161,286 research outputs found
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
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
Rademacher functions in Morrey spaces
No full textThe Rademacher sums are investigated in the Morrey spaces Mp,wMp,w on [0,1][0,1] for 1≤p<∞1≤p<∞ and weight w being a quasi-concave function. They span l2l2 space in Mp,wMp,w if and only if the weight w is smaller than View the MathML sourcelog2−1/22t on (0,1)(0,1). Moreover, if 1<p<∞1<p<∞ the Rademacher subspace Rp,wRp,w is complemented in Mp,wMp,w if and only if it is isomorphic to l2l2. However, the Rademacher subspace R1,wR1,w is not complemented in M1,wM1,w for any quasi-concave weight w . In the last part of the paper geometric structure of Rademacher subspaces in Morrey spaces Mp,wMp,w is described. It turns out that for any infinite-dimensional subspace X of Rp,wRp,w the following alternative holds: either X is isomorphic to l2l2 or X contains a subspace which is isomorphic to c0c0 and is complemented in Rp,wRp,w.Validerad; 2016; Nivå 2; 20160815 (andbra)</p
Rademacher functions in Cesaro type spaces
No full textThe Rademacher sums are investigated in the Cesaro spaces Ces(p) (1 1 and when w is such that the span of the Rademacher functions is isomorphic to l(2), this span is a complemented subspace in K-p,K-w.Validerad; 2010; 20100627 (ysko
Postfazione: I tre Dorian Gray
No full textPostfazione alla traduzione italiana della prima versione del Dorian Gray wildeano che riprercorre le vicende editoriali dell'opera e la sua diffusione in Italia
Evidence for intramolecular OH⋯π hydrogen bonding in unsaturated alcohols from UV photoelectron spectroscopy
No full textThe gas phase He(I) photoelectron (PE) spectra of several unsaturated alcohols (1-11) have been measured and analysed with respect to intramolecular OH . . . pi hydrogen bonding. Evidence for such a hydrogen bond has been detected in the spectra of 2-allylphenol (1) and 2-phenylethan-1-ol (3). 1 exists as a conformational mixture of a hydrogen bonded form la and an open form Ib in a composition of roughly 2:1. A strong ionization band (IPnu = 10.01 eV; where IPnu is the vertical ionization potential) is assigned to the ethylenic C=C double bond in the major conformer (la) and a weak band (IPnu = 9.72 eV) to that of the minor conformer (Ib). The latter IP coincides with the corresponding ionization of allylbenzene. In the series of omega -phenylalkan-1-ols, compound 3 exhibits an unusually low n(pi)(O) ionization indicating hydrogen bonding between the OH group and the pi electron system of the phenyl ring. The higher homologs 4 and 5 prefer 'open' conformations without such interaction. The PE spectra of alkenols such as but-3-en-1-ol (7) and pent-4-en-1-ol (8) as well as of alkynols such as but-3-yn-1-ol (10) and pent-4-yn-1-ol (11) are consistent with OH . . . pi hydrogen bonded conformers. The methanol/ethylene heterodimer has a T-shaped structure, as indicated by B3LYP/6-311++G(d) calculations, with a binding energy of 5.65 kJ mol(-1). (C) 2001 Elsevier Science B.V. All rights reserved
Japanese design law and practice Max Planck series on Asian intellectual property law ;, 18./ edited by Christoph Rademacher & Tsukasa Aso
No full text"Max Planck Institute for Innovation and Competition"Includes bibliographical referencesHistory of Japanese design law and relevant international instruments / Mayoko Nakano, Kumi Takada & Masanori Yabumoto -- Purpose of the design law system and the definition of 'design' under the Design Act / Tsukasa Aso -- Ownership of design rights / Tatsuyuki Suemune -- Similarity of designs / Nao Nakatsuji -- Requirements for design protection / Etsuko Yoshida -- Application process for design registration / Nao Nakatsuji -- Special design registration systems / Asuka Gomi -- Trials and appeals / Kodai Kimura -- Design infringement and scope of protection / Kensuke Murata -- International jurisdiction and governing law / Christoph Rademacher -- Design protection and competition law / Kazuhiko Fuchikawa -- Overlap of protection under the Design Act and other intellectual property and related laws / Tsukasa Aso -- Design rights and commercial transactions / Kodai Kimura -- Design of furniture used in public spaces / Naoshige Akita -- Home appliance design / Yoshitaka Sugimoto -- Cell phone design / Nobu Miake -- Car design / Yasushi Kato -- Advertising design / Toshifumi Saito -- Product packaging design / Masahiro Kiyosumi -- Web design / Kiriko Toh -- Typeface design / Shigenobu Fujita -- Noteworthy features of Japanese design law from the perspective of European law / Tsukasa Aso & Christoph Rademacher1 online resource (xliii, 366 pages)
Prohexadione-Ca: Modes of Action of a Multifunctional Plant Bioregulator for Fruit Trees
No full textProhexadione-Ca is a plant bioregulator that is primarily used to inhibit excessive vegetative growth in fruit trees and other crop plants. Additionally, effects on the incidence of bacterial and fungal diseases and on insect pests are often observed. Further, the compound may reduce abortion of fruitlets thereby increasing fruit set. Prohexadione-Ca is relatively short-lived and possesses very favorable toxicological and ecotoxicological features. The compound acts as a structural mimic of 2-oxoglutaric acid. Therefore, distinct dioxygenases involved in gibberellin biosynthesis, which require this compound as a co-substrate, are blocked (e.g. GA20 3ß-hydroxylase). As a result, less growth-active gibberellins are formed and treated plants remain compact. 2-Oxoglutaric acid-dependent dioxygenases are also involved in flavonoid metabolism. In shoots of apples and pears, prohexadione-Ca causes considerable changes in the formation of flavonoids and their phenolic precursors by inhibiting flavanone 3-hydroxylase. Prohexadione-Ca triggers pathogen resistance by inducing the formation of 3-deoxyflavonoids, in particular luteoforol, with phytoalexin-like properties. A similar mechanism may explain the lowered incidence of insect pests. Finally, treatments with prohexadione-Ca lead to reduced ethylene formation. This is due to structural similarities with ascorbic acid, the co-substrate of aminocyclopropanecarboxylic acid oxidase, another dioxygenase, which is involved in ethylene biosynthesis. Lowered ethylene levels explain increases in fruit se
PHOSPHORUS(III) DOUBLE-BOND SYSTEMS, CARBENE AND ALKENE ANALOGS - THE ELECTRONIC-STRUCTURE OF IMINO-PHOSPHANES AND METHYLENE-PHOSPHANES
No full textNIECKE E, GUDAT D, Schoeller W, RADEMACHER P. PHOSPHORUS(III) DOUBLE-BOND SYSTEMS, CARBENE AND ALKENE ANALOGS - THE ELECTRONIC-STRUCTURE OF IMINO-PHOSPHANES AND METHYLENE-PHOSPHANES. JOURNAL OF THE CHEMICAL SOCIETY-CHEMICAL COMMUNICATIONS. 1985;(15):1050-1051
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