Hurwitz rational functions

A generalization of Hurwitz stable polynomials to real rational functions is considered. We establishe an analogue of the Hurwitz stability criterion for rational functions and introduce a new type of determinants that can be treated as a generalization of the Hurwitz determinants.Comment: 10 page

On linear combinations of two idempotent matrices over an arbitrary field

Given an arbitrary field K and non-zero scalars a and b, we give necessary and sufficient conditions for a matrix A in M_n(K) to be a linear combination of two idempotents with coefficients a and b. This extends results previously obtained by Hartwig and Putcha in two ways: the field K considered here is arbitrary (possibly of characteristic 2), and the case a is different from b and -b is taken into account.Comment: 18 pages (minor corrections

Exact treatment of linear difference equations with noncommutative coefficients

The exact solution of a Cauchy problem related to a linear second-order difference equation with constant noncommutative coefficients is reported.Comment: 7 pages, 0 figure

Orientation of non-spherical particles in an axisymmetric random flow

The dynamics of non-spherical rigid particles immersed in an axisymmetric random flow is studied analytically. The motion of the particles is described by Jeffery's equation; the random flow is Gaussian and has short correlation time.The stationary probability density function of orientations is calculated exactly. Four regimes are identified depending on the statistical anisotropy of the flow and on the geometrical shape of the particle. If {\lambda} is the axis of symmetry of the flow, the four regimes are: rotation about {\lambda}, tumbling motion between {\lambda} and -{\lambda}, combination of rotation and tumbling, and preferential alignment with a direction oblique to {\lambda}.Comment: 18 pages, 8 figure

The inverse eigenvalue problem for symmetric anti-bidiagonal matrices

The inverse eigenvalue problem for real symmetric matrices of the form 0 0 0 . 0 0 * 0 0 0 . 0 * * 0 0 0 . * * 0 . . . . . . . 0 0 * . 0 0 0 0 * * . 0 0 0 * * 0 . 0 0 0 is solved. The solution is shown to be unique. The problem is also shown to be equivalent to the inverse eigenvalue problem for a certain subclass of Jacobi matrices.Comment: 6 pages; miscalculation corrected; acknowledgments adde

Invariance of simultaneous similarity and equivalence of matrices under extension of the ground field

We give a new and elementary proof that simultaneous similarity and simultaneous equivalence of families of matrices are invariant under extension of the ground field, a result which is non-trivial for finite fields and first appeared in a paper of Klinger and Levy.Comment: 10 pages (minor corrections

The asymptotic behavior of least pseudo-Anosov dilatations

For a surface $S$ with $n$ marked points and fixed genus $g\geq2$, we prove that the logarithm of the minimal dilatation of a pseudo-Anosov homeomorphism of $S$ is on the order of $(\log n)/n$. This is in contrast with the cases of genus zero or one where the order is $1/n$.Comment: 21 pages, 12 figure

Distances on a one-dimensional lattice from noncommutative geometry

In the following paper we continue the work of Bimonte-Lizzi-Sparano on distances on a one dimensional lattice. We succeed in proving analytically the exact formulae for such distances. We find that the distance to an even point on the lattice is the geometrical average of the ``predecessor'' and ``successor'' distances to the neighbouring odd points.Comment: LaTeX file, few minor typos corrected, 9 page

Generalized inversion of the Hochschild coboundary operator and deformation quantization

Using a derivative decomposition of the Hochschild differential complex we define a generalized inverse of the Hochschild coboundary operator. It can be applied for systematic computations of star products on Poisson manifolds.Comment: 9 pages, misprints correcte

Bounds on minors of binary matrices

We prove an upper bound on sums of squares of minors of {+1, -1} matrices. The bound is sharp for Hadamard matrices, a result due to de Launey and Levin (2009), but our proof is simpler. We give several corollaries relevant to minors of Hadamard matrices, and generalise a result of Turan on determinants of random {+1,-1} matrices.Comment: 9 pages, 1 table. Typo corrected in v2. Two references and Theorem 2 added in v