Results 61 to 70 of about 12,820,749 (293)

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
openaire   +3 more sources

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, Hiroshi Kaminaga, Philippe Fraisse, Gentiane Venture   +3 more
wiley   +1 more source

On flux integrals for generalized Melvin solution related to simple finite-dimensional Lie algebra

European Physical Journal C: Particles and Fields, 2017
A generalized Melvin solution for an arbitrary simple finite-dimensional Lie algebra $$\mathcal G$$ G is considered. The solution contains a metric, n Abelian 2-forms and n scalar fields, where n is the rank of $$\mathcal G$$ G .
V. D. Ivashchuk
doaj   +1 more source

ITERATION OF QUADRATIC POLYNOMIALS OVER FINITE FIELDS [PDF]

Mathematika, 2017
For a finite field of odd cardinality $q$, we show that the sequence of iterates of $aX^2+c$, starting at $0$, always recurs after $O(q/\log\log q)$ steps. For $X^2+1$ the same is true for any starting value. We suggest that the traditional "Birthday Paradox" model is inappropriate for iterates of $X^3+c$, when $q$ is 2 mod 3.
openaire   +3 more sources

Force–Displacement Characterization of PNIPAM Microactuators

Advanced Robotics Research, EarlyView.
A method to experimentally establish a force–displacement diagram of poly(N‐isopropyl acrylamide) (PNIPAM) microactuators, printed by 2PP, is presented herein. PNIPAM is a hydrogel whose volume and stiffness change with temperature due to the absorption or release of water.
Manon Cassignol, Esra Yalcinkaya, Adam Chafaï, Jérémy Odent, Pierre Lambert   +4 more
wiley   +1 more source

On the Irreducibility of Some Composite Polynomials

Journal of Mathematical Extension, 2012
. In this paper we study the irreducibility of some composite polynomials, constructed by a polynomial composition method over finite fields. Finally, a recurrent method for constructing families of irreducible polynomials of higher degree from given ...
M. Alizadeh
doaj  

On the Dispersions of the Polynomial Maps over Finite Fields [PDF]

The Electronic Journal of Combinatorics, 2008
We investigate the distributions of the different possible values of polynomial maps ${\Bbb F}_q^n\longrightarrow{\Bbb F}_q$, $x\longmapsto P(x)$. In particular, we are interested in the distribution of their zeros, which are somehow dispersed over the whole domain ${\Bbb F}_q^n$.
openaire   +3 more sources

Microscale Mapping of Fiber Strain and Damage in Composite Wrinkled Laminates Using Computed Tomography Assisted Wide‐Angle X‐Ray Scattering

Advanced Science, EarlyView.
This study combines full‐field tomography with diffraction mapping to quantify radial (ε002$\varepsilon _{002}$) and axial (ε100$\varepsilon _{100}$) lattice strain in wrinkled carbon‐fiber specimens for the first time. Radial microstrain gradients (−14.5 µεMPa$\varepsilon \mathrm{MPa}$−1) are found to signal damage‐prone zones ahead of failure, which ...
Hoang Minh Luong, James Trevarthen, Igor Dolbnya, Wadwan Singhapong, Nicholas Pilato, Richard Butler, Jiraphant Srisuriyachot, Alexander J. G. Lunt   +7 more
wiley   +1 more source

Real-World Applications of a Newly Designed Root-Finding Algorithm and Its Polynomiography

IEEE Access, 2021
Solving non-linear equations in different scientific disciplines is one of the most important and frequently appearing problems. A variety of real-world problems in different scientific fields can be modeled via non-linear equations. Iterative algorithms
Amir Naseem, M. A. Rehman, Thabet Abdeljawad   +2 more
doaj   +1 more source

Gauss factorials of polynomials over finite fields

, 2017
In this paper, we initiate a study on Gauss factorials of polynomials over finite fields, which are the analogues of Gauss factorials of positive integers.
Min Sha, Xiumei Li
core   +1 more source