Results 111 to 120 of about 133,676 (303)

Discrete Entropies of Chebyshev Polynomials

Mathematics
Because of its flexibility and multiple meanings, the concept of information entropy in its continuous or discrete form has proven to be very relevant in numerous scientific branches. For example, it is used as a measure of disorder in thermodynamics, as
Răzvan-Cornel Sfetcu, Sorina-Cezarina Sfetcu, Vasile Preda   +2 more
doaj   +1 more source

On the ω-multiple Meixner polynomials of the first kind

Journal of Inequalities and Applications, 2020
In this study, we introduce a new family of discrete multiple orthogonal polynomials, namely ω-multiple Meixner polynomials of the first kind, where ω is a positive real number.
Sonuç Zorlu Oğurlu, İlkay Elidemir
doaj   +1 more source

Higher analogues of the discrete-time Toda equation and the quotient-difference algorithm

, 2011
The discrete-time Toda equation arises as a universal equation for the relevant Hankel determinants associated with one-variable orthogonal polynomials through the mechanism of adjacency, which amounts to the inclusion of shifted weight functions in the ...
Bareiss E H, Bressoud D, Brezinski C, Brezinski C, Brezinski C, Brezinski C, Chihara T S, Draux A, Erdelyi A, Frank W Nijhoff, Henrici P, Kowalewski G, Krichever I M, Krichever I M, Lomont J S, Malaschonok G I, Malaschonok G I, Muir T, Paul E Spicer, Peter H van der Kamp, Spicer P E, Suetin P K, Toda M, van der Kamp P H, van der Kamp P H, Veselov A P, Viallet C   +26 more
core   +1 more source

Discrete orthogonal polynomials on Gauss–Lobatto Chebyshev nodes

Journal of Approximation Theory, 2007
This paper deals with explicit formulas for discrete orthogonal polynomials over the so-called Gauss-Lobatto Chebyshev nodes \[ X_n=\{x_k=-\cos((k-1)\pi/(n-1))\},\quad k=1, 2, \ldots ,n. \] The orthogonal polynomials \(p_k(x)\) (\(k=1, 2, \dots ,n\)) with respect to the discrete inner product \(\langle f,g\rangle=\sum_{k=1}^nf(x_k)g(x_k)\) on the set \(
Eisinberg A, FEDELE, Giuseppe
openaire   +2 more sources

Vector Field‐Based Collision‐Free Navigation in Tunnel‐Like Environments

Journal of Field Robotics, EarlyView.
ABSTRACT Tunnel‐like environments, renowned for their vast scale, confined spaces, and limited visibility, present significant challenges for autonomous robot navigation. This study addresses the critical issue of guiding robots through such environments while ensuring collision‐free navigation and maintaining a specified safety margin from both tunnel
Bao Jianjun, Licheng Feng, Yueqi Wang, Kai Zhao, Binghao Li, Liao Wu   +5 more
wiley   +1 more source

Efficient algorithms for construction of recurrence relations for the expansion and connection coefficients in series of quantum classical orthogonal polynomials

Journal of Advanced Research, 2010
Formulae expressing explicitly the q-difference derivatives and the moments of the polynomials Pn(x ; q) ∈ T (T ={Pn(x ; q) ∈ Askey–Wilson polynomials: Al-Salam-Carlitz I, Discrete q-Hermite I, Little (Big) q-Laguerre, Little (Big) q-Jacobi, q-Hahn ...
Eid H. Doha, Hany M. Ahmed
doaj   +1 more source

Using $\D$-operators to construct orthogonal polynomials satisfying higher order difference or differential equations [PDF]

, 2013
We introduce the concept of $\D$-operators associated to a sequence of polynomials $(p_n)_n$ and an algebra $\A$ of operators acting in the linear space of polynomials.
Durán, Antonio J.
core  

Discrete Orthogonal Polynomial Expansions of Averaged Functions

Journal of Mathematical Analysis and Applications, 1995
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openaire   +2 more sources

3D Customized Silica‐Based AFM Probes Fabricated by Selective Laser Etching

Small Methods, EarlyView.
Selective laser etching (SLE) enables the monolithic fabrication of customized, fully 3D silica AFM probes integrating both cantilever and tip with controlled 3D geometries. The process allows the production of either sharp or spherical tips with high design flexibility, reproducibility, and yield.
Koutayba Saada, David Bourrier, Juliette Lignieres, Etienne Dague, Laurent Malaquin   +4 more
wiley   +1 more source

A Discrete Cramér–Von Mises Statistic Related to Hahn Polynomials with Application to Goodness-of-Fit Testing for Hypergeometric Distributions

Axioms
We give the Karhunen–Loève expansion of the covariance function of a family of discrete weighted Brownian bridges, appearing as discrete analogues of continuous Gaussian processes related to Cramér –von Mises and Anderson–Darling statistics. This analogy
Jean-Renaud Pycke
doaj   +1 more source