548 research outputs found
Geometry and Singularities of the Prony mapping
Prony mapping provides the global solution of the Prony system of equations
This system
appears in numerous theoretical and applied problems arising in Signal
Reconstruction. The simplest example is the problem of reconstruction of linear
combination of -functions of the form
, with the unknown parameters $a_{i},\
x_{i},\ i=1,...,n,m_{k}=\int x^{k}g(x)dx.x_{i}.$ The investigation of this type of
singularities has been started in \cite{yom2009Singularities} where the role of
finite differences was demonstrated.
In the present paper we study this and other types of singularities of the
Prony mapping, and describe its global geometry. We show, in particular, close
connections of the Prony mapping with the "Vieta mapping" expressing the
coefficients of a polynomial through its roots, and with hyperbolic polynomials
and "Vandermonde mapping" studied by V. Arnold.Comment: arXiv admin note: text overlap with arXiv:1301.118
One step multiderivative methods for first order ordinary differential equations
A family of one-step multiderivative methods based on Padé approximants to the exponential function is developed.
The methods are extrapolated and analysed for use in PECE mode.
Error constants and stability intervals are calculated and the combinations compared with well known linear multi-step combinations and combinations using high accuracy Newton-Cotes quadrature formulas as correctors.
w926020
Finite element formulation for modelling nonlinear viscoelastic elastomers
Nonlinear viscoelastic response of reinforced elastomers is modeled using a three-dimensional mixed
finite element method with a nonlocal pressure field. A general second-order unconditionally stable
exponential integrator based on a diagonal Padé approximation is developed and the Bergström–Boyce
nonlinear viscoelastic law is employed as a prototype model. An implicit finite element scheme with consistent
linearization is used and the novel integrator is successfully implemented. Finally, several viscoelastic
examples, including a study of the unit cell for a solid propellant, are solved to demonstrate the
computational algorithm and relevant underlying physics
Systems of Markov type functions: normality and convergence of Hermite-Padé approximants
This thesis deals with Hermite-Padé approximation of analytic and merophorphic
functions. As such it is embeded in the theory of vector rational approximation of
analytic functions which in turn is intimately connectd with the theory of multiple
orthogonal polynomials. All the basic concepts and results used in this thesis involving
complex analysis and measure theory may found in classical textbooks...........Programa Oficial de Doctorado en IngenierÃa MatemáticaPresidente: Francisco José Marcellán Español; Vocal: Alexander Ivanovich Aptekarev; Secretario: Andrei MartÃnez Finkelshtei
Cosmology with gamma-ray bursts: II Cosmography challenges and cosmological scenarios for the accelerated Universe
Context. Explaining the accelerated expansion of the Universe is one of the
fundamental challenges in physics today. Cosmography provides information about
the evolution of the universe derived from measured distances, assuming only
that the space time ge- ometry is described by the
Friedman-Lemaitre-Robertson-Walker metric, and adopting an approach that
effectively uses only Taylor expansions of basic observables. Aims. We perform
a high-redshift analysis to constrain the cosmographic expansion up to the
fifth order. It is based on the Union2 type Ia supernovae data set, the
gamma-ray burst Hubble diagram, a data set of 28 independent measurements of
the Hubble param- eter, baryon acoustic oscillations measurements from galaxy
clustering and the Lyman-{\alpha} forest in the SDSS-III Baryon Oscillation
Spectroscopic Survey (BOSS), and some Gaussian priors on h and {\Omega}M .
Methods. We performed a statistical analysis and explored the probability
distributions of the cosmographic parameters. By building up their regions of
confidence, we maximized our likelihood function using the Markov chain Monte
Carlo method. Results. Our high-redshift analysis confirms that the expansion
of the Universe currently accelerates; the estimation of the jerk parameter
indicates a possible deviation from the standard {\Lambda}CDM cosmological
model. Moreover, we investigate implications of our results for the
reconstruction of the dark energy equation of state (EOS) by comparing the
standard technique of cosmography with an alternative approach based on
generalized Pad\'e approximations of the same observables. Because these
expansions converge better, is possible to improve the constraints on the
cosmographic parameters and also on the dark matter EOS. Conclusions. The
estimation of the jerk and the DE parameters indicates at 1{\sigma} a possible
deviation from the {\Lambda}CDM cosmological model.Comment: 10 pages, 7 figures, accepted for publication in A &
- …