Criss-cross mapping BD+30 3639: a new kinematic analysis technique

We present a new analysis of kinematic data of the young planetary nebula BD+30 3639. The data include spectroscopic long-slit and internal proper motion measurements. In this paper we also introduce a new type of mapping of kinematic proper motion data that we name "criss-cross" mapping. It basically consists of finding all points where extended proper motion vectors cross converge. From the crossing points a map is generated which helps to interpret the kinematic data. From the criss-cross mapping of BD+30 3639, we conclude that the kinematic center is approximately 0.5 arcsec offset to the South-East from the central star. The mapping does also show evidence for a non-homologous expansion of the nebula that is consistent with a disturbance aligned with the bipolar molecular bullets.Comment: 4 pages, to appear in the proceedings of the conference "Asymmetrical Planetary Nebulae V", eds. Zijlstra, et al., editorial: Ebrar

Maximum Δ\Delta-edge-colorable subgraphs of class II graphs

A graph $G$ is class II, if its chromatic index is at least $\Delta+1$. Let $H$ be a maximum $\Delta$-edge-colorable subgraph of $G$. The paper proves best possible lower bounds for $\frac{|E(H)|}{|E(G)|}$, and structural properties of maximum $\Delta$-edge-colorable subgraphs. It is shown that every set of vertex-disjoint cycles of a class II graph with $\Delta\geq3$ can be extended to a maximum $\Delta$-edge-colorable subgraph. Simple graphs have a maximum $\Delta$-edge-colorable subgraph such that the complement is a matching. Furthermore, a maximum $\Delta$-edge-colorable subgraph of a simple graph is always class I.Comment: 13 pages, 2 figures, the proof of the Lemma 1 is correcte

Spatial discretization of restricted group algebras

We consider spatial discretizations by the finite section method of the restricted group algebra of a finitely generated discrete group, which is represented as a concrete operator algebra via its left-regular representation. Special emphasis is paid to the quasicommutator ideal of the algebra generated by the finite sections sequences and to the stability of sequences in that algebra. For both problems, the sequence of the discrete boundaries plays an essential role. Finally, for commutative groups and for free non-commutative groups, the algebras of the finite sections sequences are shown to be fractal

Helicity Asymmetry in gamma p -> pi+ n with FROST

The main objective of the FROST experiment at Jefferson Lab is the study of baryon resonances. The polarization observable E for the reaction gamma p to pi+n has been measured as part of this program. A circularly polarized tagged photon beam with energies from 0.35 to 2.35 GeV was incident on a longitudinally polarized frozen-spin butanol target. The final-state pions were detected with the CEBAF Large Acceptance Spectrometer. Preliminary polarization data agree fairly well with present SAID and MAID partial-wave analyses at low photon energies. In most of the covered energy range, however, significant deviations are observed. These discrepancies underline the crucial importance of polarization observables to further constrain these analyses.Comment: Contribution to the Proceedings of NSTAR 2011 - The 8th International Workshop on the Physics of Excited Nucleons, May 17-20, 2011, Thomas Jefferson National Accelerator Facility, Newport News, Virginia US

Schmidt Games and Conditions on Resonant Sets

Winning sets of Schmidt's game enjoy a remarkable rigidity. Therefore, this game (and modifications of it) have been applied to many examples of complete metric spaces (X, d) to show that the set of "badly approximable points", with respect to a given collection of resonant sets in X, is a winning set. For these examples, strategies were deduced that are, in most cases, strongly adapted to the specific dynamics and properties of the underlying setting. We introduce a new modification of Schmidt's game which is a combination and generalization of the ones of [18] and [20]. This modification allows us to axiomatize conditions on the collection of resonant sets under which there always exists a winning strategy. Moreover, we discuss properties of winning sets of this modification and verify our conditions for several examples - among them, the set of badly approximable vectors in the Euclidian space and the p-adic integers with weights and, as a main example, the set of geodesic rays in proper geodesic CAT(-1) spaces which avoid a suitable collection of convex subsets.Comment: 30 pages, Comments are welcome