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

Leibniz 2-algebras and twisted Courant algebroids

In this paper, we give the categorification of Leibniz algebras, which is equivalent to 2-term sh Leibniz algebras. They reveal the algebraic structure of omni-Lie 2-algebras introduced in \cite{omniLie2} as well as twisted Courant algebroids by closed 4-forms introduced in \cite{4form}. We also prove that Dirac structures of twisted Courant algebroids give rise to 2-term $L_\infty$-algebras and geometric structures behind them are exactly $H$-twisted Lie algebroids introduced in \cite{Grutzmann}.Comment: 22 pages, to appear in Comm. Algebr

Next-to-leading order QCD predictions for pair production of neutral Higgs bosons at the CERN Large Hadron Collider

We present the calculations of the complete NLO inclusive total cross sections for pair production of neutral Higgs bosons through $b\bar b$ annihilation in the minimal supersymmetric standard model at the CERN Large Hadron Collider. In our calculations, we used both the DREG scheme and the DRED scheme and found that the NLO total cross sections in the above two schemes are the same. Our results show that the $b\bar b$-annihilation contributions can exceed ones of $gg$ fusion and $q\bar q$ annihilation for $h^0H^0$, $A^0h^0$ and $A^0H^0$ productions when $\tan\beta$ is large. In the case of $\mu>0$, the NLO corrections enhance the LO total cross sections significantly, which can reach a few tens percent, while for $\mu<0$, the corrections are relatively small, and are negative in most parameter space. Moreover, the NLO QCD corrections can reduce the dependence of the total cross sections on the renormalization/factorization scale, especially for $\mu<0$. We also use the CTEQ6.1 PDF sets to estimate the uncertainty of LO and NLO total cross sections, and find that the uncertainty arising from the choice of PDFs increases with the increasing $m_{A^0}$.Comment: 43 pages, 16 figures, minor changes, some references added, a version to appear in PR

Threshold Resummation Effects in Direct Top Quark Production at Hadron Colliders

We investigate the threshold-enhanced QCD corrections to the cross sections for direct top quark productions induced by model-independent flavor changing neutral current couplings at hadron colliders. We use the soft-collinear effective theory to describe the incoming massless partons and use the heavy quark effective theory to treat the top quark. Then we construct the flavor changing operator based on the above effective theories, and resum the large logarithms near threshold arising from soft gluon emission. Our results show that the resummed QCD corrections further enhance the next-to-leading order cross sections significantly. Moreover, the resummation effects vastly reduce the dependence of the cross sections on the renormalization and factorization scales, especially in cases where the next-to-leading order results behave worse than the leading order results. Our results are more sensitive to the new physics effects. If signals of direct top quark production are found in future experiments, it is more appropriate to use our results as the theoretical inputs for extracting the anomalous couplings.Comment: 5 pages, 4 figures, use revtex4 and amsmath; version to appear in Phys. Rev.

QCD Effects in High Energy Processes

In this talk, some important QCD effects in Higgs physics, supersymmetry and top physics, as well as the factorization and resummation techniques in QCD are reviewed.Comment: LaTeX, 13 pages, uses ws-ijmpa.cls. Based on an invited talk at the International Conference on QCD and Hadronic Physics, Beijing, China, June 16--20, 2005. Minor change

Next-to-Leading Order QCD Corrections to the Direct Top Quark Production via Model-independent FCNC Couplings at Hadron Colliders

We calculated the next-to-leading order (NLO) QCD corrections to the cross sections for direct top quark productions induced by model--independent flavour changing neutral current couplings at hadron colliders. The NLO results increase the experimental sensitivity to the anomalous couplings. Our results show that the NLO QCD corrections enhance the leading order (LO) total cross sections at the Tevatron Run 2 about 60% for both of $\kappa_{tc}^g$ and $\kappa_{tu}^g$ couplings, and enhance the LO total cross sections at the LHC about 40% for $\kappa_{tc}^g$ couplings and 50% for $\kappa_{tu}^g$ couplings, respectively. Moreover, the NLO QCD corrections vastly reduce the dependence of the total cross sections on the renormalization or factorization scale, which leads to increased confidence in predictions based on these results.Comment: 15 pages, 4 figures; published versio

Dense blocks of energetic ions driven by multi-petawatt lasers

Laser-driven ion accelerators have the advantages of compact size, high density, and short bunch duration over conventional accelerators. Nevertheless, it is still challenging to simultaneously enhance the yield and quality of laser-driven ion beams for practical applications. Here we propose a scheme to address this challenge via the use of emerging multi-petawatt lasers and a density-modulated target. The density-modulated target permits its ions to be uniformly accelerated as a dense block by laser radiation pressure. In addition, the beam quality of the accelerated ions is remarkably improved by embedding the target in a thick enough substrate, which suppresses hot electron refluxing and thus alleviates plasma heating. Particle-in-cell simulations demonstrate that almost all ions in a solid-density plasma of a few microns can be uniformly accelerated to about 25% of the speed of light by a laser pulse at an intensity around 1022 W/cm2. The resulting dense block of energetic ions may drive fusion ignition and more generally create matter with unprecedented high energy density.Comment: 18 pages, 4 figure

Mesons and Nucleons in Soft-Wall AdS/QCD with Constrained Infrared Background

The purpose of this paper is to further study the soft-wall AdS/QCD model with constrained IR background. By including a quartic bulk scalar potential we study various meson and nucleon spectra. This model naturally realizes the asymptotical linearity of these mass spectra simultaneously, together with correctly pattern of explicit and dynamical chiral symmetry breaking. The agreement between the theoretical calculations and the experimental data is good.Comment: 17 pages,5 table