Zobrazeno 1 - 10
of 255
pro vyhledávání: '"TAKAO KOMATSU"'
Autor:
Jiaxin Mu, Takao Komatsu
Publikováno v:
Axioms, Vol 13, Iss 9, p 608 (2024)
Many people, including Horadam, have studied the numbers Wn, satisfying the recurrence relation Wn=uWn−1+vWn−2 (n≥2) with W0=0 and W1=1. In this paper, we study the p-numerical semigroups of the triple (Wi,Wi+2,Wi+k) for integers i,k(≥3). For
Externí odkaz:
https://doaj.org/article/8ed7c2e72bb94e98bc08eec44a57a536
Publikováno v:
Symmetry, Vol 16, Iss 8, p 1090 (2024)
In this paper, we give closed-form expressions of the p-Frobenius number for the triple of the generalized star numbers an(n−1)+1 for an integer a≥4. When a=6, it is reduced to the famous star number. For the set of given positive integers {a1,a2
Externí odkaz:
https://doaj.org/article/124aef191d1c40b48ef46cac4d0bacda
Autor:
Ruze Yin, Takao Komatsu
Publikováno v:
Symmetry, Vol 16, Iss 7, p 855 (2024)
We give an explicit formula for the p-Frobenius number of triples associated with Diophantine Equations x2−y2=zr (r≥2), that is, the largest positive integer that can only be represented in p ways by combining the three integers of the solutions
Externí odkaz:
https://doaj.org/article/238dab33db92483db8485a80de309e19
Autor:
Takao Komatsu, Haotian Ying
Publikováno v:
Mathematical Biosciences and Engineering, Vol 20, Iss 2, Pp 3455-3481 (2023)
In this paper we study a certain kind of generalized linear Diophantine problem of Frobenius. Let a1,a2,…,al be positive integers such that their greatest common divisor is one. For a nonnegative integer p, denote the p-Frobenius number by gp(a1,a2
Externí odkaz:
https://doaj.org/article/1ca5e9ba937243c592b5a3ac8fd00526
Autor:
Takao Komatsu, Ram Krishna Pandey
Publikováno v:
AIMS Mathematics, Vol 6, Iss 7, Pp 6630-6646 (2021)
In 1875, Glaisher gave several interesting determinant expressions of numbers, including Bernoulli, Cauchy, and Euler numbers. Cauchy numbers can be generalized to the hypergeometric Cauchy numbers. Recently, Barman et al. study more general numbers
Externí odkaz:
https://doaj.org/article/125de655950c4d548a3a4c963a6231f1
Autor:
Takao Komatsu, Haotian Ying
Publikováno v:
Symmetry, Vol 15, Iss 7, p 1328 (2023)
For given positive integers a1,a2,⋯,ak with gcd(a1,a2,⋯,ak)=1, the denumerant d(n)=d(n;a1,a2,⋯,ak) is the number of nonnegative solutions (x1,x2,⋯,xk) of the linear equation a1x1+a2x2+⋯+akxk=n for a positive integer n. For a given nonnegati
Externí odkaz:
https://doaj.org/article/6bbde30ec0724e4f939d580517a766db
Publikováno v:
Symmetry, Vol 15, Iss 4, p 852 (2023)
For a nonnegative integer p, we give explicit formulas for the p-Frobenius number and the p-genus of generalized Fibonacci numerical semigroups. Here, the p-numerical semigroup Sp is defined as the set of integers whose nonnegative integral linear co
Externí odkaz:
https://doaj.org/article/4141f6b6e64c4af7a5b61e8a82e289b9
Autor:
Takao Komatsu, Wenpeng Zhang
Publikováno v:
AIMS Mathematics, Vol 5, Iss 6, Pp 5939-5954 (2020)
The truncated Bernoulli-Carlitz numbers and the truncated Cauchy-Carlitz numbers are defined as analogues of hypergeometric Bernoulli numbers and hypergeometric Cauchy numbers, and as extensions of Bernoulli-Carlitz numbers and the Cauchy-Carlitz num
Externí odkaz:
https://doaj.org/article/c49e972c55df4d7f86b3052ed278c3d7
Autor:
Takao Komatsu, Huilin Zhu
Publikováno v:
AIMS Mathematics, Vol 5, Iss 2, Pp 1284-1303 (2020)
In this paper, we introduce the hypergeometric Euler number as an analogue of the hypergeometric Bernoulli number and the hypergeometric Cauchy number. We study several expressions and sums of products of hypergeometric Euler numbers. We also introdu
Externí odkaz:
https://doaj.org/article/74560da02ef547bd91a0fdd328046100
Autor:
Takao Komatsu, Víctor F. Sirvent
Publikováno v:
Symmetry, Vol 15, Iss 2, p 354 (2023)
In this article, mainly from the analytical aspect, we introduce poly-Cauchy numbers with higher levels (level s) as a kind of extensions of poly-Cauchy numbers with level 2 and the original poly-Cauchy numbers and investigate their properties. Such
Externí odkaz:
https://doaj.org/article/0425fe6a374d494a88906c0204941d5c