Observables in a noncommutative approach to the unification of quanta and gravity: a finite model

We further develop a noncommutative model unifying quantum mechanics and general relativity proposed in Gen. Rel. Grav. (36, 111–126 (2004)). Generalized symmetries of the model are defined by a groupoid given by the action of a finite group on a space E. The geometry of the model is constructed in terms of suitable (noncommutative) algebras on . We investigate observables of the model, especially its position and momentum observables. This is not a trivial thing since the model is based on a noncommutative geometry and has strong nonlocal properties. We show that, in the position representation of the model, the position observable is a coderivation of a corresponding coalgebra, coparallelly to the well-known fact that the momentum observable is a derivation of the algebra. We also study the momentum representation of the model. It turns out that, in the case of the algebra of smooth, quickly decreasing functions on , the model in its quantum sector is nonlocal, i.e., there are no nontrivial coderivations of the corresponding coalgebra, whereas in its gravity sector such coderivations do exist. They are investigated.This revised version was published online in April 2005. The publishing date was inserted.     

Anisotropic nonlinear Neumann problems

We consider nonlinear Neumann problems driven by the p(z)-Laplacian differential operator and with a p-superlinear reaction which does not satisfy the usual in such cases Ambrosetti?CRabinowitz condition. Combining variational methods with Morse theory, we show that the problem has at least three nontrivial smooth solutions, two of which have constant sign (one positive, the other negative). In the process, we also prove two results of independent interest. The first is about the L ^??-boundedness of the weak solutions. The second relates W ^1,p(z) and C ¹ local minimizers.     

Chlorophyll a π-Cation Radical as Redox Mediator in Superoxide Dismutase (SOD) Mimetics

The extensive speciation of copper(II) chloride in organic solvents varies with concentration, temperature, pressure and oxygen content, providing the ability to switch between different chlorophyll transmetalation pathways. We found that one of them is exceptionally suitable for the formation and stabilisation of the chlorophyll π-cation radical. This is due to unique redox cycling, which is coupled to the generation and transformation of various reactive oxygen species. In the presence of a proton donor, our system shows behavior which resembles that of superoxide dismutase (SOD). Regardless of light, chlorophyll acts as an electron transfer mediator.     

Preparation and Oxidative-Chlorination Splitting of Nitro Derivatives OF 1,4-Dithiino[2,3-C:5,6-C′]Diquinoline as a Source of 4-Substituted 5- and 8-Nitro-3-Quinolinesulfonic Acid Derivatives

Abstract

Treatment of 1,4-dithiino[2,3-c:5,6-c′]diquinoline (a thioquinanthrene) (1a) with an excess of nitrating mixture (0 °C, 14 days) led to a mixture of mono- and dinitrothioquinanthrene 7-oxides 2b–e and 2f–h. This mixture was: (i) reduced to a mixture of mono- and dinitrothioquinanthrenes 1b– e, or (ii) oxidatively chlorinated with a gaseous chlorine/80% acetic acid/hydrochloric acid system to a mixture of 4-chloro-3-chlorosulfonylquinoline 3a and its 5- and 8-nitroderivatives 3b and 3d. Sulfochlorides 3a– d were independently synthesized from 3,4′-diquinolinyl sulfides 4 and converted to the respective 4-dimethylamino-3-quinoline-N,N-dimethylsulfonamides 9a–d.     

Reaction of Lewisite-1 with Alcohols,Diols, and Thiols in Water—A Simple Method of Derivatization of Thiodiglycol

Reaction of 2-chlorovinyldichloroarsine (Lewisite-1) with alcohols, thiols, diols, and hydroxy thiols in water at 40°C has been examined. The expected derivatization products, dialkyl 2-chlorovinylarsonites or corresponding arsonodithiolites, were obtained with alcohols and thiols, whereas reactions with bifunctional diols and hydroxythiols produced analogous cyclic esters. All derivatives may be easily detected using gas chromatography. This reaction was found useful to easily transform bis(2-hydroxyethyl) sulfide (thiodiglycol), a sulfur mustard decomposition product, to a stable eight-membered cyclic arsonite derivative. After extraction with dichloromethane, the derivative may be easily and selectively detected using GC/MS at a 100 ppb level thiodiglycol content in water matrices, eliminating tedious evaporation of water and then silylation. This method may be applied to analyze Chemical Weapons Convention related environmental water samples.     

Determination of the optimum conditions for the synthesis of praseodymium(III) chloride

In the present work, we have synthesized praseodymium(III) chloride, PrCl₃, from the praseodymium oxide, Pr₆O₁₁, by dry method in the presence of ammonium chloride, NH₄Cl. This study includes the establishment of an assembly synthesis under inert gas. The thermal decomposing process of pure NH₄Cl was investigated by TG–DTG. The results showed that NH₄Cl begins to lose weight at 188 °C, large loss of weight ending at 302 °C when NH₄Cl is heated at the rate of 10 °C/min under N₂ atmosphere. For chlorination, NH₄Cl participates directly in the reaction, and HCl decomposed from NH₄Cl also contributes to the chlorination reaction. The influence of various synthesis parameters (temperature, contact time and chemical composition) on the reaction yield was studied, and the optimum conditions for synthesis were, thus, determined and discussed.