6,298 research outputs found
A note on higher-dimensional magic matrices
We provide exact and asymptotic formulae for the number of unrestricted,
respectively indecomposable, -dimensional matrices where the sum of all
matrix entries with one coordinate fixed equals 2.Comment: AmS-LaTeX, 9 page
Galois groups of multivariate Tutte polynomials
The multivariate Tutte polynomial of a matroid is a
generalization of the standard two-variable version, obtained by assigning a
separate variable to each element of the ground set . It encodes
the full structure of . Let \bv = \{v_e\}_{e\in E}, let be an
arbitrary field, and suppose is connected. We show that is
irreducible over K(\bv), and give three self-contained proofs that the Galois
group of over K(\bv) is the symmetric group of degree , where
is the rank of . An immediate consequence of this result is that the
Galois group of the multivariate Tutte polynomial of any matroid is a direct
product of symmetric groups. Finally, we conjecture a similar result for the
standard Tutte polynomial of a connected matroid.Comment: 8 pages, final version, to appear in J. Alg. Comb. Substantial
revisions, including the addition of two alternative proofs of the main
resul
Partial pressure gauges
The determination of partial pressures in vacuum systems is usually performed by mass spectrometers. The most common type is the QMS. Quadrupole mass spectrometers were developed decades ago and have been used by vacuum specialists as a diagnostic tool since then. In the first part of the paper the principles of these mass spectrometers are briefly reviewed together with the key features of the instruments. This is necessary to operate these instruments. In the second part the boundary conditions which arise from the application as residual gas analyser in UHV/XHV plants are described. These lead to special versions of mass spectrometers. Results obtained with these instruments and typical artefacts in mass spectra obtained in the UHV are discussed
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