has good storage stability and exhibits good activity for ethylene polymerization. The polymer chains grow linearly during ca. 1 h, giving an average molecular weight of up to 2.5 × 10⁶ which indicates that practically no β-elimination occurs. The activity of the catalyst at 50°C, based on Ti(III), is 7.6 × 10⁶ PE/mol Ti h bar and based on the quantity of polyethylene formed it is 1.25 × 10⁶ g PE/mol Ti h bar. The molecular weight of the polymer can be controlled with the addition of hydrogen, under 0.5 bar hydrogen, polyethylene with a molecular weight of 411,000 and a relatively low polydispersity index of 2.2 is obtained. The catalyst shows good thermal stability; the Arrhenius activation energy is 31.8 kJ/mol for the polymerization. The catalyst is also active for propylene polymerization, giving 3 × 10⁶ g PP/mol Ti h bar with the high isotacticity of 93%. © 1994 John Wiley & Sons, Inc.     

Variants of Visibility and their Complexity

First we give an overview about variants of visibility and related problems. Then we prove that some guarding and covering problems are NP-hard for ortho-polygons with holes, using a so-called vertex cover technique.