Approximate solutions and error estimates for a Stokes boundary value problem

The aim of this paper is the numerical treatment of a boundary value problem for the system of Stokes' equations. For this we extend the method of approximate approximations to boundary value problems. This method was introduced by V. Maz'ya in 1991 and has been used until now for the approximation of smooth functions defined on the whole space and for the approximation of volume potentials. In the present paper we develop an approximation procedure for the solution of the interior Dirichlet problem for the system of Stokes' equations in two dimensions. The procedure is based on potential theoretical considerations in connection with a boundary integral equations method and consists of three approximation steps as follows. In a first step the unknown source density in the potential representation of the solution is replaced by approximate approximations. In a second step the decay behavior of the generating functions is used to gain a suitable approximation for the potential kernel, and in a third step Nyström's method leads to a linear algebraic system for the approximate source density. For every step a convergence analysis is established and corresponding error estimates are given.

On Solutions of Holonomic Divided-Difference Equations on Non-Uniform Lattices

The main aim of this paper is the development of suitable bases (replacing the power basis x^n (n\in\IN_\le 0) which enable the direct series representation of orthogonal polynomial systems on non-uniform lattices (quadratic lattices of a discrete or a q-discrete variable). We present two bases of this type, the first of which allows to write solutions of arbitrary divided-difference equations in terms of series representations extending results given in [16] for the q-case. Furthermore it enables the representation of the Stieltjes function which can be used to prove the equivalence between the Pearson equation for a given linear functional and the Riccati equation for the formal Stieltjes function. If the Askey-Wilson polynomials are written in terms of this basis, however, the coefficients turn out to be not q-hypergeometric. Therefore, we present a second basis, which shares several relevant properties with the first one. This basis enables to generate the defining representation of the Askey-Wilson polynomials directly from their divided-difference equation. For this purpose the divided-difference equation must be rewritten in terms of suitable divided-difference operators developed in [5], see also [6].

Controlling the transport of an ion: classical and quantum mechanical solutions

The accurate transport of an ion over macroscopic distances represents a challenging control problem due to the different length and time scales that enter and the experimental limitations on the controls that need to be accounted for. Here, we investigate the performance of different control techniques for ion transport in state-of-the-art segmented miniaturized ion traps. We employ numerical optimization of classical trajectories and quantum wavepacket propagation as well as analytical solutions derived from invariant based inverse engineering and geometric optimal control. The applicability of each of the control methods depends on the length and time scales of the transport. Our comprehensive set of tools allows us make a number of observations. We find that accurate shuttling can be performed with operation times below the trap oscillation period. The maximum speed is limited by the maximum acceleration that can be exerted on the ion. When using controls obtained from classical dynamics for wavepacket propagation, wavepacket squeezing is the only quantum effect that comes into play for a large range of trapping parameters. We show that this can be corrected by a compensating force derived from invariant based inverse engineering, without a significant increase in the operation time.

Perceptually-based Comparison of Image Similarity Metrics

The image comparison operation ??sessing how well one image matches another ??rms a critical component of many image analysis systems and models of human visual processing. Two norms used commonly for this purpose are L1 and L2, which are specific instances of the Minkowski metric. However, there is often not a principled reason for selecting one norm over the other. One way to address this problem is by examining whether one metric better captures the perceptual notion of image similarity than the other. With this goal, we examined perceptual preferences for images retrieved on the basis of the L1 versus the L2 norm. These images were either small fragments without recognizable content, or larger patterns with recognizable content created via vector quantization. In both conditions the subjects showed a consistent preference for images matched using the L1 metric. These results suggest that, in the domain of natural images of the kind we have used, the L1 metric may better capture human notions of image similarity.

Compositional data analysis of archaeological glass: problems and possible solutions

Presentation in CODAWORK'03, session 4: Applications to archeometry

Actividades para la ense??anza de ingl??s a trav??s de contenidos en secundaria (II)

El Programa PALE (programa de apoyo al aprendizaje de lenguas extranjeras), cofinanciado por el Ministerio de Educaci??n y Ciencia y las Comunidades Aut??nomas, pretende dar respuesta, desde el Sistema Educativo, a las necesidades derivadas de la mejora de la ense??anza y el aprendizaje de lenguas extranjeras en una sociedad como la actual, donde las lenguas se consideran conocimientos b??sicos que precisa la ciudadan??a europea para su formaci??n, para mejorar sus posibilidades de empleo, para la promoci??n del intercambio cultural y para la realizaci??n persona. El material incluido en este Cd-Rom ha sido realizado en la tercera fase del curso PALE 2008 para Secundaria del CPR de Oviedo, tras la formaci??n recibida en Asturias y en el extranjero, mediante la constituci??n de un grupo de trabajo. Consta de una serie de presentaciones realizadas durante el desarrollo del curso PALE, de once unidades did??cticas en relaci??n con distintas ??reas en las que se ejemplifica la forma de trabajar la ense??anza a trav??s de contenidos, CLIL ('Content and Language Integrated Learning'), de una gu??a para la realizaci??n de presentaciones orales y de un listado de frases ??tiles para el profesorado. Las materias y las unidades trabajadas son: 1) Art: Multimedia language: building images. 2) Biology: Healthy habits and healthy life y 'Health and disease'. 3) Chemistry: 'Chemical reactions'. 4) Citizenship and Ethics: 'Conflicts and solutions' y 'The rights of our body'. 5) Maths: 'Equations' y 'Similarity'. 6) Music: 'The singing voice'. 7). Physical Education: 'Welcome to the world of PE' y 'Health related fitness'.

Classification of sags according to their origin based on the waveform similarity

A statistical method for classification of sags their origin downstream or upstream from the recording point is proposed in this work. The goal is to obtain a statistical model using the sag waveforms useful to characterise one type of sags and to discriminate them from the other type. This model is built on the basis of multi-way principal component analysis an later used to project the available registers in a new space with lower dimension. Thus, a case base of diagnosed sags is built in the projection space. Finally classification is done by comparing new sags against the existing in the case base. Similarity is defined in the projection space using a combination of distances to recover the nearest neighbours to the new sag. Finally the method assigns the origin of the new sag according to the origin of their neighbours

Building Software Solutions

This presentation explains how we move from a problem definition to an algorithmic solution using simple tools like noun verb analysis. It also looks at how we might judge the quality of a solution through coupling, cohesion and generalisation.

"Thematically Analysing Social Network Content During Disasters Through the Lens of the Disaster Management Lifecycle" & "Investigating Similarity Between Privacy Policies of Social Networking Sites as a Precursor for Standardization"

Abstract 1: Social Networks such as Twitter are often used for disseminating and collecting information during natural disasters. The potential for its use in Disaster Management has been acknowledged. However, more nuanced understanding of the communications that take place on social networks are required to more effectively integrate this information into the processes within disaster management. The type and value of information shared should be assessed, determining the benefits and issues, with credibility and reliability as known concerns. Mapping the tweets in relation to the modelled stages of a disaster can be a useful evaluation for determining the benefits/drawbacks of using data from social networks, such as Twitter, in disaster management.A thematic analysis of tweets’ content, language and tone during the UK Storms and Floods 2013/14 was conducted. Manual scripting was used to determine the official sequence of events, and classify the stages of the disaster into the phases of the Disaster Management Lifecycle, to produce a timeline. Twenty- five topics discussed on Twitter emerged, and three key types of tweets, based on the language and tone, were identified. The timeline represents the events of the disaster, according to the Met Office reports, classed into B. Faulkner’s Disaster Management Lifecycle framework. Context is provided when observing the analysed tweets against the timeline. This illustrates a potential basis and benefit for mapping tweets into the Disaster Management Lifecycle phases. Comparing the number of tweets submitted in each month with the timeline, suggests users tweet more as an event heightens and persists. Furthermore, users generally express greater emotion and urgency in their tweets.This paper concludes that the thematic analysis of content on social networks, such as Twitter, can be useful in gaining additional perspectives for disaster management. It demonstrates that mapping tweets into the phases of a Disaster Management Lifecycle model can have benefits in the recovery phase, not just in the response phase, to potentially improve future policies and activities. Abstract2: The current execution of privacy policies, as a mode of communicating information to users, is unsatisfactory. Social networking sites (SNS) exemplify this issue, attracting growing concerns regarding their use of personal data and its effect on user privacy. This demonstrates the need for more informative policies. However, SNS lack the incentives required to improve policies, which is exacerbated by the difficulties of creating a policy that is both concise and compliant. Standardization addresses many of these issues, providing benefits for users and SNS, although it is only possible if policies share attributes which can be standardized. This investigation used thematic analysis and cross- document structure theory, to assess the similarity of attributes between the privacy policies (as available in August 2014), of the six most frequently visited SNS globally. Using the Jaccard similarity coefficient, two types of attribute were measured; the clauses used by SNS and the coverage of forty recommendations made by the UK Information Commissioner’s Office. Analysis showed that whilst similarity in the clauses used was low, similarity in the recommendations covered was high, indicating that SNS use different clauses, but to convey similar information. The analysis also showed that low similarity in the clauses was largely due to differences in semantics, elaboration and functionality between SNS. Therefore, this paper proposes that the policies of SNS already share attributes, indicating the feasibility of standardization and five recommendations are made to begin facilitating this, based on the findings of the investigation.

Dynamic programming for stochastic target problems, Viscosity solutions and hedging in markets with Portfolio constraints and large investors

The purpose of this expository arti le is to present a self- ontained overview of some results on the hara terization of the optimal value fun tion of a sto hasti target problem as (dis ontinuous) vis osity solution of a ertain dynami programming PDE and its appli ation to the problem of hedging ontingent laims in the presen e of portfolio onstraints and large investors

Phonological short term memory in deaf children fitted with a cochlear implant : effects of phonological similarity, word lenght and lipreading cues. 'La memoria fonológica a corto plazo en niños sordos con implante coclear : efectos de la similitud fonológica, la longitud de la palabra y la lectura labial'.

Resumen basado en el de la publicación. Resumen en español

500 activities for the primary classroom: inmediate ideas and solutions.

Compendio de actividades para profesores de niños entre cuatro y doce años. El recurso se divide en diez secciones que reflejan las áreas clave en la enseñanza del idioma: la escucha y el habla, la lectura y la escritura, vocabulario y gramática, cuentos y teatro, juegos, rimas, cantos y canciones, el arte y la artesanía, el aprendizaje basado en contenidos, las TIC y multimedia, y aprender a aprender. Cada actividad incluye el rango de edad para la que puede ser adecuada.

Standard level Mathematics: worked solutions CD developed for the IB Diploma.

Este práctico CD-ROM de ejercicios cubre las necesidades básicas para conseguir el Diploma de Bachillerato Internacional en estudios de matemáticas. Los temas de los ejercicios del CD-ROM son: álgebra y números (ecuaciones de segundo grado), lógica y probabilidad, funciones (funciones exponenciales y gráficos), geometría y trigonometría (la regla del seno y el área de un triángulo, la regla del coseno), estadísticas (clasificación de datos, tablas de frecuencia y polígonos), cálculo diferencial (ecuaciones de línea tangentes), matemáticas financieras.

A quantum molecular similarity analysis of changes in molecular electron density caused by basis set flotation and electric field application

Quantum molecular similarity (QMS) techniques are used to assess the response of the electron density of various small molecules to application of a static, uniform electric field. Likewise, QMS is used to analyze the changes in electron density generated by the process of floating a basis set. The results obtained show an interrelation between the floating process, the optimum geometry, and the presence of an external field. Cases involving the Le Chatelier principle are discussed, and an insight on the changes of bond critical point properties, self-similarity values and density differences is performed