Results 41 to 50 of about 12,820,749 (293)

Functional graphs of polynomials over finite fields

Journal of Combinatorial Theory, Series B, 2016
Given a function $f$ in a finite field ${\mathbb F}_q$ of $q$ elements, we define the functional graph of $f$ as a directed graph on $q$ nodes labelled by the elements of ${\mathbb F}_q$ where there is an edge from $u$ to $v$ if and only if $f(u) = v$.
Sergei V. Konyagin, Florian Luca, Bernard Mans, Luke Mathieson, Min Sha, Igor E. Shparlinski   +5 more
openaire   +4 more sources

Visibly Irreducible Polynomials over Finite Fields [PDF]

The American Mathematical Monthly, 2020
11 pages.
openaire   +2 more sources

Primitive polynomials with prescribed second coefficient [PDF]

, 2006
The Hansen-Mullen Primitivity Conjecture (HMPC) (1992) asserts that, with some (mostly obvious) exceptions, there exists a primitive polynomial of degree n over any finite fieldwith any coefficient arbitrarily prescribed.
Cohen, Stephen D., Presern, M., Cohen, S.D., Prešern, Mateja   +3 more
core   +1 more source

Wearable Smart Patches on Sustainable Chitosan With Reversible Microbial Growth‐Inhibitory Properties

Advanced Functional Materials, EarlyView.
ABSTRACT Chitosan, a polysaccharide upcycled from biowaste, has long promised sustainable, biocompatible, and antimicrobial films and devices, an appeal reinforced by its recent regulatory recognition, with several chitosan‐based antibacterial dressings gaining clearance through the Food and Drug Administration's 510(k) pathway.
Jacopo Nicoletti, Kubra Kocak, Andrea Michel, Enrico Cavarzerani, Ali Raza, Petr Rohzin, Nouha Loudhaief, Saimir Frroku, Nicolò Baldovin, Hazrat Bilal, Alvise Perosa, Maurizio Selva, Flavio Rizzolio, Luca Sbuelz, Sabrina Tamburini, Domenico De Fazio, Giovanni Antonio Salvatore   +16 more
wiley   +1 more source

Fixed Points of the Dickson Polynomials of the Second Kind

Journal of Applied Mathematics, 2013
The permutation behavior of Dickson polynomials of the first kind has been extensively studied, while such behavior for Dickson polynomials of the second kind is less known.
Adama Diene, Mohamed A. Salim
doaj   +1 more source

Exceptional Electro‐Optic Coefficient Unlocked via Polarization Swaying in KNbO3 Thin Films

Advanced Functional Materials, EarlyView.
We present the largest reported electro‐optic response in any material to date, guided by a new design principle that exploits ultralow coercive field polarization swaying enabled by low‐symmetry ferroelectric phases in monoclinic KNbO3 thin films for energy‐efficient classical and quantum photonic integrated circuits. ABSTRACT The electro‐optic effect
Sankalpa Hazra, Aiden Ross, Brynn Brower, Tobias Schwaigert, Ian Reed Philippi, Albert Suceava, Himirkanti Sarkar, Muhammed Aminul Haque Chowdhury, Suchismita Sarker, Darrell G. Schlom, Long‐Qing Chen, Venkatraman Gopalan   +11 more
wiley   +1 more source

Efficient Algorithm for Finding Roots of Error-Locator Polynomials

IEEE Access, 2021
A novel method for finding roots of polynomials over finite fields has been proposed. This method is based on the cyclotomic discrete Fourier transform algorithm. The improvement is achieved by using the normalized cyclic convolutions, which have a small
Sergei Valentinovich Fedorenko
doaj   +1 more source

Dickson Polynomials and Irreducible Polynomials Over Finite Fields

Journal of Number Theory, 1994
For the finite field of order \(q\), \(\mathbb{F}_ q\), let \[ D_ n(x,a)= \sum_{j=0}^{\lfloor n/2\rfloor} {\textstyle {n \over {n-j}}} \left( \begin{smallmatrix} n-j\\ j\end{smallmatrix} \right) (-a)^ j x^{n-2j} \] denote the Dickson polynomial of degree \(n\) with parameter \(a\in \mathbb{F}_ q\).
Gao, S.H., Mullen, G.L.
openaire   +2 more sources

On maximal curves and linearized permutation polynomials over finite fields

, 2001
The purpose of this paper is to construct maximal curves over large finite fields using linearized permutation polynomials.
Özbudak, Ferruh, Ferruh Özbudak
core   +1 more source

Universal Conductance Fluctuations in Quantum Anomalous Hall Insulators

Advanced Materials, EarlyView.
Universal conductance fluctuations are observed in mesoscopic quantum anomalous Hall insulators. Two distinct fluctuation patterns are identified, arising from different interference processes of bulk and chiral edge states, respectively. These findings unveil rich quantum interference phenomena in quantum anomalous Hall insulators and provide insights
Peng Deng, Peng Zhang, Gang Qiu, Ting‐Hsun Yang, Chang Niu, Yaochen Li, Wenqiang Cui, Yang Feng, Peide D. Ye, Ke He, Kai Chang, Kang L. Wang   +11 more
wiley   +1 more source