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.

Nuclear relaxation contribution to static and dynamic (infinite frequency approximation) nonlinear optical properties by means of electrical property expansions: Application to HF, CH4, CF4, and SF6

Electrical property derivative expressions are presented for the nuclear relaxation contribution to static and dynamic (infinite frequency approximation) nonlinear optical properties. For CF4 and SF6, as opposed to HF and CH4, a term that is quadratic in the vibrational anharmonicity (and not previously evaluated for any molecule) makes an important contribution to the static second vibrational hyperpolarizability of CF4 and SF6. A comparison between calculated and experimental values for the difference between the (anisotropic) Kerr effect and electric field induced second-harmonic generation shows that, at the Hartree-Fock level, the nuclear relaxation/infinite frequency approximation gives the correct trend (in the series CH4, CF4, SF6) but is of the order of 50% too small

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

Technological Solutions Potentially Influencing the Future of Long-Term Care. ENEPRI Research Report No. 114, April 2012

This report provides a forecast of the potential direct and indirect influences of various kinds of technologies on the LTC milieu, answering the following question: from a technology-driven perspective: “Consider each technological solution. What could be its future usage in the LTC sector?” Future technological deployments will induce changes in the respective roles of the care recipient and of the formal and informal carers, with an impact on three major concerns: the transformation of the care recipient into a proactive subject, the augmented potentiality for home care and the new functions that informal carers could assume.

The euro crisis: ten roots, but fewer solutions. Bruegel Policy Contribution 2012/17, October 2012

Many factors have contributed to the euro crisis. Some have been addressed by policymakers, even if belatedly, and European Union member states have been willing to improve the functioning of the euro area by agreeing to relinquish national sovereignty in some important areas. However, the most pressing issue threatening the integrity, even the existence, of the euro, has not been addressed: the deepening economic contraction in southern euro-area member states. The common interest lies in preserving the integrity of the euro area and in offering these countries improved prospects. Domestic structural reform and appropriate fiscal consolidation, wage increases and slower fiscal consolidation in economically stronger euro-area countries, a weaker euro exchange rate, debt restructuring and an investment programme should be part of the arsenal. In the medium term, more institutional change will be necessary to complement the planned overhaul of the euro area institutional framework. This will include the deployment of a euro-area economic stabilising tool, managing the overall fiscal stance of the euro area, some form of Eurobonds and measures to make euro-area level decision making bodies more effective and democratically legitimate.

On the convergence of the no response test

The no response test is a new scheme in inverse problems for partial differential equations which was recently proposed in [D. R. Luke and R. Potthast, SIAM J. Appl. Math., 63 (2003), pp. 1292–1312] in the framework of inverse acoustic scattering problems. The main idea of the scheme is to construct special probing waves which are small on some test domain. Then the response for these waves is constructed. If the response is small, the unknown object is assumed to be a subset of the test domain. The response is constructed from one, several, or many particular solutions of the problem under consideration. In this paper, we investigate the convergence of the no response test for the reconstruction information about inclusions D from the Cauchy values of solutions to the Helmholtz equation on an outer surface $\partial\Omega$ with $\overline{D} \subset \Omega$. We show that the one‐wave no response test provides a criterion to test the analytic extensibility of a field. In particular, we investigate the construction of approximations for the set of singular points $N(u)$ of the total fields u from one given pair of Cauchy data. Thus, the no response test solves a particular version of the classical Cauchy problem. Also, if an infinite number of fields is given, we prove that a multifield version of the no response test reconstructs the unknown inclusion D. This is the first convergence analysis which could be achieved for the no response test.