Esta tese aborda o problema de regulação para sistemas lineares sujeitos a saltos Markovianos de tempo discreto com matrizes de transição incertas. Considera-se que as incertezas são limitadas em norma e os estados da cadeia de Markov podem não ser completamente observados pelo controlador. No cenário com observação completa dos estados, a solução é deduzida com base em um funcional quadrático dado em termos das probabilidades de transição incertas. Enquanto que no cenário sem observação, a solução é obtida por meio da reformulação do sistema Markoviano como um sistema determinístico, independente da cadeia de Markov. Três modelos são propostos para essa reformulação: um modelo é baseado no primeiro momento do sistema Markoviano, o segundo é obtido a partir da medida de Dirac e resulta em um sistema aumentado, e o terceiro fornece um sistema aumentado singular. Os reguladores recursivos robustos são projetados a partir de critérios de custo quadrático, dados em termos de problemas de otimização restritos. A solução é derivada da técnica de mínimos quadrados regularizados robustos e apresentada em uma estrutura matricial. A recursividade é estabelecida por equações de Riccati, que se assemelham às soluções dos reguladores clássicos, para essa classe de sistemas, quando não estão sujeitos a incertezas. / This thesis deals with regulation problem for discrete-time Markovian jump linear systems with uncertain transition matrix. The uncertainties are assumed to be normbounded type. The states of the Markov chain can not be completely observed by the controller. In the scenario with complete observation of the states, the solution is deduced based on a quadratic functional given in terms of uncertain transition probabilities. While in the scenario without observation, the solution is obtained from reformulation of the Markovian system as a deterministic system, independent of the Markov chain. Three models are proposed for the reformulation process: a model is based on the first moment of the Markovian system, the second is obtained from Dirac measure which results in an augmented system, and the third provides a singular augmented system. Recursive robust regulators are designed from quadratic cost criteria given in terms of constrained optimization problems. The solution is derived from the robust regularized least-square approach, whose framework is given in terms of a matrix structure. The recursiveness is established by Riccati equations which resemble the solutions of standard regulators for this class of systems, when they are not subject to uncertainties.

Esta tese aborda o problema de regulação para sistemas lineares sujeitos a saltos Markovianos de tempo discreto com matrizes de transição incertas. Considera-se que as incertezas são limitadas em norma e os estados da cadeia de Markov podem não ser completamente observados pelo controlador. No cenário com observação completa dos estados, a solução é deduzida com base em um funcional quadrático dado em termos das probabilidades de transição incertas. Enquanto que no cenário sem observação, a solução é obtida por meio da reformulação do sistema Markoviano como um sistema determinístico, independente da cadeia de Markov. Três modelos são propostos para essa reformulação: um modelo é baseado no primeiro momento do sistema Markoviano, o segundo é obtido a partir da medida de Dirac e resulta em um sistema aumentado, e o terceiro fornece um sistema aumentado singular. Os reguladores recursivos robustos são projetados a partir de critérios de custo quadrático, dados em termos de problemas de otimização restritos. A solução é derivada da técnica de mínimos quadrados regularizados robustos e apresentada em uma estrutura matricial. A recursividade é estabelecida por equações de Riccati, que se assemelham às soluções dos reguladores clássicos, para essa classe de sistemas, quando não estão sujeitos a incertezas. / This thesis deals with regulation problem for discrete-time Markovian jump linear systems with uncertain transition matrix. The uncertainties are assumed to be normbounded type. The states of the Markov chain can not be completely observed by the controller. In the scenario with complete observation of the states, the solution is deduced based on a quadratic functional given in terms of uncertain transition probabilities. While in the scenario without observation, the solution is obtained from reformulation of the Markovian system as a deterministic system, independent of the Markov chain. Three models are proposed for the reformulation process: a model is based on the first moment of the Markovian system, the second is obtained from Dirac measure which results in an augmented system, and the third provides a singular augmented system. Recursive robust regulators are designed from quadratic cost criteria given in terms of constrained optimization problems. The solution is derived from the robust regularized least-square approach, whose framework is given in terms of a matrix structure. The recursiveness is established by Riccati equations which resemble the solutions of standard regulators for this class of systems, when they are not subject to uncertainties.

A scheme, analogous to the linear combination of atomic orbitals (LCAO), is used to calculate rates of reactions for the fusion of nuclei con¯ned in molecules. As an example, the possibility of nuclear fusion in rotationally excited H2O molecules of angular momentum 1¡ is estimated for the p + p + 16O ! 18Ne¤(4:522; 1¡) nuclear transition. Due to a practically exact agreement of the energy of the Ne resonance and of the p + p + 16O threshold, the possibility of an enhanced transition probability is investigated. / Physics / M.Sc.

Title: Microscopic nuclear models for open-shell nuclei Author: Jakub Herko Institute: Institute of Particle and Nuclear Physics Supervisor: Mgr. František Knapp, Ph.D., Institute of Particle and Nuclear Physics Abstract: Since the nucleus is a quantum many-body system consisting of con- stituents whose mutual interaction is not satisfactorily known, it is necessary to use approximate methods when describing the nucleus. Basic approximate approaches in the microscopic theory of the nucleus are the Hartree-Fock the- ory, Tamm-Dancoff approximation and random phase approximation. They are described in the first chapter of this thesis. The main aim was to develop mi- croscopic models for open-shell nuclei with two valence particles or holes. They are described in the second chapter, which contains detailed derivations of the relevant formulae. These methods have been numerically implemented. The re- sults of the calculations of the nuclear spectra and the electromagnetic transition probabilities are presented in the third chapter. Keywords: Tamm-Dancoff approximation, random phase approximation, open- shell nuclei, nuclear spectra, electromagnetic transition probabilities ii

Problem statement: Accurate and reliable forecasts of trends in the housing market can be useful information for market participants as well as policy makers. This information may be useful to minimize risk related to market uncertainty. Since the burst of the housing bubble in the early 1990s the price level of single-family houses has risen sharply in Sweden. The Swedish housing market has experienced an unusually long period of high growth rates in transaction prices which has opened up for discussions about the risk of another housing bubble. Business and property cycles have shown to contain asymmetries, which linear models are unable to pick up and therefore inappropriate to analyze cycles. Approach: Therefore, this study uses non-linear models which are able to pick up the asymmetries. The estimated models are variations of the Markov-switching regression model, i.e. the Markov-switching autoregressive (MS-AR) model and the Markov-switching dynamic regression (MS-DR) model. Results: Our ndings show that the MS-AR(4) model allowing for varying variance across regimes estimated using the growth rate of FASTPI produce superior forecasts over other MSAR models as well as variations of the MS-DR model. The average expected duration to remain in a positive growth regime is between 6.3 and 7.3 years and the average expected duration to remain in a negative growth regime is between 1.2 to 2.5 years. Conclusion: The next regime shift in the Swedish housing market is projected to occur between 2018 and 2019, counting the contraction period in 2012 as the most recent negative regime. Our ndings support other studies ndings which indicate that the longer the market has remained in one state, the greater is the risk for a regime shift. / Problemformulering: Noggranna och tillforlitliga prognoser om utvecklingen pa bostadsmarknaden kan vara anvandbar information for marknadsaktorer samt beslutsfattare. Denna information kan vara anvandbar for att minimera risken relaterad till osakerheten pa marknaden. Sen bostadsbubblan sprack i borjan av 1990-talet har prisnivan for smahus okat kraftigt i Sverige. Den svenska bostadsmarknaden har upplevt en ovanligt lang period av hog tillvaxt i transaktionspriser som har oppnat upp for diskussioner om risken for en ny bostadsbubbla. Konjunkturoch fastighetscykler har visat sig innehalla asymmetrier som linjara modeller inte kan uppfanga och darfor visat sig vara olampliga for att analysera cykler. Tillvagagangssatt: Darfor anvander den har studien icke-linjara modeller som kan uppfanga dessa asymmetrier. De skattade modellerna ar variationer av Hamiltons Markov-switchingmodell, dvs. en autoregressiv Markov-switchingmodell (MS-AR) och en dynamisk Markov-switchingmodell (MS-DR). Resultat: Resultatet visar att MS-AR(4)-modellen som tar hansyn till varierande varians over regimerna estimerad med tillvaxten av FASTPI producerar overlagsna prognoser jamfort med andra MS-AR-modeller samt variationer av MS-DR-modellen. Den genomsnittliga forvantade varaktigheten att benna sig i en positiv regim ar mellan 6,3 och 7,3 ar och den  genomsnittliga forvantade varaktigheten att benna sig i en negativ regim ar mellan 1,2 till 2,5 ar. Slutsats: Nasta regimskifte pa den svenska bostadsmarknaden beraknas ske mellan 2018 och 2019, antaget att nedgangen under 2012 ar den senaste negativa regimen. Resultatet stodjer tidigare studier, som tyder pa att ju langre marknaden har varit i ett tillstand, desto storre ar risken for ett regimskifte.