Ramsey partitions of integers and pair divisions

Ifk ₁ andk ₂ are positive integers, the partitionP = (₁,₂,..., _n ) ofk ₁+k ₂ is said to be a Ramsey partition for the pairk ₁,k ₂ if for any sublistL ofP, either there is a sublist ofL which sums tok ₁ or a sublist ofP –L which sums tok ₂. Properties of Ramsey partitions are discussed. In particular it is shown that there is a unique Ramsey partition fork ₁,k ₂ having the smallest numbern of terms, and in this casen is one more than the sum of the quotients in the Euclidean algorithm fork ₁ andk ₂.An application of Ramsey partitions to the following fair division problem is also discussed: Suppose two persons are to divide a cake fairly in the ratiok ₁k ₂. This can be done trivially usingk ₁+k ₂-1 cuts. However, every Ramsey partition ofk ₁+k ₂ also yields a fair division algorithm. This method yields fewer cuts except whenk ₁=1 andk ₂=1, 2 or 4.     

A theoretical study of angiotensin-converting enzyme inhibitors

Summary INDO molecular orbital calculations are reported for 35 selected angiotensin-converting enzyme inhibitors. QSARs are developed between pI₅₀ data and molecular electronic indices. The QSARs obtained reflect the importance of both charge-charge interactions between inhibitor and receptor and of specific interactions between groups on the inhibitor with points around the molecule which are postulated to correspond to binding sites at the receptor.     

The oxidative decarboxylation of polyaminocarboxylic acids

Summary The rates of oxidation of four chelating agents, NTA, EDTA, CDTA, and DTPA with Ce(IV), in sulfuric acid media, were determined spectrophotometrically by a stopped-flow technique. The reductive ability is in the order CDTA > EDTA > DTPA > NTA. The influence of varying the acidity of the medium was studied, and in each case a maximum in the rate constant vs. [H⁺] plot was observed. A possible interpretation of the reactivities and the influence of acidity is advanced.

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Oxydative Decarboxylierung von PolyaminocarbonsäurenII. Vergleichende kinetische Untersuchung der Oxydation von NTA, ÄDTA, CDTA und DTPA mit Ce(IV) in saurer Lösung

Zusammenfassung Die Oxydationsgeschwindigkeiten von 4 Chelaten (NTA, ÄDTA, CDTA und DTPA) mit Ce(IV) in saurer Lösung wurden spektrophotometrisch mit Hilfe der stopped-flow-Technik bestimmt. Die Reduzierfähigkeit nimmt in der Reihenfolge CDTA > ÄDTA > DTPA > NTA ab. Der Einfluß verschiedener Säuregehalte in der Lösung wurde untersucht, und in jedem Fall wurde ein Maximum in der graphischen Darstellung der Geschwindigkeitskonstante gegen [H⁺] beobachtet. Eine mögliche Erklärung des Reaktionsvermögens und des Säureeinflusses wird gegeben.

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Part I: Z. Anal. Chem. 246, 231 (1969).     

Rearrangement of epoxynitriles: a convenient homologation of acyclic and cyclic ketones to carboxylic acids

A convenient two-step homologation of both aliphatic and aromatic ketones to the corresponding carboxylic acid has been developed. First ketones were converted to epoxynitriles with the Darzens reaction. Second, a Lewis acid mediated rearrangement of these epoxynitriles with lithium bromide was achieved to give homologated secondary alkanoic acids (as well as aryl-alkanoic) in good yields. The mechanism and the scope of the rearrangement reaction were investigated. This strategy constitutes a two-step homologation of ketones to secondary carboxylic acids.     

Interaction potentials of the RG-I anions, neutrals, and cations (RG = He, Ne, Ar)

Interaction potentials of the iodine atom, atomic cation, and anion with light rare-gas atoms from He to Ar are calculated within the unified ab initio approach using the unrestricted coupled-cluster with singles and doubles and perturbative treatment of triples correlation treatment, relativistic small-core pseudopotential, and an extended basis set. Ab initio points are fit to a flexible analytical function. The calculated potentials are compared with available literature data, assessed in the I(-)-and I+-ion mobility calculations and the Ar-I(-)-anion zero electron kinetic-energy spectra simulations, and analyzed using the correlation rules. The results indicate a high precision of the reported potentials.     

Synthesis of TiO2 based on hydrothermal methods using elevated pressures and microwave conditions

Titanium dioxide (TiO₂), especially in its anatase form, is an effective photocatalyst under ultraviolet (UV) light. The particle size of TiO₂ is a critical factor to determine its photoactivity based on its quantum effectiveness under light irradiations. Thus, nanocrystalline TiO₂ has been widely accepted to significantly enhance this effect. The sol–gel method is generally used to synthesize the anatase form of nanocrystalline TiO₂. In this study, we expanded the synthesis method of TiO₂ to high pressures under direct heating (hydrothermal method) and indirect heating (microwave-assisted method). It was found that pH value is one of the major factors to control nano-sizes of TiO₂ particles, and the neutral condition in all methods is preferable for controlling the sizes of the prepared TiO₂ particles. The microwave-assisted method further improves quality of synthesized nano-size TiO₂ below 10 nm. These results have been confirmed by both the direct size measurement using TEM images and indirect determination using XRD peaks. The collected samples are further analyzed using UV–Vis spectroscopy to identify the particle size-dependent photoreactivity and to confirm the effectiveness of microwave-assisting under neutral conditions. DSC is also a powerful tool to identify the crystalline transition of TiO₂.     

Poling and crosslinking processes in NLO polymers

A series of photocrosslinkable polymers bearing hyperpolarizable side chain chromophores was synthesized, poled and evaluated on the basis of the thermal stability of Second Harmonic Generation (SHG). Photoinitiation allowed for control of the onset of curing. Crosslinking was monitored by infrared spectroscopy and optimal conversion was achieved by applying a slow temperature ramp during exposure. The ultimate stability of the poled polymers was directly related to the number of crosslinking substituents that were attached to the chromophore pendant group. With two reactive groups per chromophore significant SHG was retained at temperatures above the initial polymer glass transition temperature. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 2769–2775     

Interface broadening during ion plating

Radiation damaged fluorite single crystals iso-thermally annealed showed an oscillating structure of the intensity of a diffracted neutron beam. This is in accord with previous report on crystalline cobaltic compound examined for reconstitution of parent complex ions from recoil hot atoms and for annealing of radiation damage by neutron diffraction. The oscillation phenomenon already found by radiochemical means in various solids irrespectively of their chemical constitution combined by a pure physical method as the neutron diffraction, greatly supports a hypothesis of a spatial temporal oscillatory diffusion of defects in isothermal annealing of radiation damaged crystalline lattice.