8,497 research outputs found
Relations for zeros of special polynomials associated to the Painleve equations
A method for finding relations for the roots of polynomials is presented. Our
approach allows us to get a number of relations for the zeros of the classical
polynomials and for the roots of special polynomials associated with rational
solutions of the Painleve equations. We apply the method to obtain the
relations for the zeros of several polynomials. They are: the Laguerre
polynomials, the Yablonskii - Vorob'ev polynomials, the Umemura polynomials,
the Ohyama polynomials, the generalized Okamoto polynomials, and the
generalized Hermite polynomials. All the relations found can be considered as
analogues of generalized Stieltjes relations.Comment: 17 pages, 5 figure
The investigation of flow instabilities on a rotating disk with curvature in the radial direction
The major objective is to explore any visible differences of the flow field with wall curvature of the test body, including possible interaction between Taylor-Gortler instabilities present along concave walls and the inflexional instabilities investigated here. An experimental study was conducted with emphasis placed on making visual observations and recording photographically the flow instabilities present under three different rotating bodies: a flat disk, a concave paraboloid, and a convex paraboloid. The data collected for the three test bodies lead to the conclusion that the wall curvature of the concave and convex paraboloids did not alter the observed flow field significantly from that observed on the flat disk
M-Branes on k-center Instantons
We present analytic solutions for membrane metric function based on
transverse -center instanton geometries. The membrane metric functions
depend on more than two transverse coordinates and the solutions provide
realizations of fully localized type IIA D2/D6 and NS5/D6 brane intersections.
All solutions have partial preserved supersymmetries.Comment: 22 pages, 5 figure
Galaxy correlations and the BAO in a void universe: structure formation as a test of the Copernican Principle
A suggested solution to the dark energy problem is the void model, where
accelerated expansion is replaced by Hubble-scale inhomogeneity. In these
models, density perturbations grow on a radially inhomogeneous background. This
large scale inhomogeneity distorts the spherical Baryon Acoustic Oscillation
feature into an ellipsoid which implies that the bump in the galaxy correlation
function occurs at different scales in the radial and transverse correlation
functions. We compute these for the first time, under the approximation that
curvature gradients do not couple the scalar modes to vector and tensor modes.
The radial and transverse correlation functions are very different from those
of the concordance model, even when the models have the same average BAO scale.
This implies that if void models are fine-tuned to satisfy average BAO data,
there is enough extra information in the correlation functions to distinguish a
void model from the concordance model. We expect these new features to remain
when the full perturbation equations are solved, which means that the radial
and transverse galaxy correlation functions can be used as a powerful test of
the Copernican Principle.Comment: 12 pages, 8 figures, matches published versio
- …