On the weak Roman domination number of lexicographic product graphs

A vertex $v$ of a graph $G=(V,E)$ is said to be undefended with respect to a function $f: V \longrightarrow \{0,1,2\}$ if $f(v)=0$ and $f(u)=0$ for every vertex $u$ adjacent to $v$. We call the function $f$ a weak Roman dominating function if for every $v$ such that $f(v)=0$ there exists a vertex $u$ adjacent to $v$ such that $f(u)\in \{1,2\}$ and the function $f': V \longrightarrow \{0,1,2\}$ defined by $f'(v)=1$, $f'(u)=f(u)-1$ and $f'(z)=f(z)$ for every $z\in V \setminus\{u,v\}$, has no undefended vertices. The weight of $f$ is $w(f)=\sum_{v\in V(G) }f(v)$. The weak Roman domination number of a graph $G$, denoted by $\gamma_r(G)$, is the minimum weight among all weak Roman dominating functions on $G$. Henning and Hedetniemi [Discrete Math. 266 (2003) 239-251] showed that the problem of computing $\gamma_r(G)$ is NP-Hard, even when restricted to bipartite or chordal graphs. This suggests finding $\gamma_r(G)$ for special classes of graphs or obtaining good bounds on this invariant. In this article, we obtain closed formulae and tight bounds for the weak Roman domination number of lexicographic product graphs in terms of invariants of the factor graphs involved in the product

Single-particle versus pair condensation of hard-core bosons with correlated hopping

We investigate the consequences of correlated hopping on the ground state properties of hard-core bosons on a square lattice as revealed by extensive exact diagonalizations and quantum Monte Carlo simulations. While for non interacting hard-core bosons the effective attraction induced by the correlated hopping leads to phase separation at low density, we show that a modest nearest-neighbor repulsion suppresses phase separation, leading to a remarkable low-density pairing phase with no single particle Bose-Einstein condensation but long-range two-particle correlations, signaling a condensation of pairs. We also explain why the unusual properties of the pairing phase are a real challenge for standard one-worm quantum Monte Carlo simulations.Comment: 8 pages, 7 figure

Electronic Correlations in CoO2, the Parent Compound of Triangular Cobaltates

A 59Co NMR study of CoO2, the x=0 end member of AxCoO2 (A = Na, Li...) cobaltates, reveals a metallic ground state, though with clear signs of strong electron correlations: low-energy spin fluctuations develop at wave vectors q different from 0 and a crossover to a Fermi-liquid regime occurs below a characteristic temperature T*~7 K. Despite some uncertainty over the exact cobalt oxidation state n this material, the results show that electronic correlations are revealed as x is reduced below 0.3. The data are consistent with NaxCoO2 being close to the Mott transition in the x -> 0 limit.Comment: 4 pages, submitte

High-throughput synthesis of thermoelectric Ca3_3Co4_4O9_9 films

Properties of complex oxide thin films can be tuned over a range of values as a function of mismatch, composition, orientation, and structure. Here, we report a strategy for growing structured epitaxial thermoelectric thin films leading to improved Seebeck coefficient. Instead of using single-crystal sapphire substrates to support epitaxial growth, Ca$_3$Co$_4$O$_9$ films are deposited, using the Pulsed Laser Deposition technique, onto Al$_2$O$_3$ polycrystalline substrates textured by Spark Plasma Sintering. The structural quality of the 2000 \AA thin film was investigated by Transmission Electron Microscopy, while the crystallographic orientation of the grains and the epitaxial relationships were determined by Electron Back Scatter Diffraction. The use of a polycrystalline ceramic template leads to structured films that are in good local epitaxial registry. The Seebeck coefficient is about 170 $\mu$V/K at 300 K, a typical value of misfit material with low carrier density. This high-throughput process, called combinatorial substrate epitaxy, appears to facilitate the rational tuning of functional oxide films, opening a route to the epitaxial synthesis of high quality complex oxides.Comment: Submitted to Applied Physics Letters (2013

Large Liquid Rocket Testing: Strategies and Challenges

Rocket propulsion development is enabled by rigorous ground testing in order to mitigate the propulsion systems risks that are inherent in space flight. This is true for virtually all propulsive devices of a space vehicle including liquid and solid rocket propulsion, chemical and non-chemical propulsion, boost stage and in-space propulsion and so forth. In particular, large liquid rocket propulsion development and testing over the past five decades of human and robotic space flight has involved a combination of component-level testing and engine-level testing to first demonstrate that the propulsion devices were designed to meet the specified requirements for the Earth to Orbit launchers that they powered. This was followed by a vigorous test campaign to demonstrate the designed propulsion articles over the required operational envelope, and over robust margins, such that a sufficiently reliable propulsion system is delivered prior to first flight. It is possible that hundreds of tests, and on the order of a hundred thousand test seconds, are needed to achieve a high-reliability, flight-ready, liquid rocket engine system. This paper overviews aspects of earlier and recent experience of liquid rocket propulsion testing at NASA Stennis Space Center, where full scale flight engines and flight stages, as well as a significant amount of development testing has taken place in the past decade. The liquid rocket testing experience discussed includes testing of engine components (gas generators, preburners, thrust chambers, pumps, powerheads), as well as engine systems and complete stages. The number of tests, accumulated test seconds, and years of test stand occupancy needed to meet varying test objectives, will be selectively discussed and compared for the wide variety of ground test work that has been conducted at Stennis for subscale and full scale liquid rocket devices. Since rocket propulsion is a crucial long-lead element of any space system acquisition or development, the appropriate plan and strategy must be put in place at the outset of the development effort. A deferment of this test planning, or inattention to strategy, will compromise the ability of the development program to achieve its systems reliability requirements and/or its development milestones. It is important for the government leadership and support team, as well as the vehicle and propulsion development team, to give early consideration to this aspect of space propulsion and space transportation work

Australian Sphingidae – DNA Barcodes Challenge Current Species Boundaries and Distributions

© 2014 Rougerie et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. The attached file is the published version of the article