Diagonal forms, linear algebraic methods and Ramsey-type problems

This thesis focuses mainly on linear algebraic aspects of combinatorics. Let N_t(H) be an incidence matrix with edges versus all subhypergraphs of a complete hypergraph that are isomorphic to H. Richard M. Wilson and the author find the general formula for the Smith normal form or diagonal form of N_t(H) for all simple graphs H and for a very general class of t-uniform hypergraphs H.

As a continuation, the author determines the formula for diagonal forms of integer matrices obtained from other combinatorial structures, including incidence matrices for subgraphs of a complete bipartite graph and inclusion matrices for multisets.

One major application of diagonal forms is in zero-sum Ramsey theory. For instance, Caro's results in zero-sum Ramsey numbers for graphs and Caro and Yuster's results in zero-sum bipartite Ramsey numbers can be reproduced. These results are further generalized to t-uniform hypergraphs. Other applications include signed bipartite graph designs.

Research results on some other problems are also included in this thesis, such as a Ramsey-type problem on equipartitions, Hartman's conjecture on large sets of designs and a matroid theory problem proposed by Welsh.

Utilization of some aquatic macrophytes in Nigeria in-land water bodies: a review

Aquatic vegetation is an essential component of the aquatic ecosystem with both positive and negative implications on the water body. Efforts are always made to curtail the excessive growth of aquatic plants in order to prevent them from becoming a nuisance in the ecosystem. One of the ways of solving such problem is the positive economic use of such plants. Utilization as a method of weed control within the aquatic ecosystem is considered to be one of the safest methods of weed control as this provides the riparian communities double advantages in terms of save environment and personal benefits of the plant. The flora diversity of freshwater and brackish environments posses a great potential to both man and higher animals alike. Due to this fact, this paper attempt to review the exploited and unexploited aquatic plants resources of many of our water bodies in Nigeria both economica/ly and socially, to the populace. Recommendations are also advanced for further studies that will enhance sound management of the resources for maximum benefits and sustainability

Development of selection methods for steels and their heat treatments

Designers who want to manufacture a hardenable steel component need to select both the steel and its heat treatment. This project aims to develop a selection methodology for steels and process routes as an aid to designers. Three studies were conducted: - production of software to calculate the "equivalent diameter" and "equivalent Jominy distance" for simple shapes of a steel component; - prediction of semi-empirical Jominy curves (as-cooled) using CCT diagrams and process modelling methods, which were validated by experiment on plain carbon steels; - investigation of tempering of Jominy bars to explore the potential for semi-empirical models for the hardness after tempering.

Methods of multiparameter inversion of seismic data using the acoustic and elastic born approximations

This thesis presents two different forms of the Born approximations for acoustic and elastic wavefields and discusses their application to the inversion of seismic data. The Born approximation is valid for small amplitude heterogeneities superimposed over a slowly varying background. The first method is related to frequency-wavenumber migration methods. It is shown to properly recover two independent acoustic parameters within the bandpass of the source time function of the experiment for contrasts of about 5 percent from data generated using an exact theory for flat interfaces. The independent determination of two parameters is shown to depend on the angle coverage of the medium. For surface data, the impedance profile is well recovered.

The second method explored is mathematically similar to iterative tomographic methods recently introduced in the geophysical literature. Its basis is an integral relation between the scattered wavefield and the medium parameters obtained after applying a far-field approximation to the first-order Born approximation. The Davidon-Fletcher-Powell algorithm is used since it converges faster than the steepest descent method. It consists essentially of successive backprojections of the recorded wavefield, with angular and propagation weighing coefficients for density and bulk modulus. After each backprojection, the forward problem is computed and the residual evaluated. Each backprojection is similar to a before-stack Kirchhoff migration and is therefore readily applicable to seismic data. Several examples of reconstruction for simple point scatterer models are performed. Recovery of the amplitudes of the anomalies are improved with successive iterations. Iterations also improve the sharpness of the images.

The elastic Born approximation, with the addition of a far-field approximation is shown to correspond physically to a sum of WKBJ-asymptotic scattered rays. Four types of scattered rays enter in the sum, corresponding to P-P, P-S, S-P and S-S pairs of incident-scattered rays. Incident rays propagate in the background medium, interacting only once with the scatterers. Scattered rays propagate as if in the background medium, with no interaction with the scatterers. An example of P-wave impedance inversion is performed on a VSP data set consisting of three offsets recorded in two wells.

Engineering enzyme systems by recombination

Homologous recombination is a source of diversity in both natural and directed evolution. Standing genetic variation that has passed the test of natural selection is combined in new ways, generating functional and sometimes unexpected changes. In this work we evaluate the utility of homologous recombination as a protein engineering tool, both in comparison with and combined with other protein engineering techniques, and apply it to an industrially important enzyme: Hypocrea jecorina Cel5a.

Chapter 1 reviews work over the last five years on protein engineering by recombination. Chapter 2 describes the recombination of Hypocrea jecorina Cel5a endoglucanase with homologous enzymes in order to improve its activity at high temperatures. A chimeric Cel5a that is 10.1 °C more stable than wild-type and hydrolyzes 25% more cellulose at elevated temperatures is reported. Chapter 3 describes an investigation into the synergy of thermostable cellulases that have been engineered by recombination and other methods. An engineered endoglucanase and two engineered cellobiohydrolases synergistically hydrolyzed cellulose at high temperatures, releasing over 200% more reducing sugars over 60 h at their optimal mixture relative to the best mixture of wild-type enzymes. These results provide a framework for engineering cellulolytic enzyme mixtures for the industrial conditions of high temperatures and long incubation times.

In addition to this work on recombination, we explored three other problems in protein engineering. Chapter 4 describes an investigation into replacing enzymes with complex cofactors with simple cofactors, using an E. coli enolase as a model system. Chapter 5 describes engineering broad-spectrum aldehyde resistance in Saccharomyces cerevisiae by evolving an alcohol dehydrogenase simultaneously for activity and promiscuity. Chapter 6 describes an attempt to engineer gene-targeted hypermutagenesis into E. coli to facilitate continuous in vivo selection systems.