Directed networks and self-similar systems

[1] M. Hata and M. Yamaguti, The Takagi function and its generalization,

Japan J. Appl. Math., 1(1984), 183–199.

Directed networks and self-similar systems

31

[2] Y. Kamiya, T. Okada, T. Sekiguchi and Y. Shiota, Power and exponential sums for generalized code systems by a measure theoretic approach,

Theoret. Comput. Sci. 592 (2015) 23–38.

[3] Z. Kobayashi, Digital Sum Problems for the Gray Code Representation

of Natural Numbers, Interdisciplinary Information Sciences, 8(2002),

167–175.

[4] Z. Kobayashi, T. Kuzumaki, T. Okada, T. Sekiguchi and Y. Shiota,

A probability measure which has Markov property, Acta Mathematica

Hungarica, 121(2008), 1-2.

[5] Z. Kobayashi, K. Muramoto, T. Okada, T. Sekiguchi and Y. Shiota,

An explicit formula of the Newman-Coquet exponential sum, Interdisciplinary Information Sciences, 13(2007), 1-6.

[6] Z. Kobayashi, T. Okada, T. Sekiguchi and Y. Shiota, On exponential

sums of digital sums related to Gelfond’s theorem, Diophantine Analysis and Related Fields DARF 2007/2008 (Kyoto 2008),AIP Conference

Proceedings, 976(2008), 176-189.

[7] N. Kˆono, On self-affine functions, Japan J. Appl. Math., 3(1986),

259–269.

[8] N. Kˆono, On self-affine functions II, Japan J. Appl. Math., 8(1988),

441–445.

[9] K. Muramoto, T. Okada, T. Sekiguchi and Y. Shiota, Digital sum

problems for the p-adic expansion of natural numbers, Interdisciplinary

Information Sciences, 6(2000), 105-109.

[10] K. Muramoto, T. Okada, T. Sekiguchi and Y. Shiota, An explicit formula of subblock occurrences for the p-adic expansion, Interdisciplinary

Information Sciences, 8 (2002), 115–121.

[11] K. Muramoto, T. Okada, T. Sekiguchi and Y. Shiota, Power

and exponential sums of digital sums with information per digits,

Math. Rep. Toyama Univ., 26(2003), 35-44.

32

Katsushi Muramoto and Takeshi Sekiguchi

[12] T. Okada, T. Sekiguchi and Y. Shiota, Applications of binomial measures to power sums of digital sums, J. Number Theory, 52(1995), pp.

256–266.

[13] T. Okada, T. Sekiguchi and Y. Shiota, An explicit formula of the exponential sums of digital sums, Japan J. Indust. Appl. Math., 12(1995),

pp. 425–438.

[14] T. Okada, T. Sekiguchi and Y. Shiota, A generalization of Hata–

Yamaguti’s results on the Takagi function II: Multinomial case, Japan

J. Indust. Appl. Math., 13(1996), pp. 435–463.

[15] T. Okada, T. Sekiguchi and Y. Shiota, Multifractal spectrum of Multinomial measures, Proc. Japan Acad., 7(1997), Ser.A, 123-150.

[16] T. Sekiguchi and Y. Shiota, Hausdorff dimension of graph of some

Rademacher series, Japan J. Math., 7(1990), 121-129.

[17] T. Sekiguchi and Y. Shiota, A generalization of Hata–Yamaguti’s results on the Takagi function, Japan J. Indust. Appl. Math., 8(1991),

203–219.

[18] G. de Rham, Sur quelques courbes definites par des equations fonctionnelles, Rend. Sem. Mat. Torino,16 (1957), 101–113.

Katsushi Muramoto

Kawaijuku Educational Institution

2-49-7 Minamiikebukuro Toshima-ku, 171-0022, Japan

Takeshi Sekiguchi

Information Science

Tohoku Gakuin University

Sendai 981-3105, Japan

(Received July 24, 2019)

...