The Cover Pebbling Number of Graphs

A pebbling move on a graph consists of taking two pebbles off of one vertex and placing one pebble on an adjacent vertex. In the traditional pebbling problem we try to reach a specified vertex of the graph by a sequence of pebbling moves. In this paper we investigate the case when every vertex of the graph must end up with at least one pebble after a series of pebbling moves. The cover pebbling number of a graph is the minimum number of pebbles such that however the pebbles are initially placed on the vertices of the graph we can eventually put a pebble on every vertex simultaneously. We find the cover pebbling numbers of trees and some other graphs. We also consider the more general problem where (possibly different) given numbers of pebbles are required for the vertices.Comment: 12 pages. Submitted to Discrete Mathematic

Design Improvements Enhance Dry Gas Seal's Ability To Handle Reverse Pressurization.

LecturePg. 149-156Within the past three years, refrigeration compressors operating intermittently at subatmospheric pressures have experienced two dry gas seal failures which have been attributed, either all or in part, to reverse pressurization of the seal. Failures of this type occur while operating at subatmospheric suction pressures and/or high seal vent pressures (flare header). These failures have resulted in significant production losses and maintenance costs. The design of the seal and buffer system controls, failure analysis, corrective actions implemented by seal design changes, and buffer gas control improvements are discussed herein. Emphasis is given to the seal manufacturer's advanced modelling capabilities and operating/ testing experience which has allowed refinements in the seal's design to tolerate reverse pressurization. Limitations of these design changes are also discussed

Dry Gas Seal Retrofit.

LecturePg. 221-230Conventionally lubricated shaft sealing systems have long been known to be unreliable, high in maintenance and in some cases hazardous in centrifugal compressors. Labyrinth sealing systems, while generally low in maintenance, are extremely high in operating costs (product loss and steam costs). Dry gas lubricated sealing systems retrofitted into centrifugal compressors are now recognized as a cost effective means of improving equipment performance. Step by step requirements for a successful retrofit of a centrifugal compressor with dry running gas lubricated seals is presented based upon experience and the review of numerous retrofit projects in which dry gas seals are now operating. A description and the advantages of dry gas seals are provided, along with a feasibility study to determine whether or not a retrofit is technically, environmentally, and economically desirable. A detailed proposal request narrative and steps suggested in awarding the contract are shown. This is followed by installation procedures for the dry gas seals along with the commissioning of the newly retrofitted machine. The significant issues presented are based on actual case histories

Pseudomonas aeruginosa Population Structure Revisited

At present there are strong indications that Pseudomonas aeruginosa exhibits an epidemic population structure; clinical isolates are indistinguishable from environmental isolates, and they do not exhibit a specific (disease) habitat selection. However, some important issues, such as the worldwide emergence of highly transmissible P. aeruginosa clones among cystic fibrosis (CF) patients and the spread and persistence of multidrug resistant (MDR) strains in hospital wards with high antibiotic pressure, remain contentious. To further investigate the population structure of P. aeruginosa, eight parameters were analyzed and combined for 328 unrelated isolates, collected over the last 125 years from 69 localities in 30 countries on five continents, from diverse clinical (human and animal) and environmental habitats. The analysed parameters were: i) O serotype, ii) Fluorescent Amplified-Fragment Length Polymorphism (FALFP) pattern, nucleotide sequences of outer membrane protein genes, iii) oprI, iv) oprL, v) oprD, vi) pyoverdine receptor gene profile (fpvA type and fpvB prevalence), and prevalence of vii) exoenzyme genes exoS and exoU and viii) group I pilin glycosyltransferase gene tfpO. These traits were combined and analysed using biological data analysis software and visualized in the form of a minimum spanning tree (MST). We revealed a network of relationships between all analyzed parameters and non-congruence between experiments. At the same time we observed several conserved clones, characterized by an almost identical data set. These observations confirm the nonclonal epidemic population structure of P. aeruginosa, a superficially clonal structure with frequent recombinations, in which occasionally highly successful epidemic clones arise. One of these clones is the renown and widespread MDR serotype O12 clone. On the other hand, we found no evidence for a widespread CF transmissible clone. All but one of the 43 analysed CF strains belonged to a ubiquitous P. aeruginosa “core lineage” and typically exhibited the exoS+/exoU− genotype and group B oprL and oprD alleles. This is to our knowledge the first report of an MST analysis conducted on a polyphasic data set

Determination of Solvent Effects on Keto-Enol Equilibria of 1,3-Dicarbonyl Compounds Using NMR - Revisiting a Classic Physical Chemistry Experiment

The use of proton NMR to determine the equilibrium position of tautomeric 1,3-dicarbonyl compounds in various solvents has been a classic physical chemistry experiment. We are presenting an expansion of the excellent description of this experiment by Garland, Shoemaker, and Nibler. Often the assumption is made that the keto tautomer is always the more polar tautomer and hence the concentration of the keto tautomer is greater in polar solvents. However, the keto tautomers of acyclic 1,3-dicarbonyl molecules such as acetyl acetone are often not the more polar of the two tautomers, so this cannot be the only important factor that determines this equilibrium. Rather there are several factors that contribute to the tautomeric equilibrium of which solute dipole moment is just one. The study of the cyclic 1,3-diketone dimedone is especially helpful in this regard. The student is asked to analyze his/her results based on these factors. Molecular modeling is used as an aid in this analysis