The joint universality theorem for a pair of Hurwitz zeta functions

In this paper we investigate the joint functional distribution for a pair of Hurwitz zeta functions ζ(s,αj) (j=1,2) in the case that real transcendental numbers α₁ and α₂ satisfy α₂∈Q(α₁). Especially we establish the joint universality theorem for these zeta functions.     

Synthesis and X-ray crystal structure of a difunctionalized pillar[5]arene at A1/B2 positions by in situ cyclization and deprotection

The reaction of 1,4-dimethoxybenzene and paraformaldehyde using AlBr(3) yields multiple-deprotected pillar[5]arenes. A1/B2 di-deprotected pillar[5]arene can be isolated by silica gel chromatography and washing procedures. The X-ray structure and polymerization of the A1/B2 di-deprotected pillar[5]arene are reported.     

Seven New Monoterpenoid Indole Alkaloids from Gelsemium elegans

Seven new indole alkaloids were isolated from the roots of Gelsemium elegans Benth. and their structures were determined by spectroscopic analysis and chemical transformation from known alkaloids. Kounaminal ( 1 ) is a new koumine‐type alkaloid that contains an unusual aminal moiety. Humantenoxenine ( 2 ) and 15‐hydroxyhumantenoxenine ( 3 ) are humantenine‐type alkaloids that contain a novel β‐amino‐α,β‐unsaturated ketone residue. The other four novel alkaloids are two gelsedilam‐related and two gelsenicine‐related alkaloids.     

Characterization of rankings generated by linear discriminant analysis

Pairwise linear discriminant analysis can be regarded as a process to generate rankings of the populations. But in general, not all rankings are generated. We give a characterization of generated rankings. We also derive some basic properties of this model.     

Syntheses of tetraoxaquaterene derivatives

Several new dimethyl and tetramethyl tetraoxaquaterenes, 3d and 3e , have been prepared in order to synthesize the oxygen analogues of porphyrin. The reaction between furan and a ketone using an acidic catalyst gave the cyclic tetramer, tetraquaterene, and oligomers. On the other hand, in the case of furan and an aldehyde, only linear oligomers were isolated. The condensation of furan-containing dimers with carbonyl compounds, both ketone and aldehyde, except formaldehyde, gave the tetraoxaquaterene. In the case of formaldehyde, the yield of cyclic tetramer was negligible.     

Some realistic calculations on the migration process of hydrogen isotopes in bcc metals

By adopting the empirical interaction potential between hydrogen and metal atoms determined in our previous paper, calculations have been performed of the 2T configuration, in which two neighboring tetrahedral (T) sites are equally shared by a hydrogen (H) atom. The tunneling matrix element J and the activation energy are estimated by calculating the excitation energy of the H atom for the 2T state and the energy difference between the 2T and 1T state, respectively.From these calculations, it is suggested that H atoms in V and Fe migrate between the ground states of neighboring T sites by adiabatic transitions, whereas in the lower temperature region in Ta by non-adiabatic tunneling process.     

A new method for the synthesis of α-arylalkanoic acids by the use of 1,2-rearrangement of the aryl group

A simple synthetic method of α-arylalkanoic acids was accomplished by the use of a novel 1,2-rearrangement of the aryl group and this method was applied to the syntheses of some biologically important substances.     

The morphology of polyethylene prepared by γ-ray-induced polymerization in various solvents

Polyethylenes were prepared by γ-ray-induced polymerization in ethyl and n-butyl alcohols, tert-butyl alcohol containing 5 vol-% of water, 2,2,5-trimethylhexane, 2,2,4-trimethylpentane, and cyclohexane in the temperature range 25–90°C. The morphology of the polymers as-polymerized and studied by electron microscopy depends on three factors through the degree of undercooling: the affinity of the solvent, polymerization temperature, and the polymer molecular weight. Large lamellar crystals are formed even in the alcohols when at least two of them are chosen properly.     

Soft x-ray spectroscopy of Ba24Ge100: electronic phase transition and Ba-atom rattling

The electronic states of Ba24Ge100 are studied by soft x-ray photoelectron spectroscopy (XPS) at a high-energy photon factory. A large reduction in the density of states (DOS) at the Fermi level is clearly shown before and after the electronic phase transition at 200 K. The changes in the spectrum widths and the fine structures of the core-level Ba 4d spectra give a very reasonable indication of the Ba-atom rattlings in the clathrate polyhedra. On-resonance experiments using the excitation from Ba 3d to 4f levels display that the wave functions of Ba 5d and 6s orbitals give only a small contribution to make a Fermi surface through the hybridization with the Ge20 cluster orbitals. Importantly, reliable values of the DOS at the Fermi level NEF are successfully deduced, using two data sets of DOS obtained from high-resolution XPS and the total magnetic susceptibilities by a superconducting quantum interference device, to be 0.149 and 0.0427 states eV(-1) (Ge atom)(-1) for a high-temperature and for a low-temperature phase.     

Stereoselective synthesis of tetrahydrofuran-3-carbaldehyde

Trans-tetrahydrofuran-3-carbaldehydes are prepared by ruthenium-catalyzed isomerization of 4,7-dihydro-1,3-dioxepines and subsequent Lewis acid-catalyzed 1,3-alkyl migration.