Family of symplectic implicit Runge-Kutta formulae

A family of formulae for the sympletic IRK method is investigated. Specifically, focus is given to general solutions for formula parameters of IRK under the symplectic and the order conditions. Examples of such formulae are constructed for up to three stages.     

Listening difficulty as a subjective measure for evaluation of speech transmission performance in public spaces

Listening difficulty ratings, using words with high word familiarity, are proposed as a new subjective measure for the evaluation of speech transmission in public spaces to provide realistic and objective results. Two listening tests were performed to examine their validity, compared with intelligibility scores. The tests included a reverberant signal and noise as detrimental sounds. The subject was asked to repeat each word and simultaneously to rate the listening difficulty into one of four categories: (1) not difficult, (2) a little difficult, (3) fairly difficult, and (4) extremely difficult. After the tests, the four categories were reclassified into, not difficult [response (1)] and some level of difficulty, (the other 3 responses). Listening difficulty is defined as the percentage of the total number of responses indicating some level of difficulty [i.e. not (1)]. The results of two listening tests demonstrated that listening difficulty ratings can evaluate speech transmission performance more accurately and sensitively than intelligibility scores for sound fields with higher speech transmission performance.     

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.     

Parallel Implementation of Successive Convex Relaxation Methods for Quadratic Optimization Problems

As computing resources continue to improve, global solutions for larger size quadrically constrained optimization problems become more achievable. In this paper, we focus on larger size problems and get accurate bounds for optimal values of such problems with the successive use of SDP relaxations on a parallel computing system called Ninf (Network-based Information Library for high performance computing).