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On Denjoy-Dunford and Denjoy-Pettis integrals.

  • Gámez Merino, José Luis
  • Mendoza Casas, José
The two main results of this paper are the following: (a) If X is a Banach space and f : [a, b] --> X is a function such that x*f is Denjoy integrable for all x* is an element of X*, then f is Denjoy-Dunford integrable, and (b) There exists a Dunford integrable function f : [a, b] --> c(0) which is not Pettis integrable on any subinterval in [a, b], while integral(J)f belongs to co for every subinterval J in [a, b]. These results provide answers to two open problems left by R. A. Gordon in [4]. Some other questions in connection with Denjoy-Dunford and Denjoy-Pettis integrals are studied.

Computing compromise sets in polyhedral framework

  • Blasco Contreras, Fernando
  • Cuchillo Ibáñez, Eduardo
  • Morón, Manuel A.
  • Romero López, Carlos
In this note, we describe the compromise set for a special polyhedral convex feasible set. This procedure gives the monotonicity of the compromise set. This scenario appears in some engineering and economic applications like the determination of the consumer's equilibrium.

Large solutions for a system of elliptic equations arising from fluid dynamics

  • Díaz Díaz, Jesús Ildefonso
  • Lazzo, M.
  • Schmidt, Paul G.
This paper is concerned with the elliptic system (0.1) Delta upsilon=phi, Delta phi=vertical bar del upsilon vertical bar(2) posed in a bounded domain Omega subset of R-N, N is an element of N. Specifically, we are interested in the existence and uniqueness or multiplicity of "large solutions," that is, classical solutions of (0.1) that approach infinity at the boundary of Omega. Assuming that Omega is a ball, we prove that the system (0.1) has a unique radially symmetric and nonnegative large solution with v(0) = 0 (obviously, v is determined only up to an additive constant). Moreover, if the space dimension N is sufficiently small, there exists exactly one additional radially symmetric large solution with v(0) = 0 (which, of course, fails to be nonnegative). We also study the asymptotic behavior of these solutions near the boundary of Omega and determine the exact blow-up rates; those are the same for all radial large solutions and independent of the space dimension. Our investigation is motivated by a problem in fluid dynamics. Under certain assumptions, the unidirectional flow of a viscous, heat-conducting fluid is governed by a pair of parabolic equations of the form (0.2) upsilon(t) -Delta upsilon=theta, theta t-Delta theta=vertical bar del upsilon vertical bar(2), where v and theta represent the fluid velocity and temperature, respectively. The system (0.1), with phi = -theta, is the stationary version of (0.2).

Triple canonical covers of varieties of minimal degree.

  • Gallego Rodrigo, Francisco Javier
  • Purnaprajna, Bangere P.
In this article we study pluriregular varieties X of general type with base-point-free canonical bundle whose canonical morphism has degree 3 and maps X onto a variety of minimal degree Y. We carry out our study from two different perspectives. First we study in Section 2 and Section 3 the canonical ring of X describing completely the degrees of its minimal generators. We apply this to the study of the projective normality of the images of the pluricanonical morphisms of X. Our study of the canonical ring of X also shows that, if the dimension of X is greater than or equal to 3, there does not exist a converse to a theorem of M. Green that bounds the degree of the generators of the canonical ring of X. This is in sharp contrast with the situation in dimension 2 where such converse exists, as proved by the authors in a previous work. Second, we study in Section 4, the structure of the canonical morphism of X. We use this to show among other things the nonexistence of some a priori plausible examples of triple canonical covers of varieties of minimal degree. We also characterize the targets of flat canonical covers of varieties of minimal degree. Some of the results of Section 4 are more general and apply to varieties X which are not necessarily regular, and to targets Y that are scrolls which are not of minimal degree.

On the Relationship between Interpolation of Banach Algebras and Interpolation of Bilinear Operators

  • Cobos, Fernando
  • Fernández-Cabrera, Luz M.
We show that if the general real method (. , .)(Gamma) preserves the Banach-algebra Structure, then a bilinear interpolation theorem holds for (. , .)(Gamma).
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A maximal description for the real interpolation method in the quasi-Banach case.

  • Bergh, Jöran
  • Cobos, Fernando
We give a maximal description in the sense of Aronszajn-Gagliardo for the real method in the category of quasi-Banach spaces.
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On rings of semialgebraic functions

  • Gamboa, J. M.
  • Ruiz Sancho, Jesús María
The authors study some properties of the ring of abstract semialgebraic functions over a constructible subset of the real spectrum of an excellent ring. To be more precise, let X be a constructible subset of the real spectrum of a ring A. The ring S(X) of abstract semialgebraic functions over X was introduced bz N. Schwartz [see Mem. Am. Math. Soc. 397 (1989; Zbl 0697.14015)], as a generalization of continuous functions with semialgebraic graph to the context of real spectra. Unfortunately the utility of this functions is not yet quite established. The main result of the paper states that if A is excellent, the Krull dimension of S(X) equals the dimension of X (defined as the maximum of the heights of the supports of points lying in X), which in turn, as J. M. Ruiz showed in C. R. Acad. Sci. Paris, S´er. I 302, 67-69 (1986; Zbl 0591.13017) coincides with its topological dimension. This was first shown by M. Carral and M. Coste [J. Pure Appl. Algebra 30, 227-235 (1983; Zbl 0525.14015)] for the particular case of X being a ‘true’ semialgebraic subset which is locally closed, and the result extends readily to abstract locally closed constructible sets. Then the authors use the compactness of the constructible topology of real spectra and the properties of excellent rings to reduce the general case to the locally closed one. The paper finishes by characterizing the finitely generated prime ideals of S(X), namely they are the ideals of the open constructible points of X whose closure in X is open of dimension 6= 1.
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Distributed Dynamic Host Configuration Protocol (D2HCP)

  • García Villalba, Luis Javier
  • García Matesanz, Julián
  • Sandoval Orozco, Ana Lucila
  • Márquez Díaz, José Duván
Mobile Ad Hoc Networks (MANETs) are multihop wireless networks of mobile nodes without any fixed or preexisting infrastructure. The topology of these networks can change randomly due to the unpredictable mobility of nodes and their propagation characteristics. In most networks, including MANETs, each node needs a unique identifier to communicate. This work presents a distributed protocol for dynamic node IP address assignment in MANETs. Nodes of a MANET synchronize from time to time to maintain a record of IP address assignments in the entire network and detect any IP address leaks. The proposed stateful autoconfiguration scheme uses the OLSR proactive routing protocol for synchronization and guarantees unique IP addresses under a variety of network conditions, including message losses and network partitioning. Simulation results show that the protocol incurs low latency and communication overhead for IP address assignment

Aplicaciones de los mapas geomorfológicos a la planificación urbana con un ejemplo de Tenerife

  • González de Vallejo, Luis I.
Se consideran las principales aplicaciones de los mapas geomorfológicos y se discuten sus características más importantes, en orden a proporcionar la información más relevante para diversos fines de aplicación y, en especial, la planificación urbana como ejemplo, se presenta el mapa geomorfológico de Santa Cruz. La Laguna (Tenerife)

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