First analysis of an OH survey of inner Galaxy: evidence for a stellar Bar

Part of a large survey of the inner galactic Plane ( $| \ell | < 45^{\circ}$ and $| b | < 3^{\circ}$ total) in the OH 1612MHz line in search for OH/IR stars is analysed. We find strong evidence for a central m=2 distortion based on geometrical considerations. The observed deviation from axisymmetry cannot be explained by lopsidedness and agrees with other recent models of the galactic Bar on length, inclination and axis ratio.Comment: 4 pages, 140 kB postscript, to appear in proceedings of IAU colloquium 157 "Barred Galaxies

Graph parameters from symplectic group invariants

In this paper we introduce, and characterize, a class of graph parameters obtained from tensor invariants of the symplectic group. These parameters are similar to partition functions of vertex models, as introduced by de la Harpe and Jones, [P. de la Harpe, V.F.R. Jones, Graph invariants related to statistical mechanical models: examples and problems, Journal of Combinatorial Theory, Series B 57 (1993) 207-227]. Yet they give a completely different class of graph invariants. We moreover show that certain evaluations of the cycle partition polynomial, as defined by Martin [P. Martin, Enum\'erations eul\'eriennes dans les multigraphes et invariants de Tutte-Grothendieck, Diss. Institut National Polytechnique de Grenoble-INPG; Universit\'e Joseph-Fourier-Grenoble I, 1977], give examples of graph parameters that can be obtained this way.Comment: Some corrections have been made on the basis of referee comments. 21 pages, 1 figure. Accepted in JCT

The Strong Arnold Property for 4-connected flat graphs

We show that if $G=(V,E)$ is a 4-connected flat graph, then any real symmetric $V\times V$ matrix $M$ with exactly one negative eigenvalue and satisfying, for any two distinct vertices $i$ and $j$, $M_{ij}<0$ if $i$ and $j$ are adjacent, and $M_{ij}=0$ if $i$ and $j$ are nonadjacent, has the Strong Arnold Property: there is no nonzero real symmetric $V\times V$ matrix $X$ with $MX=0$ and $X_{ij}=0$ whenever $i$ and $j$ are equal or adjacent. (A graph $G$ is {\em flat} if it can be embedded injectively in $3$-dimensional Euclidean space such that the image of any circuit is the boundary of some disk disjoint from the image of the remainder of the graph.) This applies to the Colin de Verdi\`ere graph parameter, and extends similar results for 2-connected outerplanar graphs and 3-connected planar graphs

Something about the structure of the Galaxy

We analyse a sample of 507 evolved stars in the inner galactic Plane. We derive average ages for subsets of this sample and use those sets as beacons for the evolution of the Galaxy. In the Bulge the oldest OH/IR stars in the plane are 7.5 Gyr, in the Disk 2.7 Gyr. The vertical distribution of almost all AGB stars in the Disk is found to be nearly exponential, with scaleheight increasing from 100 pc for stars of \lsim 1 Gyr to 500 pc for stars of \gsim 5 Gyr. There may be a small, disjunct population of OH/IR stars. The radial distribution of AGB stars is dictated by the metallicity gradient. Unequivocal morphological evidence is presented for the existence of a central Bar, but parameters can be constrained only for a given spatial-density model. Using a variety of indicators, we identify the radii of the inner ultra-harmonic (2.5 kpc) and corotation resonance (3.5 kpc). We show that the 3-kpc arm is likely to be an inner ring, as observed in other barred galaxies, by identifying a group of evolved stars that is connected to the 3-kpc HI filament. Also, using several observed features, we argue that an inner-Lindblad resonance exists, at $\sim$1-1.5 kpc. The compositions of OH/IR populations within 1 kpc from the galactic Centre give insight into the bar-driven evolution of the inner regions. We suggest that the Bar is $\sim$8 Gyr old, relatively weak (SAB) and may be in a final stage of its existence.Comment: 18 pages, 15 figures, TeX, accepted for publication in MNRA

GHG emissions of green coffee production : toward a standard methodology for carbon footprinting : report

In this project, the scope for product specific rules for carbon footprinting of (green) coffee is investigated and a proposal is drafted for further work toward actual definition and implementation of such a standard

The structure of finite meadows

A meadow is a commutative ring with a total inverse operator satisfying 0^{-1}=0. We show that the class of finite meadows is the closure of the class of Galois fields under finite products. As a corollary, we obtain a unique representation of minimal finite meadows in terms of finite prime fields.Comment: 12 page

On the existence of real R-matrices for virtual link invariants

We characterize the virtual link invariants that can be described as partition function of a real-valued R-matrix, by being weakly reflection positive. Weak reflection positivity is defined in terms of joining virtual link diagrams, which is a specialization of joining virtual link diagram tangles. Basic techniques are the first fundamental theorem of invariant theory, the Hanlon-Wales theorem on the decomposition of Brauer algebras, and the Procesi-Schwarz theorem on inequalities for closed orbits

On partition functions for 3-graphs

A {\em cyclic graph} is a graph with at each vertex a cyclic order of the edges incident with it specified. We characterize which real-valued functions on the collection of cubic cyclic graphs are partition functions of a real vertex model (P. de la Harpe, V.F.R. Jones, Graph invariants related to statistical mechanical models: examples and problems, Journal of Combinatorial Theory, Series B 57 (1993) 207--227). They are characterized by `weak reflection positivity', which amounts to the positive semidefiniteness of matrices based on the `$k$-join' of cubic cyclic graphs (for all k\in\oZ_+). Basic tools are the representation theory of the symmetric group and geometric invariant theory, in particular the Hanlon-Wales theorem on the decomposition of Brauer algebras and the Procesi-Schwarz theorem on inequalities defining orbit spaces