Twin Paradox and the Logical Foundation of Relativity Theory

We study the foundation of space-time theory in the framework of first-order logic (FOL). Since the foundation of mathematics has been successfully carried through (via set theory) in FOL, it is not entirely impossible to do the same for space-time theory (or relativity). First we recall a simple and streamlined FOL-axiomatization Specrel of special relativity from the literature. Specrel is complete with respect to questions about inertial motion. Then we ask ourselves whether we can prove the usual relativistic properties of accelerated motion (e.g., clocks in acceleration) in Specrel. As it turns out, this is practically equivalent to asking whether Specrel is strong enough to “handle” (or treat) accelerated observers. We show that there is a mathematical principle called induction (IND) coming from real analysis which needs to be added to Specrel in order to handle situations involving relativistic acceleration. We present an extended version AccRel of Specrel which is strong enough to handle accelerated motion, in particular, accelerated observers. Among others, we show that~the Twin Paradox becomes provable in AccRel, but it is not provable without IND.     

Bestimmung des Osmiums auf katalytischer Grundlage mittels einer Photokomparationsmethode

Zusammenfassung Auf Grund seiner katalytischen Wirkung auf die Lumineszenzreaktion von Luzigenin mit Wasserstoffperoxid läßt sich Osmiumtetroxid im Konzentrationsbereich von 1 bis 60g/5 ml mit Hilfe der Simultan-komparationsmethode hinreichend genau bestimmen. Die störenden Ionen des Cu, Cd, Pb, Hg, Co, Ni, Ca und Mg lassen sich mit ÄDTA maskieren.

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Summary Osmium tetroxide can be detected in the concentration range of 1 to 60g/5 ml through its luminescence reaction with hydrogen peroxide and lucigenin with sufficient precision by means of the simultaneous comparation method. The interfering ions (Cu, Cd, Pb, Hg, Co, Ni, Ca, and Mg) can be masked with EDTA.

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Résumé En utilisant l'action catalytique du tétroxyde d'osmium sur la réaction de luminescence de la lucigénine avec l'eau oxygénée, on peut le doser avec suffisamment de précision dans le domaine des concentrations allant de 1 à 60g/5 ml par la méthode de comparaison photométrique. On peut masquer par l'EDTA les ions gênants de Cu, Cd, Pb, Hg, Co, Ni, Ca et Mg.

     

Thermometrische Schnellanalyse von Martin- und Hochofenschlacken sowie anderen Silicaten

Summary A novel method has been developed for the rapid analysis of silicates. Each component is determined from the temperature variation of the solution resulting from the addition to the test solution of a selectively reacting reagent. By suitable construction of the instrument the concentration of the component to be determined can be read directly in per cent. The determination of a component takes usually 4 to 8 minutes.In the test solution a temperature change proportional to the concentration of the component to be determined has been produced by the following reagents: sulphuric acid for barium, ammonium peroxodisulphate for iron, hydrogen peroxide for titanium, hydrofluoric acid for silicic acid, potassium permanganate for sulphur, ammonium molybdate and hydrogen peroxide for phosphate, potassium permanganate for manganese, potassium oxalate for calcium, diammonium hydrogenphosphate for magnesium, ascorbic acid for chromium. The above components can be determined without any separations. Only in the case of aluminium a separation of silicic acid from aluminium by dehydrating with perchloric acid in necessary. Thereafter the aluminium can be determined with hydrofluoric acid.The precision of the determinations is practically identical with the precision of the usual plant methods.     

The ionic product of water in concentrated tetramethylammonium chloride solutions

The ionic product of water, pK(w) = - log[H(+)][OH(-)] has been determined in aqueous solutions of tetramethylammonium chloride over the concentration range of 0.1-5.5 M at 25 degrees C using high-precision glass electrode potentiometric titrations. pK(w) data relating to aqueous potassium and sodium chlorides at ionic strengths up to 5 M are markedly lower than the tetramethylammonium chloride results. These differences are almost certainly due to weak associations between potassium and (especially) sodium and hydroxide ions.     

Development of resin-to-resin transfer reactions (RRTR) using Sonogashira chemistry

Sonogashira chemistry can be used according to the ‘resin-to-resin transfer reaction’ (RRTR) concept. Two fragments, one containing the halide moiety and the second one incorporating the alkyne functionality, are anchored on different solid supports using allyl and/or Wang-type linkages. Treatment with Pd(0) cleaves the allyl-linked fragment(s) which subsequently undergo Sonogashira coupling under the same conditions.     

Non-Watson-Crick base pairing in RNA. quantum chemical analysis of the cis Watson-Crick/sugar edge base pair family

Large RNA molecules exhibit an astonishing variability of base-pairing patterns, while many of the RNA base-pairing families have no counterparts in DNA. The cis Watson-Crick/sugar edge (cis WC/SE) RNA base pairing is investigated by ab initio quantum chemical calculations. A detailed structural and energetic characterization of all 13 crystallographically detected members of this family is provided by means of B3LYP/6-31G and RIMP2/aug-cc-pVDZ calculations. Further, a prediction is made for the remaining 3 cis WC/SE base pairs which are yet to be seen in the experiments. The interaction energy calculations point at the key role of the 2'-OH group in stabilizing the sugar-base contact and predict all 16 cis WC/SE base-pairing patterns to be nearly isoenergetic. The perfect correlation of the main geometrical parameters in the gas-phase optimized and X-ray structures shows that the principle of isosteric substitutions in RNA is rooted from the intrinsic structural similarity of the isolated base pairs. The present quantum chemical calculations for the first time analyze base pairs involving the ribose 2'-OH group and unambiguously correlate the structural information known from experiments with the energetics of interactions. The calculations further show that the relative importance and absolute value of the dispersion energy in the cis WC/SE base pairs are enhanced compared to the standard base pairs. This may by an important factor contributing to the strength of such interactions when RNA folds in its polar environment. The calculations further demonstrate that the Cornell et al. force field commonly used in molecular modeling and simulations provides satisfactory performance for this type of RNA interactions.     

On-resin native chemical ligation for cyclic peptide synthesis

A novel cysteine derivative, N(alpha)-trityl-S-(9H-xanthen-9-yl)-l-cysteine [Trt-Cys(Xan)-OH] has been introduced for peptide synthesis, specifically for application to a new strategy for the preparation of cyclic peptides. The following steps were carried out to synthesize the cyclic model peptide cyclo(Cys-Thr-Abu-Gly-Gly-Ala-Arg-Pro-Asp-Phe): (i). side-chain anchoring of Fmoc-Asp-OAl via its free beta-carboxyl as a p-alkoxybenzyl ester to a solid support; (ii). stepwise chain elongation of the peptide by standard Fmoc/tBu solid-phase chemistry; (iii). removal of the N-terminal Fmoc group; (iv). coupling of Trt-Cys(Xan)-OH; (v). selective Pd(0)-promoted cleavage of the C-terminal allyl ester; (vi). coupling of the C-terminal residue, i.e., H-Phe-SBzl, preactivated as a thioester; (vii). selective removal of the N(alpha)-Trt and S-Xan protecting groups under very mild acid conditions; (viii). on-resin cyclization by native chemical ligation in an aqueous milieu; and (ix). final acidolytic cleavage of the cyclic peptide from the resin. The strategy was evaluated for three supports: poly[N,N-dimethacrylamide-co-poly(ethylene glycol)] (PEGA), cross-linked ethoxylate acrylate resin (CLEAR), and poly(ethylene glycol)-polystyrene (PEG-PS) graft resin supports. For PEGA and CLEAR, the desired cyclic product was obtained in 76-86% overall yield with initial purities of approximately 70%, whereas for PEG-PS (which does not swell nearly as well in water), results were inferior. Solid-phase native chemical ligation/cyclization methodology appears to have advantages of convenience and specificity, which make it promising for further generalization.     

Protonation and sodium ion-pairing of the sulfite ion in concentrated aqueous electrolyte solutions

A protocol has been developed for the reliable titration of aqueous sulfite solutions which minimizes photodecomposition effects. This procedure has been used to measure the protonation constants of the sulfite ion in aqueous solution by glass electrode potentiometry at 25.0‡C and ionic strengths (I) from 0.1 to 5.0M in NaCI media and atI = 1.0M in KC1 and Me₄NCl media. These measurements provided evidence of weak but significant ionpairing between SO2/3 -and Na⁺ with a formation constant of logK _Na = 0.431 in 1.0M Me₄NCl. This was in very good agreement with the value logK _Na = 0.410 measured directly by Na⁺ ion-selective electrode potentiometry. Evidence is also presented for an extremely weak association of K⁺ and SO ₂ ³ -with logK _k = 0.22 in 1.0M Me₄NCl.