Peter J.-S. Shiue

University of Nevada, Las Vegas

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i-10 index

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Co-Authors

Tian-Xiao He

Shandong University

L. C. Hsu

Dalian University of Technology

Wun-Seng Chou

Institute of Mathematics, Academia Sinica

Shen C. Huang

University of Nevada, Las Vegas

Richard S. Millman

Georgia Institute of Technology

Eric Brendan Kahn

Bloomsburg University

Gary L. Mullen

Pennsylvania State University

Rama Venkat

University of Nevada, Las Vegas

A. G. Shannon

UNSW Sydney

Tom C. Brown

Simon Fraser University

Cooperative Institutions

University of Nevada, Las Vegas

Illinois Wesleyan University

Texas A&M University

Institute of Mathematics, Academia Sinica

Academia Sinica

Pennsylvania State University

Michigan Technological University

Dalian University of Technology

UNSW Sydney

Flinders University

Author Statistics

Papers

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Novel Theorems and Algorithms Relating to the Collatz Conjecture

arXiv (Cornell University) (2021)

Michael R. Schwob Peter J.-S. Shiue Rama Venkat

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 that explore relationships and properties between the natural numbers, their peak values, and the conjecture. These contributions primarily analyze the number of Collatz iterations it takes for a given integer to reach 1 or a number less than itself, or the relationship between a starting number and its peak value.

Value (mathematics)

Natural number

10.48550/arxiv.2104.10713

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Algorithms for enumeration problem of linear congruence modulo m as sum of restricted partition numbers

Frontiers of Mathematics in China (2014)

Tian-Xiao He Peter J.-S. Shiue

Congruence (geometry)

Enumeration

Congruence relation

10.1007/s11464-014-0394-2

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Recursive sequences and girard-waring identities with applications in sequence transformation

Electronic Research Archive (2020)

Tian-Xiao He Peter J.-S. Shiue Zihan Nie Minghao Chen

<p style='text-indent:20px;'>We present here a generalized Girard-Waring identity constructed from recursive sequences. We also present the construction of Binet Girard-Waring identity and classical Girard-Waring identity by using the generalized Girard-Waring identity and divided differences. The application of the generalized Girard-Waring identity to the transformation of recursive sequences of numbers and polynomials is discussed.</p>

Sequence (biology)

10.3934/era.2020057

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Citations (4)

Polynomials and the Division Algorithm

Springer eBooks (2015)

Richard S. Millman Peter J.-S. Shiue Eric Brendan Kahn

10.1007/978-3-319-14427-6_4

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Cycle indicators and Special Functions

Annals of Combinatorics (2001)

L. C. Hsu Peter J.-S. Shiue

Special functions

Recurrence relation

10.1007/pl00001299

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Citations (17)

On the Solutions of Three Variable Frobenius Related Problems Using Order Reduction Approach

arXiv (Cornell University) (2021)

Tian-Xiao He Peter J.-S. Shiue Rama Venkat

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 variables appearing in the problem. We present two types of order reduction methods that can be applied to the problem of finding all nonnegative solutions of three variable Frobenius related problems. The first method is used to reduce the equation of order three from a three variable Frobenius related problem to be a system of equations with two fixed variables. The second method reduces the equation of order three into three equations of order two, for which an algorithm is designed with an interesting open problem on solutions left as a conjecture.

10.48550/arxiv.2106.11449

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Citations (1)

A generalized computation procedure for Ramanujan-type identities and cubic Shevelev sum

Notes on Number Theory and Discrete Mathematics (2023)

Peter J.-S. Shiue A. G. Shannon Shen C. Huang Jorge Reyes

A generalized Computation procedure for construction of the Ramanujan-type from a given general cubic equation and a cosine Ramanujan-type identity is developed from detailed analyses of the properties of Ramanujan-type cubic equations. Examples are provided together with cubic Shevelev sums.

Ramanujan tau function

10.7546/nntdm.2023.29.1.98-129

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A note on circulant transition matrices in Markov chains

Linear Algebra and its Applications (2008)

Wun-Seng Chou Bau-Sen Du Peter J.-S. Shiue

Stochastic matrix

Matrix (chemical analysis)

10.1016/j.laa.2008.05.004

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Citations (10)

Towards a Novel Generalized Chinese Remainder Algorithm for Extended Rabin Cryptosystem

IEEE Access (2020)

Justin Zhan Peter J.-S. Shiue Shen C. Huang Benjamin Lowe

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 distinct primes. This paper further proposes methods to relax the condition on the primes with trade-offs in the time complexity. The proposed algorithms can be used to provide ciphertext indistinguishability. Finally, this paper conducts extensive experimental analysis on six large data sets. The experimental results show that the proposed algorithms are asymptotically tight to the existing decryption algorithm in the Rabin cryptosystem with the key composed of two distinct primes while maintaining increased generality.

Chinese remainder theorem

Generality

10.1109/access.2020.2967396

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Citations (1)

Notes on generalized and extended Leonardo numbers

Notes on Number Theory and Discrete Mathematics (2023)

A. G. Shannon Peter J.-S. Shiue Shen C. Huang

This paper both extends and generalizes recently published properties which have been developed by many authors for elements of the Leonardo sequence in the context of second-order recursive sequences. It does this by considering the difference equation properties of the homogeneous Fibonacci sequence and the non-homogeneous properties of their Leonardo sequence counterparts. This produces a number of new identities associated with a generalized Leonardo sequence and its associated algorithm, as well as some combinatorial results which lead into elegant properties of hyper-Fibonacci numbers in contrast to their ordinary Fibonacci number analogues, and as a convolution of Fibonacci and Leonardo numbers.

Sequence (biology)

Convolution (computer science)

Pisano period

Lucas number

Lucas sequence

Recurrence relation

10.7546/nntdm.2023.29.4.752-773

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Citations (1)