Orthogonal projections of cubes and regular simplices into a plane

We show that for every \({k\ge 2}\) and \({n\ge k}\), there is an \({n}\)-dimensional unit cube in \({\mathbb{R}^n}\) which is mapped to a regular \({2k}\)-gon by an orthogonal projection in \({\mathbb{R}^n}\) onto a \({2}\)-dimensional subspace. Moreover, by increasing dimension \({n}\), arbitrary large regular \({2k}\)-gon can be obtained in such a way. On the other hand, for every \({m\ge 3}\) and \({n\ge m-1}\), there is an \({n}\)-dimensional regular simplex of unit edge in \({\mathbb{R}^n}\) which is mapped to a regular \({m}\)-gon by an orthogonal projection onto a plane. Moreover, contrary to the cube case, arbitrary small regular \({m}\)-gon can be obtained in such a way, by increasing dimension \({n}\).     

Okamoto model for necrosis and its expansions,CD38-cyclic ADP-ribose signal system for intracellular Ca2+ mobilization and Reg (Regenerating gene protein)-Reg receptor system for cell regeneration

In pancreatic islet cell culture models and animal models, we studied the molecular mechanisms involved in the development of insulin-dependent diabetes. The diabetogenic agents, alloxan and streptozotocin, caused DNA strand breaks, which in turn activated poly(ADP-ribose) polymerase/synthetase (PARP) to deplete NAD⁺, thereby inhibiting islet β-cell functions such as proinsulin synthesis and ultimately leading to β-cell necrosis. Radical scavengers protected against the formation of DNA strand breaks and inhibition of proinsulin synthesis. Inhibitors of PARP prevented the NAD⁺ depletion, inhibition of proinsulin synthesis and β-cell death. These findings led to the proposed unifying concept for β-cell damage and its prevention (the Okamoto model). The model met one proof with PARP knockout animals and was further extended by the discovery of cyclic ADP-ribose as the second messenger for Ca²⁺ mobilization in glucose-induced insulin secretion and by the identification of Reg (Regenerating gene) for β-cell regeneration. Physiological and pathological events found in pancreatic β-cells have been observed in other cells and tissues.     

On distance-biregular graphs of girth divisible by four

We apply a circuit chasing technique to distance-biregular graphs of girth divisible by four to derive a parameter restriction. As an application, we give a classification of distance-biregular graphs of girth divisible by four with trivalent vertices.     

Well-crystallized zinc oxide quantum dots with narrow size distribution

In this study, pulsed laser ablation, online annealing, and following size classification using a differential mobility analyzer (DMA) were employed to fabricate quantum dots (QDs) of zinc oxide (ZnO). The irregularly shaped ZnO particles were obtained at annealing temperature less than 873 K, which gradually transformed into spherical QDs with increasing the annealing temperature. Finally, ZnO QDs with narrow size distribution having spherical shapes were successfully obtained at temperatures above 1173 K under the DMA classification at a nominal size of 10 nm. TEM observation demonstrated that the ZnO QDs obtained by this process were well-crystallized single crystallites with a wurtzite structure. Further, ZnO QDs with average sizes in the range of 4.8–8.1 nm were successfully fabricated by reducing the specified sizes of DMA. These features of the fabricated ZnO QDs are favorable for investigation of intrinsic quantum size effect in ZnO.     

Size-selected copper oxide nanoparticles synthesized by laser ablation

Size-tuned copper oxide nanoparticles with sizes of 9, 12, and 15 nm were fabricated by laser ablation and on-line size selection using a differential mobility analyzer at a gas pressure of 666 Pa. The dependence of the particle properties on the in situ annealing temperatures and selection sizes was investigated. The crystalline phases of the nanoparticles fabricated at temperatures below 973 K were assigned to monoclinic cupric oxide (CuO) which converted into cubic cuprous oxide (Cu₂O) when the annealing temperature was above 1,173 K. This indicates that the crystalline phases can be easily controlled by changing the annealing temperature. TEM images confirmed that well-crystallized and well-dispersed CuO and Cu₂O nanoparticles with narrow size distributions were obtained using this method. This fabrication process is useful and promising for the future investigation of the intrinsic size-dependent properties of CuO and Cu₂O.     

Impurity substitution effects in BiFeO3 thin films—From a viewpoint of FeRAM applications

Impurity substitution effects in BiFeO₃ thin films are reviewed from a viewpoint of FeRAM (ferroelectric random access memory) applications, in which such characteristics as a large remanent polarization, a low coercive voltage, and excellent fatigue endurance are most important. First, it is described that substitution experiments for Bi and Fe atoms in the films have already been conducted using almost all rare earth and transition metal elements. A list of the published paper is given in a form of the periodic table of elements. Then, two typical cases, La substitution for the Bi site and Mn substitution for the Fe site, are reviewed in detail. Particular attention is paid to the role of these impurity atoms by which the ferroelectric and insulating properties of BiFeO₃ films are significantly improved. Finally, impurity effects due to substitution or co-substitution of other elements are reviewed.     

The mineralization of CO32− ions on chitin- or chitosan- metal composite beads in water

The following dry composite beads (diameter 1.0-1-2 mm) were prepared: chitin-CaCO₃, chitosan-CaCl₂. chitosan-CuCl₂, partially N-acetylated chitosan-CuCl₂, chitosan-CuSO₄, chitosan-Fe₃O₄, chitin-SiO₂. Each of chitosan-CuCl₂, chitosan-CuSO₄ and chitin-CaCl₂ composite beads was treated in aqueous K₂CO₃ at room temperature to afford a mixture of metal carbonates and hydroxides on chitin or chitosan chain.     

Magneto-Optical Properties of Silica Gel Containing Magnetite Fine Particles

The magnetic composite materials that consist of transparent matrix and magnetic fine particles are expected to have large residual magnetization and coercive force because of their fine magnetic domain structure, and also to show magneto-optical effects. Silica gels containing magnetite (Fe₃O₄) fine particles were prepared by sol-gel method. The magnetic, optical and magneto-optical properties of the composites were investigated by measurements of magnetization curves, UV-visible spectra and Faraday rotation in visible range. The saturation magnetization of the composite was almost as same as that expected from the amount of magnetite fine particles in it. Although the composites had large and broad absorption at around 400 nm, they still maintained their transparency. The origins of decrement of transparency attributed to the optical absorption of magnetite and scattering due to magnetite fine particles. The whole composites showed positive Faraday rotation under external static magnetic field due to the large contribution of diamagnetic silica gel matrix. Magnetite contributed negative Faraday rotation with maximum at around 470–480 nm to the magneto-optical spectra of the composites.     

New synthetic routes to optically active alpha-quaternary alpha-aryl amino acid derivatives via the diastereoselective Stevens and Sommelet-Hauser rearrangements

The Stevens rearrangement of N-allylic alpha-aryl amino acid-derived ammonium salts and the Sommelet-Hauser rearrangement of N-benzylic alpha-alkyl amino acid-derived ammonium salts are shown to proceed with remarkably high levels of diastereoselectivity. The methods presented in this work provide new routes to optically active alpha-quaternary alpha-aryl amino acid derivatives.     

Chiral distortion in a Mn(IV)(salen)(N3)2 derived from Jacobsen's catalyst as a possible conformation model for its enantioselective reactions

The Mn (IV)(salen)(N 3) 2 complex ( 3) from Jacobsen's catalyst is synthesized, and the X-ray crystal structures of 3 as well as the starting Mn (III)(salen)(N 3)(CH 3OH) complex ( 2) are determined in order to investigate the conformation of the high-valent Mn (IV)(salen) molecule in comparison with that of Mn (III)(salen). The asymmetric unit of the crystal of 3 contains four complexes, all of which adopt a nonplanar stepped conformation effectively distorted by the chirality of the diimine bridge. The asymmetric unit of 2 also contains four complexes. Two of them show a stepped conformation of a lesser degree, but the other two adopt a bowl-shaped conformation. Comparison of the structural parameters shows that the Mn center in 3 is coordinated from both sides by two external axial N 3 ligands with significantly shorter bond lengths, which could induce greater preference for the stepped conformation in 3. The CH 3CN solution of 3 shows circular dichroism with a significantly strong band at 275 nm as compared to 2, suggesting that 3 may adopt a more chirally distorted conformation also in solution. The circular dichroism spectrum of 3 is slightly altered with isodichroic points from 298 to 253 K and shows no further change at temperatures lower than 253 K, suggesting that the solution of 3 contains an equilibrium between two conformers, where a low-energy conformer with more chiral distortion is predominantly favored even at room temperature. Complexes 2 and 3 are thoroughly characterized using various techniques including cyclic voltammetry, magnetic susceptibility, UV-vis, electron paramagnetic resonance, (1)H NMR, infrared spectroscopy, and electrospray ionization mass spectrometry.