On the Fay identity for KdV tau functions and the identity for the Wronskian of squared solutions of Sturm-Liouville equation

We show that the well known identity for the Wronskian of squared solutions of a Sturm-Liouville equation follows from the Fay identity. We also study some odd-order (($2^n -1$)-order, $n = 2, 3, ...$) identities which are specific for tau functions, related to the KdV hierarchy.Comment: Amstex, 13 page

High-frequency high-voltage high-power DC-to-DC converters

The current and voltage waveshapes associated with the power transitor and the power diode in an example current-or-voltage step-up (buck-boost) converter were analyzed to highlight the problems and possible tradeoffs involved in the design of high voltage high power converters operating at switching frequencies in the range of 100 Khz. Although the fast switching speeds of currently available power diodes and transistors permit converter operation at high switching frequencies, the resulting time rates of changes of current coupled with parasitic inductances in series with the semiconductor switches, produce large repetitive voltage transients across the semiconductor switches, potentially far in excess of the device voltage ratings. The need is established for semiconductor switch protection circuitry to control the peak voltages appearing across the semiconductor switches, as well as to provide the waveshaping action require for a given semiconductor device. The possible tradeoffs, as well as the factors affecting the tradeoffs that must be considered in order to maximize the efficiency of the converters are enumerated

Analysis of transistor and snubber turn-off dynamics in high-frequency high-voltage high-power converters

Dc to dc converters which operate reliably and efficiently at switching frequencies high enough to effect substantial reductions in the size and weight of converter energy storage elements are studied. A two winding current or voltage stepup (buck boost) dc-to-dc converter power stage submodule designed to operate in the 2.5-kW range, with an input voltage range of 110 to 180 V dc, and an output voltage of 250 V dc is emphasized. In order to assess the limitations of present day component and circuit technologies, a design goal switching frequency of 10 kHz was maintained. The converter design requirements represent a unique combination of high frequency, high voltage, and high power operation. The turn off dynamics of the primary circuit power switching transistor and its associated turn off snubber circuitry are investigated

Keypad mobile phones are associated with a significant increased risk of microbial contamination compared to touch screen phones

The use of mobile phones in the clinical environment by healthcare workers has become widespread. Despite evidence that these devices can harbour pathogenic micro-organisms there is little guidance on how to reduce contamination. Recently touchscreen phones with a single flat surface have been introduced. We hypothesise that bacterial contamination of phones used in hospitals will be lower on touchscreen devices compared to keypad devices. Sixty seven mobile phones belonging to health care workers were sampled. The median colony count for touchscreen phones and keypad devices was 0·09 colony forming units (cfu)/cm2 (interquartile range (IQR) 0.05–0·14) and 0·77 cfu/cm2 (IQR range 0·45–3.52) respectively. Colony counts were significantly higher on the keypad phones (Fisher’s exact test p<0.001). Multivariate analysis showed the type of phone (keypad vs. touch screen) was associated with increased colony counts (F-statistic 14.13: p<0.001). Overall, nine (13%) phones grew either meticillin resistant Staphylococcus aureus or vancomycin resistant enterococci. Eight (24%) keypad phones were contaminated with these organisms compared with one touch screen phone (3%). Our data indicate that touchscreen mobile phones are less contaminated than their keypad counterparts, and they are less likely to harbour pathogenic bacteria in the clinical setting

A hybrid CA-PDE Model of chlamydia trachomatis infection in the female genital tract

Chlamydia trachomatis is amongst the most common sexually transmitted diseases in the world and when left untreated, may lead to serious sequelae particularly in women such as pelvic inflammatory disease, ectopic pregnancy and infertility. Currently, most mathematical modelling in the literature regarding Chlamydia is based on time dependent differential equations. The serious pathology associated with C. trachomatis occurs when the chlamydial infection ascends to the upper genital tract. But no modelling study has investigated the important spatial aspects of the disease. In this work, we include spatiotemporal considerations of the progression of chlamydial infection in the genital tract. This novel direction is achieved using cellular automata modelling with probabilistic decision processes. In this presentation, the modelling strategy will be described, as well as its relationship with existing models and the advances in understanding that are achieved with such a model. Such an approach provides valuable insights into disease progression and will lead to experimentally testable predictions and a basis for further investigation in this area