Quasideterminant solutions of noncommutative integrable systems

Quasideterminants are a relatively new addition to the field of integrable systems. Their simple structure disguises a wealth of interesting and useful properties, enabling solutions of noncommutative integrable equations to be expressed in a straightforward and aesthetically pleasing manner. This thesis investigates the derivation and quasideterminant solutions of two noncommutative integrable equations - the Davey-Stewartson (DS) and Sasa-Satsuma nonlinear Schrodinger (SSNLS) equations. Chapter 1 provides a brief overview of the various concepts to which we will refer during the course of the thesis. We begin by explaining the notion of an integrable system, although no concrete definition has ever been explicitly stated. We then move on to discuss Lax pairs, and also introduce the Hirota bilinear form of an integrable equation, looking at the Kadomtsev-Petviashvili (KP) equation as an example. Wronskian and Grammian determinants will play an important role in later chapters, albeit in a noncommutative setting, and, as such, we give an account of their widespread use in integrable systems. Chapter 2 provides further background information, now focusing on noncommutativity. We explain how noncommutativity can be defined and implemented, both specifically using a star product formalism, and also in a more general manner. It is this general definition to which we will allude in the remainder of the thesis. We then give the definition of a quasideterminant, introduced by Gel'fand and Retakh in 1991, and provide some examples and properties of these noncommutative determinantal analogues. We also explain how to calculate the derivative of a quasideterminant. The chapter concludes by outlining the motivation for studying our particular choice of noncommutative integrable equations and their quasideterminant solutions. We begin with the DS equations in Chapter 3, and derive a noncommutative version of this integrable system using a Lax pair approach. Quasideterminant solutions arise in a natural way by the implementation of Darboux and binary Darboux transformations, and, after describing these transformations in detail, we obtain two types of quasideterminant solution to our system of noncommutative DS equations - a quasi-Wronskian solution from the application of the ordinary Darboux transformation, and a quasi-Grammian solution by applying the binary transformation. After verification of these solutions, in Chapter 4 we select the quasi-Grammian solution to allow us to determine a particular class of solution to our noncommutative DS equations. These solutions, termed dromions, are lump-like objects decaying exponentially in all directions, and are found at the intersection of two perpendicular plane waves. We extend earlier work of Gilson and Nimmo by obtaining plots of these dromion solutions in a noncommutative setting. The work on the noncommutative DS equations and their dromion solutions constitutes our paper published in 2009. Chapter 5 describes how the well-known Darboux and binary Darboux transformations in (2+1)-dimensions discussed in the previous chapter can be dimensionally-reduced to enable their application to (1+1)-dimensional integrable equations. This reduction was discussed briefly by Gilson, Nimmo and Ohta in reference to the self-dual Yang-Mills (SDYM) equations, however we explain these results in more detail, using a reduction from the DS to the nonlinear Schrodinger (NLS) equation as a specific example. Results stated here are utilised in Chapter 6, where we consider higher-order NLS equations in (1+1)-dimension. We choose to focus on one particular equation, the SSNLS equation, and, after deriving a noncommutative version of this equation in a similar manner to the derivation of our noncommutative DS system in Chapter 3, we apply the dimensionally-reduced Darboux transformation to the noncommutative SSNLS equation. We see that this ordinary Darboux transformation does not preserve the properties of the equation and its Lax pair, and we must therefore look to the dimensionally-reduced binary Darboux transformation to obtain a quasi-Grammian solution. After calculating some essential conditions on various terms appearing in our solution, we are then able to determine and obtain plots of soliton solutions in a noncommutative setting. Chapter 7 seeks to bring together the various results obtained in earlier chapters, and also discusses some open questions arising from our work

Effect of anion type in the performance of ionic liquid/poly(vinylidene fluoride) electromechanical actuators

Low voltage actuators based on poly(vinylidene fluoride)(PVDF)with 10, 25 and 40 % 1-hexyl-3-methylimidazolium chloride ([C6mim][Cl])and 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([C6mim][NTf2]) are prepared by solvent casting in order to evaluate the effect of anion size in the bending properties. Independently of the ionic liquid type and content, its presence leads to the crystallization of PVDF in the -phase. The addition of ionic liquid into the polymer matrix decreases significantly its degree of crystallinity and the elastic modulus. It is also confirmed the good miscibility between PVDF and IL,determinedby the interaction of the CF2groups from the PVDF chains with the imidazolium ring in the ionic liquid (IL). The AC conductivity of the composites depends both on the amount of ionic liquid content and anion size. The bending movement of the IL/PVDF composites is correlated to theirdegree of crystallinity, mechanical properties and ionic conductivity value and the best value of bending response (0.53 %) being found for IL/PVDF composite with40 wt% of [C6mim][Cl] at an applied voltage of 10 volts square signal.The authors thank the FCT-Fundação para a Ciência e Tecnologia-for financial support in the framework of the Strategic Funding UID/FIS/04650/2013, projects PTDC/EEI-SII/5582/2014 and PTDC/CTM-ENE/5387/2014,and grants SFRH/BD/90215/2012 (J.C.D.), SFRH/BPD/112547/2015 (C.M.C.). The authors thank Solvay for kindly supplying the high quality materials. Financial support from the Basque Government Industry Department under the ELKARTEK Program is also acknowledged.The authorsexpress their gratitude to the Ministry of the Higher Education and Scientific Research of Tunisiafor a research fellowship

Genetic risk prediction of atrial fibrillation

Background—Atrial fibrillation (AF) has a substantial genetic basis. Identification of individuals at greatest AF risk could minimize the incidence of cardioembolic stroke. Methods—To determine whether genetic data can stratify risk for development of AF, we examined associations between AF genetic risk scores and incident AF in five prospective studies comprising 18,919 individuals of European ancestry. We examined associations between AF genetic risk scores and ischemic stroke in a separate study of 509 ischemic stroke cases (202 cardioembolic [40%]) and 3,028 referents. Scores were based on 11 to 719 common variants (≥5%) associated with AF at P-values ranging from <1x10-3 to <1x10-8 in a prior independent genetic association study. Results—Incident AF occurred in 1,032 (5.5%) individuals. AF genetic risk scores were associated with new-onset AF after adjusting for clinical risk factors. The pooled hazard ratio for incident AF for the highest versus lowest quartile of genetic risk scores ranged from 1.28 (719 variants; 95%CI, 1.13-1.46; P=1.5x10-4) to 1.67 (25 variants; 95%CI, 1.47-1.90; P=9.3x10-15). Discrimination of combined clinical and genetic risk scores varied across studies and scores (maximum C statistic, 0.629-0.811; maximum ΔC statistic from clinical score alone, 0.009-0.017). AF genetic risk was associated with stroke in age- and sex-adjusted models. For example, individuals in the highest versus lowest quartile of a 127-variant score had a 2.49-fold increased odds of cardioembolic stroke (95%CI, 1.39-4.58; P=2.7x10-3). The effect persisted after excluding individuals (n=70) with known AF (odds ratio, 2.25; 95%CI, 1.20-4.40; P=0.01). Conclusions—Comprehensive AF genetic risk scores were associated with incident AF beyond associations for clinical AF risk factors, though offered small improvements in discrimination. AF genetic risk was also associated with cardioembolic stroke in age- and sex-adjusted analyses. Efforts are warranted to determine whether AF genetic risk may improve identification of subclinical AF or help distinguish between stroke mechanisms

Tracking the Continuing Trends of the Self-Represented Litigant Phenomenon

From 2011-2013, Dr. Julie Macfarlane conducted a study about experiences of self-representation in Canada. Her results were based on interviews and/or focus group interviews with 259 self-represented litigants (SRLs). Since the release of the “The National Self-Represented Litigants Project: Identifying and Meeting the Needs of Self-Represented Litigants”, the National Self-Represented Litigants Project (NSRLP) has continued to collect data from a variety of SRLs across Canada by asking those who contact us to complete an Intake Form in Survey Monkey, linked to the website. This paper sets out to relate the new intake data to the original demographic data in the 2013 Research Repor

Energy applications of ionic liquids

Ionic liquids offer a unique suite of properties that make them important candidates for a number of energy related applications. Cation–anion combinations that exhibit low volatility coupled with high electrochemical and thermal stability, as well as ionic conductivity, create the possibility of designing ideal electrolytes for batteries, super-capacitors, actuators, dye sensitised solar cells and thermoelectrochemical cells. In the field of water splitting to produce hydrogen they have been used to synthesize some of the best performing water oxidation catalysts and some members of the protic ionic liquid family co-catalyse an unusual, very high energy efficiency water oxidation process. As fuel cell electrolytes, the high proton conductivity of some of the protic ionic liquid family offers the potential of fuel cells operating in the optimum temperature region above 100 °C. Beyond electrochemical applications, the low vapour pressure of these liquids, along with their ability to offer tuneable functionality, also makes them ideal as CO2 absorbents for post-combustion CO2 capture. Similarly, the tuneable phase properties of the many members of this large family of salts are also allowing the creation of phase-change thermal energy storage materials having melting points tuned to the application. This perspective article provides an overview of these developing energy related applications of ionic liquids and offers some thoughts on the emerging challenges and opportunities

Gene-gene Interaction Analyses for Atrial Fibrillation

Atrial fibrillation (AF) is a heritable disease that affects more than thirty million individuals worldwide. Extensive efforts have been devoted to the study of genetic determinants of AF. The objective of our study is to examine the effect of gene-gene interaction on AF susceptibility. We performed a large-scale association analysis of gene-gene interactions with AF in 8,173 AF cases, and 65,237 AF-free referents collected from 15 studies for discovery. We examined putative interactions between genome-wide SNPs and 17 known AF-related SNPs. The top interactions were then tested for association in a

Shifts in Global Security Policies: Why They Matter for the South

The global security order has been evolving since 1989, led initially by the USA to expand its post?1945 order in Europe to the rest of the world but propelled as well by competition and debates within that post?Second World War alliance, as collective victors in the Cold War, about how to define a new international order. This article identifies three US policies that began this restructuring; their parallel redefinitions of security, and the tensions provoked by this agenda and its consequences, both within the ‘North’, replacing the ‘West’, between North and ‘South’, replacing the‘East’and the resulting multiple opportunities for alternative political coalitions, North against South, between North and South, and within the South, that have yet to play themselves out fully. The resulting fluidity has not yet stabilised into a new international security order