Edge Roman domination on graphs

An edge Roman dominating function of a graph $G$ is a function $f\colon E(G) \rightarrow \{0,1,2\}$ satisfying the condition that every edge $e$ with $f(e)=0$ is adjacent to some edge $e'$ with $f(e')=2$. The edge Roman domination number of $G$, denoted by $\gamma'_R(G)$, is the minimum weight $w(f) = \sum_{e\in E(G)} f(e)$ of an edge Roman dominating function $f$ of $G$. This paper disproves a conjecture of Akbari, Ehsani, Ghajar, Jalaly Khalilabadi and Sadeghian Sadeghabad stating that if $G$ is a graph of maximum degree $\Delta$ on $n$ vertices, then $\gamma_R'(G) \le \lceil \frac{\Delta}{\Delta+1} n \rceil$. While the counterexamples having the edge Roman domination numbers $\frac{2\Delta-2}{2\Delta-1} n$, we prove that $\frac{2\Delta-2}{2\Delta-1} n + \frac{2}{2\Delta-1}$ is an upper bound for connected graphs. Furthermore, we provide an upper bound for the edge Roman domination number of $k$-degenerate graphs, which generalizes results of Akbari, Ehsani, Ghajar, Jalaly Khalilabadi and Sadeghian Sadeghabad. We also prove a sharp upper bound for subcubic graphs. In addition, we prove that the edge Roman domination numbers of planar graphs on $n$ vertices is at most $\frac{6}{7}n$, which confirms a conjecture of Akbari and Qajar. We also show an upper bound for graphs of girth at least five that is 2-cell embeddable in surfaces of small genus. Finally, we prove an upper bound for graphs that do not contain $K_{2,3}$ as a subdivision, which generalizes a result of Akbari and Qajar on outerplanar graphs

Seebeck Coefficients in Nanoscale Junctions: Effects of Electron-vibration Scattering and Local Heating

We report first-principles calculations of inelastic Seebeck coefficients in an aluminum monatomic junction. We compare the elastic and inelastic Seebeck coefficients with and without local heating. In the low temperature regime, the signature of normal modes in the profiles of the inelastic Seebeck effects is salient. The inelastic Seebeck effects are enhanced by the normal modes, and further magnified by local heating. In the high temperature regime, the inelastic Seebeck effects are weakly suppressed due to the quasi-ballistic transport.Comment: 3 Figure

The molecular evolution of PL10 homologs

<p>Abstract</p> <p>Background</p> <p><it>PL10 </it>homologs exist in a wide range of eukaryotes from yeast, plants to animals. They share a DEAD motif and belong to the DEAD-box polypeptide 3 (<it>DDX3</it>) subfamily with a major role in RNA metabolism. The lineage-specific expression patterns and various genomic structures and locations of <it>PL10 </it>homologs indicate these homologs have an interesting evolutionary history.</p> <p>Results</p> <p>Phylogenetic analyses revealed that, in addition to the sex chromosome-linked <it>PL10 </it>homologs, <it>DDX3X </it>and <it>DDX3Y</it>, a single autosomal <it>PL10 </it>putative homologous sequence is present in each genome of the studied non-rodent eutheria. These autosomal homologous sequences originated from the retroposition of <it>DDX3X </it>but were pseudogenized during the evolution. In rodents, besides <it>Ddx3x </it>and <it>Ddx3y</it>, we found not only <it>Pl10 </it>but another autosomal homologous region, both of which also originated from the <it>Ddx3x </it>retroposition. These retropositions occurred after the divergence of eutheria and opossum. In contrast, an additional X putative homologous sequence was detected in primates and originated from the transposition of <it>DDX3Y</it>. The evolution of <it>PL10 </it>homologs was under positive selection and the elevated Ka/Ks ratios were observed in the eutherian lineages for <it>DDX3Y </it>but not <it>PL10 </it>and <it>DDX3X</it>, suggesting relaxed selective constraints on <it>DDX3Y</it>. Contrary to the highly conserved domains, several sites with relaxed selective constraints flanking the domains in the mammalian <it>PL10 </it>homologs may play roles in enhancing the gene function in a lineage-specific manner.</p> <p>Conclusion</p> <p>The eutherian <it>DDX3X/DDX3Y </it>in the X/Y-added region originated from the translocation of the ancient <it>PL10 </it>ortholog on the ancestral autosome, whereas the eutherian <it>PL10 </it>was retroposed from <it>DDX3X</it>. In addition to the functional <it>PL10</it>/<it>DDX3X</it>/<it>DDX3Y</it>, conserved homologous regions on the autosomes and X chromosome are present. The autosomal homologs were also derived from <it>DDX3X</it>, whereas the additional X-homologs were derived from <it>DDX3Y</it>. These homologs were apparently pseudogenized but may still be active transcriptionally. The evolution of <it>PL10 </it>homologs was positively selected.</p

Nucleon Mass Splitting at Finite Isospin Chemical Potential

We investigate nucleon mass splitting at finite isospin chemical potential in the frame of two flavor Nambu--Jona-Lasinio model. It is analytically proved that, in the phase with explicit isospin symmetry breaking the proton mass decreases and the neutron mass increases linearly in the isospin chemical potential.Comment: 3 pages and no figure

Energetics and energy scaling of quasi-monoenergetic protons in laser radiation pressure acceleration

Theoretical and computational studies of the ion energy scaling of the radiation pressure acceleration of an ultra-thin foil by short pulse intense laser irradiation are presented. To obtain a quasi-monoenergetic ion beam with an energy spread of less than 20%, two-dimensional particle-in-cell simulations show that the maximum energy of the quasi-monoenergetic ion beam is limited by self-induced transparency at the density minima caused by the Rayleigh-Taylor instability. For foils of optimal thickness, the time over which Rayleigh-Taylor instability fully develops and transparency occurs is almost independent of the laser amplitude. With a laser power of about one petawatt, quasi-monogenetic protons with 200 MeV and carbon ions with 100 MeV per nucleon can be obtained, suitable for particle therapy applications

Perturbation-based Non-perturbative Method

This paper presents a non-perturbative method for solving eigenproblems. This method applies to almost all potentials and provides non-perturbative approximations for any energy level. The method converts an eigenproblem into a perturbation problem, obtains perturbation solutions through standard perturbation theory, and then analytically continues the perturbative solution into a non-perturbative solution

Measuring fraud in insurance industry: The case of automobile insurance in Taiwan

By conducting an extensive exploration on claim data, this paper attempts to investigate the fraud problem in Taiwan automobile physical damage insurance. Based on the different claim patterns between data in calendar year and policy year, excess claims are significantly identified in the last month of policy year. Censored regression provides robust estimation concerning the sources of the fraud payment