In this article we will describe a surprising observation that occurred in the construction of quadratic unramified extensions of a family of pure cubic number fields. Attempting to find an explanation will lead us on a magical mystery tour through the land of pure cubic number fields, Hilbert class fields, and elliptic curves.
N. N. Cencov wrote a commentary chapter included in the Appendix of the Russian translation of the Devroye and Györfi book [15] collecting some arguments supporting the <span class="tex">L<sub>1</sub></span> view of density estimation. The Cencov's work is available in Russian only and it hasn't been translated, so late Igor Vajda decided to translate the Cencov's paper and to add some remarks on the occasion of organizing the session "25 Years of the <span class="tex">L<sub>1</sub></span> Density Estimation" at the Prague Stochastics 2010 Symposium. In this paper we complete his task, i.e., we translate the Cencov's chapter and insert some remarks on the related literature focusing primarily on Igor's results. We would also like to acknowledge the excellent work of Alexandre Tsybakov who translated the Devroye and Györfi book in Russian, annotated it with valuable comments and included some related references published in Russian only.
The paper is concerned with generalized (i. e. monotone and possibly non-additive) measures. A discussion concerning the classification of these measures, according to the type and amount of non-additivity, is done. It is proved that λ-additive measures appear naturally as solutions of functional equations generated by the idea of (possible) non additivity.
In this paper, a theoretical approach of a wideband preamplifier using a high-end operation amplifier OPA847 will be presented. This device is designed to be used for a low noise, wide band measuring. The level of optimization is based on a noise model for the electrical part of the receiver. During the process of amplifier designing, all the noise components have been investigated separately, using operational amplifiers models. Although this preamplifier was designed to serve for the purposes of flame sensors evaluate, it can be also used to other purposes requiring wide band amplifier with low noise, under only a minimal modification. and V tomto příspěvku bych rád přiblížil teoretický postup návrhu
širokopásmového předzesilovače, využívajícího moderní integrovaný
předzesilovač OPA847, který je určen pro nízkošumová
měření. Stupeň optimalizace je založen na šumovém modelu pro
elektrickou část přijímače. Během návrhu zesilovače byla každá
šumová složka zkoumána zvlášť s využitím modelu operačního
zesilovače. Přestože byl tento předzesilovač navržen pro účely
měření detektorů plamene. Může být s výhodou využit všude jinde,
kde je vyžadován širokopásmový, nízkošumový předzesilovač a to
jen s minimálními úpravami.
Der vorliegende Beitrag ist eine teils gekürzte, teils überarbeitete und ergänzte Nachschrift des frei gehaltenen Vortrags. Der Charakter der freien Rede wurde durchgehend gewahrt. Der Leser möge also bedenken, daß der Status des einzelnen Wortes, des einzelnen Satzes und der Satzfolge in frei gesprochener Rede gänzlich verschieden ist von der in einem ausgearbeiteten Text. Die Zitate sind an den Vorlagen überprüft worden. Den Herstellern der Umschrift und Herrn Dr. Felix Wörner bin ich für die Ermöglichung der Veröffentlichung in dieser Form sehr dankbar