170,997 research outputs found
Die körperliche Züchtigung von Schulkindern : im Anschluss an den preuss. Ministerialerlass vom 1. Mai 1899
No full textvon C. Rademache
Rademacher Sums and Rademacher Series
No full textWe exposit the construction of Rademacher sums in arbitrary weights and describe their relationship to mock modular forms. We introduce the notion of Rademacher series and describe several applications, including the determination of coefficients of Rademacher sums and a very general form of Zagier duality. We then review the application of Rademacher sums and series to moonshine both monstrous and umbral and highlight several open problems. We conclude with a discussion of the interpretation of Rademacher sums in physics
Estimates of the Approximation Error Using Rademacher Complexity: Learning Vector-Valued Functions
No full textFor certain families of multivariable vector-valued functions to be approximated, the accuracy of approximation schemes made up of linear combinations of computational units containing adjustable parameters is investigated. Upper bounds on the approximation error are derived that depend on the Rademacher complexities of the families. The estimates exploit possible relationships among the components of the multivariable vector-valued functions. All such components are approximated simultaneously in such a way to use, for a desired approximation accuracy, less computational units than those required by componentwise approximation. An application to -stage optimization problems is discussed
The generalized Rademacher functions
No full textIn [A & G], the authors introuced the so-called generalized Rademacher functions and used the to prove that every continuous multilinear form A : x ... x
Synthesis and analysis of bimetallic nanoparticles
No full textRademacher C. Synthesis and analysis of bimetallic nanoparticles. Bielefeld: Universität Bielefeld; 2014
Gewinnen und Verlieren
No full textKurz D. Gewinnen und Verlieren. In: Quarch C, Rademacher D, eds. Deutscher Evangelischer Kirchentag. Gütersloh: Gütersloher Verl.-Haus; 2001: 607-614
The Hardy-Ramanujan-Rademacher expansion for C-PSI-M,M'(N) using ford circles
No full textThe object of this paper is to obtain the Hardy-Ramanujan-Rademacher series for the generalized Frobenius partition function c-phi(m,m), (n) using Ford circles and deduce an asymptotic formula for the same
Reciprocity formulae for general Dedekind-Rademacher sums.
No full textThe general Dedekind-Rademacher sums are defined, for positive integers a, b, c and real numbers x, y, z modulo 1, by the formula Sm, n\pmatrix a amp; b amp; c\\ x amp; y amp; z\endpmatrix= \sumh\pmod c \overline Bm \Biggl( ah+ z\over c- x\Biggr) \overline Bn\Biggl( b h+ z\over c- y\Biggr), where \overline Bm is 1-periodic and equal to the Bernoulli polynomial Bm on the unit interval. The authors prove a reciprocity theorem which is stated in terms of a generating function involving Sm, n for all pairs of non-negative integers m, n. The reciprocity theorem embraces the classical relations (due to Dedekind and Rademacher) and their generalizations (due to Apostol, Berndt, Carlitz and Mikolás) which are known up to now
A Hyperbolic Analogue of the Rademacher Symbol
No full textOne of the most famous results of Dedekind is the transformation law of . After a half-century, Rademacher modified Dedekind's result and
introduced an -conjugacy class invariant
(integer-valued) function called the Rademacher symbol. Inspired
by Ghys' work on modular knots, Duke-Imamo\={g}lu-T\'{o}th (2017) constructed a
hyperbolic analogue of the symbol.
In this article, we study their hyperbolic analogue of the Rademacher symbol
and provide its two types of explicit formulas by
comparing it with the classical Rademacher symbol. In association with it, we
contrastively show Kronecker limit type formulas of the parabolic, elliptic,
and hyperbolic Eisenstein series. These limits give harmonic, polar harmonic,
and locally harmonic Maass forms of weight 2.Comment: 38 pages. This article is published in Mathematische Annalen. It
differs from v3 with the addition of a new Appendix B. Furthermore, while
Appendix C has been removed in the published version, it remains unchanged in
this preprin
Persistence of Rademacher-type and Sobolev-to-Lipschitz properties
No full textWe consider the Rademacher-and Sobolev-to-Lipschitztype properties for arbitrary quasi-regular strongly local Dirichlet spaces. We discuss the persistence of these properties under localization, globalization, transfer to weighted spaces, tensorization, and direct integration. As byproducts, we obtain: necessary and sufficient conditions to identify a quasi-regular strongly local Dirichlet form on an extended metric topological sigma-finite possibly non-Radon measure space with the Cheeger energy of the space; the tensorization of intrinsic distances; the tensorization of the Varadhan short-time asymptotics. (c) 2025 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/)
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