Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
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This is a survey about Thurston’s geometrization conjecture of three manifolds and Perelman’s proof with the Ricci flow. In particular we review the essential contribution of Hamilton as well as some results in topology relevants for the proof.
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This is a survey of some consequences of the fact that the fundamental group of the orbifold with singular set the Borromean link and isotropy cyclic of order 4 is a universal kleinian group.
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This paper surveys some recent results concerning inverse limits of tent maps. The survey concentrates on Ingram’s Conjecture. Some motivation is given for the study of such inverse limits.
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This survey is an introduction to some of the methods, techniques and concepts from algebraic topology and related areas (homotopy theory, shape theory) which can be fruitfully applied to study problems concerning continuous dynamical systems. To this end two instances which exemplify the interaction between topology and dynamics are considered, namely, Conley’s index theory and the study of some...
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Gromov [11] and Dranishnikov [2] introduced asymptotic and coarse dimensions of proper metric spaces via quite different ways. We define coarse and asymptotic dimension of all metric spaces in a unified manner and we investigate relationships between them generalizing results of Dranishnikov [2] and Dranishnikov-Keesling-Uspienskij [5].
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We survey recent papers on the problem of backward dynamics in economics, providing along the way a glimpse at the economics perspective, a discussion of the economic models and mathematical tools involved, and a list of applicable literature in both mathematics and economics.
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Some problems in differential equations evolve towards Topology from an analytical origin. Two such problems will be discussed: the existence of solutions asymptotic to the equilibrium and the stability of closed orbits of Hamiltonian systems. The theory of retracts and the fixed point index have become useful tools in the study of these questions.
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We survey results related to the problem of the existence of equilibria in some classes of infinitely repeated two-person games of incomplete information on one side, first considered by Aumann, Maschler and Stearns. We generalize this setting to a broader one of principal-agent problems. We also discuss topological results needed, presenting them dually (using cohomology in place of homology) and...
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We first present a class of LF-spaces, extending the class of LF-spaces of Moscatelli type, for which regularity implies completeness. Then we utilize the obtained results to describe the completions of LB-spaces of Moscatelli type. In particular, we prove that the completions of LB-spaces of that type are again LB-spaces.
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LetR denote the smallest class of compact spaces containing all metric compacta and closed under limits of continuous inverse sequences of retractions. ClassR is striclty larger than the class of Valdivia compact spaces. We show that every compact connected Abelian group which is a topological retract of a space from classR is necessarily isomorphic to a product of metric compacta. This completes...
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The aim of this paper is to show that the simplest techniques of linear algebra allow us to make explicit the defining equations of the maximal real cyclotomic extensions ℚ(ζ + ζ−1 of ℚ(ζ), where ζ stands for a primitivep ν-th rooot of unity withp a rational prime and ν any positive integer.
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We obtain a relation between π, e, γ, ζ(n) and the triangular numbers based on a recursion formula forn!.
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Incidence spatial geometry is based on three-sorted structures consisting of points, lines and planes together with three intersort binary relations between points and lines, lines and planes and points and planes. We introduce an equivalent one-sorted geometrical structure, called incidence spatial frame, which is suitable for modal considerations. We are going to prove completeness by SD-Theorem...
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An application of the results of this paper proves that there is not always an economic benefit when destroying the environment for planting an alternative industrial project. Our criterion, to act, to delay or to deny the industrial investment over the environment, is given in terms of the free boundary associated to a deterministic degenerate obstacle problem (on an unbounded domain) associated...
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Carta comunicada por / Letter communicated by Vicente Montesinos Santalucía.
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In this paper, we study variational inclusions of the following form 0 ∈f(x) + g(x) + F(x) (*) wheref is differentiable in a neighborhood of a solutionx* of (*) andg is differentiable atx* and F is a set-valued mapping with closed graph acting in Banach spaces. The method introduced to solve (*) is superlinear and quadratic when ∇f is Lipschitz continuous.
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According to the great mathematician Henri Lebesgue, making direct comparisons of objects with regard to a property is a fundamental mathematical process for deriving measurements. Measuring objects by using a known scale first then comparing the measurements works well for properties for which scales of measurement exist. The theme of this paper is that direct comparisons are necessary to establish...
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Let Ω be a nonempty open set of thek-dimensional euclidean space $$ \mathbb{R}^k $$ . In this paper, we give a structure theorem on the ultradistributions of Beurling type in Ω. Also, other structure results on certain ultradistributions are obtained, in terms of complex Borel measures in Ω.
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Given two semi-regular matrices $$ \mathfrak{M} $$ and $$ \mathfrak{M}' $$ and two open subsets Ω and Ω′ [resp. two compact subsetsK andK′] of $$ \mathbb{R}^r $$ and $$ \mathbb{R}^s $$ respectively, we introduce the spaces $$ \mathcal{E}_{(\mathfrak{M} \times \mathfrak{M}')} $$ (Ω × Ω′) and $$ \mathcal{D}_{(\mathfrak{M} \times \mathfrak{M}')} $$ (Ω × Ω′) [resp. $$ \mathcal{D}_{(\mathfrak{M}...
