The converse problem for the multipotentialisation of evolution equations and systems

We propose a method to identify and classify evolution equations and systems that can be multipotentialised in given target equations or target systems. We refer to this as the {\it converse problem}. Although we mainly study a method for $(1+1)$-dimensional equations/system, we do also propose an extension of the methodology to higher-dimensional evolution equations. An important point is that the proposed converse method allows one to identify certain types of auto-B\"acklund transformations for the equations/systems. In this respect we define the {\it triangular-auto-B\"acklund transformation} and derive its connections to the converse problem. Several explicit examples are given. In particular we investigate a class of linearisable third-order evolution equations, a fifth-order symmetry-integrable evolution equation as well as linearisable systems.Comment: 31 Pages, 7 diagrams, submitted for consideratio

The Role of Lysogenic Bacteriophage in Virulence and Survival of Streptococcus Pyogenes

This thesis investigates the interactions of lysogenic bacteriophage with Streptococcus pyogenes. We were specifically interested in elucidating novel ways in which the prophage influence GrAS virulence and survival either within the host cell or within the bacterial population. In turn, we also hoped to determine how the bacteria (and possibly other integrated phage) might influence prophage activity or gene expression. Our studies focused on two polylysogenized GrAS strains, a M6 serotype (MGAS10394) and a M1 serotype (SF370). In our M6 studies, we chose a streptococcal strain lysogenized by a chimeric bacteriophage element (Φ10394.4), which contains the erythromycin resistance gene mefA, in order to elucidate why genomes of certain erythromycin-resistant isolates of group A streptococci are resistant to SmaI endonuclease cleavage. In the work presented here, we identified a restriction modification system contained on the bacteriophage chimeric-element and successfully characterized the first methyltransferase (M.SpyI) encoded in S. pyogenes. In the M1 strain, allelic recombination techniques were used to begin to analyze the role and regulation of a bacteriophage-encoded potential superantigen, SpeH. Next, we designed a novel system to specifically select for the loss of integrated phages entirely from the genome. This technique allowed us to study the novel role that two SF370 phage play in regulating GrAS chromosomal genes involved in bacterial metabolism, DNA repair and mutagenesis. We were also able to begin to elucidate the effects that individual and multiple phage loss have on SF370 virulence and survival, as we successfully constructed the first strain of GrAS that is completely devoid of bacteriophages. In the course of these studies, we also manipulated lytic bacteriophage genes from two different Staphylococcus phage genomes to genetically engineer a novel chimeric endolysin (ClyS). We demonstrated the antimicrobial lytic activity of ClyS against methicillin-resistant Staphylococcus aureus (MRSA) in both in vivo colonization and septicemia models, and were also able to show its synergistic activity with oxacillin in in vitro and in vivo models. This work highlights the potential of ClyS as a novel therapeutic agent for the treatment of MRSA and other staphylococcal infections

The use of high-resolution terrain data in gravity field prediction

Different types of gravity prediction methods for local and regional gravity evaluation are developed, tested, and compared. Four different test areas were particularly selected in view of different prediction requirements. Also different parts of the spectrum of the gravity field were considered

Piezoelectric-based apparatus for strain tuning

We report the design and construction of piezoelectric-based apparatus for applying continuously tuneable compressive and tensile strains to test samples. It can be used across a wide temperature range, including cryogenic temperatures. The achievable strain is large, so far up to 0.23% at cryogenic temperatures. The apparatus is compact and compatible with a wide variety of experimental probes. In addition, we present a method for mounting high-aspect-ratio samples in order to achieve high strain homogeneity.Comment: 8 pages, 8 figure

A tree of linearisable second-order evolution equations by generalised hodograph transformations

We present a list of (1+1)-dimensional second-order evolution equations all connected via a proposed generalised hodograph transformation, resulting in a tree of equations transformable to the linear second-order autonomous evolution equation. The list includes autonomous and nonautonomous equations.Comment: arXiv version is already officia

Statistical Technique for Intermediate and Long-Range Estimation of 13-Month Smoothed Solar Flux and Geomagnetic Index

This report documents the Marshall Space Flight Center (MSFC) 13-month smoothed solar flux (F(sub 10.7)) and geomagnetic index (A(sub p)) intermediate (months) and long-range (years) statistical estimation technique, referred to as the MSFC Lagrangian Linear Regression Technique (MLLRT). Estimates of future solar activity are needed as updated input to upper atmosphere density models used for satellite and spacecraft orbital lifetime predictions. An assessment of the MLLRT computer program's products is provided for 5-year periods from the date estimates were made. This was accomplished for a number of past solar cycles

Reconstructing Generalized Exponential Laws by Self-Similar Exponential Approximants

We apply the technique of self-similar exponential approximants based on successive truncations of continued exponentials to reconstruct functional laws of the quasi-exponential class from the knowledge of only a few terms of their power series. Comparison with the standard Pad\'e approximants shows that, in general, the self-similar exponential approximants provide significantly better reconstructions.Comment: Revtex file, 21 pages, 21 figure

On nonlocal symmetries, nonlocal conservation laws and nonlocal transformations of evolution equations

We discuss nonlocal symmetries and nonlocal conservation laws that follow from the systematic potentialisation of evolution equations. Those are the Lie point symmetries of the auxiliary systems, also known as potential symmetries. We define higher-degree potential symmetries which then lead to nonlocal conservation laws and nonlocal transformations for the equations. We demonstrate our approach by the Burgers' hierarchy and the Calogero-Degasperis-Ibragimov-Shabat hierarchy

Viking navigation

A comprehensive description of the navigation of the Viking spacecraft throughout their flight from Earth launch to Mars landing is given. The flight path design, actual inflight control, and postflight reconstruction are discussed in detail. The preflight analyses upon which the operational strategies and performance predictions were based are discussed. The inflight results are then discussed and compared with the preflight predictions and, finally, the results of any postflight analyses are presented