Results 81 to 90 of about 1,820,249 (291)

The Bernstein Constant and Polynomial Interpolation at the Chebyshev Nodes

Journal of Approximation Theory, 2002
By giving explicit upper bounds, the author shows that the Bernstein constants \[ B_{\lambda,p} := \lim_{n\to\infty} n^{\lambda+1/p} \inf_{c_k} \Biggl\| | x| ^\lambda - \sum^n_{k=0} c_k x^k\Biggl\|_{L_p[-1,1]} \] are finite for all \(\lambda > 0\) and \(p\in (1/3,\infty)\). For \(p = 1\), the upper bounds turn out to be sharp.
openaire   +3 more sources

A remark on simultaneous inclusions of the zeros of a polynomial by Gershgorin's theorem [PDF]

, 1973
Elsner L. A remark on simultaneous inclusions of the zeros of a polynomial by Gershgorin's theorem. Numerische Mathematik. 1973;21(5):425-427.By using Gershgorin's theorem and the theorems on minimal Gershgorin disks a posteriori error bounds for the ...
Elsner, Ludwig
core   +1 more source

Elastomeric 3D‐Printed Microenvironments Enable Nanonewton Force Measurements in Healthy and Diseased Human Pluripotent Stem Cell‐Derived Neuroepithelial Cells

Advanced Materials, EarlyView.
We present elastomeric three‐dimensional (3D) microstructures fabricated via two‐photon polymerization (2PP) and post‐processed through wet etching, for quantifying nanonewton (nN)‐scale forces applied by healthy and diseased neural cells. The mechanically characterized free‐standing beam architectures enable measurement of traction forces of ...
Pieter F. J. van Altena, Lucia Castillo Ransanz, Ruben H. Guis, Giulia Bergamaschi, Nanne J. Paauw, Urs Staufer, Vivi M. Heine, Angelo Accardo   +7 more
wiley   +1 more source

On some constants in simultaneous approximation

International Journal of Mathematics and Mathematical Sciences, 1995
Pointwise estimates for the error which is feasible in simultaneous approximation of a function and its derivatives by an algebraic polynomial were originally pursued from theoretical motivations, which did not immediately require the estimation of the ...
K. Balázs, T. Kilgore
doaj   +1 more source

Descriptors to Dynamics: A Materials and Device Perspective on in‐Materio Physical Reservoir Computing for Neuromorphic Edge Intelligence

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, Alif Syafiq Kamarol Zaman, Muzhen Xu, Yuki Usami, Saptarshi Das, Hirofumi Tanaka   +5 more
wiley   +1 more source

Solution of the least squares method problem of pairwise comparison matrices [PDF]

, 2008
Pairwise comparison matrix, Least squares approximation, Polynomial system, Homotopy method, Incomplete pairwise comparison matrix,
Bozóki, Sándor, Sándor Bozóki
core   +1 more source

Spin Transport Across Interfaces With the Non‐Collinear Antiferromagnet Mn3Sn

Advanced Materials, EarlyView.
We study spin transport with Mn3Sn|Metal${\rm Mn}_3{\rm Sn}\vert{\rm Metal}$ heterostructures. For Mn3Sn|Pt${\rm Mn}_3{\rm Sn}\vert{\rm Pt}$ heterostructures, ultrafast spin current generation by optical pumping of Mn3Sn${\rm Mn}_3{\rm Sn}$ is explored, while for Mn3Sn|NiFe${\rm Mn}_3{\rm Sn}\vert{\rm NiFe}$ heterostructures, we probe the spin–charge ...
Paul A. Marschall, Wolfgang Hoppe, Prajwal Rigvedi, Börge Göbel, Franziska Ziolkowski, Samir Lounis, Banabir Pal, Stuart S. P. Parkin, Georg Woltersdorf   +8 more
wiley   +1 more source

Generalized Chebyshev Polynomials

Discussiones Mathematicae - General Algebra and Applications, 2018
Let h(x) be a non constant polynomial with rational coefficients. Our aim is to introduce the h(x)-Chebyshev polynomials of the first and second kind Tn and Un. We show that they are in a ℚ-vectorial subspace En(x) of ℚ[x] of dimension n.
Abchiche Mourad, Belbachir Hacéne
doaj   +1 more source

Polynomials with constant Hessian determinant

Journal of Pure and Applied Algebra, 1991
The author proves the Jacobian conjecture for polynomial mappings \(F:\mathbb{C}^ 2\to\mathbb{C}^ 2\) with symmetric Jacobian matrix. He uses the fact that, in this case, there exists a polynomial \(P:\mathbb{C}^ 2\to\mathbb{C}\) such that \(F=\text{grad}(P)\) (then \(P\) has constant Hessian determinant), and next, he gives the explicit form of such \(
openaire   +1 more source

The Sidon constant for homogeneous polynomials

, 2009
The Sidon constant for the index set of nonzero m-homogeneous polynomials P in n complex variables is the supremum of the ratio between the l^1 norm of the coefficients of P and the supremum norm of P in D^n. We present an estimate which gives the right order of magnitude for this constant, modulo a factor depending exponentially on m.
Ortega-Cerdà, Joaquim, Ounaïes, Myriam, Seip, Kristian   +2 more
openaire   +2 more sources