Edge-dominating cycles in graphs

AbstractA set S of vertices in a graph G is said to be an edge-dominating set if every edge in G is incident with a vertex in S. A cycle in G is said to be a dominating cycle if its vertex set is an edge-dominating set. Nash-Williams [Edge-disjoint hamiltonian circuits in graphs with vertices of large valency, Studies in Pure Mathematics, Academic Press, London, 1971, pp. 157–183] has proved that every longest cycle in a 2-connected graph of order n and minimum degree at least 13(n+2) is a dominating cycle. In this paper, we prove that for a prescribed positive integer k, under the same minimum degree condition, if n is sufficiently large and if we take k disjoint cycles so that they contain as many vertices as possible, then these cycles form an edge-dominating set. Nash-Williams’ Theorem corresponds to the case of k=1 of this result

Interplay between structure and magnetism in Mo12S9I9Mo_{12} S_9 I_9 nanowires

We investigate the equilibrium geometry and electronic structure of Mo$_{12}$S$_{9}$I$_{9}$ nanowires using ab initio Density Functional calculations. The skeleton of these unusually stable nanowires consists of rigid, functionalized Mo octahedra, connected by flexible, bi-stable sulphur bridges. This structural flexibility translates into a capability to stretch up to approximate 20% at almost no energy cost. The nanowires change from conductors to narrow-gap magnetic semiconductors in one of their structural isomers.Comment: 4 pages with PRL standards and 3 figure

A protocol to construct RNA-protein devices for photochemical translational regulation of synthetic mRNAs in mammalian cells

Here, we describe a protocol for the translational regulation of transfected messenger RNAs (mRNAs) using light in mammalian cells. We detail the steps for photocaged ligand synthesis, template DNA preparation, and mRNA synthesis. We describe steps for mRNA transfection, treatment of cells with a photocaged ligand followed by light irradiation, and analysis of the transgene expression. The protocol enables spatiotemporally regulated transgene expression without the risk of insertional mutagenesis

Prospect for Future MeV Gamma-ray Active Galactic Nuclei Population Studies

While the X-ray, GeV gamma-ray, and TeV gamma-ray skies have been extensively studied, the MeV gamma-ray sky is not well investigated after the Imaging Compton Telescope (COMPTEL) scanned the sky about two decades ago. In this paper, we investigate prospects for active galactic nuclei population studies with future MeV gamma-ray missions using recent spectral models and luminosity functions of Seyfert and flat spectrum radio quasars (FSRQs). Both of them are plausible candidates as the origins of the cosmic MeV gamma-ray background. If the cosmic MeV gamma-ray background radiation is dominated by non-thermal emission from Seyferts, the sensitivity of 10^-12 erg cm^-2 s^-1 is required to detect several hundred Seyferts in the entire sky. If FSRQs make up the cosmic MeV gamma-ray background, the sensitivity of ~4 x 10^-12 erg cm^-2 s^-1 is required to detect several hundred FSRQs following the recent FSRQ X-ray luminosity function. However, based on the latest FSRQ gamma-ray luminosity function, with which FSRQs can explain up to ~30% of the MeV background, we can expect several hundred FSRQs even with the sensitivity of 10^-11 erg cm^-2 s^-1 which is almost the same as the sensitivity goal of the next generation MeV telescopes.Comment: 9 pages, 5 figures, accepted for publication in PAS

Detection of extended millimeter emission in the host galaxy of 3C273 and its implications for QSO feedback via high dynamic range ALMA imaging

We estimate the amount of negative feedback energy injected into the ISM of the host galaxy of 3C273, a prototypical radio loud quasar. We obtained 93, 233 and 343 GHz continuum images with the Atacama Large Millimeter/Sub-millimeter Array (ALMA). After self calibration and point source subtraction, we reach an image dynamic range of $\sim 85000$ at 93\ GHz, $\sim 39000$ at 233\ GHz and $\sim 2500$ at 343\ GHz. These are currently the highest image dynamic range obtained using ALMA. We detect spatially extended millimeter emission associated with the host galaxy, cospatial with the Extended Emission Line Region (EELR) observed in the optical. The millimeter spectral energy distribution and comparison with centimeter data show that the extended emission cannot be explained by dust thermal emission, synchrotron or thermal bremsstrahlung arising from massive star formation. We interpret the extended millimeter emission as thermal bremsstrahlung from gas directly ionized by the central source. The extended flux indicates that at least $\sim 7\%$ of the bolometric flux of the nuclear source was used to ionize atomic hydrogen in the host galaxy. The ionized gas is estimated to be as massive as $10^{10}$ to $10^{11}\ \mathrm{M_\odot}$, but the molecular gas fraction with respect to the stellar mass is consistent with other ellipticals, suggesting that direct ionization ISM by the QSO may not be sufficient to suppress star formation, or we are witnessing a short timescale before negative feedback becomes observable. The discovery of a radio counterpart to EELRs provides a new pathway to studying the QSO-host ISM interaction

Stationary Rotating Strings as Relativistic Particle Mechanics

Stationary rotating strings can be viewed as geodesic motions in appropriate metrics on a two-dimensional space. We obtain all solutions describing stationary rotating strings in flat spacetime as an application. These rotating strings have infinite length with various wiggly shapes. Averaged value of the string energy, the angular momentum and the linear momentum along the string are discussed.Comment: 20pages, 7 figure