The Heun equation and the Calogero-Moser-Sutherland system V: generalized Darboux transformations

We obtain isomonodromic transformations for Heun's equation by generalizing Darboux transformation, and we find pairs and triplets of Heun's equation which have the same monodromy structure. By composing generalized Darboux transformations, we establish a new construction of the commuting operator which ensures finite-gap property. As an application, we prove conjectures in part III.Comment: 24 page

Two-component radiation model of the sonoluminescing bubble

Based on the experimental data from Weninger, Putterman & Barber, Phys. Rev. (E), 54, R2205 (1996), we offer an alternative interpretation of their experimetal results. A model of sonoluminescing bubble which proposes that the electromagnetic radiation originates from two sources: the isotropic black body or bramsstrahlung emitting core and dipole radiation-emitting shell of accelerated electrons driven by the liquid-bubble interface is outlined.Comment: 5 pages Revtex, submitted to Phys. Rev.

A Survey of the Life, Cost, and Storage of Textbooks in the First Class Districts of the State of Washington, Grades One Through Six

It was the purpose of this study (1) to compare the cost of textbooks for grades one through six for the first class school districts in the State of Washington; (2) to establish an ideal textbook budget for optimum learning; (3) to find the useful life of a textbook as limited by durability and need for revision in certain subject areas, and (4) to investigate storage procedures, particularly central storage versus individual building storage, to determine the most efficient use of the basic and supplemental texts owned by a district

A mathematical model of low-head oxygenators

AbstractA mathematical model is presented that predicts the performance of low-head oxygenators (LHO). Experimentally determined values of G20 for a single hole in a flooded orifice plate were used as the basis to develop a mathematical model that can be used to predict LHO performance under a variety of design and operating conditions. Model predictions were compared to two published studies. The model predicted the published data for dissolved oxygen levels in the departing effluent within 2–3%, oxygen absorption efficiencies within 5–6%, and total gas pressures within 1%. The mathematical model is thoroughly developed including an analysis of numerical stability and necessary restrictions to assure stability and accuracy. Convergence based solely upon effluent values was not sufficient to produce accurate results, but required additional criteria of requiring a minimum number of chamber flushings prior to convergence checking. The model was used to demonstrate its utility in predicting the effects of G/L ratio on gas absorption efficiency, effluent gas conditions and the effects of number of LHO chambers used. This model allows the designer or operator of an LHO to easily make design and operational decisions by modifying the input parameters and observing the exit conditions and performance indicators

Genome Investigation of Urinary Gardnerella Strains and Their Relationship to Isolates of the Vaginal Microbiota

Gardnerella is a frequent member of the urogenital microbiota. Given the association between Gardnerella vaginalis and bacterial vaginosis (BV), significant efforts have been focused on characterizing this species in the vaginal microbiota. However, Gardnerella also is a frequent member of the urinary microbiota. In an effort to characterize the bacterial species of the urinary microbiota, we present here 10 genomes of urinary Gardnerella isolates from women with and without lower uri- nary tract symptoms. These genomes complement those of 22 urinary Gardnerella strains previously isolated and sequenced by our team. We included these genomes in a comparative genome analysis of all publicly available Gardnerella genomes, which include 33 urinary isolates, 78 vaginal isolates, and 2 other isolates. While once this genus was thought to consist of a single species, recent comparative ge- nome analyses have revealed 3 new species and an additional 9 groups within Gardnerella. Based upon our analysis, we suggest a new group for the species. We also find that distinction between these Gardnerella species/groups is possible only when considering the core or whole-genome sequence, as neither the sialidase nor vaginolysin genes are sufficient for distinguishing between species/groups despite their clinical importance. In contrast to the vaginal microbiota, we found that only five Gardnerella species/groups have been detected within the lower urinary tract. Although we found no association between a particular Gardnerella species/group(s) and urinary symptoms, further sequencing of urinary Gardnerella isolates is needed for both comprehensive taxonomic characterization and etiological classification of Gardnerella in the urinary tract. Importance Prior research into the bacterium Gardnerella vaginalis has largely focused on its association with bacterial vaginosis (BV). However, G. vaginalis is also frequently found within the urinary microbiota of women with and without lower urinary tract symptoms as well as individuals with chronic kidney disease, interstitial cystitis, and BV. This prompted our investigation into Gardnerella from the urinary microbiota and all publicly available Gardnerella genomes from the urogenital tract. Our work suggests that while some Gardnerella species can survive in both the urinary tract and vagina, others likely cannot. This study provides the foundation for future studies of Gardnerella within the urinary tract and its possible contribution to lower urinary tract symptoms