


 Department of Computer Software 
 Mathematical Foundation of Computer Science Laboratory 

  
 Hidesada kanda Professor  Nobuyoshi Asai Assistant Professor 


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 NavierStokes Equation in complexshaped flow felds. Differential geometry, tensor analysis, and grid generation are also studied as needed. He succeeded in the calculation of the minimum critical Reynolds number of 1230 for transition from laminar to turbulent flow between parallel plates in 2002 for the first time in history.

 Prof.Asai's major research fronts may be described as follows:


 1.  Matrixtheoretic highperformance algorithm construction, with application to the numerical computation of critically important quantities associated with diAEcult special functions occurring from 3D 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.


 2.  Construction of hyper English word study dictionary: it is available at http://hidic.uaizu.ac.jp/. This represents a longrange 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 IndoEuropean Roots, Second Edition, Houghton Miffin, 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 IndoEuropean 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 socalled synonyms "anger, rage and wrath" can be clearly explained by tracing them back to their respective IndoEuropean 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).



 [nasai01:2003]  Y. Miyazaki, N. Asai, Y. Kikuchi, D. Cai, and Y. Ikebe. Computation of Multiple Eigenvalues if Infinite Tridiagonal matrices. Mathe matics of Computation, 73(246):719730, 2004.



 [nasai01:2003]  Y. Miyazaki, N. Asai, Y. Kikuchi, D. Cai, and Y. Ikebe. Computation of Multiple Eigenvalues if Infinite Tridiagonal matrices. Mathe matics of Computation, 73(246):719730, 2004.


 Refereed Proceeding Papers 

 [nasai02:2003]  Y. Ikebe, T. Enomoto, D. S. Cai, N. Asai, Y. Miyazaki, and Y. Ikebe. Special Training Programs for Total QualityWriting(TQW). In Human Interface Symposium 2003, pages 659662. Human Interface Gakkai, Oct. 2003.

 [nasai03:2003]  Y. Ikebe, D. S. Cai, N. Asai, Y. Miyazaki, and Y. Ikebe. Scripting Elearning Contents (for Linear Algebra). In Journal of Japan Distance Learning Association Vol.4, pages 4349. Japan Distance Learning Association, May 2003.



 [kanda01:2003]  T. Yanagiya and H. Kanda. Veriflcation of Transition from laminar to Turbulent Flow in Circular Pipe by ColorDye Experiment. In The Japan Society of Mechanical Engineers (JSME), editor, Proceedings of Fluids Engineering Conference 2003, page 215. JSME, JSME, September 2003.

 [kanda02:2003]  Iwamoto. T. and H. Kanda. 3D Hyperbolic Grid Generation: Implementation and Generation. In IPSJ Tohoku Region, editor, Proceedings of IPSJ Tohoku Chapter Workshop (2003 1st), pages 1619.IPSJ  Tohoku Region, IPSJ  Tohoku Region, November 2003.

 [kanda03:2003]  A. Ohba and H. Kanda. 3D Hyperbolic Grid Generation for ConcaveShape Geometry. In IPSJ Tohoku Region, editor, Proceedings of IPSJ Tohoku Chapter Workshop (2003 1st), pages 20{23. IPSJ  Tohoku Region, IPSJ  Tohoku Region, November 2003.

 [kanda04:2003]  H. Kanda. Verification of Transition from laminar to Turbulent Flow in Circular Pipe by ColorDye Experiment. In The American Physical Society (APS), editor, Bulletin of the American Physical Society, 56th Annual Meeting of the Division of Fluid Dynamics, page 126. APS, APS, November 2003.

 [kanda05:2003]  H. Kanda. Experimental Conditions for the Minimum Critical Reynolds Number in Pipe Flow. In The Physical Society of Japan (JPS), editor, Meeting Abstracts of the Physical Society of Japan, 59th Annual Meeting, page 284. JPS, JPS, March 2004.

 [nasai04:2003]  N. Asai, Y.Miyazaki, D. Cai, and Y. Ikebe. Computation of Eigenvalues of Lame Equation. In 32nd NUmerical Analysis Symposium, pages 7578, May 2003.



 [kanda06:2003]  H. Kanda. Information Synergy Center of Tohoku University, 2003.



 [kanda07:2003]  H. Kanda, November 2003. Coordinator, IPSJ Tohoku Chapter Workshop (2003 1st)

