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Systematic analysis of the incoming quark energy loss in cold nuclear matter

The investigation into the fast parton energy loss in cold nuclear matter is crucial for a good understanding of the parton propagation in hot-dense medium. By means of four typical sets of nuclear parton distributions and three parametrizations of quark energy loss, the parameter values in quark energy loss expressions are determined from a leading order statistical analysis of the existing experimental data on nuclear Drell-Yan differential cross section ratio as a function of the quark momentum fraction. It is found that with independence on the nuclear modification of parton distributions, the available experimental data from lower incident beam energy rule out the incident-parton momentum fraction quark energy loss. Whether the quark energy loss is linear or quadratic with the path length is not discriminated. The global fit of all selected data gives the quark energy loss per unit path length {\alpha} = 1.21\pm0.09 GeV/fm by using nuclear parton distribution functions determined only by means of the world data on nuclear structure function. Our result does not support the theoretical prediction: the energy loss of an outgoing quark is three times larger than that of an incoming quark approaching the nuclear medium. It is desirable that the present work can provide useful reference for the Fermilab E906/SeaQuest experiment

Cooling mechanical resonators to quantum ground state from room temperature

Ground-state cooling of mesoscopic mechanical resonators is a fundamental requirement for test of quantum theory and for implementation of quantum information. We analyze the cavity optomechanical cooling limits in the intermediate coupling regime, where the light-enhanced optomechanical coupling strength is comparable with the cavity decay rate. It is found that in this regime the cooling breaks through the limits in both the strong and weak coupling regimes. The lowest cooling limit is derived analytically at the optimal conditions of cavity decay rate and coupling strength. In essence, cooling to the quantum ground state requires $Q_{\mathrm{m}}>2.4n_{\mathrm{th}}$, with $Q_{\mathrm{m}}$ being the mechanical quality factor and $n_{\mathrm{th}}$ being the thermal phonon number. Remarkably, ground-state cooling is achievable starting from room temperature, when mechanical $Q$-frequency product $Q_{\mathrm{m}}{\nu>1.5}\times10^{13}$, and both of the cavity decay rate and the coupling strength exceed the thermal decoherence rate. Our study provides a general framework for optimizing the backaction cooling of mesoscopic mechanical resonators

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

Spin alignment of vector meson in e+e- annihilation at Z0 pole

We calculate the spin density matrix of the vector meson produced in e+e- annihilation at Z^0 pole. We show that the data imply a significant polarization for the antiquark which is created in the fragmentation process of the polarized initial quark and combines with the fragmenting quark to form the vector meson. The direction of polarization is opposite to that of the fragmenting quark and the magnitude is of the order of 0.5. A qualitative explanation of this result based on the LUND string fragmentation model is given.Comment: 15 pages, 2 fgiures; submitted to Phys. Rev.