Rellich’s theorem for spherically symmetric repulsive Hamiltonians

For spherically symmetric repulsive Hamiltonians we prove Rellich’s theorem, or identify the largest weighted space of Agmon–Hörmander type where the generalized eigenfunctions are absent. The proof is intensively dependent on commutator arguments. Our novelty here is a use of conjugate operator associated with some radial flow, not with dilations and not with translations. Our method is simple and elementary, and does not employ any advanced tools such as the operational calculus or the Fourier analysis.

     

Water revealed as molecular mirror when measuring low concentrations of sugar with near infrared light

Near infrared spectroscopy is an overtone spectroscopy regarded as a quick and non-destructive method that provides analytical solutions for components that represent approximately 1% or more of the total mass of the investigated composite samples. Aquaphotomics offers the possibility for disentanglement of information remaining hidden in the spectra when conventional data evaluation methods are used, since this concept utilizes changes of the water structure induced by the measured solute as specific molecular vibrations at water bands. Here, near infrared technique and aquaphotomics are applied for non-destructive identification and quantification of mono- and di-saccharide solutes at 100–0.02 mM concentration that is accepted as unachievable with near infrared spectroscopy. The results presented in this study support the aquaphotomics' water molecular mirror concept that explores spectral changes related to water molecular rearrangements caused by minute changes of the solutes in the aqueous systems. The method provides quick and accurate alternative for classical analytical measurements of saccharides even at millimolar concentration levels.     

Vacuum birefringence in strong magnetic fields: (I) Photon polarization tensor with all the Landau levels

Photons propagating in strong magnetic fields are subject to a phenomenon called the “vacuum birefringence” where refractive indices of two physical modes both deviate from unity and are different from each other. We compute the vacuum polarization tensor of a photon in a static and homogeneous magnetic field by utilizing Schwinger’s proper-time method, and obtain a series representation as a result of double integrals analytically performed with respect to proper-time variables. The outcome is expressed in terms of an infinite sum of known functions which is plausibly interpreted as summation over all the Landau levels of fermions. Each contribution from infinitely many Landau levels yields a kinematical condition above which the contribution has an imaginary part. This indicates decay of a sufficiently energetic photon into a fermion–antifermion pair with corresponding Landau level indices. Since we do not resort to any approximation, our result is applicable to the calculation of refractive indices in the whole kinematical region of a photon momentum and in any magnitude of the external magnetic field.     

Morphological studies of a hydrogen-bonded LC polymer obtained by photopolymerization in LC solvents

Anisotropic morphologies and the phase behaviour of a hydrogen-bonded LC polymer obtained by photopolymerization in two kinds of LC solvent are discussed. The hydrogen-bonded LC monomer, 4-(6-acryloyloxyhexyloxy) benzoic acid (A6OBA), was photopolymerized in 4-cyano-4′-hexyloxybiphenyl (6OCB) and in 4-cyano-4′-undecyloxybiphenyl (11OCB), which show a nematic phase and a smectic A phase, respectively. After photo-polymerization, the LC media were removed by extraction and the pure polymer was observed by scanning electron microscopy. SEM images showed that the polymer possessed fibrous morphology with a fibre diameter of a few micrometers, based on polymerization-induced phase separation. The overall geometries reflected typical LC characteristics such as schlieren and focal-conic fan textures. It was found that the hydrogen bond between benzoic acid groups in the monomer was rigid enough to fix the anisotropic phase-separated structure forming during the early stage of phase separation; however, it could not permanently maintain the fibre structure due to dissociation at elevated temperature. X-ray measurements revealed that a well developed layer structure of the hydrogen-bonded mesogen existed in the polymer obtained from the smectic phase of 11OCB, whereas a polymer layer structure could develop only partially from the nematic phase of 6OCB.     

Ammonium chiral borate salt catalyzed asymmetric Friedel-Crafts alkylation of indoles with α,β-disubstituted enals

In the presence of a catalytic amount of ammonium chiral borate salt, asymmetric Friedel-Crafts alkylation of indoles with α,β-disubstituted enals proceeded to give the corresponding 1,4-addition products with moderate enantioselectivities.     

Fluorine in Shark Teeth: Its Direct Atomic‐Resolution Imaging and Strengthening Function

Atomic‐resolution imaging of beam‐sensitive biominerals is extremely challenging, owing to their fairly complex structures and the damage caused by electron irradiation. Herein, we overcome these difficulties by performing aberration‐corrected electron microscopy with low‐dose imaging techniques, and report the successful direct atomic‐resolution imaging of every individual atomic column in the complex fluorapatite structure of shark tooth enameloid, which can be of paramount importance for teeth in general. We demonstrate that every individual atomic column in shark tooth enameloid can be spatially resolved, and has a complex fluorapatite structure. Furthermore, ab initio calculations show that fluorine atoms can be covalently bound to the surrounding calcium atoms, which improves understanding of their caries‐reducing effects in shark teeth.     

A Novel Synthesis of α-Tellanyl α,β-Unsaturated Aldehydes Using α-Tellanyl β-Alkoxyalkenyl Lithiums

Abstract

β-Ethoxy-α-phenyltellanylvinyl lithiums were successfully generated in situ from phenyltellanylacetaldehyde diethyl acetal with lithium 2,2,6,6-tetrame-thylpiperidide (LTMP) and underwent methylation or nucleophilic addition with aldehydes and ketones. The successive dehydration of the allylic alcohols with trimethylsilyl trifluoromethanesulfonate (TMSOTf) gave α-phenyltellanyl α,β-unsaturated aldehydes, which transformed to some useful compounds.