14 resultados para Numerical Evaluation of Special Functions

em Aston University Research Archive


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Adult illiteracy rates are alarmingly high worldwide. The portability, affordability, and ease of use of mobile (or handheld) devices offer a realistic opportunity to provide novel, context-sensitive literacy resources to adults with limited literacy skills. To this end, we developed the concept of ALEX – a mobile Adult Literacy support application for EXperiential learning (Lumsden et al., 2005). On the basis of a medium-fidelity prototype of this application, we conducted an evaluation of ALEX using participants from our in tended user group. This evaluation had two goals: (a) to assess the usefulness of the ALEX concept and the usability of its current design; and (b) to reflect on the appropriateness of our evaluation process given the literacy-related needs of our participants. This paper outlines our approach to this evaluation as well as the results we obtained and our reflections on the process.

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Comparing the Poincaré plots of the Tokamap and the underlying Hamiltonian system reveals large differences. This stems from the particular choice of evaluation of the singular perturbations present in the system (a series of δ functions). A symmetric evaluation approach is proposed and shown to yield results that almost perfectly match the Hamiltonian system. © 2005 The American Physical Society.

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A new numerical model which incorporates Brillouin shift frequency variations arising from fibre inhomogeneities has been developed for stimulated Brillouin scattering in optical fibres. This enables simulations of backscattered and transmitted power as functions of input power based only on known physical and material parameters as well as the polarisation factor and the measured Brillouin gain linewidth for the fibre. Agreement between modelled and experimental power characteristics for a CW input is excellent.

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This thesis presents theoretical investigation of three topics concerned with nonlinear optical pulse propagation in optical fibres. The techniques used are mathematical analysis and numerical modelling. Firstly, dispersion-managed (DM) solitons in fibre lines employing a weak dispersion map are analysed by means of a perturbation approach. In the case of small dispersion map strengths the average pulse dynamics is described by a perturbation approach (NLS) equation. Applying a perturbation theory, based on the Inverse Scattering Transform method, an analytic expression for the envelope of the DM soliton is derived. This expression correctly predicts the power enhancement arising from the dispersion management.Secondly, autosoliton transmission in DM fibre systems with periodical in-line deployment of nonlinear optical loop mirrors (NOLMs) is investigated. The use of in-line NOLMs is addressed as a general technique for all-optical passive 2R regeneration of return-to-zero data in high speed transmission system with strong dispersion management. By system optimisation, the feasibility of ultra-long single-channel and wavelength-division multiplexed data transmission at bit-rates ³ 40 Gbit s-1 in standard fibre-based systems is demonstrated. The tolerance limits of the results are defined.Thirdly, solutions of the NLS equation with gain and normal dispersion, that describes optical pulse propagation in an amplifying medium, are examined. A self-similar parabolic solution in the energy-containing core of the pulse is matched through Painlevé functions to the linear low-amplitude tails. The analysis provides a full description of the features of high-power pulses generated in an amplifying medium.

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The generally accepted paradigm of 'inert' and 'mono functional' excipient in dosage form has been recently challenged with the development of individual excipients capable of exhibiting multiple functions (e.g. binder-disintegrants, surfactant which affect P-gp function). The proposed study has been designed within the realm of multifunctionality and is the first and novel investigation towards evaluation of aspartic acid as a filler and disintegration enhancing agent for the delivery of biopharmaceutical class IV model drug trimethoprim. The study investigated powder characteristics using angle of repose, laser diffractometry and scanning electron microscopy (SEM). The prepared tablets were characterised using Heckel analysis, disintegration time and tensile strength measurements. Although Heckel analysis revealed that both TMP and TMP aspartate salt have high elasticity, the salt form produced a stronger compact which was attributed to the formation of agglomerates. Aspartic acid was found to have high plasticity, but its incorporation into the formulations was found to have a negative impact on the compaction properties of TMP and its salt. Surface morphology investigations showed that mechanical interlocking plays a vital role in binding TMP crystals together during compaction, while the small particle size of TMP aspartate agglomerates was found to have significant impact on the tensile strength of the tablets. The study concluded that aspartic acid can be employed as filler and disintegrant and that compactability within tablets was independent of the surface charge of the excipients.

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The purpose of the present study is to make a comparative evaluation of the legislative controls on unfairness in the context of B2B, B2C and small businesses contracts in England and Brazil. This work will focus on the examination of statutes and relevant case law which regulate exemption clauses and terms on the basis of their ‘unfairness’. The approach adopted by legislation and courts towards the above controls may vary according to the type of contract. Business contracts are more in line with the classical model of contract law according to which parties are presumably equals and able to negotiate terms. As a consequence interventions should be avoided for the sake of freedom of contract even if harmful terms were included. Such assumption of equality however is not applicable to small businesses contracts because SMEs are often in a disadvantageous position in relation to their larger counterparties. Consumer contracts in their turn are more closely regulated by the English and Brazilian legal systems which recognised that vulnerable parties are more exposed to unfair terms imposed by the stronger party as a result of the inequality of bargaining power. For this reason those jurisdictions adopted a more interventionist approach to provide special protection to consumers which is in line with the modern law of contract. The contribution of this work therefore consists of comparing how the law of England and Brazil tackles the problem of ‘unfairness’ in the above types of contracts. This study will examine the differences and similarities between rules and concepts of both jurisdictions with references to the law of their respective regional trade agreements (EU and the Mercosul). Moreover it will identify existing issues in the English and Brazilian legislation and recommend lessons that one system can learn from the other.

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We investigate the problem of determining the stationary temperature field on an inclusion from given Cauchy data on an accessible exterior boundary. On this accessible part the temperature (or the heat flux) is known, and, additionally, on a portion of this exterior boundary the heat flux (or temperature) is also given. We propose a direct boundary integral approach in combination with Tikhonov regularization for the stable determination of the temperature and flux on the inclusion. To determine these quantities on the inclusion, boundary integral equations are derived using Green’s functions, and properties of these equations are shown in an L2-setting. An effective way of discretizing these boundary integral equations based on the Nystr¨om method and trigonometric approximations, is outlined. Numerical examples are included, both with exact and noisy data, showing that accurate approximations can be obtained with small computational effort, and the accuracy is increasing with the length of the portion of the boundary where the additionally data is given.

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We consider the problem of stable determination of a harmonic function from knowledge of the solution and its normal derivative on a part of the boundary of the (bounded) solution domain. The alternating method is a procedure to generate an approximation to the harmonic function from such Cauchy data and we investigate a numerical implementation of this procedure based on Fredholm integral equations and Nyström discretization schemes, which makes it possible to perform a large number of iterations (millions) with minor computational cost (seconds) and high accuracy. Moreover, the original problem is rewritten as a fixed point equation on the boundary, and various other direct regularization techniques are discussed to solve that equation. We also discuss how knowledge of the smoothness of the data can be used to further improve the accuracy. Numerical examples are presented showing that accurate approximations of both the solution and its normal derivative can be obtained with much less computational time than in previous works.

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In 1998 the Accounting Standards Board (ASB) published FRS 13, ‘Derivatives and other Financial Instruments: Disclosures’. This laid down the requirements for disclosures of an entity’s policies, objectives and strategies in using financial instruments, their impact on its risk, performance and financial condition, and details of how risks are managed. FRS 13 became effective in March 1999, and this paper uses the 1999 annual reports of UK banks to evaluate the usefulness of disclosures from a user’s perspective. Usefulness is measured in terms of the criteria of materiality, relevance, reliability, comparability and understandability as defined in the ASB’s Statement of Principles (ASB, 1999). Our findings suggest that the narrative disclosures are generic in nature, the numerical data incomplete and not always comparable, and that it is difficult for the user to combine both narrative and numerical information in order to assess the banks’ risk profile. Our overall conclusion is therefore that current UK financial reporting practices are of limited help to users wishing to assess the scale of an institution’s financial risk exposure.

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Plant oxylipins are a large family of metabolites derived from polyunsaturated fatty acids. The characterization of mutants or transgenic plants affected in the biosynthesis or perception of oxylipins has recently emphasized the role of the so-called oxylipin pathway in plant defense against pests and pathogens. In this context, presumed functions of oxylipins include direct antimicrobial effect, stimulation of plant defense gene expression, and regulation of plant cell death. However, the precise contribution of individual oxylipins to plant defense remains essentially unknown. To get a better insight into the biological activities of oxylipins, in vitro growth inhibition assays were used to investigate the direct antimicrobial activities of 43 natural oxylipins against a set of 13 plant pathogenic microorganisms including bacteria, oomycetes, and fungi. This study showed unequivocally that most oxylipins are able to impair growth of some plant microbial pathogens, with only two out of 43 oxylipins being completely inactive against all the tested organisms, and 26 oxylipins showing inhibitory activity toward at least three different microbes. Six oxylipins strongly inhibited mycelial growth and spore germination of eukaryotic microbes, including compounds that had not previously been ascribed an antimicrobial activity such as 13-keto-9(Z),11(Z),15(Z)- octadecatrienoic acid and 12-oxo-10,15(Z)-phytodienoic acid. Interestingly this first large-scale comparative assessment of the antimicrobial effects of oxylipins reveals that regulators of plant defense responses are also the most active oxylipins against eukaryotic microorganisms, suggesting that such oxylipins might contribute to plant defense through their effects both on the plant and on pathogens, possibly through related mechanisms. © 2005 American Society of Plant Biologists.

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An iterative method for the parabolic Cauchy problem in planar domains having a finite number of corners is implemented based on boundary integral equations. At each iteration, mixed well-posed problems are solved for the same parabolic operator. The presence of corner points renders singularities of the solutions to these mixed problems, and this is handled with the use of weight functions together with, in the numerical implementation, mesh grading near the corners. The mixed problems are reformulated in terms of boundary integrals obtained via discretization of the time-derivative to obtain an elliptic system of partial differential equations. To numerically solve these integral equations a Nyström method with super-algebraic convergence order is employed. Numerical results are presented showing the feasibility of the proposed approach. © 2014 IMACS.

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We show, by numerical simulation, that the impact of tight optical filtering in high speed coherent 50% RZ-BPSK systems can be greatly reduced by offsetting the filter (equivalent to laser detuning). We show that by offsetting the filter by up to half the filter bandwidth, that system performance is improved by > 2.5 dB in the calculated 'Q' for an OSNR of 12 dB. © 2013 IEEE.

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A numerical method for the Dirichlet initial boundary value problem for the heat equation in the exterior and unbounded region of a smooth closed simply connected 3-dimensional domain is proposed and investigated. This method is based on a combination of a Laguerre transformation with respect to the time variable and an integral equation approach in the spatial variables. Using the Laguerre transformation in time reduces the parabolic problem to a sequence of stationary elliptic problems which are solved by a boundary layer approach giving a sequence of boundary integral equations of the first kind to solve. Under the assumption that the boundary surface of the solution domain has a one-to-one mapping onto the unit sphere, these integral equations are transformed and rewritten over this sphere. The numerical discretisation and solution are obtained by a discrete projection method involving spherical harmonic functions. Numerical results are included.