Showing papers in "Revista Matematica Complutense in 1996"

Estabilidad orbital de satélites estacionarios

Abstract: Se establecen las condiciones, para un satelite alrededor de un planeta en rotacion alrededor de su eje de inercia de mayor mo inento, bajo las que puede aparecer, en un sistema de referencia fijo en el planeta, dos posiciones de equilibrio con exponentes carac teristicos imaginarios puros. En este caso, despu& de la apropiada normalizacion mediante una transformacion de Lic, efectuada de forma mecanica con un procesador algebraico simbolico, se aplica el teorema de Arnold sobre formas cuadraticas no definidas. Se concluye que los equilibrios son estables en el sentido de Liapunov. Las condiciones de estabilidad se verifican en el caso de la Tierra.

On the Intersection of Finitely Generated Subgroups of Free Groups

Abstract: Howson [41praved that the intersection of twa finitely generated subgroups H and 1< of ranks m and it respectively is finitely generated. HepravedthattherankNofffflKisatmast2litit—m—it+l. H. Neumann [8,9] gaye a better bound of 2mn — 2it — 2m + 3. Burns [2]further impraved the general upper haund to N < 2mn — 3m — 2n + 4 (for m =it). Imrich [6]gaye shorter proof of Neumann>s result and also Nickolas [10] gaye simple praof for Burn’s result. Servatius [12] gaye graphical praof far Burn’s result. Burns [1]showed that the stranger baund N < mit — it — m + 2 holds if 11 or 1< is of finite index in E. In this paper it is shown tbat stronger bound N < mit — it — m + 2 always hold. In section 1 we gaye basic concepts about free groups, graphs and cayley graphs. 1991 Mathematics Subject Classification: 2aEal Servicio publicaciones Univ. Complutense. Madrid, 1996. 1 would like to thank the referee br lis helpful suggestions. http://dx.doi.org/10.5209/rev_REMA.1996.v9.n1.17603

Multiplicative characterization of Hilbert spaces and other interesting classes of Banach spaces

Abstract: For a Banach space X, we show how the existence ob a norinone element u in X and a norm-one continuous bilinear mapping f : X xX —.~ X satisfying f(xu) = f(u,x) = x for aH x luX, togetber with sorne more intrinsic conditions, can be utiliza! to characterize A? as a member of some relevant subclass of the class ob Banach spaces.

Stokeslet and the Operator Extensions Theory

Abstract: Operator version of the stokeslet method in tbe theory of creeping flow is suggested. TIle approach is analogous to the zero-range po- tential one in quantum mechanics and ja basal on the thecry of self-adjoint operator extensions in the apace L 2 and in the Pontryagin's apace with an in- definite metric. The problem of Stokes llow in two channeis connected through a amail openinga ja considered in the framework of thia approach. The case of a periodic system of amail openinga jastudied too. The picture of streamlines for such flow ja obtained.

Localization of bounded sets in tensor products.

Abstract: The problern of topologies of Grothendieck is considered for complete tensor products of Frechet spaces endowed with the topology defined by an arbitrary tensor norm. Sorne consequences on the stability of certain locally convex properties ja spaces of operators are also given.

Complemented subspaces of sums and products of copies of L 1[0,1]

Abstract: We prove that the direct sum and the product of countably many copies of L1¡O, 1] are prirnary locally convex spacn. We also give sorne related results. For a whule it was an open problem whether a complemented subspace of a countable product of Banach spaces can be written as a product of Banach spaces. This question has been solved in negative by M. 1. Ostrovskii [12], but it is still open for XN where X is a ciassical Banach space. The only countable products of classical Banaeh spaces whose complemented subspaces have been fully described are: ¿o; (iP)N, 1 =p =oc, aud (co)N ([5], [91) and for these the answer is positive. Moreover, in [11it was shown that, for 1

Biorthogonal systems in certain Banach spaces

Abstract: Let A? be an Asplund space. We show iii this paper that X admits a total biorthogonal system, (xi, u?)?ci such that the closed linear hulI of {x~ : j E I} is a weakly compacti>’ generated Banach space. We also prove that it’ Y in a weakly compactly convexdetermined nonned subspace of a Banach space A?with dens Y > devis ,K then there is a total biortbogonal system (x?,~?»cI for X such that the linear huIl {z~ :1 E l} is a dense subspace of Y. Titrougitout titis paper ali vector spaces are suppose to be real ones. Tite set of positive integers is denote it>’IV and tite set of real numbers by IR. When no confusion occurs, i~ - will reprcaent tite norm in a norma! space A?; unless stated, B(A?) is tite closed unit bali of A?. We write A? bor tite conjugate space of A?; A? for tite conjugate of A?, and we identify A?, in tite usual wa>’, witit a subspace of A?t If A is a subsel of A?, A0 stands for sucit a subset equipa! witit tite induced weak-star topolog>’ of A?; A1 is tite subspace of A? ortitogonal tu A, and A0 is tite polar set of A in A?. ~>‘ .c -,-> we represent tite usual dualit>’ between A? and A?, Le., if x E A?aud u E A?’, = u(x). For a subset M of A?, M’ will be tite subspace of X ortitogonal to M, aud M0 tite polar of M in A?; afro, lin M wil> denote tite linear span ob M. Tite

A "Universal" Class of 4-Coloured Graphs

Abstract: A family of 4—cohoured grapbs depending on three integers b, 1,1 and on a transitive pair of permutations a, y E Eh is constructed. Each asisociated topological space turns out to he a b-fohd branched covering of elther a 6or a handcuff-graph, with embedding depending on 1 and 1, or a two-hridge knot or hink of type (1,1). Moreover, the monodromy map is phetehy defined by a and r. La particuhar, when 1 = 2 aud t = 1, the space is homcomorphic to the (possibly singuhar) manifoid N(o, r), which is the branched covering of the Montesinos universah graph, associated to the pair a, r. This allows us to ohtain a “universal” chass of 4—coloured graphs representing ah orientable 3-djmensionah singular manifolds. Further, the nec~sary and sufllcient condition for the graph to represent a manifohd is ohtaiaed and a topohogical interpretation of a similar construction of A. Cavicchiohi is given. 1991 M,thematics Subject Classification Primary 57M25, 57M12; Secondary 57M15. Servicio publicaciones Univ. Complutense. Madrid, 1996. Work performed under the auspices of the GNSAGA-CNR, .vithin tite project “Ceon.etrfa reale e complessa” of the MURST and under the supervision of Prof. Massimo Ferri. http://dx.doi.org/10.5209/rev_REMA.1996.v9.n1.17620

Chaos made visual

Abstract: In tbis paper we sbow how the main properties of chaos can be fuil>' visualized at the light ob a ver>' easy to handie object, tbe tent bunction. Although ver>' concrete, this case is representative of a ver>' large nurnber of examples, with more or leas the same properties. Discrete chaotic dynamical systems .11 (M, p) is a metric space and E : M —. M is a continuous function, F is calla! chaotic on M, according to R.Devaney, witen tite following titree conditions are satisfled: 1) Tite function F is topologicalí>' transitive, i.e., for eacit two open sets U, V of M, there is some iteration Fkof F such titat Fle(U) fl y ~ ~. (One can express this fact by saying titat tite iterations of E mix tite open sets of M). 2) Titere is sensitive dependence with respect to small perturbations, i.e. titere is sorne a > O sucit that for each open set U of M, no matter itow small, titere are two points x,y in U and titere exists sorne k sucit that p(Fk(x), Fk(y)) > a.(One calls titis propert>' tite butterfly effect).

Approximation de la solution de viscosité d'un problème d'Hamilton-Jacobi.

Abstract: We consider the Cauchy problem for a parabolic equation tu oc (v)Av+ i Vv i2 +E(v), where oc (y) is a “small enough” non negative continucus function; we prove uniform estimate of the modulus of continuity of a classical solution y, existence of viscosity solutions y, and convergence, as oc — O in appropriate sense, of these solutions tia the viscosity solution of tIme Caucby problem for =1 Vv i2 +E(v).

Some geometric properties concerning fixed point theory

Abstract: The Fixed Point Theory bar nonexpansive mappings is strongly based upan the geometry ob tite ambient Banach space. Fn Section 1 we state tite role which is played by the muitidirnensional convexity and smoothness in this tbeory. Iri Section 2 we study tite computation of the normal structure coefflcient in finite dimensional tp—SpaceS and ite connection with severa! clasaje geometrie problems.

Unknotting number and knot diagram

Abstract: TImis note is acontinuation of [Nl], Wbere we have discusged tbe unknotting number of knots With rspect tia knot diagrams. Wc wilI show that for every minimum-crossing knot-diagram among ah unknotting-number-one two-bridge knot there exist crossings whose exchangeyields tIme trivial knot, ib tbe tbird Tait conjecture is true.

A note on the extensions of Eratosthenes' sieve.

Abstract: Given A~ E IN, let Sk denote the set of natural numbers relatively prime to the first k primes. The k-extension of the Sieve of Eratos- thenes, recently found, provides a set of rules that govern the positions in 8k of the multiples of tbe elements of Sk. In this paper we provide an alternative approach to the k-extension which yields an easier implementation in parallel processing. In addition it is shown that, with an appropriate layout of the set Sk, the rules governing the sieving process can he made similar to those in the original sieve.

Calderón weights and the real interpolation method

Abstract: Interpelation theory is a pewerful teel te study operatera in functien spaces. In particular it providea methods te ebtain new estimates frem initial estirnates. The theory originated with the coixvexity theorem of Riesz-Thorin (1926, 1939), which atates that ifan operator T is beunded en the cemplex spaces LP* .~÷ ~ i — 0, 1, then it is alse beunded fin all the range of intermediate values of p. Therefore, we may cenclude that T is beunded frem L~ —* L’~, whenever there exista O 6 (0, 1) such that 1 1—6 6 1 1—O O P PO Pi q qo q~

Bases of the homology spaces of the Hilbert scheme of points in an algebraic surface

Abstract: For a complex surface S , proper, smooth and connected, the authors find two bases of the spaces of rational homology H n (Hilb d S) Q of the Hilbert scheme of subschemes of S of length d . The idea of the proof of the main theorem is to prove that the elements of the two candidates have as cardinalities the known Betti numbers of Hilb d S and to show that both intersect in a triangular matrix of nonzero diagonal entries. Papers on the subject which have a close connection with the present one are by B. Fantechi ["Base of the homology groups of the Hilbert scheme of points on a surface'', Preprint; per bibl.] and L. Gottsche [Math. Ann. 286 (1990), no. 1-3, 193–207 ].

A unified approach for commutators theorems in interpolation theory, a survey

Abstract: We review the main facta that are behind a unified construction for the commutator theorem of the main interpolation metheds.

Le Genre de Heegaard de 3-variétés orientables

Abstract: Wecorisiderirreducible, closed, oriented, connected 3-manifolde With a nontrivial fundamental group, and link Heegaard genus to fundamental domajus. We ahail show that the Heegaard genus is the least positive integer h(M) for which tIme manifoid has a fundamental domain with 2 . h(M) faces.

Orthonormal bases for spaces of continuous and continuosly differentiable functions defined on a subset of Z(p)

Abstract: Let K be a non-archimedean valued fleld which contains 4, and suppose that K is complete for the valuation ¡ . ¡, which extends the p-adic valuation. V~ is the closure of the set {aq¶n 0,1,2, . . . } where a and q are two units of 4, q not a root of unity. CQ4 + Rl) (resp. C’(Vq -4 K)) is the Banacb space of continuoua funetiona (resp. continuously differentiable functions) from Vq to K. Oir aim is to flnd orthonormal bases for C(Vq —. Rl) and —, Rl).