Results 61 to 70 of about 43,755 (258)

The arithmetic of genus two curves with (4,4)-split Jacobians

, 2011
In this paper we study genus 2 curves whose Jacobians admit a polarized (4,4)-isogeny to a product of elliptic curves. We consider base fields of characteristic different from 2 and 3, which we do not assume to be algebraically closed.
Bolza, Bosma, Donagi, Frey, Frey, Gaudry, Igusa, Igusa, J.-B., Kani, Kani, Kevin Doerksen, Krazer, Kuhn, L.-C., Magaard, Milne, Murabayashi, Nils Bruin, Shaska, Shaska, Silverberg   +21 more
core   +1 more source

Polar Derivative Versions of Polynomial Inequalities

Advances in Pure Mathematics, 2015
Let be a polynomial of degree n and for a complex number , let  denote the polar derivative of the polynomial  with respect to . In this paper, first we extend as well as generalize the result proved by Dewan and Mir [Inter. Jour. Math. and Math. Sci., 16 (2005), 2641-2645] to polar derivative. Besides, another result due to Dewan et al. [J. Math. Anal.
openaire   +2 more sources

Direct Photocurrent Detection of Optical Vortex Based on the Orbital Photo Galvanic Effect: Progress, Challenge, and Perspective

Advanced Science, EarlyView.
Direct orbital angular momentum (OAM) detection through the orbital photogalvanic effect offers a scalable route for integrated optoelectronics. This perspective evaluates symmetry‐driven material selection and demonstrates how electrode matrices enable the resolution of complex, mixed OAM modes.
Jinluo Cheng, Dehong Yang, Weiming Wang, Chang Xu, Zipu Fan, Dong Sun   +5 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

Spin-Singlet Quantum Hall States and Jack Polynomials with a Prescribed Symmetry

, 2011
We show that a large class of bosonic spin-singlet Fractional Quantum Hall model wave-functions and their quasi-hole excitations can be written in terms of Jack polynomials with a prescribed symmetry.
Ardonne, Ardonne, Ardonne, Ardonne, Ardonne, B. Andrei Bernevig, Baker, Benoit Estienne, Bernard, Bernevig, Bernevig, Bernevig, Bernevig, Bernevig, Calogero, Cherednik, di Francesco, Estienne, Estienne, Estienne, Estienne, Feigin, Gepner, Grosfeld, Halperin, Kasatani, Kasatani, Laughlin, Moore, Nakai, Read, Read, Read, Read, Simon, Sutherland, Sutherland, Thomale   +37 more
core   +1 more source

Bicomplex polar weighted homogeneous polynomials

We study the topology of real polynomial maps $\mathbb{R}^{4n} \longrightarrow \mathbb{R}^{4}$ expressed in terms of bicomplex variables and their conjugates, which we refer to as bicomplex mixed polynomials. We introduce the notion of polar weighted homogeneity, a property that generalizes the concept of weighted homogeneity in the complex setting ...
Bravo, Yesenia, Rabelo, Inácio, Romano-Velázquez, Agustín   +2 more
openaire   +2 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

On Polar Jacobi Polynomials

Mathematics
In the present work, we investigate certain algebraic and differential properties of the orthogonal polynomials with respect to a discrete–continuous Sobolev-type inner product defined in terms of the Jacobi measure.
openaire   +3 more sources

Active Metamaterials with Tunable Shear Nonreciprocity and Nonlinear Dynamics

Advanced Science, EarlyView.
Active gear‐based mechanical metamaterials enable simultaneous control of translational and torsional stiffnesses by 30–100×, break shear reciprocity under positive versus negative loads, broadly tune resonant frequencies, and offer programmable dynamic responses.
Xin Fang, Miao Yu, Dianlong Yu, Li Cheng
wiley   +1 more source

Some Bounds for the Polar Derivative of a Polynomial [PDF]

International Journal of Mathematics and Mathematical Sciences, 2018
The polar derivative of a polynomial p(z) of degree n with respect to a complex number α is a polynomial np(z)+α-zp′(z), denoted by Dαp(z). Let 1≤R≤k. For a polynomial p(z) of degree n having all its zeros in z≤k, we investigate a lower bound of modulus of Dαp(z) on z=R.
Jiraphorn Somsuwan, Keaitsuda Maneeruk Nakprasit   +1 more
openaire   +3 more sources