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Let F (let + f)
Selected AbstractsClass groups of dihedral extensionsMATHEMATISCHE NACHRICHTEN, Issue 6 2005Franz Lemmermeyer Abstract Let L/F be a dihedral extension of degree 2p, where p is an odd prime. Let K/F and k/F be subextensions of L/F with degrees p and 2, respectively. Then we will study relations between the p -ranks of the class groups Cl(K) and Cl(k). (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Chromatic numbers of products of graphs: The directed and undirected versions of the Poljak-Rödl functionJOURNAL OF GRAPH THEORY, Issue 1 2006Claude Tardif Abstract Let f(n),=,min{,(G,×,H),:,G and H are n -chromatic digraphs} and g(n),=,min{,(G,×,H),:,G and H are n -chromatic graphs}. We prove that f is bounded if and only if g is bounded. © 2005 Wiley Periodicals, Inc. J Graph Theory [source] The covering number and the uniformity of the ideal ,fMLQ- MATHEMATICAL LOGIC QUARTERLY, Issue 4 2006Noboru Osuga Abstract Let f, g , ,, . We will denote by g , f that for every k < ,, f (nk) , g (n ) except for finitely many n . The ideal ,f on ,2 is the collection of sets X such that, for some g , f and , , ,n <,g (n )2, every x , X satisfies , (n ) , x for infinitely many n . In the present paper, we will prove the consistency of cov(,f) < ,, and non(,f) < ,,. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Legendre polynomial kernel estimation of a density function with censored observations and an application to clinical trialsCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 8 2007Simeon M. Berman Let f(x), x , ,M, M , 1, be a density function on ,M, and X1, ,., Xn a sample of independent random vectors with this common density. For a rectangle B in ,M, suppose that the X's are censored outside B, that is, the value Xk is observed only if Xk , B. The restriction of f(x) to x , B is clearly estimable by established methods on the basis of the censored observations. The purpose of this paper is to show how to extrapolate a particular estimator, based on the censored sample, from the rectangle B to a specified rectangle C containing B. The results are stated explicitly for M = 1, 2, and are directly extendible to M , 3. For M = 2, the extrapolation from the rectangle B to the rectangle C is extended to the case where B and C are triangles. This is done by means of an elementary mapping of the positive quarter-plane onto the strip {(u, v): 0 , u , 1, v > 0}. This particular extrapolation is applied to the estimation of the survival distribution based on censored observations in clinical trials. It represents a generalization of a method proposed in 2001 by the author [2]. The extrapolator has the following form: For m , 1 and n , 1, let Km, n(x) be the classical kernel estimator of f(x), x , B, based on the orthonormal Legendre polynomial kernel of degree m and a sample of n observed vectors censored outside B. The main result, stated in the cases M = 1, 2, is an explicit bound for E|Km, n(x) , f(x)| for x , C, which represents the expected absolute error of extrapolation to C. It is shown that the extrapolator is a consistent estimator of f(x), x , C, if f is sufficiently smooth and if m and n both tend to , in a way that n increases sufficiently rapidly relative to m. © 2006 Wiley Periodicals, Inc. [source] Decay of correlations and the central limit theorem for meromorphic mapsCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 5 2006Tien-Cuong Dinh Let f be a dominant meromorphic self-map of large topological degree on a compact Kähler manifold. We give a new construction of the equilibrium measure , of f and prove that , is exponentially mixing. As a consequence, we get the central limit theorem in particular for Hölder-continuous observables, but also for noncontinuous observables. © 2005 Wiley Periodicals, Inc. [source] Mean curvature flows and isotopy of maps between spheresCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 8 2004Mao-Pei Tsui Let f be a smooth map between unit spheres of possibly different dimensions. We prove the global existence and convergence of the mean curvature flow of the graph of f under various conditions. A corollary is that any area-decreasing map between unit spheres (of possibly different dimensions) is isotopic to a constant map. © 2004 Wiley Periodicals, Inc. [source] Properly colored subgraphs and rainbow subgraphs in edge-colorings with local constraintsRANDOM STRUCTURES AND ALGORITHMS, Issue 4 2003Noga Alon We consider a canonical Ramsey type problem. An edge-coloring of a graph is called m-good if each color appears at most m times at each vertex. Fixing a graph G and a positive integer m, let f(m, G) denote the smallest n such that every m -good edge-coloring of Kn yields a properly edge-colored copy of G, and let g(m, G) denote the smallest n such that every m -good edge-coloring of Kn yields a rainbow copy of G. We give bounds on f(m, G) and g(m, G). For complete graphs G = Kt, we have c1mt2/ln t , f(m, Kt) , c2mt2, and cmt3/ln t , g(m, Kt) , cmt3/ln t, where c1, c2, c, c are absolute constants. We also give bounds on f(m, G) and g(m, G) for general graphs G in terms of degrees in G. In particular, we show that for fixed m and d, and all sufficiently large n compared to m and d, f(m, G) = n for all graphs G with n vertices and maximum degree at most d. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 2003 [source] | ||||||||||