Zobrazeno 1 - 10
of 42
pro vyhledávání: '"Peter J. S. Shiue"'
Publikováno v:
International Journal of Mathematics and Mathematical Sciences, Vol 2021 (2021)
This paper presents a new approach to determine the number of solutions of three-variable Frobenius-related problems and to find their solutions by using order reducing methods. Here, the order of a Frobenius-related problem means the number of varia
Externí odkaz:
https://doaj.org/article/c92981e6884a482b822c44c237dfc77f
Publikováno v:
International Journal of Mathematics and Mathematical Sciences, Vol 2021 (2021)
Proposed in 1937, the Collatz conjecture has remained in the spotlight for mathematicians and computer scientists alike due to its simple proposal, yet intractable proof. In this paper, we propose several novel theorems, corollaries, and algorithms t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4928371aa6b4d6d332af7e8835645560
https://doi.org/10.1155/2021/5754439
https://doi.org/10.1155/2021/5754439
Autor:
Tian-Xiao He, Peter J. S. Shiue
Publikováno v:
Special Matrices, Vol 8, Iss 1, Pp 123-130 (2020)
This note presents a new formula of Eulerian numbers derived from Toeplitz matrices via Riordan array approach.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7fb1b557fd4cdfc2d959a3b2771165ca
https://doi.org/10.1515/spma-2020-0103
https://doi.org/10.1515/spma-2020-0103
Publikováno v:
Journal of Discrete Mathematical Sciences and Cryptography. 25:335-352
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::4f91a68759835d2be0433e98ba068f20
https://doi.org/10.1080/09720529.2019.1662580
https://doi.org/10.1080/09720529.2019.1662580
Publikováno v:
IEEE Access, Vol 8, Pp 26433-26444 (2020)
This paper proposes a number of theorems and algorithms for the Chinese Remainder Theorem, which is used to solve a system of linear congruences, and the extended Rabin cryptosystem, which accepts a key composed of an arbitrary finite number of disti
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5a1b35f54f69ce4924ec7014c9493dcb
https://doi.org/10.1109/access.2020.2967396
https://doi.org/10.1109/access.2020.2967396
Autor:
Tian-Xiao He, Peter J.-S. Shiue
Publikováno v:
International Journal of Mathematics and Mathematical Sciences, Vol 2009 (2009)
Here we present a new method to construct the explicit formula of a sequence of numbers and polynomials generated by a linear recurrence relation of order 2. The applications of the method to the Fibonacci and Lucas numbers, Chebyshev polynomials, th
Externí odkaz:
https://doaj.org/article/82282bbc52c94f73890fdb376ba7060e
Autor:
Peter J.-S. Shiue, Tian-Xiao He
Publikováno v:
Electronic Research Archive. 29:3489
We present here a general rule of construction of identities for recursive sequences by using sequence transformation techniques developed in [16]. Numerous identities are constructed, and many well known identities can be proved readily by using thi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::1d65937345198ace320070a97eab94c5
https://doi.org/10.3934/era.2021049
https://doi.org/10.3934/era.2021049
Autor:
Peter J. S. Shiue, Tian-Xiao He
Publikováno v:
Frontiers of Mathematics in China. 10:69-89
We consider the congruence x1 + x2 + ... + xr ≡ c (mod m), where m and r are positive integers and c ∈ ℤm:= {0, 1, ...,m−1} (m ⩾ 2). Recently, W. -S. Chou, T. X. He, and Peter J. -S. Shiue considered the enumeration problems of this congrue
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::cbe902f4487f247be2aa27d206ac6da8
https://doi.org/10.1007/s11464-014-0394-2
https://doi.org/10.1007/s11464-014-0394-2
Publikováno v:
ISRN Discrete Mathematics. 2011:1-16
Here we present a connection between a sequence of numbers generated by a linear recurrence relation of order 2 and sequences of the generalized Gegenbauer-Humbert polynomials. Many new and known formulas of the Fibonacci, the Lucas, the Pell, and th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f431fa178f81d9e28d40bb6405263d61
https://doi.org/10.5402/2011/674167
https://doi.org/10.5402/2011/674167
Autor:
Tian-Xiao He, Peter J. S. Shiue
Publikováno v:
ISRN Algebra. 2011:1-18
Here, we present a connection between a sequence of polynomials generated by a linear recurrence relation of order 2 and sequences of the generalized Gegenbauer-Humbert polynomials. Many new and known transfer formulas between non-Gegenbauer-Humbert
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fbbb1f5a8d7bf3b5e2d22c169171500e
https://doi.org/10.5402/2011/268096
https://doi.org/10.5402/2011/268096