Related papers: Finite Gap Jacobi Matrices: A Review

We recall criteria on the spectrum of Jacobi matrices such that the corresponding isospectral torus consists of periodic operators. Motivated by those known results for Jacobi matrices, we define a new class of operators called GMP…

This short but self-contained survey presents a number of elegant matrix/operator inequalities for general convex or concave functions, obtained with a unitary orbit technique. Jensen, sub or super-additivity type inequalities are…

Some inequalities for different types of convexity are established.

A revised version with a number of corrections and refinements.

A Jacobi matrix with matrix entries is a self-adjoint block tridiagonal matrix with invertible blocks on the off-diagonals. Averaging over boundary conditions leads to explicit formulas for the averaged spectral measure which can…

We prove a conjecture due to Y. Last on Jacobi matrices.

In this paper, new inequalities connected with the celebrated Steffensen's integral inequality are proved.

In this paper we give an algorithm to determine all finite matrix groups over a number field. Our algorithm is based on the representation theory of finite groups.

This brief note gives a survey on results relating to existence of closed points on schemes, including an elementary topological characterization of the schemes with (at least one) closed point.

We correct here two errors in our earlier paper "An algebraic model for finite loop spaces" [arXiv:1212.2033]

System of alternatively orthogonalized rational functions of Jacobi type on the half line $[1, \infty)$ is defined and its properties are established. Three subsystems of proper and mixed systems of rational functions with nice properties…

We introduce a function of the density of states for periodic Jacobi matrices on trees and prove a useful formula for it. This allows new, streamlined proofs of the gap labeling and Aomoto index theorems. We prove a version of this new…

In this paper, we obtain recursion formulas for the Kamp\'e de Fe\'riet hypergeometric matrix function. We also give finite and infinite summation formulas for the Kamp\'e de Fe\'riet hypergeometric matrix function.

We study the affine ring of the affine Jacobi variety of a hyper-elliptic curve. The matrix construction of the affine hyper-elliptic Jacobi varieties due to Mumford is used to calculate the character of the affine ring. By decomposing the…

Rejoinder: Bayesian Checking of the Second Levels of Hierarchical Models [arXiv:0802.0743]

We discuss some research problems on affine monomial curves, from the perspective of computation.

Chapters : Old and new inequalities; Surfaces with $\chi=1$ and the bicanonical map; Surfaces with $p_g=4$; Surfaces isogeneous to a product, Beauville surfaces and the absolute Galois group;Lefschetz pencils and braid monodromies;DEF, DIFF…

Alternative approaches to Lebesgue integration are considered.

The Jacobi evolution method has been widely used in the QCD analysis of structure function data. However a recent paper claims that there are serious problems with its convergence and stability. Here we briefly review the evidence for the…

This is an expository paper about the topics listed in the title.