Which point sets admit a k-angulation?

For k >= 3, a k-angulation is a 2-connected plane graph in which every internal face is a k-gon. We say that a point set P admits a plane graph G if there is a straight-line drawing of G that maps V(G) onto P and has the same facial cycles and outer face as G. We investigate the conditions under which a point set P admits a k-angulation and find that, for sets containing at least 2k^2 points, the only obstructions are those that follow from Euler's formula.Comment: 13 pages, 7 figure

Containing Hydrogen Deflagrations

PresentationSchroeder and Holtappels (2005) published data on the explosion characteristics of hydrogen-air mixtures, looking at the effect of pressure and temperature on upper and lower explosive limits and the effect of pressure, temperature, and composition on explosion ratio, PEX/PO. They showed that the effect of increasing pressure on UEL and LEL is negligible to slightly advantageous, while the effect of increasing temperature was disadvantageous. They also showed that the explosion ratio was largely independent of operating pressure, but very dependent on temperature and composition of hydrogen-air mixtures. However, they did not develop their data to the point that it could be used as the basis of design and risk assessment. This paper uses the data published by Schroeder and Holtappels to develop equations that can be used to predict the extent of a hydrogen-air deflagration in a vessel and correlates those predictions to the nature of pressure vessel failures that are likely to be experienced as a result of such a deflagration

Thoughts on Barnette's Conjecture

We prove a new sufficient condition for a cubic 3-connected planar graph to be Hamiltonian. This condition is most easily described as a property of the dual graph. Let $G$ be a planar triangulation. Then the dual $G^*$ is a cubic 3-connected planar graph, and $G^*$ is bipartite if and only if $G$ is Eulerian. We prove that if the vertices of $G$ are (improperly) coloured blue and red, such that the blue vertices cover the faces of $G$, there is no blue cycle, and every red cycle contains a vertex of degree at most 4, then $G^*$ is Hamiltonian. This result implies the following special case of Barnette's Conjecture: if $G$ is an Eulerian planar triangulation, whose vertices are properly coloured blue, red and green, such that every red-green cycle contains a vertex of degree 4, then $G^*$ is Hamiltonian. Our final result highlights the limitations of using a proper colouring of $G$ as a starting point for proving Barnette's Conjecture. We also explain related results on Barnette's Conjecture that were obtained by Kelmans and for which detailed self-contained proofs have not been published.Comment: 12 pages, 7 figure

Renormalization Group Evolution in the type I + II seesaw model

We carefully analyze the renormalization group equations in the type I + II seesaw scenario in the extended standard model (SM) and minimal supersymmetric standard model (MSSM). Furthermore, we present analytic formulae of the mixing angles and phases and discuss the RG effect on the different mixing parameters in the type II seesaw scenario. The renormalization group equations of the angles have a contribution which is proportional to the mass squared difference for a hierarchical spectrum. This is in contrast to the inverse proportionality to the mass squared difference in the effective field theory case.Comment: 13 pages, 4 figures; corrected error due to wrong superfield normalization in RG equations (24-28,C1-4) as well as error in RG equations of mixing parameters (38,43); RG equations of mixing angles depend on Majorana phase

Hybrid Deterministic-Stochastic Methods for Data Fitting

Many structured data-fitting applications require the solution of an optimization problem involving a sum over a potentially large number of measurements. Incremental gradient algorithms offer inexpensive iterations by sampling a subset of the terms in the sum. These methods can make great progress initially, but often slow as they approach a solution. In contrast, full-gradient methods achieve steady convergence at the expense of evaluating the full objective and gradient on each iteration. We explore hybrid methods that exhibit the benefits of both approaches. Rate-of-convergence analysis shows that by controlling the sample size in an incremental gradient algorithm, it is possible to maintain the steady convergence rates of full-gradient methods. We detail a practical quasi-Newton implementation based on this approach. Numerical experiments illustrate its potential benefits.Comment: 26 pages. Revised proofs of Theorems 2.6 and 3.1, results unchange

Effect of Benzene and Ethylbenzene on the Transcription of methyl-\u3cem\u3etert\u3c/em\u3e-butyl Ether Degradation Genes of \u3cem\u3eMethylibium petroleiphilum\u3c/em\u3e PM1

Methyl-tert-butyl ether (MTBE) and its degradation by-product, tert-butyl alcohol (TBA), are widespread contaminants detected frequently in groundwater in California. Since MTBE was used as a fuel oxygenate for almost two decades, leaking underground fuel storage tanks are an important source of contamination. Gasoline components such as BTEX (benzene, toluene, ethylbenzene and xylenes) are often present in mixtures with MTBE and TBA. Investigations of interactions between BTEX and MTBE degradation have not yielded consistent trends, and the molecular mechanisms of BTEX compounds’ impact on MTBE degradation are not well understood. We investigated trends in transcription of biodegradation genes in the MTBE-degrading bacterium, Methylibium petroleiphilum PM1 upon exposure to MTBE, TBA, ethylbenzene and benzene as individual compounds or in mixtures. We designed real-time quantitative PCR assays to target functional genes of strain PM1 and provide evidence for induction of genes mdpA (MTBE monooxygenase), mdpJ (TBA hydroxylase) and bmoA (benzene monooxygenase) in response to MTBE, TBA and benzene, respectively. Delayed induction of mdpA and mdpJ transcription occurred with mixtures of benzene and MTBE or TBA, respectively. bmoA transcription was similar in the presence of MTBE or TBA with benzene as in their absence. Our results also indicate that ethylbenzene, previously proposed as an inhibitor of MTBE degradation in some bacteria, inhibits transcription of mdpA, mdpJ and bmoAgenes in strain PM1

Gene \u3cem\u3emdpC\u3c/em\u3e Plays a Regulatory Role in the Methyl-\u3cem\u3etert\u3c/em\u3e-butyl Ether Degradation Pathway of \u3cem\u3eMethylibium petroleiphilum\u3c/em\u3e Strain PM1

Among the few bacteria known to utilize methyl tert-butyl ether (MTBE) as a sole carbon source, Methylibium petroleiphilum PM1 is a well-characterized organism with a sequenced genome; however, knowledge of the genetic regulation of its MTBE degradation pathway is limited. We investigated the role of a putative transcriptional activator gene, mdpC, in the induction of MTBE-degradation genes mdpA (encoding MTBE monooxygenase) and mdpJ (encoding tert-butyl alcohol hydroxylase) of strain PM1 in a gene-knockout mutant mdpC−. We also utilized quantitative reverse transcriptase PCR assays targeting genes mdpA, mdpJ and mdpC to determine the effects of the mutation on transcription of these genes. Our results indicate that gene mdpC is involved in the induction of both mdpA and mdpJ in response to MTBE and tert-butyl alcohol (TBA) exposure in PM1. An additional independent mechanism may be involved in the induction of mdpJ in the presence of TBA

The Decomposition of Hydrazine in the Gas Phase and over an Iridium Catalyst

Hydrazine is an important rocket fuel, used as both a monopropellant and a bipropellant. This paper presents theoretical results to complement the extensive experimental studies of the gas phase and Ir catalyzed decompositions involved in the monopropellant applications of hydrazine. Gas phase electronic structure theory calculations that include electron correlation predict that numerous molecular and free radical reactions occur within the same energy range as the basic free radical pathways: NN bond breaking around 65 kcal/mol and NH bond breaking around 81 kcal/mol. The data suggest that a revision to existing kinetics modeling is desirable, based on the energetics and the new elementary steps reported herein. A supported Ir6 octahedron model for the Shell 405 Iridium catalyst used in thrusters was developed. Self-Consistent Field and electron correlation calculations (with core potentials and associated basis sets) find a rich chemistry for hydrazine on this catalyst model. The model catalyst provides dramatically lower NN and NH bond cleavage energies and an even smaller barrier to breaking the NH bond by NH2 abstractions. Thus, the low temperature decomposition over the catalyst is interpreted in terms of consecutive NH2 abstractions to produce ammonia and nitrogen. The higher temperature channel, which has hydrogen and nitrogen products, may be due to a mixture of two mechanisms. These two mechanisms are successive NH cleavages with surface H + H recombinations, and the same type of assisted H2 eliminations found to occur in the gas phase part of this study

Bringing Darkness to Light: The Influence of Auditor Quality and Audit Committee Expertise on the Timeliness of Financial Statement Restatement Disclosures

This study investigates whether auditor quality and audit committee expertise are associated with improved financial reporting timeliness as measured by the duration of a financial statement restatement’s ‘‘dark period.’’ The restatement dark period represents the length of time between a company’s discovery that it will need to restate financial data and the subsequent disclosure of the restatement’s effect on earnings. For a sample of dark restatements disclosed between 2004 and 2009, we find that companies that engage Big 4 auditors have shorter dark periods than companies that do not engage Big 4 auditors. We also find that companies with more financial experts on the audit committee have shorter dark periods, but only when such financial expertise relates specifically to accounting. Finally, companies with audit committee chairs that have accounting financial expertise provide the most timely disclosures, as the dark periods for these firms are reduced by approximately 38 percent. Our results suggest that both auditor and audit committee expertise are associated with the timely disclosure of restatement details

Does Methane Invert through Square Planar?

MCSCF calculations using a triple-t basis set augmented with diffuse and polarization functions are used to probe that part of the singlet methane potential energy surface that pertains to the inversion of CH4 from one t~trahedral structure t.o another. The true inversion transition state is found to have a distorted C, structure, quite different both ge?me.tncally ~nd energetically from the previously presumed square planar saddle point. At the secondorder configuration mte.ractl~n.level of theory, the barrier to inversion is predicted to be just 7-8 kcaljmol higher in energy than the bond diSSOCiation energy for the first C-H bond cleavage in methane