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- Matthias Beck, Ira M. Gessel, Takao Komatsu
- Electr. J. Comb.
- 2001

Given a set of positive integers A = {a 1 ,. .. , a n }, we study the number p A (t) of nonnegative integer solutions (m 1 ,. .. , m n) to n j=1 m j a j = t. We derive an explicit formula for the polynomial part of p A. Let A = {a 1 ,. .. , a n } be a set of positive integers with gcd(a 1 ,. .. , a n) = 1. The classical Frobenius problem asks for the… (More)

We discuss the partial infinite sum ∞ k=n u −s k for some positive integer n, where u k satisfies a recurrence relation of order s, u n = au n−1 + u n−2 + · · · + u n−s (n ≥ s), with initial values u 0 ≥ 0, u k ∈ N (0 ≤ k ≤ s − 1), where a and s(≥ 2) are positive integers. If a = 1, s = 2, and u 0 = 0, u 1 = 1, then u k = F k is the k-th Fibonacci number.… (More)

We provide a fairly simple and straightforward argument yielding all substitution invariant Beatty sequences.

- Takao Komatsu
- Ars Comb.
- 2011

In this paper we consider infinite sums derived from the reciprocals of the Fibonacci numbers, and infinite sums derived from the reciprocals of the square of the Fibonacci numbers. Applying the floor function to the reciprocals of these sums, we obtain equalities that involve the Fibonacci numbers.

We obtain the values concerning M(θ, φ) = lim inf |q|→∞ |q||qθ−φ using the algorithm by Nishioka, Shiokawa and Tamura. In application, we give the values M(θ, 1/2), M(θ, 1/a), M(θ, 1/ ab(ab + 4)) and so on when θ = (ab(ab + 4) − ab)/(2a) = [0; a, b, a, b,. . .]. 1. Introduction. Let θ be irrational and φ real. We suppose throughout that qθ − φ is never… (More)

- Tomokazu Ohnuma, Takao Komatsu, Shinji Nakayama, Takahito Nishiyama, Kenichiro Ogura, Akira Hiratsuka
- Archives of biochemistry and biophysics
- 2009

In the present study, we isolated falcarindiol from Notopterygium incisum and investigated the effect of falcarindiol on the expression of antioxidant enzymes (AOEs), such as catalase, and phase 2 drug-metabolizing enzymes (DMEs), such as glutathione S-transferase and NAD(P)H:quinone oxidoreductase 1, in a cultured cell line from normal rat liver, Clone 9… (More)

- Masumi Ito, Takaichi Hamano, Takao Komatsu, Kaori Asamitsu, Tomio Yamakawa, Takashi Okamoto
- Modern rheumatology
- 2014

OBJECTIVES
To evaluate the therapeutic efficacy of a novel inhibitor for IκB kinase alpha (IKKα), noraristeromycin (NAM), for murine experimental model of rheumatoid arthritis, collagen- induced arthritis (CIA).
METHODS
NAM has been chemically synthesized as reported earlier. CIA was induced in DBA/1JNCrlj mice by intradermal inoculation of bovine type II… (More)

- Takao Komatsu, Florian Luca, Yohei Tachiya
- 2013

Here, we show that if s �∈ {1, 2, 4} is a fixed positive integer and m and n are coprime positive integers such that the multiplicative order of Fn+1/Fn modulo Fm is s, where Fk is the kth Fibonacci number, then m < 500s2.

- Takao Komatsu
- Math. Comput.
- 2005

For any given real number, its corresponding continued fraction is unique. However, given an arbitrary continued fraction, there has been no general way to identify its corresponding real number. In this paper we shall show a general algorithm from continued fractions to real numbers via infinite sums representations. Using this algorithm, we obtain some… (More)