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Professor |
Professor |
Associate Professor |
Assistant Professor |
- Matrix-theoretic high-performance algorithm construction, with application to the numerical computation of critically important quantities associated with difficult special functions occurring from 3-D wave equations, such as regular Coulomb wave functions, Mathieu functions, spheroidal wave functions, Lame functions, ellipsoidal wave functions. The Bessel function of the first kind, an easier function serves as a model case, where two types of computational problems were solved in the complex domain as well as real domain: given a complex order Bessel function, compute a given number of zeros closest to the origin to a specified accuracy; and given a complex number find a specified number of orders of Bessel functions closest to the origin, to a specified accuracy. There are no comparable algorithms known elsewhere which give as accurate an error estimate as ours.
- Construction of hyper English word study dictionary: it is available at http://hidic.u-aizu.ac.jp/. This represents a long-range project, aiming at compiling a database for the study of English words for Japanese students. The main feature is that the dictionary is organized to bring out the best fruits of comparative linguistics in the past century: the usefulness of IndoEuropean roots as presented in the wonderful book by Calvert Watkins, The American Heritage Dictionary of Indo-European Roots, Second Edition, HoughtonMifflin, 2000. Example: The organizing principle of the dictionary will tell you that the following words are best studied as a group: riddle, garble, crime, decree, discern, secret, hypocrisy (they are all derivatives from the same Indo-European root krei-, meaning "to sieve", indicating that a group of seemingly unrelated words come from the same notion "to sieve"). Another example: the usage of the so-called synonyms "anger, rage and wrath" can be clearly explained by tracing them back to their respective Indo-European root: anger to angh-, meaning painful, rage to rebh-, meaning violent, impetuous, and wrath to wreit-, meaning to turn, twist (anger is akin to angst, angina, rage is akin to rabid, rabies, and wrath is akin to wreath, writhe).
We conduct research works extensively related to the fundamental theories and advanced
applications of mathematics, especially in numerical computation. |
| Prof. Kanda's research interests are mainly in numerical analysis of partial differential
equations, and emphasis is placed on the development of program codes for Navier-Stokes
Equation in complex-shaped
ow elds. Differential geometry, tensor analysis, and grid
generation are also studied as needed. |
| In 1883, Osborne Reynolds observed the transition between laminar and turbulent
ows in circular pipes; the critical values of Rc were 12,830 for the color-dye method and
2030 for the pressure method. These values have yet to be theoretically obtained. Hence,
Prof. Kanda succeeded in the calculation of the minimum critical Reynolds number,
Rc(min), of 2040 in 1999 for the rst time in history. Then, he wanted to con rm the Rc
of 12,830 experimentally before starting calculations, but it is very difficult to reproduce
Rc. Therefore, he has been carrying out experiments similar to Reynolds color-dye
experiment everyday and every weekends since March 2003 to x physical constants
for Rc. Thus, he realized in 2004 that studies of science take three steps of analysis:
veri cation of real phenomena, building of physical model, and calculation based on
mathematical model. |
| Prof. Asai's major research fronts may be described as follows:
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Unreferred Papers
| [nasai-01:2007] |
N. Asai, Y. Miyazaki, and Y. Ikebe. Derivation of an Error Estimate for the Eigenvalue Problem of Lame Equation. In SciCADE07(Scienti c Compu- tation And Differential Equation 07) poster presentation, Sant. Malo, France, 2007. |
| [nasai-02:2007] |
Nobuyoshi Asai, Yoshinori Miyazaki, and Yasuhiko Ikebe. Eigenvalue Problem of Lame EquationL. In Proceedings of the 2007 Annual Conference of the Japan Society for Industrial and Applied Mathematics, pages 106{107, 2007. |
| [nasai-03:2007] |
Nobuyoshi Asai, Yoshinori Miyazaki, and Yasuhiko Ikebe. E-Contents for Linear Algebra and Implementation of Equation Editor on Moodle. In Scienti c Seminar, Annual Meeting of Japan e-Learning Association 2007, 2007. |
| [nasai-04:2007] |
Nobuyoshi Asai, Yoshinori Miyazaki, and Yasuhiko Ikebe. A Consideration of Open Contents Decoding Papers on Society. In Proceedings of the 36th Numerical Analysis Symposium 2007, pages 75{78, 2007. |
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