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

Molecular epidemiological study of clinical Acinetobacter baumannii isolates: phenotype switching of antibiotic resistance

BackgroundThe presence of clinical Acinetobacter baumannii (A. baumannii) isolates with differing antibiotic resistance phenotypes in the same patient causes difficulties and confusion in treatment. This phenomenon may be caused by reasons such as cross-infection from neighboring patients that switches to different A. baumannii strain, natural mutation of A. baumannii, inducing of different antibiotic resistance genes expression or acquisition of genes conferring resistance from another source. To elucidate this question, clinical A. baumannii strains, isolated from the same individual patients, showed antibiotic resistance phenotypes switching during the same hospitalization period, were attentively collected for further analysis. Molecular approaches for phylogenetic analysis, including pulsed field gel electrophoresis, multilocus sequence typing, and short tandem repeat analysis, were employed for the chronological studies.FindingsOur results showed that antibiotic resistance phenotype switching could have occurred as a result through both cross-infection and natural mutation roots. Our results also suggest that rapid phenotype switching between paired isolates could occur during one single course of antibiotic treatment.ConclusionsThough cross infection caused antibiotic resistance phenotype switching does occur, natural mutation of A. baumannii isolates is particularly cautious for antibiotic treatment

Risk factor analysis for extended-spectrum β-lactamase-producing Enterobacter cloacae bloodstream infections in central Taiwan

BackgroundEnterobacter cloacae (E.cloacae) bloodstream infection (EcBSI) is an important cause of morbidity and mortality, with an increasing incidence in our hospital. We wanted to elucidate the risk factors of mortality among patients with ESBL-positive EcBSI in central Taiwan.MethodsWe ordered the clinical and microbiological data of cases with diagnosis of EcBSI, and analyzed the isolates by using antibiotyping, detection of ESBL, detection of class 1 integron and genomic fingerprinting by pulsed-field gel electrophoresis (PFGE).ResultsSeventy episodes of EcBSI from 70 patients (56 hospital-acquired infections) were enrolled. Significant differences were found between ESBL-positive and ESBL-negative isolates with regard to risk factors, including the diseases severity (p = 0.03), category of health care-associated infection (p = 0.04), prior use of antibiotics (p = 0.023), and prior use of a ventilator (p = 0.037). A significant difference in mortality between two groups (p = 0.004) was determined using the chi-square test, and a trend in mortality between two groups (p = 0.006, OR = 4.750, 95% C.I.=1.573-14.344) was determined using univariate logistic regression analysis. The predominant clone in ESBL-positive strains was associated with a higher mortality rate but not with the presence of the integron.ConclusionsThe study disclosed four types of clinical characteristics to obtain ESBL-positive EcBSI, and there was a trend in mortality too. We suggested the need to review antibiotic prescription practices, and the possible need to consider ESBL-positive strains in empirical treatment of bloodstream infection

Quantum Radiation Properties of Dirac Particles in General Nonstationary Black Holes

Quantum radiation properties of Dirac particles in general nonstationary black holes in the general case are investigated by both using the method of generalized tortoise coordinate transformation and considering simultaneously the asymptotic behaviors of the first-order and second-order forms of Dirac equation near the event horizon. It is generally shown that the temperature and the shape of the event horizon of this kind of black holes depend on both the time and different angles. Further, we give a general expression of the new extra coupling effect in thermal radiation spectrum of Dirac particles which is absent from the thermal radiation spectrum of scalar particles. Also, we reveal a relationship that is ignored before between thermal radiation and nonthermal radiation in the case of scalar particles, which is that the chemical potential in thermal radiation spectrum is equal to the highest energy of the negative energy state of scalar particles in nonthermal radiation for general nonstationary black holes