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Certain Applications of the Theory of Polar-Composite Polynomials [PDF]

Proceedings of the American Mathematical Society, 1982
In a recent paper [5] the authors have, for the first time, given a detailed account of the theory of polar-composite polynomials in algebraically closed fields of characteristic zero. In another paper [6], we have given some applications of this theory and have obtained a few results for a new variety of composite polynomials which have been derived ...
Zaheer, Neyamat, Alam, Mahfooz
openaire   +2 more sources

Hard‐Magnetic Soft Millirobots in Underactuated Systems

Advanced Robotics Research, EarlyView.
This review provides a comprehensive overview of hard‐magnetic soft millirobots in underactuated systems. It examines key advances in structural design, physics‐informed modeling, and control strategies, while highlighting the interplay among these domains.
Qiong Wang, Zixuan Zhang, Bingyan Li, Junkai Wang, Hongcheng Gu   +4 more
wiley   +1 more source

Lower Bound of the Complexity of Functions over Finite Field of Order 4 in the Class of Polarized Polynomials

Известия Иркутского государственного университета: Серия "Математика", 2016
The representations, including polynomial, of functions over final fields have been actively investigated. The complexity of such representations is the main stream of research.
A. Baliuk, A.S. Zinchenko
doaj  

Inequalities for the polar derivative of a complex polynomial

Filomat, 2022
Let P(z):= ?n v=0 avzv be a univariate complex coefficient polynomial of degree n. Then as a generalization of a well-known classical inequality of Tur?n [25], it was shown by Govil [7] that if P(z) has all its zeros in |z| ? k, k ? 1, then max |z|=1 |P?(z)| ? n/1 + kn max |z|=1 |P(z)|, whereas, if P(z) , 0 in |z| < k, k ?
Abdullah Mir, Imtiaz Dar
openaire   +1 more source

Physical Origin of Temperature Induced Activation Energy Switching in Electrically Conductive Cement

Advanced Science, EarlyView.
The temperature‐induced Arrhenius activation energy switching phenomenon of electrical conduction in electrically conductive cement originates from structural degradation within the biphasic ionic‐electronic conduction architecture and shows percolation‐governed characteristics: pore network opening dominates the low‐percolation regime with downward ...
Jiacheng Zhang, Xinyuan Ke, Andrew Heath, Richard J. Ball, Jiawei Xie, Jinchen Fan, Guisheng Li, Kevin Paine   +7 more
wiley   +1 more source

Inequalities for the Polar Derivative of a Polynomial

Advances in Pure Mathematics, 2011
If is a polynomial of degree , having all its zeros in |z|≤K, K≥1 , then it was proved by Aziz and Rather [2] that for every real or complex number with |a| ≥K, .
Gulshan Singh, W. M. Shah, Yash Paul
openaire   +2 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

Phase Diagrams and Piezoelectric Properties of Wurtzite Al1−x−yScxGdyN Heterostructural Alloys

Advanced Science, EarlyView.
This study demonstrates ferroelectricity and piezoelectric properties improvement of quaternary wurtzite Al1−x−yScxGdyN${\rm Al}_{1-x-y}{\rm Sc}_x{\rm Gd}_y{\rm N}$ films, guided by density functional theory calculations. Wurtzite Al1−x−yScxGdyN${\rm Al}_{1-x-y}{\rm Sc}_x{\rm Gd}_y{\rm N}$ films have a high optical bandgap, enhanced piezoelectric ...
Julia L. Martin, Cheng‐Wei Lee, Nate S.P. Bernstein, Thi Nguyen, Ande Bryan, Eli Cooper, John S. Mangum, Sage R. Bauers, Andriy Zakutayev, Keisuke Yazawa, Prashun Gorai, Rebecca W. Smaha   +11 more
wiley   +1 more source

On the polar derivative of lacunary type polynomials

Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics
Let $p(z)=a_nz^n+\sum_{l=\nu}^na_{n-l}z^{n-l}$, where $1\leq \nu \leq n$, be a polynomial of degree $n$ having all its zeros in $|z|\leq k\leq 1$. For polar derivative $D_{\alpha}p(z)$, it is known that for each $|\alpha|\leq 1$ on $|z|=1$, \begin{align*} |D_{\alpha}p(z)|\leq \frac{n}{1+k^{\nu}}\Big\{(|\alpha|+k^{\nu})\|p\|_{\infty}-\frac{1 ...
Ahmad Motamednezhad, Fatemeh Mohammadi
openaire   +3 more sources

Atomic Defects in Layered Transition Metal Dichalcogenides for Sustainable Energy Storage and the Intelligent Trends in Data Analytics

Advanced Science, EarlyView.
This review comprehensively summarizes the atomic defects in TMDs for their applications in sustainable energy storage devices, along with the latest progress in ML methodologies for high‐throughput TEM data analysis, offering insights on how ML‐empowered microscopy facilitates bridging structure–property correlation and inspires knowledge for precise ...
Zheng Luo, Ying Yang, Zizhen Fu, Fengqi Liu, Susu Fang, Kele Xu, Shanshan Wang   +6 more
wiley   +1 more source