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Castrillón López, Marco ; Díaz-Cano Ocaña, Antonio ; Etayo Gordejuela, J. Javier ; Folgueira, Marta ; Infante del Río, Juan Antonio ; Pozo Coronado, Luis Miguel ; Rey Cabezas, Jose María | No publicado | 2013Material elaborado por profesores de la UCM para la asignatura de este nombre del grado en Ingeniería Matemáticas, el grado en Matemáticas y el grado en Matemáticas y Estadística. Contenidos: - Números enteros. Dígitos de control y criptografía[...]![]()
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The author describes such things as the Poincaré conjecture, Waldhausen's generalization of it, and the dimension 4 Poincaré conjecture. Then he turns to the finite-infinite and discrete-continuous dichotomies. For the former he gives examples i[...]![]()
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Leiva Cuadrado, Javier | 2016-02-24Este trabajo contiene los principales resultados sobre Números Normales de Borel, como son los teoremas sobre su medida en el intervalo unitario y algunas caracterizaciones y definiciones alternativas. Se exponen también los ejemplos más conocid[...]![]()
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In this paper we get an effective algorithm to compute all odd orders and ramification indices of homeomorphisms![]()
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We determine all complete intersection surface germs whose Pythagoras number is 2, and find that they are all embedded in R-3 and have the property that every positive semidefinite analytic function germ is a sum of squares of analytic function [...]![]()
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We study in this paper a modification of continued fractions defined by the author, such that its lexicographic order coincides with the linear order of real numbers. This fact has beautiful consequences in Topology. Indeed, it gives the possibi[...]![]()
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Using some elementary theory of convex sets we prove a necessary and a sufficient condition for f ? R[x„ . . ., x„](R being the real numbers) to be a finite sum of 2m-th powers of rational functions in x1, . . ., x n over R[i.e.f ? ? R(x)2 m]![]()
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Castrillón López, Marco ; Gadea, P.M. ; Muñoz Masqué, Jaime | the American Romanian Academy of Arts and Sciences (USA) | 1999The paper is a survey of several results by the authors, the main one of them being the following characterization of homogeneous algebraic distributions: Let us consider a vertical distribution D on the vector bundle p:E?M locally spanned by ve[...]![]()
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This is a nice expository paper at an elementary level which describes the type of mathematics used inWiles’ proof of Fermat’s Last Theorem. The first section of the paper is a discussion about tessellations of the plane with several nice exampl[...]![]()
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It is known [J. F. Ritt, Trans. Am. Math. Soc. 23, 51-66 (1922; JFM 48.0079.01), H. T. Engstrom, Am. J. Math. 63, 249–255 (1941; Zbl 0025.10403), H.Levi, ibid. 64, 389–400 (1942; Zbl 0063.03512), F. Dorey and G. Whaples, J. Algebra 28, 88-101 (1[...]![]()
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The author describes such things as the Poincaré conjecture, Waldhausen's generalization of it, and the dimension 4 Poincaré conjecture. Then he turns to the finite-infinite and discrete-continuous dichotomies. For the former he gives examples i[...]![]()
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We define a modification of continued fractions such that the lexicographic order coincides with the linear order of real numbers. Using this representation, we obtain a new proof of the theorem which shows that the Sorgenfrey line is not totall[...]![]()
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Among the invariant factors g of a positive semidefinite analytic function f on R-3, those g whose zero set Y is a curve are called special. We show that if each special g is a sum of squares of global meromorphic functions on a neighbourhood of[...]![]()
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We show that the Pythagoras number of a real analytic curve is the supremum of the Pythagoras numbers of its singularities, or that supremum plus 1. This includes cases when the Pythagoras number is infinite.