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Some measures for asymmetry of distributions

REA Auditado

We propose several measures, functional and scalar, for asymmetry of distributions by comparing the behavior of probability densities to the right and left of the mode(s) and show how to generate classes of equivalent distributions from a given distribution, allowing for varying asymmetry but retaining some information theoretic properties of the original distribution, such as the entropy.

Tema: general: 

• Ciencias›Matemáticas

On Émery's Inequality and a Variation-of-Constants Formula

REA Auditado

A generalization of Émery's inequality for stochastic integrals is shown for convolution integrals of the form
$\left( \int_0^t g(t-s) Y(s-) dZ(s)\right)_{t \geq 0}$, where Z is a semimartingale, Y an adapted càdlàg process, and g a deterministic function. An even more general inequality for processes with two parameters is proved. The inequality is used to prove existence and uniqueness of solutions of equations of variation-of-constants type.

Tema: general: 

• Ciencias›Matemáticas

An Algorithm for the Complete Solution of Quadratic Eigenvalue Problems

REA Auditado

We develop a new algorithm for the computation of all the eigenvalues and optionally the right and left eigenvectors of dense quadratic matrix polynomials.
It incorporates scaling of
the problem parameters prior to the computation of eigenvalues, a choice of linearization with favorable
conditioning and backward stability properties,
and a preprocessing step that
reveals and deflates the zero and infinite eigenvalues contributed by singular
leading and trailing matrix coefficients.
The algorithm is backward stable for quadratics that are not too heavily damped.
Numerical experiments sh

Tema: general: 

• Ciencias›Matemáticas

An Algorithm for the Complete Solution of Quadratic Eigenvalue Problems

REA Auditado

We develop a new algorithm for the computation of all the eigenvalues and optionally the right and left eigenvectors of dense quadratic matrix polynomials.
It incorporates scaling of
the problem parameters prior to the computation of eigenvalues, a choice of linearization with favorable
conditioning and backward stability properties,
and a preprocessing step that
reveals and deflates the zero and infinite eigenvalues contributed by singular
leading and trailing matrix coefficients.
The algorithm is backward stable for quadratics that are not too heavily damped.
Numerical experiments sh

Tema: general: 

• Ciencias›Matemáticas

An Algorithm for the Complete Solution of Quadratic Eigenvalue Problems

REA Auditado

We develop a new algorithm for the computation of all the eigenvalues and optionally the right and left eigenvectors of dense quadratic matrix polynomials.
It incorporates scaling of
the problem parameters prior to the computation of eigenvalues, a choice of linearization with favorable
conditioning and backward stability properties,
and a preprocessing step that
reveals and deflates the zero and infinite eigenvalues contributed by singular
leading and trailing matrix coefficients.
The algorithm is backward stable for quadratics that are not too heavily damped.
Numerical experiments sh

Tema: general: 

• Ciencias›Matemáticas

Generating H*(BO(3), F2) as a module over the Steenrod algebra

REA Auditado

This paper continues the investigation of the hit problem, started in [5], for the algebra of symmetric polynomials B(n) viewed as a left ${\cal A}$-module graded by degree, where ${\cal A}$ denotes the Steenrod algebra over the field of two elements ${\bb F}_2$. We recall that a homogeneous element f of grading d in a graded left ${\cal A}$-module M is hit if there is a hit equation in the form of a finite sum $f=\sum_{k>0}Sq^{k}(h_k)$, where the homogeneous elements hk in M have grading less than d and the Sqk are the Steenrod squares, which generate ${\cal A}$.

Tema: general: 

• Ciencias›Matemáticas