A comparative evaluation of the legislative controls on unfair terms and exemption clauses in consumer and business contracts in England and Brazil

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.

On the numerical solution of a Cauchy problem for the Laplace equation via a direct integral equation approach

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.

Fast reconstruction of harmonic functions from Cauchy data using integral equation techniques

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.

Accounting for derivatives:an evaluation of reporting practice by UK banks

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.

Evaluation of the antimicrobial activities of plant oxylipins supports their involvement in defense against pathogens

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.

Partial Quasi-Bilateral Generating Function Involving some Special Functions

A group-theoretic method of obtaining more general class of generating functions from a given class of partial quasi-bilateral generating functions involving Hermite, Laguerre and Gegenbaur polynomials are discussed.

Generalizing of Neural Nets: Functional Nets of Special Type

Special generalizing for the artificial neural nets: so called RFT – FN – is under discussion in the report. Such refinement touch upon the constituent elements for the conception of artificial neural network, namely, the choice of main primary functional elements in the net, the way to connect them(topology) and the structure of the net as a whole. As to the last, the structure of the functional net proposed is determined dynamically just in the constructing the net by itself by the special recurrent procedure. The number of newly joining primary functional elements, the topology of its connecting and tuning of the primary elements is the content of the each recurrent step. The procedure is terminated under fulfilling “natural” criteria relating residuals for example. The functional proposed can be used in solving the approximation problem for the functions, represented by its observations, for classifying and clustering, pattern recognition, etc. Recurrent procedure provide for the versatile optimizing possibilities: as on the each step of the procedure and wholly: by the choice of the newly joining elements, topology, by the affine transformations if input and intermediate coordinate as well as by its nonlinear coordinate wise transformations. All considerations are essentially based, constructively and evidently represented by the means of the Generalized Inverse.

Numerical solution of parabolic Cauchy problems in planar corner domains

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.

Evaluation of Pareto/D/1/k Queue by Simulation

The finding that Pareto distributions are adequate to model Internet packet interarrival times has motivated the proposal of methods to evaluate steady-state performance measures of Pareto/D/1/k queues. Some limited analytical derivation for queue models has been proposed in the literature, but their solutions are often of a great mathematical challenge. To overcome such limitations, simulation tools that can deal with general queueing system must be developed. Despite certain limitations, simulation algorithms provide a mechanism to obtain insight and good numerical approximation to parameters of queues. In this work, we give an overview of some of these methods and compare them with our simulation approach, which are suited to solve queues with Generalized-Pareto interarrival time distributions. The paper discusses the properties and use of the Pareto distribution. We propose a real time trace simulation model for estimating the steady-state probability showing the tail-raising effect, loss probability, delay of the Pareto/D/1/k queue and make a comparison with M/D/1/k. The background on Internet traffic will help to do the evaluation correctly. This model can be used to study the long- tailed queueing systems. We close the paper with some general comments and offer thoughts about future work.

On Two Saigo’s Fractional Integral Operators in the Class of Univalent Functions

2000 Mathematics Subject Classification: Primary 26A33, 30C45; Secondary 33A35

Fractional Integration of the Product of Bessel Functions of the First Kind

Dedicated to 75th birthday of Prof. A.M. Mathai, Mathematical Subject Classification 2010:26A33, 33C10, 33C20, 33C50, 33C60, 26A09

Generalized Fractional Calculus, Special Functions and Integral Transforms: What is the Relation?

Виржиния С. Кирякова - В този обзор илюстрираме накратко наши приноси към обобщенията на дробното смятане (анализ) като теория на операторите за интегриране и диференциране от произволен (дробен) ред, на класическите специални функции и на интегралните трансформации от лапласов тип. Показано е, че тези три области на анализа са тясно свързани и взаимно индуцират своето възникване и по-нататъшно развитие. За конкретните твърдения, доказателства и примери, вж. Литературата.

Numerical Issues in Using MATLAB

Михаил Константинов, Весела Пашева, Петко Петков - Разгледани са някои числени проблеми при използването на компютърната система MATLAB в учебната дейност: пресмятане на тригонометрични функции, повдигане на матрица на степен, спектрален анализ на целочислени матрици от нисък ред и пресмятане на корените на алгебрични уравнения. Причините за възникналите числени трудности могат да се обяснят с особеностите на използваната двоичната аритметика с плаваща точка.

Comparison of Multivariate and Univariate Models for Genetic Evaluation of Milk Yield based on Test Day Data

2000 Mathematics Subject Classification: 62H12, 62P99

Performance evaluation of strongly filtered asymmetric 42.7 Gb/s coherent 50%RZ-BPSK system

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.