Results 1 to 10 of about 435,489 (102)
Simulating Cardiac Electrophysiology Using Unstructured All-Hexahedra Spectral Elements. [PDF]
Biomed Res Int, 2015 We discuss the application of the spectral element method to the monodomain and bidomain equations describing propagation of cardiac action potential. Models of cardiac electrophysiology consist of a system of partial differential equations coupled with a system of ordinary differential equations representing cell membrane dynamics.
Cuccuru G +3 more
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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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Bivariate Generalized Shifted Gegenbauer Orthogonal System
Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021 For K0, K1 ≥ 0, λ > −(1/2), we examine Cr∗λ,K0,K1x, generalized shifted Gegenbauer orthogonal polynomials, with reference to the weight Wλ,K0,K1x=2λΓ2λ/Γλ+12/2x−x2λ−12/Ix∈0,1dx+K0δ0+K1δ1, where the indicator function is denoted by Ix∈0,1 and δx indicates the Dirac δ−measure.
Mohammad A. Alqudah +3 more
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A new family of orthogonal polynomials in three variables
Journal of Inequalities and Applications, 2020 In this paper we introduce a six-parameter generalization of the four-parameter three-variable polynomials on the simplex and we investigate the properties of these polynomials.
Rabia Aktaş +2 more
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The Fractional Orthogonal Derivative
Mathematics, 2015 This paper builds on the notion of the so-called orthogonal derivative, where an n-th order derivative is approximated by an integral involving an orthogonal polynomial of degree n.
Enno Diekema
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Symmetry, Integrability and Geometry: Methods and Applications, 2013 We present a semi-infinite q-boson system endowed with a four-parameter boundary interaction. The n-particle Hamiltonian is diagonalized by generalized Hall-Littlewood polynomials with hyperoctahedral symmetry that arise as a degeneration of the ...
Jan Felipe van Diejen, Erdal Emsiz
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The dynamical U(n) quantum group
International Journal of Mathematics and Mathematical Sciences, Volume 2006, Issue 1, 2006., 2006 We study the dynamical analogue of the matrix algebra M(n), constructed from a dynamical R‐matrix given by Etingof and Varchenko. A left and a right corepresentation of this algebra, which can be seen as analogues of the exterior algebra representation, are defined and this defines dynamical quantum minor determinants as the matrix elements of these ...
Erik Koelink, Yvette Van Norden
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Some details of proofs of theorems related to the quantum dynamical Yang‐Baxter equation
International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 12, Page 793-806, 2000., 2000 This paper of tutorial nature gives some further details of proofs of some theorems related to the quantum dynamical Yang‐Baxter equation. This mainly expands proofs given in “Lectures on the dynamical Yang‐Baxter equation” by Etingof and Schiffmann, math.QA/9908064.
Tom H. Koornwinder
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Differential representations of dynamical oscillator symmetries in discrete Hilbert space
Discrete Dynamics in Nature and Society, Volume 5, Issue 2, Page 97-106, 2000., 2000 As a very important example for dynamical symmetries in the context of q‐generalized quantum mechanics the algebra aa† − q−2a†a = 1 is investigated. It represents the oscillator symmetry SUq(1, 1) and is regarded as a commutation phenomenon of the q‐Heisenberg algebra which provides a discrete spectrum of momentum and space, i.e., a discrete Hilbert ...
Andreas Ruffing
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Wavelet transforms in generalized Fock spaces
International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 4, Page 657-672, 1997., 1996 A generalized Fock space is introduced as it was developed by Schmeelk [1‐5], also Schmeelk and Takači [6‐8]. The wavelet transform is then extended to this generalized Fock space. Since each component of a generalized Fock functional is a generalized function, the wavelet transform acts upon the individual entry much the same as was developed by ...
John Schmeelk, Arpad Takači
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