Exercise sheet 8

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Exam 86 pdf

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Exam 87 pdf

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Exam 87

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Exam 86

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271 Exam 84

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Exam 83

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Exercise sheet 2 pdf

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Exam 83 pdf

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Exam 88 pdf

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Exam 84

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Análisis estratégico sector de transporte de carga por carretera

En este trabajo se desarrolla el modelo de Análisis Estructural de Sectores Estratégicos y un estudio de las fuerzas del mercado del sector de transporte de carga por Carreteras. Para el desarrollo de estos modelos se requiere de información financiera, información del sector, información interna de la empresa y conocimiento de términos estratégicos. Adicionalmente, se hizo un estudio estratégico de la compañía de transporte EXXE y se determinaron los encajes, las renuncias y las singularidades de esta compañía. Este es un ejercicio que le servirá a muchas compañías del sector como ejemplo para poder identificar el estado en el que se encuentran y tomar las decisiones adecuadas y con fundamentos teóricos y estratégicos.

A ponderação de bens em Direito Administrativo

Quando duas normas jurídicas entram em conflito não resolúvel por inexistência de normas de conflito (o que acontece em especial no domínio dos direitos fundamentais ou quando se tentam aplicar princípios jurídicos), a solução em direito não pode ser por subsunção, tem de ser através da ponderação. A ponderação não deve ser subjetiva, mas objetiva, baseada num sistema controlável externamente. O sistema neste momento internacionalmente mais reputado de fazer a ponderação é a fórmula do peso de Robert Alexy. Aqui explica-se em que consiste a ponderação de bens, a sua origem e expressão noutros países, a sua admissibilidade, a referida fórmula, e defende-se a aplicação de um sistema alternativo baseado na teoria psicológica da pirâmide das necessidades humanas, de Abraham Maslow. Verifica-se a validade das teses testando-as em casos concretos. Faz-se ainda a aplicação destes princípios a problemas próprios do direito administrativo.

Efficient evaluation of highly oscillatory acoustic scattering surface integrals

We consider the approximation of some highly oscillatory weakly singular surface integrals, arising from boundary integral methods with smooth global basis functions for solving problems of high frequency acoustic scattering by three-dimensional convex obstacles, described globally in spherical coordinates. As the frequency of the incident wave increases, the performance of standard quadrature schemes deteriorates. Naive application of asymptotic schemes also fails due to the weak singularity. We propose here a new scheme based on a combination of an asymptotic approach and exact treatment of singularities in an appropriate coordinate system. For the case of a spherical scatterer we demonstrate via error analysis and numerical results that, provided the observation point is sufficiently far from the shadow boundary, a high level of accuracy can be achieved with a minimal computational cost.

Perspex machine IX: transreal analysis

We introduce transreal analysis as a generalisation of real analysis. We find that the generalisation of the real exponential and logarithmic functions is well defined for all transreal numbers. Hence, we derive well defined values of all transreal powers of all non-negative transreal numbers. In particular, we find a well defined value for zero to the power of zero. We also note that the computation of products via the transreal logarithm is identical to the transreal product, as expected. We then generalise all of the common, real, trigonometric functions to transreal functions and show that transreal (sin x)/x is well defined everywhere. This raises the possibility that transreal analysis is total, in other words, that every function and every limit is everywhere well defined. If so, transreal analysis should be an adequate mathematical basis for analysing the perspex machine - a theoretical, super-Turing machine that operates on a total geometry. We go on to dispel all of the standard counter "proofs" that purport to show that division by zero is impossible. This is done simply by carrying the proof through in transreal arithmetic or transreal analysis. We find that either the supposed counter proof has no content or else that it supports the contention that division by zero is possible. The supposed counter proofs rely on extending the standard systems in arbitrary and inconsistent ways and then showing, tautologously, that the chosen extensions are not consistent. This shows only that the chosen extensions are inconsistent and does not bear on the question of whether division by zero is logically possible. By contrast, transreal arithmetic is total and consistent so it defeats any possible "straw man" argument. Finally, we show how to arrange that a function has finite or else unmeasurable (nullity) values, but no infinite values. This arithmetical arrangement might prove useful in mathematical physics because it outlaws naked singularities in all equations.