Publications:

Real analysis of fractal functions:

[1] Two or three precautions concerning real functions with fractal character. Sugaku, Mathematical Society of Japan, 49, No.3, 301-303 (1997). (in Japanese).

[2] On the classification of self-similar sets determined by two contractions on the plane, J. Math. Kyoto University, 42, no.2, pp 255-286 (2002).

[3] Extreme values of some continuous nowhere differentiable functions, Math. Proc. Camb. Phil. Soc. 140, no. 2, pp269-295 (2006) (With P.Allaart)

[4] On the coordinate functions of Levy’s dragon curve, Real Analysis Exchange, 31, no. 1, pp 295-308 (2005/06) (With P.Allaart).

[5] Dimensions of coordinate functions of space-filling curves, J. Math. Anal. Appl. 335, pp 1161-1176 (2007) (with P.Allaart).

[6] On Weierstrass-like Takagi functions, In preparation.

Computability of fractal sets:

[1] Computability of Koch curve and Koch island, Algorithm, 54, pp 1-8 (1996) (with H. Kamo).

[2] Computability of self-affine sets, Annual Reports of Graduate School of Human Culture of Nara Women's Univ. 12, pp 135-150, (1997) (with H. Kamo).

[3] Computability of self-similar sets, Mathematical Logic Quarterly, 45, pp 23-30 (1999) (with H. Kamo).

[4] Computational complexity of fractal sets, Real Analysis Exchange, 26, no. 2, pp 773-793 (2000/01) (With H. Kamo and I. Takeuti).

Reports in Conference Proceedings:

[1] Real Function with Fractal Property (communicated by Prof. A. Tsutsumi), 35^th International Symposium on Functional Equations, Aequationes Math. Vol. 55, pp 309-310 (1998).

[2] Hausdorff dimension and Computational Complexity, 3^rd Workshop on Computability and Complexity in Analysis, Informatik Berichte of Fern Universitat Vol. 235, pp 41-50 (1999)

[3] On the classification of self-similar sets, 37^th International Symposium on Functional Equations, Aequationes Math. Vol. 60, pp 182, 192, 196 (2000).

[4] Computational complexity of self-similar sets, 25^th Summer Symposium Conference, Real Anal.Exchange (2000).

[5] Extreme values of some nowhere differentiable functions, 29^th Summer Symposium Conference, Real Anal. Exchange, pp 61- 64 (2005).

[6] The coordinate functions of Levy’s dragon curve, 29^th Summer Symposium Conference, Real Anal. Exchange, pp55-60 (2005).

Invited research talks:

[1] Computability of self-similar sets, JES meeting, Special session on Chaos and Computation, Tokyo, Japan (October, 1997).

[2] Four classes of functions with self-similarity, Symposium on Real Analysis and Functional Analysis, Tokyo, Japan (May,1998).

[3] Hausdorff dimension and computational complexity, The third Satellite workshop on Computability and Complexity in Analysis, Bruno, Czech Republic (August, 1998).

[4] On the classification of self-similar sets, The 37^th International Symposium on Functional Equations, Hutchington, West Virginia, U.S. (May, 1999).

Recent research talks (selection):

[1] Computational complexity of self-similar sets, The 24^th Summer Symposium in Real Analysis Exchange, Denton, Texas, U.S. (May, 2000).

[2] Extreme values of some nowhere differentiable functions, The 29^th Summer Symposium in Real Analysis Exchange, Walla Walla, Washington, U.S. (June, 2005).

[3] Extreme values of some nowhere differentiable functions, Fractal on mathematics 2006, Kyoto, Japan (September, 2006).

Other scholarly activities:

Referee for American Mathematical Monthly, Reviewer for Mathematical reviews.

Grants awarded:

[1] International Information Science Foundation, 1998

[2] Japan Association for Mathematical Sciences, 2000