Properties of sparse random matrices over finite fields

Typical properties of sparse random matrices over finite (Galois) fields are studied, in the limit of large matrices, using techniques from the physics of disordered systems. For the case of a finite field GF(q) with prime order q, we present results for the average kernel dimension, average dimension of the eigenvector spaces and the distribution of the eigenvalues. The number of matrices for a given distribution of entries is also calculated for the general case. The significance of these results to error-correcting codes and random graphs is also discussed.

Prediction of the equilibrium structures and photomagnetic properties of the Prussian blue analogue RbMn[Fe(CN)6] by density functional theory

A periodic density functional theory method using the B3LYP hybrid exchange-correlation potential is applied to the Prussian blue analogue RbMn[Fe(CN)6] to evaluate the suitability of the method for studying, and predicting, the photomagnetic behavior of Prussian blue analogues and related materials. The method allows correct description of the equilibrium structures of the different electronic configurations with regard to the cell parameters and bond distances. In agreement with the experimental data, the calculations have shown that the low-temperature phase (LT; Fe(2+)(t(6)2g, S = 0)-CN-Mn(3+)(t(3)2g e(1)g, S = 2)) is the stable phase at low temperature instead of the high-temperature phase (HT; Fe(3+)(t(5)2g, S = 1/2)-CN-Mn(2+)(t(3)2g e(2)g, S = 5/2)). Additionally, the method gives an estimation for the enthalpy difference (HT LT) with a value of 143 J mol(-1) K(-1). The comparison of our calculations with experimental data from the literature and from our calorimetric and X-ray photoelectron spectroscopy measurements on the Rb0.97Mn[Fe(CN)6]0.98 x 1.03 H2O compound is analyzed, and in general, a satisfactory agreement is obtained. The method also predicts the metastable nature of the electronic configuration of the high-temperature phase, a necessary condition to photoinduce that phase at low temperatures. It gives a photoactivation energy of 2.36 eV, which is in agreement with photoinduced demagnetization produced by a green laser.

The effect of blending on selected physical properties of crude oils and their products

A study was made of the effect of blending practice upon selected physical properties of crude oils, and of various base oils and petroleum products, using a range of binary mixtures. The crudes comprised light, medium and heavy Kuwait crude oils. The properties included kinematic viscosity, pour point, boiling point and Reid vapour pressure. The literature related to the prediction of these properties, and the changes reported to occur on blending, was critically reviewed as a preliminary to the study. The kinematic viscosity of petroleum oils in general exhibited non-ideal behaviour upon blending. A mechanism was proposed for this behaviour which took into account the effect of asphaltenes content. A correlation was developed, as a modification of Grunberg's equation, to predict the viscosities of binary mixtures of petroleum oils. A correlation was also developed to predict the viscosities of ternary mixtures. This correlation showed better agreement with experimental data (< 6% deviation for crude oils and 2.0% for base oils) than currently-used methods, i.e. ASTM and Refutas methods. An investigation was made of the effect of temperature on the viscosities of crude oils and petroleum products at atmospheric pressure. The effect of pressure on the viscosity of crude oil was also studied. A correlation was developed to predict the viscosity at high pressures (up to 8000 psi), which gave significantly better agreement with the experimental data than the current method due to Kouzel (5.2% and 6.0% deviation for the binary and ternary mixtures respectively). Eyring's theory of viscous flow was critically investigated, and a modification was proposed which extends its application to petroleum oils. The effect of blending on the pour points of selected petroleum oils was studied together with the effect of wax formation and asphaltenes content. Depression of the pour point was always obtained with crude oil binary mixtures. A mechanism was proposed to explain the pour point behaviour of the different binary mixtures. The effects of blending on the boiling point ranges and Reid vapour pressures of binary mixtures of petroleum oils were investigated. The boiling point range exhibited ideal behaviour but the R.V.P. showed negative deviations from it in all cases. Molecular weights of these mixtures were ideal, but the densities and molar volumes were not. The stability of the various crude oil binary mixtures, in terms of viscosity, was studied over a temperature range of 1oC - 30oC for up to 12 weeks. Good stability was found in most cases.

The chemical structure and mechanical properties of phenolic resins and related polymers

Paper-based phenolic laminates are used extensively in the electrical industry. Many small components are fabricated from these materials by the process known as punching. Recently an investigation was carried out to study the effect of processing variables on the punching properties. It was concluded that further work would be justified and that this should include a critical examination of the resin properties in a more controlled and systematic manner. In this investigation an attempt has been made to assess certain features of the resin structure in terms of thermomechanical properties. The number of crosslinks in the system was controlled using resins based on phenol and para-cresol formulations. Intramolecular hydrogen bonding effects were examined using substituted resins and a synthetically derived phenol based on 1,3-di-(o-hydroxyphenyl) propane.. A resin system was developed using the Friedel Crafts reaction to examine inter-molecular hydrogen bonding at the resin-paper interface. The punching properties of certain selected resins were assessed on a qualitative basis. In addition flexural and dynamic mechanical properties were determined in a general study of the structure-property relationships of these materials. It has been shown that certain features of the resin structure significantly influenced mechanical properties. :F'urther, it was noted that there is a close relationship between punching properties, mechanical damping and flexural strain. This work includes a critical examination of the curing mechanism and views are postulated in an attempt to extend knowledge in this area of the work. Finally, it is argued that future work should be based on a synthetic approach and that dynamic mechanical testing would provide a powerful tool In developing a deeper understanding of the resin fine structure.

Enterotoxigenic Escherichia coli infection of pigs: expression, extraction, purification and the adhesive properties of the K88 fimbrial adhesin

The ability of Escherichia coli to express the K88 fimbrial adhesin was satisfactorily indicated by the combined techniques of ELISA, haemagglutination and latex agglutination. Detection of expression by electron microscopy and the ability to metabolize raffinose were unsuitable. Quantitative expression of the K88 adhesin was determined by ELISA. Expression was found to vary according to the E.coli strain examined, media type and form. In general it was found that the total amount was greater, while the amount/cfu was less on agar than in broth cultures. Expression of the K88 adhesin during unshaken batch culture was related to the growth rate and was maximal during late logarithmic to early stationary phase. A combination of heat extraction, ammonium sulphate and isoelectric precipitation was found suitable for both large and small scale preparation of purified K88ab adhesin. Extraction of the K88 adhesin was sensitive to pH and it was postulated that this may affect the site of colonisation of by ETEC in vivo. Results of haemagglutination experiments were consistent with the hypothesis that the K88 receptor present on erythrocytes is composed of two elements, one responsible for the binding of K88ab and K88ac and a second responsible for the binding of the K88ad adhesin. Comparison of the haemagglutinating properties of cell-free and cell-bound K88 adhesin revealed some differences probably indicating a minor conformational change in the K88 adhesin on its isolation. The K88ab adhesin was found to bind to erythrocytes over a wide pH range (PH 4-9) and was inhibited by αK88ab and αK88b antisera. Inhibition of haemagglutination was noted with crude heparin, mannan and porcine gastric mucin, chondrosine and several hexosamines, glucosamine in particular. The most potent inhibitor of haemagglutination was n-dodecyl-β-D-glucopyranoside, one of a series of glucosides found to have inhibitory properties. Correlation between hydrophobicity of glucosides tested and degree of inhibition observed suggested hydrophobic forces were important in the interaction of the K88 adhesin with its receptor. The results of Scatchard and Hill plots indicated that binding of the K88ab adhesin to porcine enterocytes in the majority of cases is a two-step, three component system. The first K88 receptor (or site) had a K2. of 1.59x1014M-1 and a minimum of 4.3x104 sites/enterocyte. The second receptor (or site) had a K2 of 4.2x1012M-1 with a calculated 1.75x105 sites/enterocyte. Attempts to inhibit binding of cell-free K88 adhesin to porcine enterocytes by lectins were unsuccessful. However, several carbohydrates including trehalose, lactulose, galactose 1→4 mannopyranoside, chondrosine, galactosamine, stachyose and mannan were inhibitory. The most potent inhibitor was found to be porcine gastric mucin. Inhibition observed with n-octyl-α-D-glucopyranose was difficult to interpret in isolation because of interference with the assay, however, it agreed with the results of haemagglutination inhibition experiments.

The compressive creep and load relaxation properties of a series of high aluminium zinc-based alloys

A new family of commercial zinc alloys designated as ZA8, ZA12, and ZA27 and high damping capacity alloys including Cosmal and Supercosmal and aluminium alloy LM25 were investigated for compressive creep and load relaxation behaviour under a series of temperatures and stresses. A compressive creep machine was designed to test the sand cast hollow cylindrical test specimens of these alloys. For each compressive creep experiment the variation of creep strain was presented in the form of graphs plotted as percentage of creep strain () versus time in seconds (s). In all cases, the curves showed the same general form of the creep curve, i.e. a primary creep stage, followed by a linear steady-state region (secondary creep). In general, it was observed that alloy ZA8 had the least primary creep among the commercial zinc-based alloys and ZA27 the greatest. The extent of primary creep increased with aluminium content to that of ZA27 then declined to Supercosmal. The overall creep strength of ZA27 was generally less than ZA8 and ZA12 but it showed better creep strength than ZA8 and ZA12 at high temperature and high stress. In high damping capacity alloys, Supercosmal had less primary creep and longer secondary creep regions and also had the lowest minimum creep rate among all the tested alloys. LM25 exhibited almost no creep at maximum temperature and stress used in this research work. Total creep elongation was shown to be well correlated using an empirical equation. Stress exponent and activation energies were calculated and found to be consistent with the creep mechanism of dislocation climb. The primary α and β phases in the as-cast structures decomposed to lamellar phases on cooling, with some particulates at dendrite edges and grain boundaries. Further breakdown into particulate bodies occurred during creep testing, and zinc bands developed at the highest test temperature of 160°C. The results of load relaxation testing showed that initially load loss proceeded rapidly and then deminished gradually with time. Load loss increased with temperature and almost all the curves approximated to a logarithmic decay of preload with time. ZA alloys exhibited almost the same load loss at lower temperature, but at 120°C ZA27 improved its relative performance with the passage of time. High damping capacity alloys and LM25 had much better resistance to load loss than ZA alloys and LM25 was found to be the best against load loss among these alloys. A preliminary equation was derived to correlate the retained load with time and temperature.

The structural properties of glassfibre reinforced plastics

The research work described in this thesis is concerned with the development of glassfibre reinforced plastics for structural uses in Civil Engineering construction. The first stage was primarily concerned with the design of GRP lamintes with structura1 properties and method of manufacture suitable for use with relatively large structural components. A cold setting, pressure moulding technique was developed which proved to be efficient in reducing the void content in the composite and minimising the exothermic effect due to curing. The effect of fibre content and fibre arrangement on strength and stiffness of the cornposite was studied and the maximum amount of' fibre content that could be reached by the adopted type of moulding technique was determined. The second stage of the project was concerned with the introduction of steel-wire "sheets" into the GRP cornposites, to take advantage of the high modulus of steel wire to improve the GRP stiffness and to reduce deformation. The experimental observations agreed reasonably well with theoretical predictions in both first and second stages of the work. The third stage was concerned with studying the stability of GRP flat rectangular plates subjected to uniaxial compression or pure shear, to simulate compression flanges or shear webs respectively. The investigation was concentrated on the effect of fibre arrangement in the plate on buckling load. The effect of the introduction of steel-wire sheets on the plate stability in compression was also investigated. The boundary conditions were chosen to be close to those usually assumed in built-up box-sections for both compression flanges and webs. The orthotropic plate and the mid-plane symmetric were used successfully in predicting the buckling load theoretically. In determining the buckling load experimentally, two methods were used. The Southwell plot method and electrical strain gauge method. The latter proved to be more reliable in predicting the buckling load than the former, especially for plates under uniaxial compression. Sample design charts for GRP plates that yield and buckle simultaneously under compression are also presented in the thesis. The final stage of the work dealt with the design and test of GRP beams. The investigation began by finding the optimum cross-section for a GRP beam. The cross-section which was developed was a thin walled corrugated section which showed higher stiffness than other cross-sections for the same cross-sectional area (i.e. box, I, and rectangular sections). A cold setting, hand layings technique was used in manufacturing these beams wbich were of nine types depending on the type of glass reinforcement employed and the arrangement of layers in the beam. The simple bending theory was used in the beam design and proved to be satisfactory in predicting the stresses and deflections. A factor of safety of 4 was chosen for design purposes and considered to be suitable for long term use under static load. Because of its relatively low modulus, GRP beams allowable deflection was limited to 1/120th of the span which was found to be adequate for design purposes. A general discussion of the behaviour of GRP composites and their place relative to the more conventional structural material was also presented in the thesis.

The effect of thermochemical treatment on the fatigue properties of alloy steels

The effect of thermochemical treatment namely carburising on the fatigue behaviour of one carbon and two alloy steels has been studied in rotating and unidirectional bending. The effect of carbon profile on the unidirect¬ional bending fatigue strength of 63SA14 was assessed, and it was found that single stage carburising with a surface carbon content of 0.8% has resulted in a higher fatigue strength than other types of carbon profiles. Residual stresses and other metallurgical variables arising from different carbon profiles, were also considered. The highest compressive stresses h~e resulted from boost-diffuse-carburising. On the other hand surface decarburisation was associated with tensile residual stresses and a reduced fatigue strength. Retained austenite was found to be detrimental in unidirectional bending fatigue; however its presence in carburised 83SAIS did not seem to influence the rotating bending fatigue strength. Carbide particles in globular and/or intergranular form were detrimental to compressive residual stresses; the unidirectional bending fatigue strength is markedly lowered. The highest fatigue strength was accomplished by vacuum carburising. The absence of internal oxidation was the key factor in the increased fatigue strength; the presence of uniformly distributed fine carbide particles did not upset the superior fatigue strength of vacuum carburised pieces. The effect of mean stress on the fatigue strength of carburised 63SA14 was studied. Increasing the mean stress as would be expected resulted in a decreased fatigue strength. Carburisation showed its advantages at low mean stress, but at high mean stress it offers little advantage over the uncarburised hardened conditions. Notch effect was also studied in unidirectional bending of carburised 080MlS. The general trend showed that the fatigue strength decreases with increasing the stress concentration factor. But different carburising conditions have different effect on notch sensitivity.

The synthesis and properties of some hydrazines

A new synthetic method, applicable to the preparation of a wide range of hydrazine derivatives, is described. This involves the diborane reduction of a hydrazone, or, more conveniently, the reductive-condensation of a hydrazine and the appropriate aldehyde (or ketone). The method gives high yields and provides a particularly simple route to the relatively inaccessible 1,2-disubstituted hydrazines bearing a different group on each nitrogen. The new method has also been applied to the preparation of 1,2-disubstituted hydrazines with the same group on both nitrogens (via the azine), the very rare 1 ,2-disubstituted hydrazines bearing a tert-butyl group, trisubstituted hydrazines and monosubstituted hydrazines. Application of the reaction to the preparation of diaziridines has also been investigated. A mechanism for the reduction, supported by the isolation of a boron-containing intermediate, is suggested. Some limitations of the procedure are discussed. A general i.r. method of distinguishing the isomeric disubstituted hydrazines, as stable salts, has been developed. This has the advantages of speed and simplicity over previous methods. The mass spectra of a series of monosubstituted hydrazines, a series of 1,2-disubstituted hydrazines and some 1-benzoyl 2-alkylhydrazines have been examined in detail. The spectra are generally dominated byα -cleavage processes and the compounds show a variety of interesting rearrangement reactions. The mass spectra of some 1, 1-disubstituted hydrazines and some trisubstituted hydrazines have also been examined. Rearrangement processes occurring in the mass spectrum of tropylium fluoroborate have been examined. Similar rearrangements have been found in the spectrum of trityl fluoroborate and may be of general occurrence in the mass spectra of aromatic fluoroborates. Chemical shift values for some groups on hydrazine nitrogen are recorded and the results of tumour inhibitory tests on some hydrazines are also given.

Impact of the counterion on the solubility and physicochemical properties of salts of carboxylic acid drugs

Aim: Salt formation is a widely used approach to improve the physicochemical and solid state properties of an active pharmaceutical ingredient. In order to better understand the relationships between the active drug, the selected counterion and the resultant salt form, crystalline salts were formed using four different carboxylic acid drugs and a closely related series of amine counterions. Thirty-six related crystalline salts were prepared, characterized and the relationship between solubility and dissolution behaviour and other properties of the salt and the counterion studied. Methods: Salts of four model acid drugs, gemfibrozil, flurbiprofen, ibuprofen and etodolac were prepared using the counterions butylamine, hexylamine, octylamine, benzylamine, cyclohexylamine, tert-butylamine, 2-amino-2-methylpropan-1-ol, 2-amino-2-methylpropan-1,3-diol andtris(hydroxymethyl)aminomethane. Salt formation was confirmed, the salts were characterized and their corresponding solubilities determined and rationalized with respect to the counterions' properties. Results and conclusion: The properties of the salt highly dependent on the nature of the counterion and, although there is considerable variation, some general conclusion can be drawn. For the alkyl amines series, increasing chain length leads to a reduction in solubility across all the acidic drugs studied and a reduction in melting point, thus contradicting simplistic relationships between solubility and melting point. Small, compact counterions consistently produce crystalline salts with high melting point accompanied with a modest improvement in solubility and the nature of hydrogen bonding between the ions has a major impact on the solubility. © 2012 Informa Healthcare USA, Inc.

Discovering properties of new DNA-binding activity of proteins

Protein-DNA interactions are an essential feature in the genetic activities of life, and the ability to predict and manipulate such interactions has applications in a wide range of fields. This Thesis presents the methods of modelling the properties of protein-DNA interactions. In particular, it investigates the methods of visualising and predicting the specificity of DNA-binding Cys2His2 zinc finger interaction. The Cys2His2 zinc finger proteins interact via their individual fingers to base pair subsites on the target DNA. Four key residue positions on the a- helix of the zinc fingers make non-covalent interactions with the DNA with sequence specificity. Mutating these key residues generates combinatorial possibilities that could potentially bind to any DNA segment of interest. Many attempts have been made to predict the binding interaction using structural and chemical information, but with only limited success. The most important contribution of the thesis is that the developed model allows for the binding properties of a given protein-DNA binding to be visualised in relation to other protein-DNA combinations without having to explicitly physically model the specific protein molecule and specific DNA sequence. To prove this, various databases were generated, including a synthetic database which includes all possible combinations of the DNA-binding Cys2His2 zinc finger interactions. NeuroScale, a topographic visualisation technique, is exploited to represent the geometric structures of the protein-DNA interactions by measuring dissimilarity between the data points. In order to verify the effect of visualisation on understanding the binding properties of the DNA-binding Cys2His2 zinc finger interaction, various prediction models are constructed by using both the high dimensional original data and the represented data in low dimensional feature space. Finally, novel data sets are studied through the selected visualisation models based on the experimental DNA-zinc finger protein database. The result of the NeuroScale projection shows that different dissimilarity representations give distinctive structural groupings, but clustering in biologically-interesting ways. This method can be used to forecast the physiochemical properties of the novel proteins which may be beneficial for therapeutic purposes involving genome targeting in general.

Optimising catalytic properties of supported sulfonic acid catalysts

Siliceous mesoporous molecular sieves (SBA-15) have been functionalised with propylsulfonic acid groups by both co-condensing 3-mercaptopropyltrimethoxysilane with the solid at the synthesis (sol-gel) stage and by grafting the same compound to pre-prepared SBA-15, followed, in both cases, by oxidation to sulfonic acid. The acidic and catalytic properties of the supported sulfonic acids prepared in the two ways have been compared, using ammonia adsorption calorimetry and the benzylation reaction between benzyl alcohol and toluene. Using a combination of X-ray photoelectron spectroscopy and other analytical techniques, the level of functionalisation and the extent of subsequent oxidation of tethered thiol to sulfonic acid, both in the bulk and close to the surface of SBA-15 particles, have been assessed. The research shows that the co-condensing route leads to higher levels of functionalisation than the grafting route. The extent of oxidation of added thiol to acid groups is similar using the two routes, about 70% near the surface and only 50% in the bulk. Comparison is made with polymer supported sulfonic acid catalysts, Amberlysts 15 and 35, and Nafion. Nafion shows the highest acid strength and the highest specific catalytic activity of all materials studied. Amongst the other materials, average acid strengths are broadly similar but there appears to be a relationship between the concentration of acid sites on the catalysts and their specific activity in the benzylation reaction. A model is proposed to explain this, in which clustering of sulfonic acid groups, even to a small extent, leads to disproportionately enhanced catalytic activity. © 2009 Elsevier B.V. All rights reserved.

Revealing statistical properties of quasi-CW fibre lasers in bandwidth-limited measurements

We introduce a general technique how to reveal in experiments of limited electrical bandwidth which is lower than the optical bandwidth of the optical signal under study, whether the statistical properties of the light source obey Gaussian distribution or mode correlations do exist. To do that one needs to perform measurements by decreasing the measurement bandwidth. We develop a simple model of bandwidth-limited measurements and predict universal laws how intensity probability density function and intensity auto-correlation function of ideal completely stochastic source of Gaussian statistics depend on limited measurement bandwidth and measurement noise level. Results of experimental investigation are in good agreement with model predictions. In particular, we reveal partial mode correlations in the radiation of quasi-CW Raman fibre laser.

Improved methodology to evaluate fracture properties of warm-mix asphalt using overlay test

This study developed a reliable and repeatable methodology to evaluate the fracture properties of asphalt mixtures with an overlay test (OT). In the proposed methodology, first, a two-step OT protocol was used to characterize the undamaged and damaged behaviors of asphalt mixtures. Second, a new methodology combining the mechanical analysis of viscoelastic force equilibrium in the OT specimen and finite element simulations was used to determine the undamaged properties and crack growth function of asphalt mixtures. Third, a modified Paris's law replacing the stress intensity factor by the pseudo J-integral was employed to characterize the fracture behavior of asphalt mixtures. Theoretical equations were derived to calculate the parameters A and n (defined as the fracture properties) in the modified Paris's law. The study used a detailed example to calculate A and n from the OT data. The proposed methodology was successfully applied to evaluate the impact of warm-mix asphalt (WMA) technologies on fracture properties. The results of the tested specimens showed that Evotherm WMA technology slightly improved the cracking resistance of asphalt mixtures, while foaming WMA technology provided comparable fracture properties. In addition, the study found that A decreased with the increase in n in general. A linear relationship between 2log(A) and n was established.