Polynomial solutions of qKZ equation and ground state of XXZ spin chain at Delta = -1/2
, 2007 Integral formulae for polynomial solutions of the quantum Knizhnik-Zamolodchikov equations associated with the R-matrix of the six-vertex model are considered.
A V Razumov +33 more
core +1 more source
Tracing Student Activity Patterns in E-Learning Environments: Insights into Academic Performance
Future InternetIn distance learning educational environments like Moodle, students interact with their tutors, their peers, and the provided educational material through various means.
Evgenia Paxinou +5 more
doaj +1 more source
Singular and non-singular eigenvectors for the Gaudin model [PDF]
J.Math.Phys. 42 (2001) 3497, 2002 We present a method to construct a basis of singular and non-singular common eigenvectors for Gaudin Hamiltonians in a tensor product module of the Lie algebra SL(2). The subset of singular vectors is completely described by analogy with covariant differential operators. The relation between singular eigenvectors and the Bethe Ansatz is discussed.
arxiv +1 more source
Spectral analysis of q-fractional Sturm-Liouville operators
Electronic Journal of Differential Equations, 2017 In this article, we study q-fractional Sturm-Liouville operators. Using by the functional method, we pass to a new operator. Then, showing that this operator is a maximal operator and constructing a self-adjoint dilation of the maximal dissipative ...
Bilender P. Allahverdiev, Huseyin Tuna
doaj
Spectra of chains connected to complete graphs [PDF]
arXiv, 2020 We characterize the spectrum of the Laplacian of graphs composed of one or two finite or infinite chains connected to a complete graph. We show the existence of localized eigenvectors of two types, eigenvectors that vanish exactly outside the complete graph and eigenvectors that decrease exponentially outside the complete graph.
arxiv
Mine exogenous fire monitoring method using the fusion of infrared visual features
矿业科学学报In order to solve the problems of high false positive and false negative rates of external fire monitoring in complex mine environments, a monitoring algorithm using infrared visual feature fusion was proposed.
LI Xiaoyu +3 more
doaj +1 more source
Finite sample approximation results for principal component analysis: a matrix perturbation approach
, 2009 Principal component analysis (PCA) is a standard tool for dimensional reduction of a set of $n$ observations (samples), each with $p$ variables. In this paper, using a matrix perturbation approach, we study the nonasymptotic relation between the ...
Nadler, Boaz
core +2 more sources
A Note on Surgical Eigenstructure Assignment via State Feedback [PDF]
arXiv, 2020 Assignability of all eigenvalues and a subset of key eigenvectors/generalized eigenvectors of a linear time-invariant system via state feedback is considered. We clarify that, if the key eigenvectors/generalized eigenvectors and their associated eigenvalues satisfy the classical conditions for full eigenstructure assignment, the remaining eigenvalues ...
arxiv
Universal eigenvector statistics in a quantum scattering ensemble
, 2000 We calculate eigenvector statistics in an ensemble of non-Hermitian matrices describing open quantum systems [F. Haake et al., Z. Phys. B 88, 359 (1992)] in the limit of large matrix size.
B. Mehlig +16 more
core +1 more source
Analytical solutions to some generalized and polynomial eigenvalue problems
Special Matrices, 2021 It is well-known that the finite difference discretization of the Laplacian eigenvalue problem −Δu = λu leads to a matrix eigenvalue problem (EVP) Ax =λx where the matrix A is Toeplitz-plus-Hankel.
Deng Quanling
doaj +1 more source