9,216 research outputs found
Can an infinite left-product of nonnegative matrices be expressed in terms of infinite left-products of stochastic ones?
If a left-product of square complex matrices converges to a
nonnull limit when and if the belong to a finite set, it is
clear that there exists an integer such that the , , have
a common right-eigenvector for the eigenvalue 1. Now suppose that the
are nonnegative and that has positive entries. Denoting by the
diagonal matrix whose diagonal entries are the entries of , the stochastic
matrices satisfy , so the problem of the convergence of reduces
to the one of . In this paper we still suppose that the
are nonnegative but we do not suppose that has positive entries. The first
section details the case of the matrices, and the last gives a first
approach in the case of matrices.Comment: 8 page
Infinite products of nonnegative matrices by nonnegative vectors
Given a finite set of nonnegative
matrices and a nonnegative column-vector , we associate to each
the sequence of the column-vectors
. We give the necessary and sufficient condition on the
matrices and the vector for this sequence to converge for all
\hbox{} such that $\forall n,\
M_{\omega_1}\dots M_{\omega_n}V\ne\begin{pmatrix}0\\0\end{pmatrix}$.Comment: 8 page
Infinite products of matrices and the Gibbs properties of Bernoulli convolutions
We consider the infinite sequences (A\_n)\_{n\in\NN} of matrices
with nonnegative entries, where the are taken in a finite set of
matrices. Given a vector V=\pmatrix{v\_1\cr v\_2} with , we give
a necessary and sufficient condition for to converge uniformly. In application we prove that the
Bernoulli convolutions related to the numeration in Pisot quadratic bases are
weak Gibbs
Weak Gibbs property and system of numeration
We study the selfsimilarity and the Gibbs properties of several measures
defined on the product space \Omega\_r:=\{0,1,...,\break r-1\}^{\mathbb N}.
This space can be identified with the interval by means of the
numeration in base . The last section is devoted to the Bernoulli
convolution in base , called the Erd\H os measure, and
its analogue in base , that we study by means of a
suitable system of numeration
Singular inextensible limit in the vibrations of post-buckled rods: Analytical derivation and role of boundary conditions
In-plane vibrations of an elastic rod clamped at both extremities are studied. The rod is modeled as an extensible planar Kirchhoff elastic rod under large displacements and rotations. Equilibrium configurations and vibrations around these configurations are computed analytically in the incipient post-buckling regime. Of particular interest is the variation of the first mode frequency as the load is increased through the buckling threshold. The loading type is found to have a crucial importance as the first mode frequency is shown to behave singularly in the zero thickness limit in the case of prescribed axial displacement, whereas a regular behavior is found in the case of prescribed axial load.This publication is based in part upon work supported by Award no. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST) (A.G.). A.G. is a Wolfson/Royal Society Merit Award holder. Support from the Royal Society, through the International Exchanges Scheme (Grant IE120203), is also acknowledge
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