Indivisibility of Class Numbers of Real Quadratic Fields

Let D denote the fundamental discriminant of a real quadratic field, and let h(D) denote its associated class number. If p is prime, then the Cohen and Lenstra Heuristics give a probability that ph(D). If pgt;3 is prime, then subject to a mild condition, we show that

ESR studies on the formation of p-benzosemiquinone anions over manganese dioxide

The reaction between a hydroquinone aqueous solution and manganese dioxide has been investigated by electron paramagnetic resonance spectroscopy. A very stable p-benzosemiquinone anion is formed when an aqueous solution of hydroquinone is passed through a column of manganese dioxide. The kinetics for the reaction between hydroquinone and manganese dioxide follow the equation where A₀ is the initial concentration of hydroquinone, C is the concentration of p-benzosemiquinone anions, W is the amount of manganese dioxide, F is the feed rate of a hydroquinone aqueous solution, and k₁⁰ and k₂⁰ are constants; k₁⁰ = 3.1 × 10^?2 (cm³/g MnO₂· min), k₂⁰ = 3.2 (cm³/g MnO₂·min). A mechanism for the reaction is proposed such that Mn(IV) in manganese dioxide is reduced to Mn (II) with hydroquinone from which the semiquinone anion is formed via a neutral semiquinone. The formation of semiquinone anions from several substituted hydroquinones is also discussed.     

Subwavelength optical imaging through a metallic nanorod array

We propose a subwavelength imaging system without a lens or a mirror but with an array of metallic nanorods. The near-field components of dipole sources were plasmonically transferred through the rod array to reproduce the source distribution in the other side. We calculated the field distribution at the different planes of imaging process using the finite-difference time-domain algorithm and found that the spatial resolution was 40 nm given by the rod size and spacing. A typical configuration is a hexagonal arrangement of silver rods of 50 nm height and 20 nm diameter. We also show that the image formation highly depends on the coherence and the polarization of the source distribution and the source-array distance.     

Direct observation of excitons and a continuum of one-dimensional Mott insulators: a reflection-type third-harmonic-generation study of Ni-halogen chain compounds

The third-harmonic-generation (THG) spectrum was measured for a NiBr-chain compound, which is a one-dimensional Mott insulator, in a reflection configuration. A sharp peak and a shoulder structure in the THG spectrum are attributed to three-photon resonance to an exciton and a continuum, respectively. The band-edge energy, the exciton binding energy, and the spectral weights for the exciton and the continuum were determined from comparative studies of linear absorption, THG, and electroreflectance spectra. The excitonic effect is more pronounced in the NiCl chain than in the NiBr chain.     

Evolution of the Hall coefficient and the peculiar electronic structure of the cuprate superconductors

Although the Hall coefficient R(H) is an informative transport property of metals and semiconductors, its meaning in the cuprate superconductors has been ambiguous because of its unusual characteristics. Here we show that a systematic study of R(H) in La2-xSrxCuO4 single crystals over a wide doping range establishes a qualitative understanding of its peculiar evolution, which turns out to reflect a two-component nature of the electronic structure caused by an unusual development of the Fermi surface recently uncovered by photoemission experiments.     

Chiral phosphinooxazolidine ligands for palladium- and platinum-catalyzed asymmetric Diels-Alder reactions

Cationic palladium (Pd)- and platinum (Pt)-phosphinooxazolidine catalysts 13a-c, 15a-d, 17a-c, and 19a-c were prepared from phosphinooxazolidine ligands 1-3, MCl(2) (M = Pd and Pt), and counterions, and the activities of the catalysts in the asymmetric Diels-Alder (DA) reactions of cyclic or acyclic dienes with imide dienophiles were investigated. These catalysts demonstrated high levels of catalytic activity. The cationic Pd-POZ complex 13c provided particularly excellent enantioselectivity (98% ee) in the DA reactions of cyclopentadiene with acryloyl-, crotonyl-, and fumaroyl-1,3-oxazolidin-2-ones (20a-c).     

Novel spirocyclic trichothecanes, spirotenuipesine A and B, isolated from entomopathogenic fungus, Paecilomyces tenuipes

Entomopathogenic fungi forming fruiting bodies have been employed as tonics and antitussives from ancient times. Paecilomyces tenuipes, which is also called Isaria japonica, is a very popular entomopathogenic fungus and is often considered a health food in northeast Asian countries such as China, Korea, and Japan. We cultivated the fruiting bodies of Paecilomyces tenuipes. Among the large-scale cultivations, fruiting body grown in barley grain contained two novel spirocyclic trichothecane derivatives, spirotenuipesine A (1) and B (2), and known trichothecane mycotoxins. Compounds 1 and 2 showed potent activity in neurotrophic factor biosynthesis in glial cells. The isolation of these compounds indicated that P. tenuipes is a promising source for producing various biologically active substances including trichothecanes. It is noteworthy that trichothecane mycotoxins are present in Paecilomyces tenuipes, which is typically used in medicinal health food.