Results 51 to 60 of about 12,115,560 (297)
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.
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Advanced Functional Materials, EarlyView.Two‐photon grayscale lithography (2GL) enables high‐speed and precise 3D printing of thermolyzed silica glass microstructures with optical‐grade surface quality, high quality factors, and mechanical strength utilizing a custom‐made pre‐glass resist based on polyhedral oligomeric silsesquioxane (POSS) modified with a high‐sensitivity Norrish type II ...
Jonathan L. G. Schneider +4 more
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Factoring Polynomials Over Finite Fields: A Survey
Journal of Symbolic Computation, 2001 The paper surveys several algorithms for the factorization of univariate polynomials over finite fields, emphasizing the main ideas of the methods. The problem addressed is: Given a monic univariate polynomial \(f\in F_q [x]\), find the complete factorization \(f = f_1^{e_1} f_2^{e_2}\cdots f_k^{e_k}\) where \(f_1,\dots,f_k\) are pairwise distinct ...
Joachim von zur Gathen, Daniel Panario
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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 +11 more
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A New Construction of Multisender Authentication Codes from Polynomials over Finite Fields
Journal of Applied Mathematics, 2013 Multisender authentication codes allow a group of senders to construct an authenticated message for a receiver such that the receiver can verify the authenticity of the received message.
Xiuli Wang
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Roots of sparse polynomials over a finite field [PDF]
LMS Journal of Computation and Mathematics, 2016 For a$t$-nomial$f(x)=\sum _{i=1}^{t}c_{i}x^{a_{i}}\in \mathbb{F}_{q}[x]$, we show that the number of distinct, nonzero roots of$f$is bounded above by$2(q-1)^{1-\unicode[STIX]{x1D700}}C^{\unicode[STIX]{x1D700}}$, where$\unicode[STIX]{x1D700}=1/(t-1)$and$C$is the size of the largest coset in$\mathbb{F}_{q}^{\ast }$on which$f$vanishes completely ...
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Advanced Materials, EarlyView.Intrinsic material dynamics are harnessed as computational resources for neuromorphic in‐materio physical reservoir computing. Defects, ionic motion, interfaces, percolation, geometry, and biasing shape transient states that provide fading memory, nonlinearity, and high‐dimensional projection for simple readout. A descriptor‐to‐dynamics framework links
Kshitij RB Singh +5 more
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Unimodular polynomial matrices over finite fields [PDF]
Journal of Algebraic Combinatorics, 2020 14 ...
Akansha Arora +2 more
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A group action on multivariate polynomials over finite fields
, 2018 Seja Fq o corpo finito com q elementos, onde q é a potência de um primo p. Recentemente, uma ação particular do grupo GL2 (Fq) sobre polinômios irredutíveis em Fq [X] foi introduzida e muitas questões relativas aos polinômios invariantes foram discutidas.
Lucas da Silva Reis
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Compliant Pneumatic Feet with Real‐Time Stiffness Adaptation for Humanoid Locomotion
Advanced Robotics Research, EarlyView.A compliant pneumatic foot with real‐time variable stiffness enables humanoid robots to adapt to changing terrains. Using onboard vision and pressure control, the foot modulates stiffness within each gait cycle, reducing impact forces and improving balance. The design, cast in soft silicone with embedded air chambers and Kevlar wrapping, offers durable,
Irene Frizza +3 more
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