Minimum Weight Resolving Sets of Grid Graphs

For a simple graph $G=(V,E)$ and for a pair of vertices $u,v \in V$, we say that a vertex $w \in V$ resolves $u$ and $v$ if the shortest path from $w$ to $u$ is of a different length than the shortest path from $w$ to $v$. A set of vertices ${R \subseteq V}$ is a resolving set if for every pair of vertices $u$ and $v$ in $G$, there exists a vertex $w \in R$ that resolves $u$ and $v$. The minimum weight resolving set problem is to find a resolving set $M$ for a weighted graph $G$ such that$\sum_{v \in M} w(v)$ is minimum, where $w(v)$ is the weight of vertex $v$. In this paper, we explore the possible solutions of this problem for grid graphs $P_n \square P_m$ where $3\leq n \leq m$. We give a complete characterisation of solutions whose cardinalities are 2 or 3, and show that the maximum cardinality of a solution is $2n-2$. We also provide a characterisation of a class of minimals whose cardinalities range from $4$ to $2n-2$.Comment: 21 pages, 10 figure

Influence of trace erythromycin and eryhthromycin-H2O on carbon and nutrients removal and on resistance selection in sequencing batch reactors (SBRs).

Three sequencing batch reactors (SBRs) were operated in parallel to study the effects of trace erythromycin (ERY) and ERY-H2O on the treatment of a synthetic wastewater. Through monitoring (1) daily effluents and (2) concentrations of nitrogen (N) and phosphorous (P) in certain batch cycles of the three reactors operated from transient to steady states, the removal of carbon, N, and P was affected negligibly by ERY (100 microg/L) or ERY-H2O (50 microg/L) when compared with the control reactor. However, through analyzing microbial communities of the three steady state SBRs on high-density microarrays (Phylo-Chip), ERY, and ERY-H2O had pronounced effects on the community composition of bacteria related to N and P removal, leading to diversity loss and abundance change. The above observations indicated that resistant bacteria were selected upon exposure to ERY or ERY-H2O. Shortterm batch experiments further proved the resistance and demonstrated that ammonium oxidation (56-95%) was inhibited more significantly than nitrite oxidation (18-61%) in the presence of ERY (100, 400, or 800 microg/L). Therefore, the presence of ERY or ERY-H2O (at microg/L levels) shifted the microbial community and selected resistant bacteria, which may account for the negligible influence of the antibiotic ERY or its derivative ERY-H2O (at microg/L levels) on carbon, N, and P removal in the SBRs

Band structure analysis of the conduction-band mass anisotropy in 6H and 4H SiC

The band structures of 6H and 4H SiC calculated by means of the FP-LMTO method are used to determine the effective mass tensors for their conduction-band minima. The results are shown to be consistent with recent optically detected cyclotron resonance measurements and predict an unusual band filling dependence for 6H-SiC.Comment: 5 pages including 4 postscript figures incorporated with epsfig figs. available as part 2: sicfig.uu self-extracting file to appear in Phys. Rev. B: Aug. 15 (Rapid Communications

Microstructural Effects During Chemical Mechanical Planarization of Copper

Novel die-stacking schema using through-wafer interconnects require vias to be filled with electroplated Cu, resulting in thick copper films, and requiring an aggressive first-step CMP. This work investigates the effects of microstructure on CMP of copper films, which are not presently well understood. Bulk and local removal rates were investigated for several different microstructures. Surface orientation maps were created and the orientations of individual grains were correlated with topographical data to elucidate local removal behavior. Cu removal depends on the details of the microstructure, and certain microstructures allowed for either faster or more uniform removal of thick Cu films

Observational Tests and Predictive Stellar Evolution II: Non-standard Models

We examine contributions of second order physical processes to results of stellar evolution calculations amenable to direct observational testing. In the first paper in the series (Young et al. 2001) we established baseline results using only physics which are common to modern stellar evolution codes. In the current paper we establish how much of the discrepancy between observations and baseline models is due to particular elements of new physics. We then consider the impact of the observational uncertainties on the maximum predictive accuracy achievable by a stellar evolution code. The sun is an optimal case because of the precise and abundant observations and the relative simplicity of the underlying stellar physics. The Standard Model is capable of matching the structure of the sun as determined by helioseismology and gross surface observables to better than a percent. Given an initial mass and surface composition within the observational errors, and no additional constraints for which the models can be optimized, it is not possible to predict the sun's current state to better than ~7%. Convectively induced mixing in radiative regions, seen in multidimensional hydrodynamic simulations, dramatically improves the predictions for radii, luminosity, and apsidal motions of eclipsing binaries while simultaneously maintaining consistency with observed light element depletion and turnoff ages in young clusters (Young et al. 2003). Systematic errors in core size for models of massive binaries disappear with more complete mixing physics, and acceptable fits are achieved for all of the binaries without calibration of free parameters. The lack of accurate abundance determinations for binaries is now the main obstacle to improving stellar models using this type of test.Comment: 33 pages, 8 figures, accepted for publication in the Astrophysical Journa