Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 6 of 6
Full-Text Articles in Physical Sciences and Mathematics
Art And Math Via Cubic Polynomials, Polynomiography And Modulus Visualization, Bahman Kalantari
Art And Math Via Cubic Polynomials, Polynomiography And Modulus Visualization, Bahman Kalantari
LASER Journal
Throughout history, both quadratic and cubic polynomials have been rich sources for the discovery and development of deep mathematical properties, concepts, and algorithms. In this article, we explore both classical and modern findings concerning three key attributes of polynomials: roots, fixed points, and modulus. Not only do these concepts lead to fertile ground for exploring sophisticated mathematics and engaging educational tools, but they also serve as artistic activities. By utilizing innovative practices like polynomiography—visualizations associated with polynomial root finding methods—as well as visualizations based on polynomial modulus properties, we argue that individuals can unlock their creative potential. From crafting captivating …
The Number Systems Tower, Bill Bauldry, Michael J. Bossé, William J. Cook, Trina Palmer, Jaehee K. Post
The Number Systems Tower, Bill Bauldry, Michael J. Bossé, William J. Cook, Trina Palmer, Jaehee K. Post
Journal of Humanistic Mathematics
For high school and college instructors and students, this paper connects number systems, field axioms, and polynomials. It also considers other properties such as cardinality, density, subset, and superset relationships. Additional aspects of this paper include gains and losses through sequences of number systems. The paper ends with a great number of activities for classroom use.
On Sharpening And Generalization Of Rivlin's Inequality, Prasanna Kumar, Gradimir Milovanovic
On Sharpening And Generalization Of Rivlin's Inequality, Prasanna Kumar, Gradimir Milovanovic
Turkish Journal of Mathematics
n inequality due to T. J. Rivlin from 1960 states that if $P(z)$ is a polynomial of degree $n$ having no zeros in $ z
On The Growth Of Maximum Modulus Of Rational Functions With Prescribed Poles, Lubna Wali Shah
On The Growth Of Maximum Modulus Of Rational Functions With Prescribed Poles, Lubna Wali Shah
Turkish Journal of Mathematics
In this paper we prove a sharp growth estimate for rational functions with prescribed poles and restricted zeros in the Chebyshev norm on the unit disk in the complex domain. In particular we extend a polynomial inequality due to Dubinin (2007) to rational functions which also improves a result of Govil and Mohapatra (1998).
On Cauchy's Bound For Zeros Of A Polynomial, V. K. Jain
On Cauchy's Bound For Zeros Of A Polynomial, V. K. Jain
Turkish Journal of Mathematics
In this note, we improve upon Cauchy's classical bound, and upon some recent bounds for the moduli of the zeros of a polynomial.
Valuations Of Polynomials, Sorasak Leeratanavalee
Valuations Of Polynomials, Sorasak Leeratanavalee
Turkish Journal of Mathematics
A tree is a connected (undirected) graph that contains no cycles. Trees play an important role in Computer Science. There are many applications in this field. Ordered binary decision diagrams are trees in the language of Boolean algebras. For the applications, it is important to measure the complexity of a tree or of a polynomial. The complexity of a polynomial over an arbitrary algebra can be regarded as a valuation. The concept of the valuations of terms was introduced by K. Denecke and S. L. Wismath in [5]. In [6], the author defined the depth of a polynomial which is …