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.     

Simple Extraction and HPLC Determination of UV-A and UV-B Filters in Sunscreen Products

The determination of 11 organic UV filters, worldwide authorised in sunscreen formulations, was performed by HPLC with UV spectrophotometric detection. The filters determined were: phenylbenzimidazole sulfonic acid, benzophenone-4, benzophenone-3, 4-methylbenzylidene camphor, ethylhexyl methoxycinnamate, octocrylene, methylene bis-benzotriazolyl tetramethylbutyl phenol, butyl methoxydibenzoylmethane, bis-ethylhexyloxyphenol methoxyphenyltriazine, ethylhexyl triazone, and diethylamino hydroxybenzoyl hexyl benzoate. Three analytical methods were developed which were based on an ultrasonic extraction of the sample in methanol/1% aqueous acetic acid (70:30, v/v) or dimethylacetamide/propan-2-ol (1:1, v/v) in dependence of the water or fat-solubility of the filter, followed by HPLC separation and quantitation. HPLC was carried out using three different columns and eluting conditions. Standard calibration curves were linear for all the analytes over the concentration range 0.5–100 μg mL^?1. UV measurements were carried out at 280, 300, 310 or 360 nm with the aid of a diode array detector in dependence on the maximum absorption of each filter. Quantitative recoveries were obtained for all sunscreen compounds determined in homemade formulations. The proposed analytical procedure has been successfully applied for the analysis of commercial samples in order to check the presence of UV filters and to determine their concentration.     

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.     

Rate constant for the reaction of OH radicals with CH3C(O)Cl determined by direct kinetic method

Summary The fast flow technique with OH resonance fluorescence detection has been applied at T = 298 ± 2 K to study the kinetics of the overall reaction: H + CH₃C(O)Cl → products (1) A rate constant value of k₁ = (1.02 ± 0.12) x 10¹⁰ cm³ mol^-1 s^-1 has been determined which is the first direct kinetic parameter reported for reaction (1) in the literature (the error given refers to 2σ accuracy).     

Morphology,surface roughness,electron inelastic and quasielastic scattering in elastic peak electron spectroscopy of polymers

In elastic peak electron spectroscopy (EPES), the nearest vicinity of elastic peak in the low kinetic energy region reflects electron inelastic and quasielastic processes. Incident electrons produce surface excitations, inducing surface plasmons, with the corresponding loss peaks separated by 1–20 eV energy from the elastic peak. In this work, X‐ray photoelectron spectroscopy (XPS) and helium pycnometry are applied for determining surface atomic composition and bulk density, whereas atomic force microscopy (AFM) is applied for determining surface morphology and roughness. The component due to electron recoil on hydrogen atoms can be observed in EPES spectra for selected primary electron energies. Simulations of EPES predict a larger contribution of the hydrogen component than observed experimentally, where hydrogen deficiency is observed. Elastic peak intensity is influenced more strongly by surface morphology (roughness and porosity) than by surface excitations and quasielastic scattering of electrons by hydrogen atoms. Copyright © 2007 John Wiley & Sons, Ltd.