Arimoto S.,Tsuyama National College of Technology
Journal of Mathematical Chemistry | Year: 2011
Fukui's DNA problem is a long-range target of the First and Second Generation Fukui Project, whose underlying motive has been to cultivate a new interdisciplinary region between chemistry and mathematics. The normed repeat space Xr(q, d, p) and its super space XB(q, d, p) are special Banach algebras which are fundamental in the second generation Fukui project. In the present article, keeping Fukui's DNA problem in mind, we formulate and solve a prototypal problem (problem I) of the normed repeat space Xr(q, d, p) and its super space XB(q, d, p). The present article provides also three "Challenging Problems" II-IV. These are called parallel problems in view of the structural parallelism observed when compared with the original problem I. The challenging problems, which would allow multiple approaches, are specially designed for those who are interested in interdisciplinary investigations. © 2010 Springer Science+Business Media, LLC.
Hasegawa K.,Muroran Institute of Technology |
Shimada T.,Tsuyama National College of Technology
Japanese Journal of Applied Physics | Year: 2012
A staggered grid for velocity-stress formulation is presented for modeling elastic waves in anisotropic solids by the finite-difference time domain method. To simply impose boundary conditions on numerical models, our grid is derived by applying a finite integration technique to a single control volume satisfying Newton's law instead of interleaved control volumes for conventional staggered grids. Computed results for the numerical dispersions of the new grid for propagating vertically polarized shear and longitudinal waves in an isotropic solid show that the numerical dispersions of the new grid can be suppressed to the same levels as those of the conventional staggered grids by using a third-degree bipolynomial interpolation. © 2012 The Japan Society of Applied Physics.
Ono T.,Tsuyama National College of Technology
Transactions of the North American Manufacturing Research Institution of SME | Year: 2010
Wear characteristics of small ball end mills in the micro milling process on optical glass are discussed. A method to measure loss of cutting edge is developed to observe the wear characteristics of glass milling. This method allows the loss of cutting edge to be determined from the surface profile of a machined surface with a numerical approach. Cutting tests are performed by changing of the attitude of the tool cutting edge and typical cutting conditions to verify the validity of the developed method and to observe the wear characteristics in glass milling. In this experiment, the loss of cutting edge is changed by tool attitude because the cutter velocity of actual cutting area is changed by tool attitude. On the other hand, the loss of cutting edge is not changed with the rotational speed and feed rate of the milling tool in which a crack-free surface can be obtained. In addition, diamond-coated carbide tools show high durability. However, they leave small brittle cracks on the machined surface. It is concluded that the flank wear does not grow enough to suppress the brittle crack because of the hardness of the diamond coat.
Arimoto S.,Tsuyama National College of Technology
Journal of Mathematical Chemistry | Year: 2016
The Asymptotic Linearity Theorem, which proves the Fukui conjecture in a broader context, plays a significant role in the repeat space theory, which is the central unifying theory in the first and the second generation Fukui Project. Proving the Asymptotic Linearity Theorem Extension Conjecture (ALTEC) is a fundamental problem in the repeat space theory. In the present paper, we give a proof of the ALTEC using inwardly repeating fractal structures of some functions used in Matrix Art from the Niagara Project, which is part of the second generation Fukui Project. In recent years, the Niagara Project has been extended to the broader project of Science-Art Multi-angle Network, and the second generation Fukui Project is also called the New Frontier Project. © 2015, Springer International Publishing Switzerland.
Abe T.,Tsuyama National College of Technology
International Journal of Mechanical Sciences | Year: 2014
The r-value is defined as the ratio of the width strain to the thickness strain. It was pointed out that the r-value can be defined for each grain in polycrystalline metal during plastic deformation. Based on r-value of grains, a model of plastic deformation of polycrystalline metal and surface roughening after plastic deformation is proposed in the present paper. Various experimental features of the surface roughening under uniaxial stress are well explained with the present first model. Meanwhile, the r-value is also known as a measure of formability in the sheet metal forming process. Marciniak and Kuczynski proposed the so-called M-K model which gives the analytical estimation of the formability of sheet metal under biaxial stretching considering a certain irregularity of the thickness of the sheet metal. Yamaguchi et al. showed that the experimentally measured surface roughness may correspond to the surface irregularity suggested in the M-K model. In the present paper, the formability of sheet metal under biaxial stretching is analyzed based on the surface roughening model caused by the difference of the r-value in sheet metals. © 2014 Elsevier Ltd. All rights reserved.