Learn More
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 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)
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)
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)
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)