Spectra of Abelian C*-Subalgebra Sums

Let $C_b(X)$ be the C*-algebra of bounded continuous functions on some non-compact, but locally compact Hausdorff space $X$. Moreover, let $A_0$ be some ideal and $A_1$ be some unital C*-subalgebra of $C_b(X)$. For $A_0$ and $A_1$ having trivial intersection, we show that the spectrum of their vector space sum equals the disjoint union of their individual spectra, whereas their topologies are nontrivially interwoven. Indeed, they form a so-called twisted-sum topology which we will investigate before. Within the whole framework, e.g., the one-point compactification of $X$ and the spectrum of the algebra of asymptotically almost periodic functions can be described.Comment: 12 pages, LaTeX. Extension of Section 3 in arXiv:1010.0449 (version v1

Stratification of the Generalized Gauge Orbit Space

The action of Ashtekar's generalized gauge group \Gb on the space \Ab of generalized connections is investigated for compact structure groups \LG. First a stratum is defined to be the set of all connections of one and the same gauge orbit type, i.e. the conjugacy class of the centralizer of the holonomy group. Then a slice theorem is proven on \Ab. This yields the openness of the strata. Afterwards, a denseness theorem is proven for the strata. Hence, \Ab is topologically regularly stratified by \Gb. These results coincide with those of Kondracki and Rogulski for Sobolev connections. As a by-product, we prove that the set of all gauge orbit types equals the set of all (conjugacy classes of) Howe subgroups of \LG. Finally, we show that the set of all gauge orbits with maximal type has the full induced Haar measure 1.Comment: LaTeX, 21 page

Measurement of the Iron Spectrum in Cosmic Rays with VERITAS

The elemental energy spectra of cosmic rays play an important role in understanding their acceleration and propagation. Most current results are obtained either from direct measurements by balloon or satellite detectors, or from indirect measurements by air shower detector arrays on the Earth's surface. Imaging Air Cherenkov Telescopes (IACTs), used primarily for gamma-ray astronomy, can also be used for cosmic-ray physics. They are able to measure Cherenkov light emitted both by heavy nuclei and by secondary particles produced in their air showers, and are thus sensitive to the charge and energy of cosmic ray particles with energies of tens to hundreds of TeV. A measurement of the energy spectrum of iron nuclei, based on 71 hours of data taken by the VERITAS array of IACTs between 2009 and 2012, will be presented. The energy and other properties of the primary particle are reconstructed using a template-based likelihood fit. The event selection makes use of direct Cherenkov light, which is emitted by the primary particle before starting the air shower. A multivariate method is used to estimate the remaining background. Using these methods, the iron spectrum was measured in the energy range from 20 TeV to 500 TeV.Comment: Presented at the 35th International Cosmic Ray Conference (ICRC2017), Bexco, Busan, Kore