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On the performance of active RIS-enhanced NOMA systems with spectrum sharing mechanisms. [PDF]

PLoS One
Tran M, Bui Vu M, Nguyen SQ.
europepmc   +1 more source

Multi-Objective Optimization of an Injection Molding Process for an Alvarez Freeform Lens Using an Integrated Optical System and Mold Flow Analyses. [PDF]

Polymers (Basel)
Yen PY, Lin CM, Chang Chien IH.
europepmc   +1 more source

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Multiplication theorems for orthogonal polynomials

International Journal of Quantum Chemistry, 1993
AbstractIn this paper, a general method is presented that allows the derivation of the expansion coefficients of the product of two orthogonal functions provided the generating function is known. For the three classical orthogonal polynomials, the Laguerre, the Hermite, and the Legendre polynomials, the coefficients blmn with ϕmϕn = ∑lblmnϕl are ...
H. Kleindienst, A. Lüchow
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Orthogonal Polynomials and Approximate Multiple Integration

SIAM Journal on Numerical Analysis, 1971
Let \(R_n\) denote an \(n\)-dimensional region and \(w\) a weight function defined on \(R_n\). This paper is concerned with the existence and construction of approximations of the type \(\int_{R_n} wf\cong \sum_{k=1}^N A_kf(\mu_k)\), where the approximation is precise for polynomials up to a certain degree.
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Meixner Multiple Orthogonal Polynomials on Interlacing Lattices

Mathematical Notes
The authors consider the polynomials \(P_{n_1,n_2}\), which are orthogonal with respect to two discrete measures \[ \mu_j(y)=\sum_{x\in\gamma_j+\mathbb Z_{+}}R(x)\delta(y-x), \qquad j=1,2, \] where the weight function \(R\) is defined on lattices \(\gamma_j+\mathbb Z_{+}\) as a product of two classical Meixner measures, namely \[ R(x):=R_{\gamma_1 ...
Aptekarev, A. I., Dyachenko, A. V., Lysov, V. G.   +2 more
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Multiple input orthogonal polynomial parameter estimation

Mechanical Systems and Signal Processing, 1987
The object of this paper is the development of a so-called global modal parameter estimation technique capable of analyzing frequency response functions (FRFs) between several input and response stations simultaneously. The technique analyses the FRFs in their natural domain, the frequency domain.
van der Anweraer, H., Leuridan, J.
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Asymptotic γ-forms generated by multiple orthogonal polynomials

Proceedings of the Steklov Institute of Mathematics, 2011
The authors find the \(n\)-large asymptotics of the integrals \[ q_n=\int_0^{\infty}Q_ne^{-x}\,dx \] and \[ f_n=\int_0^{\infty}Q_n(x)\ln x e^{-x}\,dx \] involving polynomials \[ Q_n(x)=\frac{1}{(n!)^2}\frac{e^x}{x-1}\frac{d^n}{dx^n}x^n\frac{d^n}{dx^n}(x-1)^{2n+1}x^ne^{-x}.
Aptekarev, A. I., Lysov, V. G.
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Multiplication of Generalized Polynomials, with Applications to Classical Orthogonal Polynomials

SIAM Journal on Algebraic Discrete Methods, 1984
The author considers the problem of writing the product of two polynomials as the sum of other polynomials. The polynomials are given as the sum of orthogonal polynomials, and he uses the comrade matrix to encode some of the calculations. The calculations are done directly using the three term recurrence relation rather than using powers of x as an ...
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Chimeric antigen receptor T‐cell therapy in multiple myeloma: A comprehensive review of current data and implications for clinical practice

Ca-A Cancer Journal for Clinicians, 2023
Rujul Parikh
exaly  

Hahn multiple orthogonal polynomials of type I: Hypergeometric expressions

Journal of Mathematical Analysis and Applications, 2023
Manuel Mañas
exaly