3,279 research outputs found
Moduli of spherical tori with one conical point
No full textWe determine the topology of the moduli space MS1;1(v) of surfaces of genus one with a Riemannian metric of constant curvature 1 and one conical point of angle 2 pi v. In particular, for v is an element of (2m-1, 2m + 1) nonodd, MS1,1(v) is connected, has orbifold Euler characteristic -1/12m(2), and its topology depends on the integer m > 0 only. For v= 2m + 1 odd, MS1,1(v) has 1/6 m(m + 1) connected components. For v= 2m even, MS1,1(v) has a natural complex structure and it is biholomorphic to H-2/G(m) for a certain subgroup Gm of SL(2, Z) of index m(2), which is nonnormal for m > 1
An upper estimate for characteristic exponent of polynomials
No full textIn (10), A. Eremenko and G. Levin have found an upper bound for the characteristic exponent of polynomials with connected Julia set. In (11), they extended their result so that it includes the polynomials of the form P\sb{c}(z)=z\sp{d}+c. In the case of polynomials with connected Julia set, the upper bound is sharp, and in the second case it is asymptotically the best possible upper bound. In this paper we extend their result to all polynomials
Rational maps with real multipliers
No full textLet f be a rational function such that the multipliers of all repelling periodic points are real. We prove that the Julia set of such a function belongs to a circle. Combining this with a result of Fatou we conclude that whenever J(f) belongs to a smooth curve, it also belongs to a circle. Then we discuss rational functions whose Julia sets belong to a circle
Determining biholomorphic type of a manifold using combinatorial and algebraic structures
No full textWe settle two problems of reconstructing a biholomorphic type of a manifold. In the first problem we use graphs associated to Riemann surfaces of a particular class. In the second one we use the semigroup structure of analytic endomorphisms of domains in [special characters omitted]. 1. We give a new proof of a theorem due to P. Doyle. The problem is to determine a conformal type of a Riemann surface of class Fq, using properties of the associated Speiser graph. Sufficient criteria of type have been given since 1930\u27s when the class Fq was introduced. Also there were necassary and sufficient results which have theoretical value, but which are hard to apply. P. Doyle\u27s theorem states that a non-compact Riemann surface of class Fq has a hyperbolic (parabolic) type, if and only if its extended Speiser graph is hyperbolic (parabolic). By a hyperbolic graph we mean a locally-finite infinite connected graph, which admits a non-constant positive superharmonic function with respect to the discrete Laplace operator. Otherwise a graph is parabolic. The usefulness of this criterion stems from the possibility of applying Rayleigh\u27s short-cut method for graphs. We apply Doyle\u27s theorem to give a counterexample to a conjecture of R. Nevanlinna that relates the type to an excess of a Speiser graph. More explicitely, the conjecture was that if the (upper) mean excess of a surface of class Fq is negative, then the surface is hyperbolic. We provide an example of a parabolic surface of class Fq with negative mean excess. 2. If there is a biholomorphic or antibiholomorphic map between two domains in [special characters omitted], then it gives rise to an isomorphism between the semigroups of analytic endomorphisms of these domains. Suppose, conversely, that we are given two domains in [special characters omitted] with isomorphic semigroups of analytic endomorphisms. Are they biholomorphically or antibiholomorphically equivalent? This question was raised by L. Rubel. Similar questions were studied in the setting of topological spaces. The case n = 1 was investigated by A. Eremenko, who showed that if we require that the domains are bounded, then the answer to the above question is positive. It was shown by A. Hinkkanen that the boundedness condition cannot be dropped. We prove that two bounded domains in [special characters omitted] with isomorphic semigroups of analytic endomorphisms are biholomorphically or antibiholomorphically equivalent. Moreover, we generalize this by requiring only the existence of an epimorphism between the semigroups
Über Funktionen in der Speiser-Klasse mit einem Trakt
No full textLet f be a transcendental entire map. A complex number w is called critical value of f if there exists a complex number z such that f'(z)=0 and f(z)=w. A complex number b is called an asymptotic value of f if there exists a curve \gamma with \gamma(t)\to\infty as t\to\infty but f(\gamma(t))\to b as t\to\infty. The singular set of f is the set consisting of all critical and asymptotic values of f. The set B of all transcendental entire functions with a bounded singular set is called Eremenko-Lyubich class. The Speiser class S consists of all functions in class B where the singular set is not only bounded but finite.
These classes have been thoroughly studied, notably, in complex dynamics, which deals with the behaviour of an entire or rational map f under iteration. Of particular interest is the construction of functions in classes B and S with prescribed behaviour. One method to obtain maps in class B is using so-called Cauchy integrals. Gwyneth Stallard used this method to prove that for any d\in(1,2) there exists a function in class B whose Julia set has Hausdorff dimension equal to d. It is the shape of the tracts of her maps which yields the desired Hausdorff dimension. Here, a tract is a connected component of the set where the modulus of the function is large.
The question arises whether Stallard's result also holds for maps in class S. While we are not able to answer this question, we show that there exist functions in class S whose tracts are in some sense similar to the tracts used by Stallard. The method of Cauchy integrals does generally not generate maps in class S. An alternative construction method is quasiconformal folding, which was recently introduced by Christopher Bishop.
We use Bishop's method to construct quasiregular maps which only grow in one parabola shaped tract which is symmetric to the real axis and are bounded otherwise. Furthermore, we prove that for each constructed quasiregular map g there exists an entire function f in class S such that g=f\circ\phi for some quasiconformal homeomorphism \phi. Thus, the tract of f, which is still symmetric to the real axis, is the quasiconformal image of the tract of g. Moreover, the quasiconformal map involved is asymptotically conformal at infinity. We use this to prove that the maximum modulus M(r,f) of f on the circle with radius r is bounded below by a function which depends on the shape of the tract. In particular, we prove that there exists an entire map f in the class S with only one tract, which is symmetric to the real axis, such that \log\log M(r,f) is bounded below by d\cdot\sqrt{r} for some d>0.Sei f eine ganz transzendente Funktion. Eine komplexe Zahl w heißt kritischer Wert der Funktion f, falls es eine kpomplexe Zahl z mit f'(z)=0 und f(z)=w gibt. Eine komplexe Zahl b heißt asymptotischer Wert von f, falls es eine Kurve \gamma mit \gamma(t)\to\infty für t\to\infty gibt, so dass f(\gamma(t))\to b gilt. Die Menge sing(f^{-1}) ist die Menge der Singularitäten der Umkehrfunktion von f und besteht aus allen kritischen und allen asymptotischen Werten von f. Die Menge B aller ganz transzendenter Funktionen derart, dass sing(f^{-1}) beschränkt ist, heißt Eremenko-Lyubich-Klasse. Die Speiser-Klasse S besteht aus allen Funktionen der Klasse B, deren Menge der Singularitäten der Umkehrfunktion sogar endlich ist.
Insbesondere in der komplexen Dynamik, die sich mit dem Verhalten einer ganzen oder rationalen Funktion unter Iteration befasst, wurden diese Funktionenklassen ausgiebig untersucht. Die Konstruktion von Funktionen in den Klassen B und S mit vorgeschriebenem Verhalten ist von besonderem Interesse. Eine Möglichkeit, Funktionen der Klasse B zu konstruieren, sind sogenannte Cauchyintegrale. Gwyneth Stallard nutzte diese Methode, um zu beweisen, dass es für jedes d\in(1,2) eine Funktion in der Klasse B gibt, deren Juliamenge Hausdorff-Dimension d hat. Die Form der Trakte ihrer Funktionen bestimmt dabei die Hausdorff-Dimension. Dabei ist ein Trakt eine Zusammenhangskomponente der Menge, auf welcher der Absolutbetrag der Funktion groß ist.
Es ergibt sich die Frage, ob Stallards Resultat auch für Funktionen der Klasse S gilt. Auch wenn wir diese Frage nicht beantworten können, so zeigen wir, dass es Funktionen in der Klasse S gibt, deren Trakte in gewissem Sinne den von Stallard genutzten Trakten ähneln. Im Allgemeinen sind Funktionen, die mithilfe von Cauchyintegralen konstruiert wurden, nicht in der Klasse S. Eine alternative Konstruktionsmethode ist die quasikonforme Faltung, die kürzlich von Christopher Bishop vorgestellt wurde.
Wir nutzen Bishops Methode, um quasireguläre Funktionen zu konstruieren, die nur in einem parabelförmigen, zur reellen Achse symmetrischen Trakt wachsen und ansonsten beschränkt sind. Des Weiteren beweisen wir, dass es zu jeder so konstruierten quasiregulären Funktion g eine ganze Funktion f in der Klasse S gibt, so dass g=f\circ\phi für eine quasikonforme Abbildung \phi gilt. Somit ist der Trakt von f, welcher ebenfalls symmetrisch zur reellen Achse ist, ein quasikonformes Bild des Traktes von g. Ferner ist die hierbei genutzte quasikonforme Abbildung asymptotisch konform bei unendlich. Wir nutzen dieses, um zu zeigen, dass der Maximalbetrag M(r,f) von f auf dem Kreis mit Radius r von unten durch eine Funktion beschränkt ist, die von der Form des Traktes abhängt. Insbesondere beweisen wir, dass es eine ganze Funktion f in der Klasse S gibt, die nur einen Trakt hat, der ferner symmetrisch zur reellen Achse ist, so dass \log\log M(r,f) von unten durch d\cdot\sqrt{r} für ein d>0 beschränkt ist
La filosofía del derecho de Alexandre Kojève
No full textThis article is a presentation of Alexandre Kojève’s philosophy of law, exposed in his Esquisse d’une phénoménologie du droit (1981). Little attention has been paid to this work. So there is a gap that has to be filled with a critical reflection of its strengths. Among them, undoubtedly, we count the fact that Kojève is introducing a conception of international justice that casts a singular light on current debates about cosmopolitanism and globalization. According to this author, citizenship is the key element of the process of global expansion of the juridical sphere. In sum, Kojève’s philosophy is useful to reflect upon the contrast between the juridical and the political, which is the basis for all philosophy of law, in order to achieve world peace and international justice.Este artículo es una presentación de la filosofía del derecho de Alexandre Kojève contenida en su Esquisse d’une phénoménologie du droit (1981). La poca atención que dicha obra ha recibido es un vacío que debiera llenarse con una reflexión crítica de sus puntos fuertes. Entre ellos destaca una concepción de la justicia internacional que proyecta una luz muy singular sobre los actuales debates en torno a la globalización y el cosmopolitismo. A ojos de este autor, la ciudadanía es el elemento clave para aquilatar la expansión global de lo jurídico. En suma, Kojève aparece como un valioso referente en la labor de pensar la contraposición entre lo jurídico y lo político que está en la base de toda filosofía del derecho, con la aspiración al logro de la justicia internacional y la paz mundial en el horizonte
Reconfiguração do consensualismo contratual: as ações tituladas nominativas e os limites à transmissão
No full textPartimos da evolução histórica do consensualismo contratual salientando os
principais carateres que, nos diversos momentos históricos, se foram evidenciando.
Numa segunda etapa exploramos os fundamentos dogmáticos do modelo de
transmissão contratual assumido pelo legislador e a sua viabilidade no sistema
jurídico global, em particular, no direito dos valores mobiliários. Constatamos a
crescente necessidade na prática mercantil e inevitabilidade no sistema jurídico
global da admissibilidade da existência de contratos de compra e venda de natureza
meramente obrigacional. Num terceiro momento desenvolvemos os principais
aspetos do regime jurídico aplicável às ações tituladas nominativas fora do mercado
regulado, em particular, os principais limites à transmissão, enquanto instrumentos/barreiras ao consensualismo contratual.We start from the historical evolution of contractual consensualism emphasizing the
main aspects that, in different historical moments, were showing up. In a second
stage we explore the dogmatic foundations of the transmission model contractual
assumed by the legislator and its viability in the global legal system, in particular, in
securities law. We note the growing need in commercial practice and inevitability in
the global legal system the admissibility of the existence of contracts of sale purely
obligatory. In the third stage we develop the main aspects of the legal regime
applicable to nominative titled actions outside the regulated market, in particular,
the main limits to the transmission, as instruments / barriers to contractual
consensualism
“Era por Alexandre tod’esto demostrado”: ¿pruebas verídicas y pruebas engañosas en el Libro de Alexandre?
No full textEl Libro de Alexandre es un texto de s. XIII, que se escribió en la España medieval. En este escrito, el autor pretende demostrar que, en el Alexandre, algunas de las situaciones que se ponen a prueba son aceptadas, pero eso no significa que el macedonio gane la prueba. El articulo esta dividido en tres apartados. En el primero, el autor da cuenta de la historia textual de la obra y también dedica ciertas líneas al Estado de la cuestión del texto; mientras que, en la segunda parte, nos guía a conceptos etimológicos de los términos prueba, evidencia y demás. En el tercer apartado se centra en algunas pruebas expuestas en el Libro de Alexandre.The Libro de Alexandre is a literary work, written during the medieval Spain. In this paper, the author tries to demonstrate that, carefully reading the L.A, some of the situations that are set as proves are accepted, but it does not mean that Alexander can be a victor. This paper is divided in three sections: firstly, the author tells the textual history of the L.A and, then, tries to update the State of art: on the other hand, in the second part, the author offers meanings about terms as: prueba and evidencia. Finally, the author focuses on certain passages contained in the Libro de Alexandre that can be taken as failed proves
Mixing the Immiscible: Improvisation within Fixed-Media Composition
No full textThis paper will explore ways in which mastered improvisation practice, with the studio as an instrument, is a proposed avenue to bridge the historical dichotomy between what Ted Gioia describe as ‘the aesthetics of perfection’ and ‘the aesthetics of imperfection’. It is proposed as a way to re-embody fixed music, as experimented by the author through the composition of his last fixed-media work. This will be put in the context of a wider trend observed amongst the current emerging generation of composers interested in the aesthesics of the work, by opposition to the previous generations that placed the value of the work in its poietics. The vital and primal importance of practice outcome as practice-based research’s main document will also be advocated for, as these trends are happening in the laboratory of live music
LANDAU’S THEOREM FOR HOLOMORPHIC CURVES IN PROJECTIVE SPACE AND THE KOBAYASHI METRIC ON HYPERPLANE COMPLEMENTS
No full textAbstract. We prove an effective version of a theorem of Dufresnoy: For any set of 2n+1 hyperplanes in general position in P n, we find an explicit constant K such that for every holomorphic map f from the unit disc to the complement of these hyperplanes, we have f # (0) ≤ K, where f # denotes the norm of the derivative measured with respect to the Fubini-Study metric. This result gives an explicit lower bound on the Royden function, i.e., the ratio of the Kobayashi metric on the hyperplane complement to the Fubini-Study metric. Our estimate is based on the potential-theoretic method of Eremenko and Sodin. 1
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