Results 21 to 30 of about 9,075 (140)
Tridiagonal pairs of q-Racah type and the q-tetrahedron algebra [PDF]
Journal of Pure and Applied Algebra, 2021 Let $\mathbb F$ denote a field, and let $V$ denote a vector space over $\mathbb F$ with finite positive dimension. We consider an ordered pair of $\mathbb F$-linear maps $A: V \to V$ and $A^*:V\to V$ such that (i) each of $A,A^*$ is diagonalizable; (ii) there exists an ordering $\lbrace V_i\rbrace_{i=0}^d$ of the eigenspaces of $A$ such that $A^* V_i ...
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Analogues of Lusztig's higher order relations for the q-Onsager algebra
, 2013 Let $A,A^*$ be the generators of the $q-$Onsager algebra. Analogues of Lusztig's $r-th$ higher order relations are proposed. In a first part, based on the properties of tridiagonal pairs of $q-$Racah type which satisfy the defining relations of the $q ...
Baseilhac, P., Vu, T. T.
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An integrable structure related with tridiagonal algebras
, 2004 The standard generators of tridiagonal algebras, recently introduced by Terwilliger, are shown to generate a new (in)finite family of mutually commuting operators which extends the Dolan-Grady construction.
Ahn +39 more
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High Relative Accuracy Computations With Covariance Matrices of Order Statistics
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT In many statistical applications, numerical computations with covariance matrices need to be performed. The error made when performing such numerical computations increases with the condition number of the covariance matrix, which is related to the number of variables and the strength of the correlation between the variables. In a recent work,
Juan Baz +3 more
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Engineering Reports, Volume 8, Issue 3, March 2026.Agricultural intensification and the increasing use of fertilizers and irrigation have significantly improved crop productivity but have also led to growing concerns over groundwater contamination and inefficient water usage. When solutes like nitrates and pesticides seep past the root zone, they not only deplete soil fertility but also endanger the ...
Wubale Demis Alamirew, Ephrem Yetbarek
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Method of studying the Bogoliubov-de Gennes equations for the superconducting vortex lattice state
, 2009 In this paper, we present a method to construct the eigenspace of the normal-state electrons moving in a 2D square lattice in presence of a perpendicular uniform magnetic field which imposes (quasi)-periodic boundary conditions for the wave functions in ...
Azbel M Ya +6 more
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Scattering theory for difference equations with operator coefficients
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract We investigate a class of second‐order difference equations featuring operator‐valued coefficients with the aim of approaching problems of stationary scattering theory. We focus on various compact perturbations of the discrete Laplacian given in a Hilbert space of bi‐infinite square‐summable sequences with entries from a fixed Hilbert space ...
David Sher +3 more
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Efficient Dynamics: Reduced‐Order Modeling of the Time‐Dependent Schrödinger Equation
Advanced Physics Research, Volume 5, Issue 2, February 2026.Reduced‐order modeling (ROM) approaches for the time‐dependent Schrödinger equation are investigated, highlighting their ability to simulate quantum dynamics efficiently. Proper Orthogonal Decomposition, Dynamic Mode Decomposition, and Reduced Basis Methods are compared across canonical systems and extended to higher dimensions.
Kolade M. Owolabi
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Towards a classification of the tridiagonal pairs
Linear Algebra and its Applications, 2008 18 ...
Nomura, Kazumasa, Terwilliger, Paul
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Tridiagonal pairs of q-Serre type and their linear perturbations
Journal of Algebra, 2022 A tridiagonal pair is an ordered pair of diagonalizable linear maps on a nonzero finite-dimensional vector space, that each act on the eigenspaces of the other in a block-tridiagonal fashion. We consider a tridiagonal pair $(A, A^*)$ of $q$-Serre type; for such a pair the maps $A$ and $A^*$ satisfy the $q$-Serre relations.
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