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.     

Calculation of cyclodextrin-mediated enantiomer ratio shifting of racem norgestrel in aqueous solutions

Enantioselective solubility of rac-norgestrel was found in the presence of γ-cyclodextrin or hydroxypropyl-γ-cyclodextrin. In both cases the efficacious enantiomer was dissolved in greater extent. Calculating the molar absorptivity and molar ellipticity spectra of the γ- and hydroxypropyl-γ-cyclodextrin aqueous complexes, a simple and rapid direct circular dichroism (CD) spectrometric method was obtained for the determination of the enantiomer ratio in aqueous solutions.     

An additive problem in the Fourier coefficients of cusp forms

 We establish an estimate on sums of shifted products of Fourier coefficients coming from holomorphic or Maass cusp forms of arbitrary level and nebentypus. These sums are analogous to the binary additive divisor sum which has been studied extensively. As an application we derive, extending work of Duke, Friedlander and Iwaniec, a subconvex estimate on the critical line for L-functions associated to character twists of these cusp forms. Received: 2 October 2001 / Revised version: 9 September 2002 / Published online: 28 March 2003 Mathematics Subject Classification (2000): Primary 11F30, 11F37; Secondary 11M41.     

Accurate determination of low pK values by (1)H NMR titration

The NMR titration methodology to determine acid dissociation constants in aqueous solutions is extended for pK(a) values between 0 and 2, where potentiometric titrations are no longer applicable. (1)H NMR spectra are acquired for single samples of constant acid concentration (e.g. 0.02M), controlled ionic strength (I=1M with HNO(3)/NaNO(3)) and varying pH. To avoid biased pH readings due to the acid error of the glass electrode, true, concentration-based pH values are deduced by combination of the charge balance equation with information from (1)H NMR chemical shifts of the investigated acid. The method has been tested on histidine (pK(1)=1.83+/-0.02) and yielded the dissociation constant of dichloroacetic acid (pK=1.06+/-0.01) for the first time with good accuracy and precision. Dichloroacetic acid is recommended as an NMR spectroscopical "indicator molecule" for in situ monitoring the pH in strong acidic solutions of other equilibrium systems.     

A fluorescent molecular imaging probe with selectivity for soluble tau aggregated protein

Soluble forms of aggregated tau misfolded protein, generally termed oligomers, are considered to be the most toxic species of the different assembly states that are the pathological components of neurodegenerative disorders. Therefore, a critical biomedical need exists for imaging probes that can identify and quantify them. We have designed and synthesized a novel fluorescent probe, pTP-TFE for which binding and selectivity profiles towards aggregated tau and Aβ proteins were assessed. Our results have shown pTP-TFE to be selective for early forms of soluble tau aggregates, with high affinity of dissociation constants (K_d) = 66 nM, and tenfold selectivity over mature tau fibrils. Furthermore, we found that pTP-TFE is selective for tau over Aβ aggregates and had good cell permeability. This selectivity of pTP-TFE towards early forms of aggregated tau protein ex vivo was also supported with studies on human brain tissue containing tau and Aβ pathology. To the best of our knowledge, this is the first fluorescent molecule to be reported to have this form of selectivity profile, which suggests that pTP-TFE is a unique probe candidate for imaging-based detection of early stages of Alzheimer''s disease and other tauopathies.

pTP-TFE imaging probe can distinguish soluble tau aggregated proteins from other aggregated proteins enabling earlier detection of neurodegenerative diseases.     

Esterification of C1−C8 carboxylic acids to n-butyl esters in aqueous solutions for their gas chromatographic analysis

Summary The esterification of C₁–C₈ fatty acid in aqueous solutions and in the presence of sulfuric or hydrochloric acid and with n-butanol is described. It has been established that the esterification can be used for the quantitative determination of these fatty acids in the concentration ratio range of [H₂O]/[n-BuOH]=0.01–5.3. In the concentration ratio range of 0.01–0.8 the water present does not interfere. In the concentration range of above 0.8 anhydrous sodium sulfate is used for binding the water, in the amount of [Na₂SO₄.anh.]/[H₂O]0.2.     

The kinetics of radical polymerization—XXVII. Investigation of the radical reactivity of 3,3′- and 4,4′-disubstituted azobenzenes in the polymerization of vinylacetate

A study was made on the inhibition by some 3,3′- and 4,4′-disubstituted azobenzenes of the polymerization of vinylacetate initiated by azoisobutyronitrile at 50°. The inhibitory effects of these substances can be attributed to their ability to engage in radical addition giving a less reactive hydrazyl type radical. The mechanism of the inhibition has been established by ESR and kinetic (stoichiometric) measurements. The value of k₅/k₂ (characteristic of the reactivity of an inhibitor) was determined for 9 substituents. The radical reactivity of the aromatic azo group was decreased by electron donor substituents and increased by electron acceptors. The substituent effect can be well interpreted by the Hammett equation; the value of the reaction constant was ? = +0.53.     

Novel method for the preparation of anionic surfactant-selective electrodes

A simple one-step synthesis is described for the functionalization of poly(vinyl chloride) used for the preparation of anionic surfactant-selective membrane electrodes. The method is based on the nucleophilic substitution of a fraction of the chlorine atoms bound to the poly(vinyl chloride) backbone by trimethylamine. The prepared slightly charged polymer gave rise to high-quality surfactant-selective electrode membranes, which had a Nernstian response, short response time, and appropriate stability.     

Iminodiacetic acid/ethylcellulose as a chelating ion exchanger : Part 1. Determination of trace metals by atomic absorption spectrometry and collection of uranium

A chelate-forming ion exchanger, iminodiacetic acid/ethylcellulose, is used for the separation of trace metals from waters and different organic solvents. Added uranium was collected from sea waters with recoveries of about 97%. Graphite-furnace atomic absorption spectrometry and solution spectrophotometry were used to quantify the metals. For the direct determination of trace metals in waters by the graphite-furnace method, a simple matrix-matching method is described. The detection limit for cadmium was 0.1 μg l^?1 and for lead 1 μg^?1 in drinking water.