82,913 research outputs found
On the integrability of the sine-Gordon system
No full textThis thesis investigates the integrability of the sine-Gordon system of nonlinear partial differential equations when the dependent variables are subject to some very particular boundary conditions. In chapter 1 the sine-Gordon system is introduced and, with N ϵ Z, P, Q ϵ R, the sets of initial-boundary value problems A(_N) and B(_P,Q) are defined. In the set A(_N) at the spatial variable x is unbounded and the boundary conditions are fixed by initially choosing the topological charge N. This set of problems is the one usually associated with the sine-Gordon system. In the set B(_P,Q) the spatial coordinate is constrained to the semi-line (-oo,0) and there exists two boundary parameters P,Q ϵ R to be chosen a priori. It is the study of this second set of initial-boundary value problems for arbitrary P, Q which forms all the original work of this dissertation. The study presented here is primarily concerned with the development of three separate inverse scattering methods for solving these sets of initial-boundary value problems. The first of these is developed in chapter 3 and is applicable to a subset of the problems in A(_N). The method is the one usually associated with the sine-Gordon system and studies the asymptotics of the initial data as x → ±oo. It is included in this thesis for completeness and as background for the original material which follows. Next, in chapters 4 and 5, the inverse scattering methods appropriate to initial-boundary value problems in subsets of B(_P,O) and B(_P,Q#O) are constructed. In these cases it is important to realise that it is only possible to study the asymptotics of the initial data as x → -oo. Once these three methods have been formulated they are used to find soliton solutions and infinite sets of integrals of motion for these boundary value problems. When a boundary is present at x = 0 the interaction of the solitons with this boundary is studied. These topics are addressed in chapter 6. Finally in chapter 7 the question of the integrability of both sets of problems is addressed. By interpreting the various inverse scattering methods in terms of canonical coordinate transformations of phase space it is seen that the existence of such methods can be viewed as a constructive proof of the integrability of these boundary value problems
Going Beyond Counting First Authors in Author Co-citation Analysis
No full textThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Dispelling the Myths Behind First-author Citation Counts
No full textWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
The complex sine-Gordon model on a half line
No full textIn this thesis, we study the complex sine-Gordon model on a half line. The model in the bulk is an integrable (l+1) dimensional field theory which is U(1) gauge invariant and comprises a generalisation of the sine-Gordon theory. It accepts soliton and breather solutions. By introducing suitably selected boundary conditions we may consider the model on a half line. Through such conditions the model can be shown to remain integrable and various aspects of the boundary theory can be examined. The first chapter serves as a brief introduction to some basic concepts of integrability and soliton solutions. As an example of an integrable system with soliton solutions, the sine-Gordon model is presented both in the bulk and on a half line. These results will serve as a useful guide for the model at hand. The introduction finishes with a brief overview of the two methods that will be used on the fourth chapter in order to obtain the quantum spectrum of the boundary complex sine-Gordon model. In the second chapter the model is properly introduced along with a brief literature review. Different realisations of the model and their connexions are discussed. The vacuum of the theory is investigated. Soliton solutions are given and a discussion on the existence of breathers follows. Finally the collapse of breather solutions to single solitons is demonstrated and the chapter concludes with a different approach to the breather problem. In the third chapter, we construct the lowest conserved currents and through them we find suitable boundary conditions that allow for their conservation in the presence of a boundary. The boundary term is added to the Lagrangian and the vacuum is reexamined in the half line case. The reflection process of solitons from the boundary is studied and the time-delay is calculated. Finally we address the existence of boundary-bound states. In the fourth chapter we study the quantum complex sine-Gordon model. We begin with a brief overview of the theory in the bulk where the semi-classical spectrum and an exact S'-matrix are presented. Following that we use the stationary phase method to derive the semi-classical spectrum of boundary bound states. The bootstrap method is used as an alternative approach to obtain the same spectrum. The results are discussed and compared. The final chapter consists of a general discussion on open questions and problems of the model, and some proposals for further research
Linear systems, Hankel products and the sinh-Gordon equation
No full textLet be a linear system in continuous time with input and output space and state space . The scattering functions determines a Hankel integral operator ; if is trace class, then the Fredholm determinant determines the tau function of . The paper establishes properties of algebras including on . Thus the paper obtains solutions of the sinh-Gordon PDE. The tau function for sinh-Gordon satisfies a particular Painl\'eve nonlinear ODE and describes a random matrix model, with asymptotic distribution found by the Coulomb fluid method to be the solution of an electrostatic variational problem on an interval
Complex sine-Gordon theory: solitons, defects and boundaries
No full textThis thesis presents research into the properties and features of the complex sine- Gordon theory. The CSG theory is a dimensional integrable held theory that admits soliton solutions which carry a Noether charge due to the U(I) invariance of the theory. Integrable CSG defects and boundaries are constructed and interactions between solitons, defects and boundaries are analysed at the classical and quantum level. The introduction of defects into the theory is facilitated by a new Backlund transformation involving two parameters. Defect conditions, constructed so they maintain the integrability of the theory and found to be exactly the BT, are used to sew two CSG theories together. How solitons interact with the defect is investigated, in particular whether as in the SG theory solitons can be absorbed and emitted by the defect. The classical time-delay and phase-shift are calculated for soliton-defect and particle-defect scattering. Using the CSG defect to dress the Dirichlet boundary a new CSG boundary theory is produced. Its integrability is checked by the explicit construction of conserved charges. The various interactions between solitons and the boundary are analysed, compared and contrasted with the defect theory. Finally aspects of the quantum CSG boundary theory are examined, culminating in a conjecture for the quantum reflection matrix for a Q = -1-1 soliton reflecting from an unexcited boundary. Reflection and boundary bootstrap procedures are used to generate the general reflection matrix for any charged soliton reflecting from any excited boundar
Quantum corrections to the classical reflection factor of the sinh-Gordon model
No full textThis thesis studies the quantum reflection factor of the sinh-Gordon model under boundary conditions consistent with integrability. First, we review the affine Toda field theory in Chapter One. In particular, the classical and quantum integrability of the theory are reviewed on the whole line and on the half-line as well, that is, in the presence of a boundary. We next consider the sinh-Gordon model which is restricted to a half-line by boundary conditions maintaining integrability in Chapter Two. A perturbative calculation of the reflection factor is given to one loop order in the bulk coupling and to first order in the difference of the two parameters introduced at the boundary. The result provides a further verification of Ghoshal's formula. The calculation is consistent with a conjecture for the general dependence of the reflection factor on the boundary parameters and the bulk coupling. In Chapter Three, quantum corrections to the classical reflection factor of the sinh-Gordon model are studied up to second order in the difference of boundary data and to one loop order in the bulk coupling. Chapter Four deals with the quantum reflection factor for the sinh-Gordon model with general boundary conditions. The model is studied under boundary conditions which are compatible with integrability and in the framework of the conventional perturbation theory generalised to the affine Toda field theory. It is found that the general form of a subset of the related quantum corrections are hypergeometric functions. Finally, we sum up this thesis in Chapter Five along with some conclusions and suggestions for further future studies
Diagnostic performance evaluation of hepatitis B e antigen rapid diagnostic tests in Malawi
No full textBackground: The World Health Organization (WHO) has targeted a reduction in viral hepatitis-related mortality by 65% and incidence by 90% by 2030, necessitating enhanced hepatitis B treatment and prevention programmes in low- and middle-income countries. Hepatitis B e antigen (HBeAg) status is used in the assessment of eligibility for antiviral treatment and for prevention of mother-to-child transmission (PMTCT). Accordingly, the WHO has classified HBeAg rapid diagnostic tests (RDTs) as essential medical devices. Methods: We assessed the performance characteristics of three commercially available HBeAg RDTs (SD Bioline, Alere, South Africa; Creative Diagnostics, USA; and Biopanda Reagents, UK) in two hepatitis B surface antigen-positive cohorts in Blantyre, Malawi: participants of a community study (n = 100) and hospitalised patients with cirrhosis or hepatocellular carcinoma (n = 94). Two investigators, blinded to the reference test result, independently assessed each assay. We used an enzyme-linked immunoassay (Monolisa HBeAg, Bio-Rad, France) as a reference test and quantified HBeAg concentration using dilutions of the WHO HBeAg standard. We related the findings to HBV DNA levels, and evaluated treatment eligibility using the TREAT-B score. Results: Among 194 HBsAg positive patients, median age was 37 years, 42% were femaleand 26% were HIV co-infected. HBeAg prevalence was 47/194 (24%). The three RDTs showed diagnostic sensitivity of 28% (95% CI 16–43), 53% (38–68) and 72% (57–84) and specificity of 96–100% for detection of HBeAg. Overall inter-rater agreement κ statistic was high at 0.9–1.0. Sensitivity for identifying patients at the threshold where antiviral treatment is recommended for PMTCT, with HBV DNA > 200,000 IU/ml (39/194; 20%), was 22, 49 and 54% respectively. Using the RDTs in place of the reference HBeAg assay resulted in 3/43 (9%), 5/43 (12%) and 8/43 (19%) of patients meeting the TREAT-B treatment criteria being misclassified as ineligible for treatment. A relationship between HBeAg concentration and HBeAg detection by RDT was observed. A minimum HBeAg concentration of 2.2–3.1 log10IU/ml was required to yield a reactive RDT. Conclusions: Commercially available HBeAg RDTs lack sufficient sensitivity to accurately classify hepatitis B patients in Malawi. This has implications for hepatitis B public health programs in sub-Saharan Africa. Alternative diagnostic assays are recommended
[Amnesty Letter] ID207 / Phillips, E. B.
No full textThis letter was written by E. B. Phillips to President Andrew Johnson in response to the President's Amnesty Proclamation of 29 May 1865. The writer indicates his county of residence as Wilkes Co., NC and does not state his occupation
Telegram, 1928 June 19,Paris, to Earhart, Stultz, Gordon, Southampton
No full textSidney Veit, President of the Paris Chapter of the National Aeronautic Association USA, telegraph to Amelia Earhart, Wilmer Stultz, and Lou Gordon, congratulations, stamped June 19, 192
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