Mathematics and Computer Science: Algorithms, Trees, by Andras Antos, Luc Devroye (auth.), Danièle Gardy, Abdelkader

By Andras Antos, Luc Devroye (auth.), Danièle Gardy, Abdelkader Mokkadem (eds.)

This is often the 1st booklet the place arithmetic and desktop technological know-how are at once faced and joined to take on elaborate difficulties in machine technological know-how with deep mathematical methods. It includes a number of refereed papers provided on the Colloquium on arithmetic and computing device technology held on the collage of Versailles-St-Quentin on September 18-20, 2000. The colloquium was once a gathering position for researchers in arithmetic and computing device technological know-how and therefore a massive chance to switch principles and issues of view, and to provide new methods and new leads to the typical components comparable to algorithms research, bushes, combinatorics, optimization, functionality assessment and possibilities. The booklet is meant for a wide public in utilized arithmetic, discrete arithmetic and desktop technological know-how, together with researchers, academics, graduate scholars and engineers. It offers an outline of the present questions in computing device technology and similar smooth mathematical tools. the variety of functions is especially extensive and reaches past laptop technological know-how.

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By Andras Antos, Luc Devroye (auth.), Danièle Gardy, Abdelkader Mokkadem (eds.)

This is often the 1st booklet the place arithmetic and desktop technological know-how are at once faced and joined to take on elaborate difficulties in machine technological know-how with deep mathematical methods. It includes a number of refereed papers provided on the Colloquium on arithmetic and computing device technology held on the collage of Versailles-St-Quentin on September 18-20, 2000. The colloquium was once a gathering position for researchers in arithmetic and computing device technological know-how and therefore a massive chance to switch principles and issues of view, and to provide new methods and new leads to the typical components comparable to algorithms research, bushes, combinatorics, optimization, functionality assessment and possibilities. The booklet is meant for a wide public in utilized arithmetic, discrete arithmetic and desktop technological know-how, together with researchers, academics, graduate scholars and engineers. It offers an outline of the present questions in computing device technology and similar smooth mathematical tools. the variety of functions is especially extensive and reaches past laptop technological know-how.

Show description

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Desk of Contents

* 1 Henri Cartan Les travaux de Koszul, I (Lie algebra cohomology)
* 2 Claude Chabauty Le théorème de Minkowski-Hlawka (Minkowski-Hlawka theorem)
* three Claude Chevalley L'hypothèse de Riemann pour les corps de fonctions algébriques de caractéristique p, I, d'après Weil (local zeta-function)
* four Roger Godement Groupe complexe unimodulaire, I : Les représentations unitaires irréductibles du groupe complexe unimodulaire, d'après Gelfand et Neumark (representation thought of the advanced exact linear group)
* five Léo Kaloujnine Sur los angeles constitution de p-groupes de Sylow des groupes symétriques finis et de quelques généralisations infinies de ces groupes (Sylow theorems, symmetric teams, limitless crew theory)
* 6. Pierre Samuel l. a. théorie des correspondances birationnelles selon Zariski (birational geometry)
* 7 Jean Braconnier Sur les suites de composition d'un groupe et los angeles journey des groupes d'automorphismes d'un groupe fini, d'après H. Wielandt (finite groups)
* eight Henri Cartan, Les travaux de Koszul, II (see 1)
* nine Claude Chevalley, L'hypothèse de Riemann pour les groupes de fonctions algébriques de caractéristique p, II,, d'après Weil (see 3)
* 10 Luc Gauthier, Théorie des correspondances birationnelles selon Zariski (see 6)
* eleven Laurent Schwartz, Sur un mémoire de Petrowsky : "Über das Cauchysche challenge für ein process linearer partieller Differentialgleichungen im gebiete nichtanalytischen Funktionen" (partial differential equations)
* 12 Henri Cartan, Les travaux de Koszul, III (see 1)
* thirteen Roger Godement, Groupe complexe unimodulaire, II : los angeles transformation de Fourier dans le groupe complexe unimodulaire à deux variables, d'après Gelfand et Neumark (see 4)
* 14 Marc Krasner, Les travaux récents de R. Brauer en théorie des groupes (finite groups)
* 15 Laurent Schwartz, Sur un deuxième mémoire de Petrowsky : "Über das Cauchysche challenge für method von partiellen Differentialgleichungen" (see 11)
* sixteen André Weil Théorèmes fondamentaux de l. a. théorie des fonctions thêta, d'après des mémoires de Poincaré et Frobenius (theta functions)
* 17 André Blanchard, Groupes algébriques et équations différentielles linéaires, d'après E. Kolchin (differential Galois theory)
* 18 Jean Dieudonné, Géométrie des espaces algébriques homogènes, d'après W. L. Chow (algebraic geometry)
* 19 Roger Godement, Sommes maintains d'espaces de Hilbert, I (functional research, direct integrals)
* 20 Charles Pisot, Démonstration élémentaire du théorème des nombres premiers, d'après Selberg et Erdös (prime quantity theorem)
* 21 Georges Reeb, Propriétés des trajectoires de certains systèmes dynamiques (dynamical systems)
* 22 Pierre Samuel, Anneaux locaux ; advent à l. a. géométrie algébrique (local rings)
* 23 Marie-Hélène Schwartz, Compte-rendu de travaux de M. Heins sur diverses majorations de l. a. croissance des fonctions analytiques et sous-harmoniques (complex research, subharmonic functions)
* 24 Charles Ehresmann, Les connexions infinitésimales dans un espace fibré différentiable (connections on fiber bundles)
* 25 Roger Godement, Sommes keeps d'espaces de Hilbert, II (see 19)
* 26 Laurent Schwartz, Sur un mémoire de ok. Kodaira : "Harmonic fields in riemannian manifolds (generalized strength theory)", I (Hodge theory)
* 27 Jean-Pierre Serre, Extensions de groupes localement compacts, d'après Iwasawa et Gleason (locally compact groups)
* 28 René Thom, Les géodésiques dans les variétés à courbure négative, d'après Hopf (geodesics)
* 29 Armand Borel, Groupes localement compacts, d'après Iwasawa et Gleason (see 27)
* 30 Jacques Dixmier, Facteurs : class, measurement, hint (von Neumann algebras)
* 31 Jean-Louis Koszul, Algèbres de Jordan (Jordan algebras)
* 32 Laurent Schwartz, Sur un mémoire de okay. Kodaira : "Harmonic fields in riemannian manifolds (generalized strength theory)", II (see 26)
* 33 Armand Borel, Sous-groupes compacts maximaux des groupes de Lie, d'après Cartan, Iwasawa et Mostow (maximal compact subgroups)
* 34 Henri Cartan, Espaces fibrés analytiques complexes (analytic geometry, fiber bundles)
* 35 Charles Ehresmann, Sur les variétés presque complexes (almost-complex manifolds)
* 36 Samuel Eilenberg, Exposition des théories de Morse et Lusternick-Schnirelmann (Morse conception, Lyusternik-Schnirelmann category)
* 37 Luc Gauthier, Quelques variétés usuelles en géométrie algébrique (algebraic geometry)
* 38 Jean-Louis Koszul, Cohomologie des espaces fibrés différentiables et connexions (Chern-Weil theory)
* 39 Jean Delsarte, Nombre de ideas des équations polynomiales sur un corps fini, d'après A. Weil (Weil conjectures)
* forty Jacques Dixmier, Anneaux d'opérateurs et représentations des groupes (operator algebras, illustration theory)
* forty-one Roger Godement, Théorie des caractères dans les groupes unimodulaires (unimodular groups)
* forty two Pierre Samuel, Théorie du corps de periods neighborhood selon G. P. Hochschild (local category box theory)
* forty three Laurent Schwartz, Les théorèmes de Whitney sur les fonctions différentiables (singularity theory)
* forty four Jean-Pierre Serre, Groupes d'homotopie (homotopy groups)
* forty five Armand Borel, Cohomologie des espaces homogènes (cohomology of homogeneous areas of Lie groups)
* forty six Samuel Eilenberg, Foncteurs de modules et leurs satellites, d'après Cartan et Eilenberg (homological algebra)
* forty seven Marc Krasner, Généralisations non-abéliennes de los angeles théorie locale des corps de periods (local fields)
* forty eight Jean Leray, los angeles résolution des problèmes de Cauchy et de Dirichlet au moyen du calcul symbolique et des projections orthogonales et obliques (Dirichlet difficulties and Cauchy difficulties for partial differential equations, symbolic calculus)
* forty nine Pierre Samuel, Sections hyperplanes des variétés normales, d'après A. Seidenberg (algebraic geometry, hyperplane sections, basic type)

Extra info for Mathematics and Computer Science: Algorithms, Trees, Combinatorics and Probabilities

Sample text

0 Lemma 7 There exists a constant Do such that Proof. We use Lemma 6 with x = 1- e-h/Uh+l) and where Do > 0 will be chosen in the sequel. h 1 '" 2"e h /(i3h+ 1 ) ((jh+1)k ( 1)k k! l 1 ) Do"fh log h (c')k k! jh - > 0) it follows that there exists Do > 0 such that (Ph: 1) ~(1J,v'Ii I"h) 0Wh: 1tv'lil"h) = Mathematics and Computer Science 50 as h ---+ 00. In a similar way we can discuss Zh+d(X). By definition (and after some algebra) we get if Do is sufficiently large. / > _c_ _"'h_+_1)DOVh logh 3 as proposed.

Observe that and that h~,z(u) = 0 if and only if u = Qy,z := e 1 1 + exp 2 (y - z) Let t > 0 and "( > O. 2, Trivially, so we can conclude h~,zCx) dx 2: 8(u - Qy,z) + ,,(r 1 / 2 ) E (0,1). and b := 1, and 2: 8,,(C 1 / 2 for all u E (a, b).

A. edu;-fill/ SVANTE JANSON Department of Mathematics, Uppsala University, Sweden. se;-svante/ JAMES ALLEN FILLI Abstract. Using Fourier analysis, we prove that the limiting distribution of the standardized random number of comparisons used by Quicksort to sort an array of n numbers has an everywhere positive and infinitely differentiable density f, and that each derivative f(k) enjoys superpolynomial decay at ±oo. In particular, each f(k) is bounded. Our method is sufficiently computational to prove, for example, that f is bounded by 16.

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