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| Zahlenlehre und Rechengesetze Teilbarkeitslehre Teilbarkeitsregeln: Quersummenregel
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In diesem Text beschäftigen wir uns mit der sogenannten Quersummenregel . Die Quersummenregel ist eine Teilbarkeitsregel in der Mathematik. Mit ihr lässt sich schnell erkennen, ob eine Zahl durch 3 , 6 , 9 oder 15 teilbar ist. Hierzu erklären wir dir in diesem Kapitel den Begriff Quersumme und wie man diese ausrechnet.

Quersummenregel Teilbarkeitsregel Quersumme

Merke

Merke

Die Quersumme einer Zahl ist die Summe aus den einzelnen Ziffern der Zahl.

einzelnen Ziffern

Eine Zahl ist durch 3 teilbar, wenn die Quersumme durch 3 teilbar ist.

Eine Zahl ist durch 6 teilbar, wenn die Quersumme durch 3 teilbar ist und die Zahl gerade ist.

gerade

Eine Zahl ist durch 9 teilbar, wenn die Quersumme durch 9 teilbar ist.

Abstract : QUBIC is an instrument aiming at measuring the B mode polarisation anisotropies at medium scales angular scales (30-200 multipoles). The search for the primordial CMB B-mode polarization signal is challenging, because of many difficulties: smallness of the expected signal, instrumental systematics that could possibly induce polarization leakage from the large E signal into B, brighter than anticip… ▽ More QUBIC is an instrument aiming at measuring the B mode polarisation anisotropies at medium scales angular scales (30-200 multipoles). The search for the primordial CMB B-mode polarization signal is challenging, because of many difficulties: smallness of the expected signal, instrumental systematics that could possibly induce polarization leakage from the large E signal into B, brighter than anticipated polarized foregrounds (dust) reducing to zero the initial hope of finding sky regions clean enough to have a direct primordial B-modes observation. The QUBIC instrument is designed to address all aspects of this challenge with a novel kind of instrument, a Bolometric Interferometer, combining the background-limited sensitivity of Transition-Edge-Sensors and the control of systematics allowed by the observation of interference fringe patterns, while operating at two frequencies to disentangle polarized foregrounds from primordial B mode polarization. Its characteristics are described in details in this Technological Design Report. △ Less

Submitted 11 May, 2017; v1 submitted 14 September, 2016; originally announced September 2016.

Comments: 139 pages ; high resolution version can be found on the qubic website (http://qubic.in2p3.fr/QUBIC/Home.html) minor changes : update author list affiliations ; correct title

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[, , other ] math.DG

The field and Killing spinor equations of M-theory and type IIA/IIB supergravity in coordinate-free notation

Authors: M. J. D. Hamilton

Abstract : We review the actions of the supergravity theory in eleven dimensions as well as the type IIA and IIB supergravities in ten dimensions and derive the bosonic equations of motion in a coordinate-free notation. We also consider the existence of supersymmetries and the associated generalized Killing spinor equations. The aim of this note is to serve as a formulary and make the equations of supergravi… ▽ More We review the actions of the supergravity theory in eleven dimensions as well as the type IIA and IIB supergravities in ten dimensions and derive the bosonic equations of motion in a coordinate-free notation. We also consider the existence of supersymmetries and the associated generalized Killing spinor equations. The aim of this note is to serve as a formulary and make the equations of supergravity more easily accessible to mathematicians. △ Less

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