Odd and even partial waves of eta pi(-) and eta 'pi(-) in pi(-) p -> eta(('))pi(-)p at 191 GeV/c

Exclusive production of eta pi(-) and eta'pi(-) in has been studied with a 191 GeV/c pi(-) beam impinging on a hydrogen target at COMPASS (CERN). Partial-wave analyses reveal different odd/even angular momentum (L) characteristics in the inspected invariant mass range up to 3 GeV/c(2). A striking similarity between the two systems is observed for the L = 2, 4, 6 intensities (scaled by kinematical factors) and the relative phases. The known resonances a(2)(1320) and a(4)(2040) are in line with this similarity. In contrast, a strong enhancement of eta'pi(-) over eta pi(-) is found for the L = 1, 3, 5 waves, which carry non-qq quantum numbers. The L = 1 intensity peaks at 1.7 GeV/c(2) in in and at 1.4 GeV/c(2) in eta pi(-), the corresponding phase motions with respect to L = 2 are different. (C) 2014 The Authors. Published by Elsevier B.V.DFG [1102]; German Bundesministerium fur Bildung und Forschung; Czech Republic MEYS [ME492, LA242]; SAIL (CSR), Govt. of India; CERN-RFBR [08-02-91009, 12-02-91500]; Portuguese FCT - Fundacao para a Ciencia e Tecnologia [CERN/FP/109323/2009, CERN/FP/116376/2010, CERN/FP/123600/2011]; MEXT; JSPS [18002006, 20540299, 18540281]; Daiko Foundation; Yamada Foundation; DFG; EU [283286]; Israel Science Foundation; Polish NCN [DEC-2011/01/M/ST2/02350

Domatic Number of a Graph and its Variants (Extended Abstract)

This chapter presents some numerical invariants of graphs that are related to the concept of domination—namely, the domatic number and its variants.. The word domatic was coined from the words dominating and chromatic in the same way as the word smog was composed from the words smoke and fog. This concept is a certain analogy of the chromatic number, but instead of independent sets, dominating sets are used in its definition. A subset D of the vertex set V(G) of an undirected graphs G is called dominating if for each x V(G) − D there exists a vertex yD adjacent to x. A domatic partition of G is a partition of V(G), all of whose classes are dominating sets in G. The maximum number of classes of a domatic partition of G is called the “domatic number” of G and denoted by d(G). R. Laskar and S. T. Hedetniemi have introduced the connected domatic number d, (G) of a graph G. It is the maximum number of classes of a partition of V(G) into dominating sets that induce connected subgraphs of G.DFG [1102]; German Bundesministerium fur Bildung und Forschung; Czech Republic MEYS [ME492, LA242]; SAIL (CSR), Govt. of India; CERN-RFBR [08-02-91009, 12-02-91500]; Portuguese FCT - Fundacao para a Ciencia e Tecnologia [CERN/FP/109323/2009, CERN/FP/116376/2010, CERN/FP/123600/2011]; MEXT; JSPS [18002006, 20540299, 18540281]; Daiko Foundation; Yamada Foundation; DFG; EU [283286]; Israel Science Foundation; Polish NCN [DEC-2011/01/M/ST2/02350