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.     

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.     

Direct analysis of thin-layer chromatographic spots of narcotics by means of diffuse reflectance Fourier transform infrared spectroscopy

The technique of diffuse reflectance Fourier transform infrared spectrometry (DRIFT) as an in situ detection method was used for the qualitative and quantitative analysis of drugs (heroin, cocaine and codeine) separated by thin layer chromatography.It was found that at a given interferometer throughput and detector sensitivity the quality of the spectrum depends strongly in the type of the chromatographic thin layer used. A detection limit of approx. 2 g was attained on a microcrystalline cellulose thin layer with a dynamically aligned Bio-Rad Digilab FTS 60A/896 type interferometer and room temperature DTGS detector. A reliable qualitative analysis can be made with as little as 10 to 15 g drug per spot.     

A simple device for continuous and selective detection of water vapour evolved during thermal decomposition reactions

A technique developed for the continuous and selective detection of water vapour formed during thermal decomposition reactions is described. The device can be connected to different types of thermoanalytical instruments without any difficulties. The detector can closely follow changes in the amount of water released during decomposition reactions, with negligible time delay. The signal curves obtained by the detector can be compared to the simultaneously recorded thermoanalytical curves and used to determine the step in which the water was released. The device as a free standing unit can be used to detect water plugs in different gas flows as well.     

Continuous determination of carbon dioxide evolved during thermal decomposition reactions

A simple device suitable for continuous monitoring of carbon dioxide evolved during thermal decomposition reactions is described. Carbon dioxide is transported by a carrier gas through the device connected to thermoanalytical equipment and absorbed by soda lime reagent. The reaction heat released is linearly proportional to the amount of carbon dioxide absorbed.     

Investigation of RuO2-IrO2-SnO2 thin film evolution

The thermal evolution process of RuO₂–IrO₂–SnO₂ mixed oxide thin films of varying noble metal contents has been investigated under in situ conditions by thermogravimetry-mass spectrometry (TG-MS), infrared emission spectroscopy (IR) and cyclic voltammetry (CV). The gel-like films prepared from aqueous solutions of the precursor compounds RuOHCl₃, H₂IrCl₆ and Sn(OH)₂(CH₃COO)_2–xCl_x on titanium metal support were heated in an atmosphere containing 20% O₂ and 80% Ar up to 600°C. Chlorine evolution takes place in a single step between 320 and 500°C accompanied with the decomposition of the acetate ligand. The decomposition of surface species formed like carbonyls, carboxylates and carbonates occurs in two stages between 200 and 500°C. The temperature of chlorine evolution and that of the final film formation increases with the increase of the iridium content in the films. The anodic peak charge shows a maximum value at 18% iridium content.     

1-D cobalt(II) spin transition compound with strong interchain interaction: [Co(pyterpy)Cl(2)].X

Cobalt(II) compounds [Co(pyterpy)Cl(2)].MeOH (1.(MeOH)) and [Co(pyterpy)Cl(2)].2H(2)O (1.(2H(2)O)) were synthesized. The compound 1.(MeOH) forms the quasi 3-D networks by making pi-pi stacking between the 1-D chains. The methanol molecules from 1.(MeOH) can be removed by heating, and substituted by absorption of water molecules. The MeOH molecules in 1.(MeOH) are removed by heating at 410 K, and they are substituted by water molecules to form 1.(2H(2)O). 1.(2H(2)O) exhibits a S = (3)/(2) (HS) left arrow over right arrow S = (1)/(2) (LS) spin transition with a thermal hysteresis. We have succeeded in constructing a guest dependent 1-D spin-crossover cobalt(II) compound.