The law of the iterated logarithm for the discrepancy of perturbed geometric progressions

Acta Mathematica Hungarica - We investigate the asymptotic distribution of perturbed geometric progression $$\{\theta^k x+ \gamma_k\}$$ given by $$\theta\in (-\infty, -1)\cup (1, \infty)$$ and...     

Ferromagnetism in hydrogenated graphene nanopore arrays

Theoretically, the so-called zigzag edge of graphenes provides localized electrons due to the presence of flat energy bands near the Fermi level. Spin interaction makes the localized spins strongly polarized, yielding ferromagnetism. However, in most experimental studies, ferromagnetism has been observed in uncontrollable and complicated carbon-based systems. Here, we fabricate graphenes with honeycomblike arrays of hexagonal nanopores, which have a large ensemble of hydrogen-terminated and low-defect pore edges that are prepared by a nonlithographic method (nanoporous alumina templates). We observe large-magnitude ferromagnetism derived from electron spins localizing at the zigzag nanopore edges. This promises to be a realization of graphene magnets and novel spintronic devices.     

Concise total synthesis of (+)-lyconadin a

The total synthesis of lyconadin A from (R)-5-methylcyclohex-2-enone was accomplished. Our synthesis features the facile construction of a highly fused tetracyclic compound through a combination of an aza-Prins reaction and an electrocyclic ring opening. Transformation of the bromoalkene moiety in the tetracycle could be achieved by either a vinylogous Pummerer rearrangement or the formation and subsequent isomerization of the nitrosoalkene to furnish an α,β-unsaturated ketone, from which the pyridone ring was constructed.     

Total synthesis of gelsemoxonine

The first total synthesis of gelsemoxonine (1) has been accomplished. Divinylcyclopropane-cycloheptadiene rearrangement of the highly functionalized substrate was successfully applied to assemble the spiro-quaternary carbon center connected to the bicyclic seven-membered core structure. A one-pot isomerization reaction of the α,β-unsaturated aldehyde to the saturated ester via the TMSCN-DBU reagent combination allowed a facile diastereoselective introduction of the latent nitrogen functionality of the unique azetidine moiety.     

Roles of electric field on toroidal magnetic confinement

Theoretical research on the influence of electric field on toroidal magnetic confinement is surveyed. The static electric field is first described. A physical picture of the radial electric field generation and its influence on confinement are shown. Neoclassical effects as well as the non-classical processes are discussed. Emphasis is made on the connection with improved confinement. Convective cells with a nonuniform potential on the magnetic surface are also discussed. The roles of the fluctuating electric field are then reviewed. Recent progress in anomalous transport theory is addressed. Through these surveys, the impact of experiments using the heavy ion beam probes on modern plasma physics is illustrated     

Study on the etching conditions of polycarbonate detectors for particle analysis of safeguards environmental samples

The fission track technique was applied to the particle analysis for safeguards environmental samples to obtain information about the isotope ratio of nuclear materials in individual particles. To detect the particles containing nuclear material with high detection efficiency and less particle loss, the influence of uranium enrichments on etching conditions of a fission track detector made of polycarbonate was investigated. It was shown that the increase in uranium enrichment shortened the suitable etching time both for particle detection and for less particle loss. From the results obtained, it was suggested that the screening of the uranium particles according to the enrichment is possible by controlling the etching time of the detector.     

An asymptotic property of gap series

Takahashi [15] gave a concrete upper bound estimate of the law of the iterated logarithm for ∑ f(n _k x). We extend this result and prove the best possibility of this bound. This revised version was published online in August 2006 with corrections to the Cover Date.     

Determination of isoniazid in tablets by second-derivative ultraviolet spectrophotometry of scraped-spot solutions from thin-layer chromatography

Isoniazid in solutions of tablets was separated by thin-layer chromatography (TLC). The portion of the precoated plate carrying the isoniazid spot was cut out and the coating was scraped off into water. The isoniazid was quantified in the solution, without separation of suspended adsorbent, by second-derivative spectrophotometry, which eliminated the background in the zero-order spectra. Relative standard deviations (n = 5) were <1%. Results obtained for commercial tablets were in good agreement with those given by a liquid-chromatographic method.     

Penning ionization electron spectroscopy and photo-electron spectroscopy of molecular solids. II. Ammonia and water

The Penning ionization electron spectra (PIES) and ultraviolet photoelectron spectra (UPS) of ammonia and water molecules condensed on a cold metal substrate have been measured using thermal He*(2³S, 2¹S) metastable atoms and He(I) (58.4 nm) photons. The shifts of the observed positions of the PIES peaks relative to those of the UPS peaks in the condensed phase are roughly equal to the corresponding shifts in the gas phase. The relative intensities of the 3a₁ and 1e orbital peaks are reversed in the PIES and UPS for both gaseous and condensed ammonia; the origin of this reversal is interpreted as the difference between the interactions with metastable atoms and photons. On the other hand, the relative intensities of the 3a₁ orbital peak in the PIES and UPS for condensed water decrease as compared to the gas-phase spectra. This implies participation of the 3a₁ orbital of water in the hydrogen bonding.     

(1-nosyl-5-nitroindol-3-yl)methyl ester: a novel protective group for carboxylic acids

The usefulness of (1-nosyl-5-nitroindol-3-yl)methyl esters as a novel protective group for carboxylic acid is fully demonstrated. The novel protective group is stable under a broad range of conditions and can easily be deprotected under the mild conditions used for removal of the nosyl (Ns) group. It is orthogonal to the existing protective groups for carboxylic acids such as t-butyl and allyl esters.