Quantum D-modules and equivariant Floer theory for free loop spaces

The objective of this paper is to clarify the relationships between the quantum D-module and equivariant Floer theory. Equivariant Floer theory was introduced by Givental in his paper ``Homological Geometry'. He conjectured that the quantum D-module of a symplectic manifold is isomorphic to the equivariant Floer cohomology for the universal cover of the free loop space. First, motivated by the work of Guest, we formulate the notion of ``abstract quantum D-module' which generalizes the D-module defined by the small quantum cohomology algebra. Second, we define the equivariant Floer cohomology of toric complete intersections rigorously as a D-module, using Givental's model. This is shown to satisfy the axioms of abstract quantum D-module. By Givental's mirror theorem [Giv3], it follows that equivariant Floer cohomology defined here is isomorphic to the quantum cohomology D-module.     

High-pressure and high-temperature generation using diamond/sic composite anvils prepared with hot isostatic pressing

Using a hot isostatic pressing (HIP) technique, we synthesized diamond/SiC composites from diamond and Si powders. At an HIP condition of 1450 °C and 100 MPa, a pressure much lower than that of the diamond stability field, diamond powders react with molten Si to form well-sintered diamond/SiC composites. Cubes of the composites with 15 mm edge length were thereby fabricated, and an application to the second stage anvils in a Kawai-type high-pressure apparatus was attempted. A hybrid anvils system using four cubes of the composites and four of the conventional WC was introduced and heating experiments up to 1600 °C became possible. Because the diamond/SiC composites are transparent to X-rays, the present system is applicable not only to diffraction studies but also to radiographic studies that need a larger window for an X-ray image.     

The boundary of higher rank numerical ranges

The rank-k-numerical range of an n×n matrix A is defined as

     

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.