Results 41 to 50 of about 2,224 (227)
The q-Laguerre matrix polynomials [PDF]
SpringerPlus, 2016 The Laguerre polynomials have been extended to Laguerre matrix polynomials by means of studying certain second-order matrix differential equation. In this paper, certain second-order matrix q-difference equation is investigated and solved. Its solution gives a generalized of the q-Laguerre polynomials in matrix variable.
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Bivariate q-Laguerre–Appell polynomials and their applications
Applied Mathematics in Science and EngineeringRecently, the monomiality principle has been extended to q-polynomials, namely, the q-monomiality principle of q-Appell polynomials has been considered.
Mohammed Fadel +3 more
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A direct Approximation Method to solve OCP Using Laguerre Functions [PDF]
Kirkuk Journal of Science, 2006 This paper presents an approximate method to solve unconstrained optimal control problem (OCP).This method is classified as a direct method in which an OCP is converted into a mathematical programming problem.The proposed direct method is employed by ...
Omar M. Al-Faour and Suha N. Al-Rawi +1 more
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Communications on Pure and Applied Mathematics, EarlyView.Abstract We consider a planar Coulomb gas ensemble of size N$N$ with the inverse temperature β=2$\beta =2$ and external potential Q(z)=|z|2−2clog|z−a|$Q(z)=|z|^2-2c \log |z-a|$, where c>0$c>0$ and a∈C$a \in \mathbb {C}$. Equivalently, this model can be realised as N$N$ eigenvalues of the complex Ginibre matrix of size (c+1)N×(c+1)N$(c+1) N \times (c+1)
Sung‐Soo Byun +2 more
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Finite sums and generalized forms of Bernoulli polynomials [PDF]
Rendiconti di Matematica e delle Sue Applicazioni, 1999 We introduce new classes of Bernoulli polynomials, useful to evaluate partial sums of Hermite and Laguerre polynomials. We also comment on the possibility of extending the class of Bernoulli numbers itself, and indicate their importance in the derivation
G. Dattoli, S. Lorenzutta, C. Cesarano
doaj
Laguerre polynomial expansions
Journal of Computational and Applied Mathematics, 1995 AbstractThe differential operator generated by the Laguerre differential equation xy″ + (1 + α − x)y′ + λy = 0 is considered for all α both in the classical setting L2(0,∞; xαe−x) and in the Sobolev space H1(0,∞;xα + 1e−x;xαe−x). In L2 a shifted operator exists for α < 1, which corresponds to the classic case α > −1.
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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
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Counting words with Laguerre polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 We develop a method for counting words subject to various restrictions by finding a combinatorial interpretation for a product of formal sums of Laguerre polynomials. We use this method to find the generating function for $k$-ary words avoiding any vincular pattern that has only ones.
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Mathematical Methods in the Applied Sciences, EarlyView.A highly accurate numerical method is given for the solution of boundary value problem of generalized Bagley‐Torvik (BgT) equation with Caputo derivative of order 0<β<2$$ 0<\beta <2 $$ by using the collocation‐shooting method (C‐SM). The collocation solution is constructed in the space Sm+1(1)$$ {S}_{m+1}^{(1)} $$ as piecewise polynomials of degree at ...
Suzan Cival Buranay +2 more
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Construction of Bernstein‐Based Words and Their Patterns
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT In this paper, with inspiration of the definition of Bernstein basis functions and their recurrence relation, we give construction of a new word family that we refer Bernstein‐based words. By classifying these special words as the first and second kinds, we investigate their some fundamental properties involving periodicity and symmetricity ...
Irem Kucukoglu, Yilmaz Simsek
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