Results 11 to 20 of about 147 (140)
The Viscous and Ohmic Damping of the Earth's Free Core Nutation. [PDF]
J Geophys Res Solid Earth, 2021 Abstract The cause for the damping of the Earth's free core nutation (FCN) and the free inner core nutation eigenmodes has been a matter of debate since the earliest reliable estimations from nutation observations were made available. Numerical studies are difficult given the extreme values of some of the parameters associated with the Earth's fluid ...
Triana SA +4 more
europepmc +2 more sources
Two Legendre-dual-Petrov-Galerkin algorithms for solving the integrated forms of high odd-order boundary value problems. [PDF]
ScientificWorldJournal, 2014 Two numerical algorithms based on dual‐Petrov‐Galerkin method are developed for solving the integrated forms of high odd‐order boundary value problems (BVPs) governed by homogeneous and nonhomogeneous boundary conditions. Two different choices of trial functions and test functions which satisfy the underlying boundary conditions of the differential ...
Abd-Elhameed WM, Doha EH, Bassuony MA.
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Sobolev‐orthogonal systems with tridiagonal skew‐Hermitian differentiation matrices
Studies in Applied Mathematics, Volume 150, Issue 2, Page 420-447, February 2023., 2023 Abstract We introduce and develop a theory of orthogonality with respect to Sobolev inner products on the real line for sequences of functions with a tridiagonal, skew‐Hermitian differentiation matrix. While a theory of such L2 ‐orthogonal systems is well established, Sobolev orthogonality requires new concepts and their analysis.
Arieh Iserles, Marcus Webb
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Parameter and q asymptotics of Lq‐norms of hypergeometric orthogonal polynomials
International Journal of Quantum Chemistry, Volume 123, Issue 2, January 15, 2023., 2023 The weighted Lq‐norms of orthogonal polynomials are determined when q and the polynomial's parameter tend to infinity. They are given in this work by the leading term of the q and parameter asymptotics of the corresponding quantities of the associated probability density. These results are not only interesting per se, but also because they control many
Nahual Sobrino, Jesus S. Dehesa
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Journal of Function Spaces, Volume 2023, Issue 1, 2023., 2023 This article is devoted to deriving a new linearization formula of a class for Jacobi polynomials that generalizes the third‐kind Chebyshev polynomials class. In fact, this new linearization formula generalizes some existing ones in the literature. The derivation of this formula is based on employing a new moment formula of this class of polynomials ...
W. M. Abd-Elhameed +3 more
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Algebraic and complexity‐like properties of Jacobi polynomials: Degree and parameter asymptotics
International Journal of Quantum Chemistry, Volume 122, Issue 6, March 15, 2022., 2022 The Cramér–Rao, Fisher–Shannon and LMC complexity‐like measures of the Jacobi polynomials are determined when the polynomial's degree and parameter tend to infinity. They are given by the leading term of the degree and parameter asymptotics of the corresponding statistical properties of the associated probability density.
Nahual Sobrino, Jesus S.‐Dehesa
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Orthogonality Property of the Discrete q‐Hermite Matrix Polynomials
Mathematical Problems in Engineering, Volume 2022, Issue 1, 2022., 2022 In this paper, we prove that the solution of the autonomous q‐difference system DqY(x) = AY(qx) with the initial condition Y(0) = Y0 where A is a constant square complex matrix, Dq is the Jackson q‐derivative and 0 < q < 1, is asymptotically stable if and only if ℜ(λ) < 0 for all λ ∈ σ(A) where σ(A) is the set of all eigenvalues of A (the spectrum of A)
Ahmed Salem +3 more
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Optimum Synthesis of Pencil Beams with Constrained Dynamic Range Ratio
International Journal of Antennas and Propagation, Volume 2022, Issue 1, 2022., 2022 In antenna array design, low dynamic range ratio (DRR) of excitation coefficients is important because it simplifies array’s feeding network and enables better control of mutual coupling. Optimization‐based synthesis of pencil beams allows explicit control of DRR.
Marko Matijascic +4 more
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Generalized Auto‐Convolution Volterra Integral Equations: Numerical Treatments
Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022 In this paper, we use the operational Tau method based on orthogonal polynomials to achieve a numerical solution of generalized autoconvolution Volterra integral equations. Displaying a lower triangular matrix for basis functions, the corresponding solution is represented in matrix form, and an infinite upper triangular Toeplitz matrix is used to show ...
Mahdi Namazi Nezamabadi +2 more
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On Approximation Properties of Fractional Integral for A‐Fractal Function
Mathematical Problems in Engineering, Volume 2022, Issue 1, 2022., 2022 In this paper, the Riemann–Liouville fractional integral of an A‐fractal function is explored by taking its vertical scaling factors in the block matrix as continuous functions from [0,1] to ℝ. As the scaling factors play a significant role in the generation of fractal functions, the necessary condition for the scaling factors in the block matrix is ...
T. M. C. Priyanka +4 more
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