Singular random matrix decompositions: distributions.

Assuming that Y has a singular matrix variate elliptically contoured distribution with respect to the Hausdorff measure, the distributions of several matrices associated to QR, modified QR, SV and Polar decompositions of matrix Y are determined, for central and non-central, non-singular and singular cases, as well as their relationship to the Wishart and Pseudo-Wishart generalized singular and non-singular distributions. We present a particular example for the Karhunen-Lòeve decomposition. Some of these results are also applied to two particular subfamilies of elliptical distributions, the singular matrix variate normal distribution and the singular matrix variate symmetric Pearson type VII distribution

Singular random matrix decompositions: Jacobians.

For a singular random matrix Y, we find the Jacobians associated with the following decompositions; QR, Polar, Singular Value (SVD), L'U, L'DM and modified QR (QDR). Similarly, we find the Jacobinas of the following decompositions: Spectral, Cholesky's, L'DL and symmetric non-negative definite square root, of the cross-product matrix S = Y'Y

Cyclic homogeneous Riemannian manifolds

In spin geometry, traceless cyclic homogeneous Riemannian manifolds equipped with a homogeneous spin structure can be viewed as the simplest manifolds after Riemannian symmetric spin spaces. In this paper, we give some characterizations and properties of cyclic and traceless cyclic homogeneous Riemannian manifolds and we obtain the classification of simply-connected cyclic homogeneous Riemannian manifolds of dimension less than or equal to four. We also present a wide list of examples of non-compact irreducible Riemannian $3$-symmetric spaces admitting cyclic metrics and give the expression of these metrics

Homogeneous spin Riemannian manifolds with the simplest Dirac operator

We show the existence of nonsymmetric homogeneous spin Riemannian manifolds whose Dirac operator is like that on a Riemannian symmetric spin space. Such manifolds are exactly the homogeneous spin Riemannian manifolds $(M,g)$ which are traceless cyclic with respect to some quotient expression $M=G/K$ and reductive decomposition $\mathfrak{g} = \mathfrak{k} \oplus \mathfrak{m}$. Using transversally symmetric fibrations of noncompact type, we give a list of them

Strategic Wage Setting and Coordination Frictions with Multiple Applications

We examine wage competition in a model where identical workers choose the number of jobs to apply for and identical firms simultaneously post a wage. The Nash equilibrium of this game exhibits the following properties: (i) an equilibrium where workers apply for just one job exhibits unemployment and absence of wage dispersion; (ii) an equilibrium where workers apply for two or for more (but not for all) jobs always exhibits wage dispersion and, typically, unemployment; (iii) the equilibrium wage distribution with a higher vacancy-to-unemployment ratio first-order stochastically dominates the wage distribution with a lower level of labor market tightness; (iv) the average wage is non-monotonic in the number of applications; (v) the equilibrium number of applications is non-monotonic in the vacancy-to-unemployment ratio; (vi) a minimum wage increase can be welfare improving because it compresses the wage distribution and reduces the congestion effects caused by the socially excessive number of applications; and (vii) the only way to obtain efficiency is to impose a mandatory wage that eliminates wage dispersion altogether.wage setting, unemployment, minimum wage, Nash equilibrium

Motivos por los que los estudiantes universitarios no practican deporte

Este estudio examinó las causas por las que los jóvenes universitarios no practican deporte. Los participantes fueron estudiantes de la Universidad de Oviedo (N = 1.916). Los resultados mostraron que aquellos que manifiestan motivos de carácter extrínseco para explicar su desvinculación activa del deporte, son estudiantes que, a pesar de todo, siguen estando interesados y predispuestos a practicar (no-practica de carácter reluctante, o también de una no-práctica contra el corazón, con mayores posibilidades de ser captados o reintegrados al deporte). Mientras que los que aducen motivos de carácter intrínseco son universitarios que han dejado de estar interesados por el deporte, les ha dejado de gustar, les resulta aburrido, etc. (no-practica por descontento, con menores posibilidades de ser captados o reincorporados). Observamos que estas dos direcciones se relacionan con el género, la percepción de las repercusiones de la práctica deporte en los estudios y la importancia que asignan al deporte en la vida universitaria. Finalmente se discuten sus implicaciones.This papers presents the reasons why university students say that they don’t practice sports. The information comes from a survey answered by students from the Universidad de Oviedo. The results show that those students who talk about external reasons to quit from sports (reluctant non-practice o against the sentiments non-practice) are students that keep an interest in sports and, eventually, could come back to sports activities. They are people with some possibilities to be active again in sports practice. Whereas those students who sustain internal reasons to quit from sports practice are people who has not interest at all in sports. They don’t like it anymore or they find it boring (non-practice by dissatisfaction). They are people with less possibilities to come again to sports practice. We can see that in both groups there are meaningful variables such as sex, students perception of the impact of sports in academic results and the importance that they give to sports in university life. The paper concludes with the discussion of the implications that the analysed classifications can have in the increase of university sports practice

SINGULAR RANDOM MATRIX DECOMPOSITIONS: DISTRIBUTIONS.

Assuming that Y has a singular matrix variate elliptically contoured distribution with respect to the Hausdorff measure, the distributions of several matrices associated to QR, modified QR, SV and Polar decompositions of matrix Y are determined, for central and non-central, non-singular and singular cases, as well as their relationship to the Wishart and Pseudo-Wishart generalized singular and non-singular distributions. We present a particular example for the Karhunen-Lòeve decomposition. Some of these results are also applied to two particular subfamilies of elliptical distributions, the singular matrix variate normal distribution and the singular matrix variate symmetric Pearson type VII distribution.