Solutions of Tikhonov functional equations and applications to multiplication operators on Szegö spaces

We consider a natural representation of solutions for Tikhonov functional equations. This will be done by applying the theory of reproducing kernels to the approximate solutions of general bounded linear operator equations (when defined from reproducing kernel Hilbert spaces into general Hilbert spaces), by using the Hilbert-Schmidt property and tensor product of Hilbert spaces. As a concrete case, we shall consider generalized fractional functions formed by the quotient of Bergman functions by Szegö functions considered from the multiplication operators on the Szegö spaces.

Regularization and Bang-bang conjugate times in optimal control

Consideramos o problema de controlo óptimo de tempo mínimo para sistemas de controlo mono-entrada e controlo afim num espaço de dimensão finita com condições inicial e final fixas, onde o controlo escalar toma valores num intervalo fechado. Quando aplicamos o método de tiro a este problema, vários obstáculos podem surgir uma vez que a função de tiro não é diferenciável quando o controlo é bang-bang. No caso bang-bang os tempos conjugados são teoricamente bem definidos para este tipo de sistemas de controlo, contudo os algoritmos computacionais directos disponíveis são de difícil aplicação. Por outro lado, no caso suave o conceito teórico e prático de tempos conjugados é bem conhecido, e ferramentas computacionais eficazes estão disponíveis. Propomos um procedimento de regularização para o qual as soluções do problema de tempo mínimo correspondente dependem de um parâmetro real positivo suficientemente pequeno e são definidas por funções suaves em relação à variável tempo, facilitando a aplicação do método de tiro simples. Provamos, sob hipóteses convenientes, a convergência forte das soluções do problema regularizado para a solução do problema inicial, quando o parâmetro real tende para zero. A determinação de tempos conjugados das trajectórias localmente óptimas do problema regularizado enquadra-se na teoria suave conhecida. Provamos, sob hipóteses adequadas, a convergência do primeiro tempo conjugado do problema regularizado para o primeiro tempo conjugado do problema inicial bang-bang, quando o parâmetro real tende para zero. Consequentemente, obtemos um algoritmo eficiente para a computação de tempos conjugados no caso bang-bang.

Valorization of solid wastes from cellulose and paper industry

This thesis reports in detail studies of industrial solid wastes valorization as alternative raw materials. All tested wastes are classified as non-hazardous and are generated in the pulp and paper process, including primary sludge, dregs, grits, lime mud and bottom ash (this generated in a process that occurs in parallel to the production of cellulose, whose aim is the production of energy to supply the plant through the combustion of forest biomass in fluidized bed). A detailed general characterization was performed at each waste and according to their characteristics, they were selected some applications in materials with potential use, specifically in Fibercement, Bituminous Mixture for regularization layer and industrial mortars (rendering mortars and cementitious-adhesive). After decided to application each waste was specifically tested to proceed the setting up of formulations containing different content of waste in replacement of the raw conventional material. As an isolated case, the bottom ash was tested not only as an alternative raw material for construction materials, but also it was tested for its use in fluidized bed in which the waste is generated as raw material. Both dregs and bottom ash had undergone special treatment to make possible to obtain a better quality of waste in order do not compromise the final product characteristics and process. The dregs were tested in bituminous mixtures as received and also washed (on the laboratory scale to remove soluble salts) and bottom ash were washed and screened in industrial scale (for removal of soluble salts, especially chlorides and coarse fraction particles elimination - particles larger than 1 mm size). The remaining residues form used in such as received avoiding additional costs. The results indicated potential and some limitations for each application to the use of these wastes as alternative raw material, but in some cases, the benefits in relation to valorization overlap with its limitations in both aspects, environmental and economic.