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The proportional coalitional Shapley value

REA Auditado

We propose a modification of the Shapley value for monotonic games with a coalition structure. The resulting coalitional value is a twofold extension of the Shapley value in the following sense: (1) the amount obtained by any union coincides with the Shapley value of the union in the quotient game; and (2) the players of the union share this amount proportionally to their Shapley value in the original game (i.e., without unions).

Tema: general: 

• Ciencias Sociales›Educación

Power and potential maps induced by any semivalue: some algebraic properties and computation by multilinear extensions

REA Auditado

The notions of total power and potential, both defined for any semivalue, give rise to two endomorphisms of the vector space of cooperative games on any given player set where the semivalue is defined. Several properties of these linear mappings are stated and the role of unanimity games as eigenvectors is described. We also relate in both cases the multilinear extension of the image game to the multilinear extension of the original game.

Tema: general: 

• Ciencias Sociales›Educación

On the 16th Hilbert problem for limit cycles on nonsingular algebraic curves

REA Auditado

We give an upper bound for the maximum number N of algebraic limit cycles that a planar polynomial vector field of degree n can exhibit if the vector field has exactly k nonsingular irreducible invariant algebraic curves. Additionally we provide sufficient conditions in order that all the algebraic limit cycles are hyperbolic. We also provide lower bounds for N.

Tema: general: 

• Ciencias Sociales›Educación

On the decay of solutions for porous-elastic systems with history

REA Auditado

In this paper we study the asymptotic behavior to an one-dimensional porous-elasticity problem with history. We show the lack of exponential stability when the porous dissipation or the elastic dissipation is absent. And we show the lack of analyticity and exponential stability when the porous viscosity and the elastic dissipation are present.

Tema: general: 

• Ciencias Sociales›Educación

On matroids determined by their Tutte polynomials

REA Auditado

A matroid is T-unique if it is determined up to isomorphism by its Tutte polynomial. Known T-unique matroids include projective and affine geometries of rank at least four, wheels, whirls, free and binary spikes, and certain generalizations of these matroids. In this paper we survey this work and give three new results. Namely, we prove the T-uniqueness of M(Km,n) and of the truncations of M(Kn), and we show the existence of exponentially large families of T-unique matroids.

Tema: general: 

• Ciencias Sociales›Educación

On the maximum number of cycles in outerplanar and series-parallel graph

REA Auditado

Let c(n) be the maximum number of cycles in an outerplanar graph with n vertices. We show that lim $c(n)^{1/n}$ exists and equals β = 1.502837 . . ., where β is a constant related to the recurrence $x_n+1$=1+$x^2_n$, $x_0$=1. The same result holds for the larger class of series–parallel graphs.

Tema: general: 

• Ciencias Sociales›Educación

Symmetries in Steinhaus triangles and in generalized Pascal triangles

REA Auditado

We give explicit formulae for obtaining the binary sequences which produce Steinhaus
triangles and generalized Pascal triangles with rotational and dihedral symmetries.

Tema: general: 

• Ciencias Sociales›Educación

Internalization and kinetics of nuclear migration of protein-only, arginine-rich nanoparticles

REA Auditado

Understanding the intracellular trafficking of nanoparticles internalized by mammalian cells is a critical issue in nanomedicine, intimately linked to therapeutic applications but also to toxicity concerns. While the uptake mechanisms of carbon nanotubes and polymeric particles have been investigated fairly extensively, there are few studies on the migration and fate of protein-only nanoparticles other than
natural viruses.

Tema: general: 

• Ciencias Sociales›Educación

Every large point set contains many collinear points or an empty pentagon

REA Auditado

We prove the following generalised empty pentagon theorem for every integer ℓ ≥ 2, every sufficiently large set of points in the plane contains ℓ collinear points or an empty pentagon. As an application, we settle the next open case of the “big line or big clique” conjecture of Kára, Pór, and Wood [Discrete Comput. Geom. 34(3):497–506, 2005].

Tema: general: 

• Ciencias Sociales›Educación

A review of higher order ionospheric refraction effects on dual frequency GPS

REA Auditado

Abstract Higher order ionospheric effects are increasingly relevant as precision
requirements on GPS data and products increase. The refractive index of the ionosphere is affected by its electron content and the magnetic field of the Earth, so the carrier phase of the GPS L1 and L2 signals is advanced and the modulated code delayed. Due to system design the polarisation is unaffected. Most of the effect is removed by expanding the refractive index as a series and eliminating the first term with a linear combination of the two signals. However, the higher order terms remain.

Tema: general: 

• Ciencias Sociales›Educación