Citations
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Book
Random matrices, Frobenius eigenvalues, and monodromy
Nicholas M. Katz,Peter Sarnak +1 more
TL;DR: In this paper, the main results of the main theorem were reformulated and reduction steps in proving the main theorems were taken in the following order: Test functions Haar measure Tail estimates Large $N$ limits and Fredholm determinants Several variables Equidistribution Monodromy of families of curves Monodromes of some other families GUE discrepancies in various families Distribution of low-lying Frobenius eigenvalues in different families Appendix AD: Densities Appendix AG: Graphs References.
Journal ArticleDOI
A high-order discontinuous Galerkin method for the unsteady incompressible Navier-Stokes equations
TL;DR: The proposed discontinuous Galerkin method with the P"k-P"k formulation is an efficient scheme for accurate and stable solution of the unsteady Navier-Stokes equations in convection-dominated flows.
Journal ArticleDOI
Fast and accurate computation of gauss-legendre and gauss-jacobi quadrature nodes and weights ∗
Nicholas Hale,Alex Townsend +1 more
TL;DR: An efficient algorithm for the accurate computation of Gauss--Legendre and Gauss-Jacobi quadrature nodes and weights is presented based on Newton's root-finding method with initial guesses and function evaluations computed via asymptotic formulae.
Journal ArticleDOI
The longest increasing subsequence in a random permutation and a unitary random matrix model
TL;DR: In this paper, it was shown that the expected length of the longest increasing subsequence in a random permutation is the same as the length of a subsequence of the shortest increasing subsequences in the unitary random matrix model.
Journal ArticleDOI
Image focus measure based on Chebyshev moments
TL;DR: It is shown that the focus measure is monotonic and unimodal with respect to image blurring and invariant to contrast changes due to the differences in the intensities of illumination.
References
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Journal ArticleDOI
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
TL;DR: This work represents the stochastic processes with an optimum trial basis from the Askey family of orthogonal polynomials that reduces the dimensionality of the system and leads to exponential convergence of the error.
Book
Random matrices, Frobenius eigenvalues, and monodromy
Nicholas M. Katz,Peter Sarnak +1 more
TL;DR: In this paper, the main results of the main theorem were reformulated and reduction steps in proving the main theorems were taken in the following order: Test functions Haar measure Tail estimates Large $N$ limits and Fredholm determinants Several variables Equidistribution Monodromy of families of curves Monodromes of some other families GUE discrepancies in various families Distribution of low-lying Frobenius eigenvalues in different families Appendix AD: Densities Appendix AG: Graphs References.
Journal ArticleDOI
An extended class of orthogonal polynomials defined by a Sturm-Liouville problem
TL;DR: In this article, two infinite sequences of polynomial eigenfunctions of a Sturm-Liouville problem are presented, and they are shown to be orthogonal with respect to a positive definite inner product defined over the compact interval [ − 1, 1 ] or the half-line [ 0, ∞ ), respectively.
Journal ArticleDOI
An extension of Bochner's problem: Exceptional invariant subspaces
TL;DR: The main theorem of the paper provides a characterization of all such differential operators and polynomial sequences based on the classification of codimension one exceptional subspaces under projective transformations.
Journal ArticleDOI
A high-order discontinuous Galerkin method for the unsteady incompressible Navier-Stokes equations
TL;DR: The proposed discontinuous Galerkin method with the P"k-P"k formulation is an efficient scheme for accurate and stable solution of the unsteady Navier-Stokes equations in convection-dominated flows.