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.

Compositional data analysis of archaeological glass: problems and possible solutions

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

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.

Soluciones isotónicas versus hipotónicas como líquidos de mantenimiento en niños en estado crítico

El desarrollo de hiponatremia aguda en los pacientes hospitalizados se ha asociado con el uso de líquidos de mantenimiento hipotónicos.3,5-7,11-13,15-21 El propósito de este estudio es determinar si el uso de soluciones hipotónicas (60 meq/l Na) como líquidos de mantenimiento en niños críticos inducen más hiponatremia aguda que soluciones isotónicas (lactato ringer). Método: Se realizó un estudio retrospectivo de cohorte, que incluyó los niños que ingresaron a la UCIP de la Fundación Cardioinfantil desde septiembre de 2009 a diciembre de 2011 con edades entre 6 meses y 10 años, quienes requirieron líquidos endovenosos de mantenimiento con 60 meq/l de sodio o lactato Ringer. Resultados: En total se estudiaron 117 pacientes de los cuales 71 niños recibieron 60 meq/L de Na y 46 recibieron lactato Ringer, las características demográficas y clínicas fueron similares en ambos grupos. De los pacientes que recibieron 60 meq/L de sodio se encontró hiponatremia en un 28,1% ( n= 20) vs 17.4% ( n=8) de los que recibieron 130 meq /l sodio, sin observar diferencias significativas ( RR 1,863 IC95% 0,779- 4,680 p=0.1302) . Conclusiones: En niños críticos que requieren líquidos de mantenimiento no se encontraron diferencias en la frecuencia de aparición de hiponatremia sintomática inducidas por el tipo de solución utilizada. El lactato de Ringer y la Dextrosa con 60 mq/lit de sodio fueron seguros y efectivos para sostener el estado de hidratación.

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

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.

Evaluating the performance of external fault ridethrough solutions used in wind farms with fixed speed induction generators when facing unbalanced faults

Na sequência da integração da energia eólica em larga escala foram estabelecidos códigos de rede pelos vários operadores de sistema, exigindo que os parques eólicos permaneçam em serviço durante e após a ocorrência de defeitos na rede a montante. Nos parques eólicos equipados com sistemas de velocidade constante este requisito pode ser assegurado pela instalação, no ponto de interligação à rede, de equipamento de compensação dinâmica de potência reactiva, controlado como fonte de tensão, sendo as funções de controlo baseadas em medidas efectuadas no ponto de interligação relativamente às componentes directas da tensão e da corrente. Como a adopção deste tipo de soluções externas é adequada ao funcionamento do sistema em regime equilibrado, este artigo foca a avaliação do desempenho da solução no caso da ocorrência de defeitos assimétricos. Os resultados obtidos através das simulações dinâmicas evidenciam o aparecimento de sobre tensões nas fases não afectadas pelo defeito que poderão colocar o parque eólico fora de serviço.

Aviation solutions

Overview Some of the Challenges - Future Technology - Capacity - Safety Working with Airports, Air Traffic Service Providers and Airlines The Role of the Regulator Air Traffic Service Providers