Results 21 to 30 of about 9,096 (136)

Tridiagonal pairs of Krawtchouk type

Linear Algebra and its Applications, 2007
Let $K$ denote an algebraically closed field with characteristic 0 and let $V$ denote a vector space over $K$ with finite positive dimension. Let $A,A^*$ denote a tridiagonal pair on $V$ with diameter $d$. We say that $A,A^*$ has Krawtchouk type whenever the sequence $\lbrace d-2i\rbrace_{i=0}^d$ is a standard ordering of the eigenvalues of $A$ and a ...
Ito, Tatsuro, Terwilliger, Paul
openaire   +2 more sources

Tridiagonal-Diagonal Reduction of Symmetric Indefinite Pairs [PDF]

SIAM Journal on Matrix Analysis and Applications, 2004
The authors consider the reduction of a symmetric indefinite matrix pair \((A, B)\), with \(B\) nonsingular, to tridiagonal-diagonal form by congruence transformations. More precisely, three different tridiagonal-diagonal reduction methods are presented. The first two algorithms proposed are an improvement over \textit{M. A.
openaire   +2 more sources

Equivalence of finite dimensional input-output models of solute transport and diffusion in geosciences [PDF]

, 2016
We show that for a large class of finite dimensional input-output positive systems that represent networks of transport and diffusion of solute in geological media, there exist equivalent multi-rate mass transfer and multiple interacting continua ...
Babey, Tristan, De Dreuzy, Jean-Raynald, Ramirez, Hector, Rapaport, Alain, Rojas-Palma, Alejandro   +4 more
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Investigation of continuous-time quantum walk by using Krylov subspace-Lanczos algorithm [PDF]

, 2006
In papers\cite{js,jsa}, the amplitudes of continuous-time quantum walk on graphs possessing quantum decomposition (QD graphs) have been calculated by a new method based on spectral distribution associated to their adjacency matrix. Here in this paper, it
Aharonov, Berman, Buonsante, Childs, Cserti, Du, Dur, Eriksen, Farhi, Farhi, Farhi, Feldman, Grover, Guhr, Jafarizadeh, Jafarizadehn, Jeong, Kakutani, Knight, Konno, Lee, M. A. Jafarizadeh, Madi, Mulken, Obata, R. Sufiani, S. Jafarizadeh, S. Salimi, Sanders, Terwilliger, Voiculescu, Wu, Zusman   +32 more
core   +2 more sources

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 ...
openaire   +3 more sources

Mass flows and angular momentum density for $p_x+ip_y$ paired fermions in a harmonic trap [PDF]

, 2007
We present a simple two-dimensional model of a $p_x+ip_y$ superfluid in which the mass flow that gives rise to the intrinsic angular momentum is easily calculated by numerical diagonalization of the Bogoliubov-de Gennes operator.
Anderson, Balatskii, Cross, Gaitan, Garg, Goldstone, Inaki Anduaga, Ishikawa, Ishikawa, Ishikawa, Kita, Kita, Leggett, Mackenzie, McClure, Mermin, Michael Stone, Read, Regal, Stone, Volovik, Volovik, Volovik   +22 more
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Affine transformations of a Leonard pair

, 2006
Let $K$ denote a field and let $V$ denote a vector space over $K$ with finite positive dimension. We consider an ordered pair of linear transformations $A : V \to V$ and $A^* : V \to V$ that satisfy (i) and (ii) below: (i) There exists a basis for $V ...
Nomura, Kazumasa, Terwilliger, Paul
core   +2 more sources

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, Albertini, Au-Yang, Baseilhac, Baseilhac, Baxter, Baxter, Bazhanov, Bazhanov, Bazhanov, Bazhanov, Bernard, Chari, Cherednik, Date, Davies, Davies, de Vega, Delius, Doikou, Dolan, Ghoshal, Ito, Ito, Klishevich, Klishevich, Lezter, Mezincescu, Onsager, Pascal Baseilhac, Perk, Sklyanin, Terwilliger, Terwilliger, Terwilliger, Terwilliger, von Gehlen, von Gehlen, Wiegmann, Zhedanov   +39 more
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Limits of spiked random matrices I

, 2011
Given a large, high-dimensional sample from a spiked population, the top sample covariance eigenvalue is known to exhibit a phase transition. We show that the largest eigenvalues have asymptotic distributions near the phase transition in the rank-one ...
Bloemendal, Alex, Virág, Bálint
core   +1 more source

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, Pedro Alonso, Juan Manuel Peña, Raúl Pérez‐Fernández   +3 more
wiley   +1 more source