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Matrix algorithm for determination of the elementary paths and elementary circuits using exotic semirings
idempotent semiring semiring of distinguished languages elementary path
2012/4/18
We propose a new method for determining the elementary paths and elementary circuits in a directed graph. Also, the Hamiltonian paths and Hamiltonian circuits are enumerated.
The poset of the nilpotent commutator of a nilpotent matrix
Jordan type nilpotent matrix commutator poset
2012/2/29
Fix an n by n nilpotent matrix B with entries in an infinite field k. Assume that B is in Jordan canonical form with associated Jordan block partition P. It is well known that the nilpotent commutator...
Series expansions from the corner transfer matrix renormalization group method: the hard squares model
Corner transfer matrix hard squares model series expansions
2011/9/30
Abstract: The corner transfer matrix renormalization group method is an efficient method for evaluating physical quantities in statistical mechanical models. It originates from Baxter's corner transfe...
Matrix Valued Orthogonal Polynomials related to (SU(2) x SU(2),diag)
Matrix Valued Orthogonal Polynomials (SU(2) x SU(2),diag)
2011/1/21
The matrix-valued spherical functions for the pair (K × K,K), K = SU(2), are studied. By
restriction to the subgroup A the matrix-valued spherical functions are diagonal. For suitable set of represen...
The largest eigenvalue of real symmetric, Hermitian and Hermitian self-dual random matrix models with rank one external source, part I
largest eigenvalue of real symmetric Hermitian and Hermitian self-dual random matrix rank one external source
2011/2/22
We consider the limiting location and limiting distribution of the largest eigenvalue in real
symmetric (β = 1), Hermitian (β = 2), and Hermitian self-dual (β = 4) random matrix models
with rank 1 e...
Loop symmetric functions and factorizing matrix polynomials
Loop symmetric functions factorizing matrix polynomials
2011/1/18
These are notes for my talk at ICCM 2010, Beijing. We survey some results, obtained jointly with Pavlo Pylyavskyy, concerning the ring of loop symmetric functions. Motivations from networks on surface...
Matrix operators for complex interferometer analysis
matrix multiplication fiber optic sensors gyroscopes integrated optics
2011/1/14
A modeling methodology and matrix formalism is presented that permits analysis of arbitrarily complex interferometric waveguide systems, including polarization and backreflection effects.
A generalized plasma and interpolation between classical random matrix ensembles
generalized plasma interpolation classical random matrix ensembles
2011/1/17
The eigenvalue probability density functions of the classical random matrix ensembles have
a well known analogy with the one component log-gas at the special couplings = 1, 2 and 4.
Some remarks on structural matrix rings and matrices with ideal entries
structural matrix ring incidence algebra pre-order quasiorder
2011/1/19
Associating to each pre-order on the indices 1, ..., n the corresponding structural matrix ring, or incidence algebra, embeds the lattice of n-element pre-orders into the lattice of n × n matrix rings...
Random matrix theory of unquenched two-colour QCD with nonzero chemical potential
Spontaneous symmetry breaking matrix models chiral Lagrangians
2011/3/3
We solve a random two-matrix model with two real asymmetric matrices whose primary purpose is to describe certain aspects of quantum chromodynamics with two colours and dynamical fermions at nonzero q...
Fuzzy Scalar Field Theory as Matrix Quantum Mechanics
Fuzzy Scalar Field Theory Matrix Quantum Mechanics
2011/3/3
We study the phase diagram of scalar field theory on a three dimensional Euclidean spacetime whose spatial component is a fuzzy sphere. The corresponding model is an ordinary one-dimensional matrix mo...
Realizability of Polytopes as a Low Rank Matrix Completion Problem
Realizability of Polytopes Low Rank Matrix Completion Problem
2011/2/22
Here we show that the problem of realizing a polytope with specified combinatorics is equivalent to a low rank matrix completion problem.This is comparable to known results reducing realizability to s...
We develop a deterministic ab-initio model for the input-output relationship of a multiple-
input multiple-output (MIMO) wireless channel, starting from the Maxwell equations com-
bined with Ohm's L...
The truncated matrix trigonometric moment problem: the operator approach
truncated matrix trigonometric moment problem operator approach
2011/1/19
The aim of this investigation is to obtain a bijective parameterization of all solutions of the truncated matrix trigonometric moment problem. Recall that the truncated matrix trigonometric moment pro...
Exotic characters of unitriangular matrix groups
Exotic characters unitriangular matrix groups
2011/1/20
Let UTn(q) denote the unitriangular group of unipotent n × n upper triangular matrices over a finite field with cardinality q and prime characteristic p. It has been known for some time that when p is...