{ "1504.05139": { "category": [ "Mathematics - Algebraic Topology", "Mathematics - Combinatorics", "05E45, 52B70, 57T99" ], "title": "Discrete Morse theory for moduli spaces of flexible polygons, or solitaire game on the circle", "authors": [ "Panina, Gaiane", "Zhukova, Alena" ], "summary": " We introduce a perfect discrete Morse function on the moduli space of a polygonal linkage. The ingredients of the construction are: (1) the cell structure on the moduli space, and (2) the discrete Morse theory approach, which allows to reduce the number of cells to the minimal possible. ", "link": "http://arxiv.org/pdf/1504.05139", "published_date": "2016-01-23", "toc": [ { "children": [], "title": "1. Introduction" }, { "children": [ { "children": [], "title": "Polygonal linkage: moduli space and the cell complex pan2" }, { "children": [], "title": "Discrete Morse function on a regular cell complex Forman" } ], "title": "2. Preliminaries" }, { "children": [ { "children": [], "title": "Step 1" }, { "children": [], "title": "Step 2" }, { "children": [], "title": "Step k" }, { "children": [], "title": "Pair search algorithm" } ], "title": "3. Pairing on the complex K: ''rules of the game''." }, { "children": [], "title": "4. Critical cells of the complex K" }, { "children": [], "title": "5. Gradient paths between critical cells" }, { "children": [ { "children": [], "title": "Path reversing construction." }, { "children": [], "title": "Two examples" } ], "title": "6. Path reversing: new discrete Morse function" }, { "children": [], "title": "References" } ] }, "1210.4430": { "category": [ "Astrophysics - Solar and Stellar Astrophysics" ], "title": "Laboratory measurement of optical constants of solid SiO and application to circumstellar dust", "authors": [ "Wetzel, Steffen", "Klevenz, Markus", "Gail, Hans-Peter", "Pucci, Annemarie", "Trieloff, Mario" ], "summary": " Silicate minerals belong to the most abundant solids in space. Their formation becomes difficult at the transition from the oxygen rich chemistry of M-stars to the carbon rich chemistry of C-stars. In the intermediate type S-stars oxygen and carbon are consumed by CO and SiO molecule formation, and left-over oxygen to build the SiO4-tetrahedra of silicates becomes scarce. Then SiO molecules may directly condense into solid SiO. The IR absorption spectrum of solid SiO differs from that of silicates by the absence of Si-O-Si bending modes at 18 mum while the absorption by Si-O bond stretching modes at 10 mum is present. Such characteristics are observed in a number of S-star spectra. We suggest that this observation may be explained by formation of solid SiO as a major dust component at C/O abundance ratios close to unity. We determine the IR absorption properties of solid SiO by laboratory transmission measurements of thin SiO films produced by vapour deposition on a Si(111) wafer. From the measured spectra the dielectric function of SiO is derived. The results are used in model calculations of radiative transfer in circumstellar dust shells with solid SiO dust. Comparison of synthetic and observed spectra shows that reasonable agreement is obtained between the main spectral characteristics of emission bands due to solid SiO and an emission band centred on 10 mum, but without accompanying 18 mum band, observed in some S-stars. We propose that solid SiO is the carrier material of this 10 mum spectral feature. ", "link": "http://arxiv.org/pdf/1210.4430", "published_date": "2012-10-16", "toc": [ { "children": [], "title": "1 Introduction" }, { "children": [ { "children": [], "title": "2.1 Experimental setup" }, { "children": [], "title": "2.2 Results" }, { "children": [], "title": "2.3 Dielectric function" } ], "title": "2 Optical properties of SiO" }, { "children": [ { "children": [], "title": "3.1 S-stars" }, { "children": [], "title": "3.2 Why solid silicon monoxide?" }, { "children": [], "title": "3.3 Growth of silicon monoxide grains" } ], "title": "3 Astrophysical applications" }, { "children": [ { "children": [], "title": "4.1 Opacity" }, { "children": [], "title": "4.2 Model calculations" }, { "children": [], "title": "4.3 Results for spectral energy distribution" }, { "children": [], "title": "4.4 Discussion" } ], "title": "4 Radiative transfer model for dust shells" }, { "children": [], "title": "5 Conclusions" }, { "children": [], "title": "A Radiative transfer model" }, { "children": [], "title": "B Relation to Voigt function" } ] }, "1504.05131": { "category": [ "Nuclear Theory" ], "title": "Three-pion exchange nucleon-nucleon potentials with virtual \$\\Delta\$-isobar excitation", "authors": [ "Kaiser, N." ], "summary": " The nucleon-nucleon interaction arising from the exchange of three pions and the excitation of \$\\Delta(1232)\$-isobars in intermediate states is studied. Approximating the \$\\Delta\$-propagator by the inverse \$\\Delta\$N mass-splitting, analytical expressions are derived for the spectral-functions of the isoscalar and isovector central, spin-spin and tensor NN-potentials in momentum-space. A trans- lation of the spectral-functions into coordinate-space potentials reveals that the main effect of these specific exchange and excitation mechanisms is a repulsive isoscalar central NN-potential. ", "link": "http://arxiv.org/pdf/1504.05131", "published_date": "2015-04-20", "toc": [ { "children": [], "title": "1 Introduction and summary" }, { "children": [], "title": "2 Preparation" }, { "children": [ { "children": [], "title": "3.1 Single -excitation of one nucleon" }, { "children": [], "title": "3.2 Single -excitation of both nucleons" }, { "children": [], "title": "3.3 Double -excitation of one nucleon" }, { "children": [], "title": "3.4 Double and single -excitation of either one nucleon" }, { "children": [], "title": "3.5 Double -excitation of both nucleons" } ], "title": "3 Calculation of spectral functions and r-space potentials" }, { "children": [], "title": "4 Conclusions" } ] } }