Results 91 to 100 of about 128,384 (219)

Semi-classical Laguerre polynomials and a third order discrete integrable equation

, 2009
A semi-discrete Lax pair formed from the differential system and recurrence relation for semi-classical orthogonal polynomials, leads to a discrete integrable equation for a specific semi-classical orthogonal polynomial weight. The main example we use is
Christoffel E B, Darboux G, Forrester P J Witte N S, Forrester P J Witte N S, Frank W Nijhoff, Freud G, Grammaticos B, Laguerre E, Laguerre E, Laguerre E, Lax P D, Magnus A P, Paul E Spicer   +12 more
core   +3 more sources

Maximum Shattering

Journal of Combinatorial Designs, EarlyView.
ABSTRACT A family ℱ ${\rm{ {\mathcal F} }}$ of subsets of [ n ] = { 1 , 2 , … , n } $[n]=\{1,2,\ldots ,n\}$ shatters a set A ⊆ [ n ] $A\subseteq [n]$ if for every A ′ ⊆ A ${A}^{^{\prime} }\subseteq A$, there is an F ∈ ℱ $F\in {\rm{ {\mathcal F} }}$ such that F ∩ A = A ' $F\cap A={A}^{\text{'}}$.
Noga Alon, Varun Sivashankar, Daniel G. Zhu   +2 more
wiley   +1 more source

On the spectrum of tridiagonal matrices with two-periodic main diagonal

Special Matrices
We find the spectrum and eigenvectors of an arbitrary irreducible complex tridiagonal matrix with two-periodic main diagonal. This is expressed in terms of the spectrum and eigenvectors of the matrix with the same sub- and superdiagonals and zero main ...
Dyachenko Alexander, Tyaglov Mikhail
doaj   +1 more source

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

Murine Supraspinatus Tendons Demonstrate Aging‐Related Changes in Multiscale Mechanics, Structure, and Gene Expression

Journal of Orthopaedic Research, EarlyView.
ABSTRACT Rotator cuff disorders are common in the aging population, often leading to pain, disability, and reduced quality of life. Age‐associated changes can occur disproportionately in regions of high mechanical stress, such as the insertion site of the supraspinatus tendon, leading to increased injury rates and tendinopathies.
Michael S. DiStefano, Jeremy D. Eekhoff, Stephanie N. Weiss, Courtney A. Nuss, Rebecca L. Betts, Andrew F. Kuntz, Louis J. Soslowsky   +6 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

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

Convergence rate for a Gauss collocation method applied to unconstrained optimal control

, 2015
A local convergence rate is established for an orthogonal collocation method based on Gauss quadrature applied to an unconstrained optimal control problem.
Hager, William W., Hou, Hongyan, Rao, Anil V.   +2 more
core   +1 more source

Orbital Angular Momentum Holography Using Neural Network and Camera in the Loop

Laser &Photonics Reviews, EarlyView.
Neural network and optimization‐based approaches are introduced for Orbital Angular Momentum (OAM) multiplexed holography, enabling high‐capacity, phase‐only image reconstruction. A Camera‐In‐The‐Loop (CITL) system learns a realistic propagation model to correct system imperfections.
Nima Asoudegi, Mo Mojahedi
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