This thesis consists of four papers and a summary. The common topic of the included papers are the pricing equations of path-dependent options. Various properties of barrier options and American options are studied, such as convexity of option prices, the size of the continuation region in American option pricing and pricing formulas for turbo warrants. In Paper I we study the effect of model misspecification on barrier option pricing. It turns out that, as in the case of ordinary European and American options, this is closely related to convexity properties of the option prices. We show that barrier option prices are convex under certain conditions on the contract function and on the relation between the risk-free rate of return and the dividend rate. In Paper II a new condition is given to ensure that the early exercise feature in American option pricing has a positive value. We give necessary and sufficient conditions for the American option price to coincide with the corresponding European option price in at least one diffusion model. In Paper III we study parabolic obstacle problems related to American option pricing and in particular the size of the non-coincidence set. The main result is that if the boundary of the set of points where the obstacle is a strict subsolution to the differential equation is C1-Dini in space and Lipschitz in time, there is a positive distance, which is uniform in space, between the boundary of this set and the boundary of the non-coincidence set. In Paper IV we derive explicit pricing formulas for turbo warrants under the classical Black-Scholes assumptions.

In 1989 Jun Kigami made an analytic construction of a Laplacian on the Sierpiński gasket, a construction that he extended to post critically finite fractals. Since then, this field has evolved into a proper theory of analysis on fractals. The new results obtained in this thesis are all in the setting of Kigami's theory. They are presented in three papers. Strichartz recently showed that there are first order linear differential equations, based on the Laplacian, that are not solvable on the Sierpiński gasket. In the first paper we give a characterization on the polynomial p so that the differential equation p(Δ)u=f is solvable on any open subset of the Sierpiński gasket for any f continuous on that subset. For general p we find the open subsets on which p(Δ)u=f is solvable for any continuous f. In the second paper we describe the infinitesimal geometric behavior of a large class of smooth functions on the Sierpiński gasket in terms of the limit distribution of their local eccentricity, a generalized direction of gradient. The distribution of eccentricities is codified as an infinite dimensional perturbation problem for a suitable iterated function system, which has the limit distribution as an invariant measure. We extend results for harmonic functions found by Öberg, Strichartz and Yingst to larger classes of functions. In the third paper we define and study intrinsic first order derivatives on post critically finite fractals and prove differentiability almost everywhere for certain classes of fractals and functions. We apply our results to extend the geography is destiny principle, and also obtain results on the pointwise behavior of local eccentricities. Our main tool is the Furstenberg-Kesten theory of products of random matrices.

In this thesis, parabolic-pseudoparabolic equations are derived coupling chemical reactions, diffusion, flow and mechanics in a heterogeneous medium using the framework of mixture theory. The weak solvability in 1-D of the obtained models is studied. Furthermore, it is numerically illustrated that approximate solutions according to the Rothe method exhibit expected realistic behaviour. For a simpler model formulation, the periodic homogenization in higher space dimensions is performed. / <p>Research is funded by the Netherlands Organisation of Scientific Research (NWO) with MPE-grant 657.000.004, and a research stay at Karlstads Universitet is funded by NWO cluster Nonlinear Dynamics in Natural Systems (NDNS+).</p>

This Master Thesis report was written by Umeå University Engineering Physics student Richard Tano during his thesis work at Ericsson Luleå. Monitoring network quality is of utmost importance to network providers. This can be done with models evaluating QoS (Quality of Service) and conforming to ITU-T Recommendations. When determining video stream quality there is of more importance to evaluatethe QoE (Quality of Experience) to understand how the user perceives the quality. This isranked in MOS (Mean opinion scores) values. An important aspect of determining the QoEis the video content type, which is correlated to the coding complexity and MOS values ofthe video. In this work the possibilities to improve quality estimation models complying to ITU-T study group 12 (q.14) was investigated. Methods were evaluated and an algorithm was developed that applies time series analysis of packet statistics for determination of videostreams MOS scores. Methods used in the algorithm includes a novel assembling of frequentpattern analysis and regression analysis. A model which incorporates the algorithm for usage from low to high bitrates was dened. The new model resulted in around 20% improvedprecision in MOS score estimation compared to the existing reference model. Furthermore an algorithm using only regression statistics and modeling of related statistical parameters was developed. Improvements in coding estimation was comparable with earlier algorithm but efficiency increased considerably. / Detta examensarbete skrevs av Richard Tano student på Umeå universitet åt Ericsson Luleå. Övervakning av nätets prestanda är av yttersta vikt för nätverksleverantörer. Detta görs med modeller för att utvärdera QoS (Quality of Service) som överensstämmer med ITU-T rekommendationer. Vid bestämning av kvaliten på videoströmmar är det mer meningsfullt att utvärdera QoE (Quality of Experience) för att få insikt i hur användaren uppfattar kvaliten. Detta graderas i värden av MOS (Mean opinion score). En viktig aspekt för att bestämma QoE är typen av videoinnehåll, vilket är korrelerat till videons kodningskomplexitet och MOS värden. I detta arbete undersöktes möjligheterna att förbättra kvalitetsuppskattningsmodellerna under uppfyllande av ITU-T studygroup 12 (q.14). Metoder undersöktes och en algoritm utvecklades som använder tidsserieanalys av paketstatistik för uppskattning av videoströmmars MOS-värden. Metoder som ingår i algoritmen är en nyutvecklad frekventa mönster metod tillsammans med regressions analys. En modell som använder algoritmen från låg till hög bithastighet definierades. Den nya modellen gav omkring 20% förbättrad precision i uppskattning av MOS-värden jämfört med existerande referensmodell. Även en algoritm som enbart använder regressionsstatistik och modellerande av statistiska parametrar utvecklades. Denna algoritm levererade jämförbara resultat med föregående algoritm men gav även kraftigt förbättrad effektivitet.

When moving into a more connected world together with machines, a mutual understanding will be very important. With the increased availability in wear- able sensors, a better understanding of human needs is suggested. The Dart- mouth Research study at the Psychiatric Research Center has examined the viability of detecting and further on predicting human behaviour and complex tasks. The field of smoking detection was challenged by using the Q-sensor by Affectiva as a prototype. Further more, this study implemented a framework for future research on the basis for developing a low cost, connected, device with Thayer Engineering School at Dartmouth College. With 3 days of data from 10 subjects smoking sessions was detected with just under 90% accuracy using the Conditional Random Field algorithm. However, predicting smoking with Electrodermal Momentary Assessment (EMA) remains an unanswered ques- tion. Hopefully a tool has been provided as a platform for better understanding of habits and behaviour.

To be successful in today&apos;s competitive market, service providers should look at user&apos;s satisfaction as a critical key. In order to gain a better understanding of customers&apos; expectations, a proper evaluations which considers intrinsic characteristics of perceived quality of service is needed. Due to the subjective nature of quality, the vagueness of human judgment and the uncertainty about the degree of users&apos; linguistic satisfaction, fuzziness is associated with quality of experience. Considering the capability of Fuzzy logic in dealing with imprecision and qualitative knowledge, it would be wise to apply it as a powerful mathematical tool for analyzing the quality of experience (QoE). This thesis proposes a fuzzy procedure to evaluate the quality of experience. In our proposed methodology, we provide a fuzzy relationship between QoE and Quality of Service (QoS) parameters. To identify this fuzzy relationship a new term called Fuzzi ed Opinion Score (FOS) representing a fuzzy quality scale is introduced. A fuzzy data mining method is applied to construct the required number of fuzzy sets. Then, the appropriate membership functions describing fuzzy sets are modeled and compared with each other. The proposed methodology will assist service providers for better decision-making and resource management.

The conversion of mechanical energy to electrical energy is done mainly with synchronous generators. They are used in hydropower generators and nuclear plants that presently account for about 80% of the electric energy production in Sweden. Because of the dominating role of the synchronous generators, it is important to minimize the power losses for efficient use of natural resources and for the economies of the electric power companies and their customers. For a synchronous machine, power loss means undesired heat production. In electric machines, there are power losses due to windage, friction in bearings, resistance in windings, remagnetization of ferromagnetic materials, and induced voltages in windings, shields and parts that are conductive but ideally should be non-conductive. The subject of this thesis is prediction of end region magnetic leakage fields in synchronous generators and the eddy current power losses they cause. The leakage fields also increase the hysteresis losses in the end regions. Magnetic flux that takes paths such that eddy current power losses increase in end regions of synchronous generators is considered to be leakage flux. Although only a small fraction of the total magnetic flux is end region leakage flux, it can cause hot spots, discoloration and reduce the service life of the insulation on the core laminations. If unattended, damaged insulation could lead to electric contact and eddy currents induced by the main flux between the outermost laminations. That gives further heating and deterioration of the insulation of laminations deeper into the core. In a severe case, the core can melt locally, cause a cavity, buckling and a short circuit of the main conductors. The whole stator may have to be replaced. However, the end region leakage flux primarily causes heating close to the main stator conductors which makes the damage possible to discover by visual inspection before it has become irrepairable.

The common topic of this thesis is boundedness of integral and supremal operators between weighted function spaces. The first type of results are characterizations of boundedness of a convolution-type operator between general weighted Lorentz spaces. Weighted Young-type convolution inequalities are obtained and an optimality property of involved domain spaces is proved. Additional provided information includes an overview of basic properties of some new function spaces appearing in the proven inequalities. In the next part, product-based bilinear and multilinear Hardy-type operators are investigated. It is characterized when a bilinear Hardy operator inequality holds either for all nonnegative or all nonnegative and nonincreasing functions on the real semiaxis. The proof technique is based on a reduction of the bilinear problems to linear ones to which known weighted inequalities are applicable. Further objects of study are iterated supremal and integral Hardy operators, a basic Hardy operator with a kernel and applications of these to more complicated weighted problems and embeddings of generalized Lorentz spaces. Several open problems related to missing cases of parameters are solved, thus completing the theory of the involved fundamental Hardy-type operators. / Operators acting on function spaces are classical subjects of study in functional analysis. This thesis contributes to the research on this topic, focusing particularly on integral and supremal operators and weighted function spaces. Proving boundedness conditions of a convolution-type operator between weighted Lorentz spaces is the first type of a problem investigated here. The results have a form of weighted Young-type convolution inequalities, addressing also optimality properties of involved domain spaces. In addition to that, the outcome includes an overview of basic properties of some new function spaces appearing in the proven inequalities.  Product-based bilinear and multilinear Hardy-type operators are another matter of focus. It is characterized when a bilinear Hardy operator inequality holds either for all nonnegative or all nonnegative and nonincreasing functions on the real semiaxis. The proof technique is based on a reduction of the bilinear problems to linear ones to which known weighted inequalities are applicable.  The last part of the presented work concerns iterated supremal and integral Hardy operators, a basic Hardy operator with a kernel and applications of these to more complicated weighted problems and embeddings of generalized Lorentz spaces. Several open problems related to missing cases of parameters are solved, completing the theory of the involved fundamental Hardy-type operators. / <p>Artikel 9 publicerad i avhandlingen som manuskript med samma titel.</p>

Spectral properties of linear operators and operator functions can be used to analyze models in nature. When dispersion and damping are taken into account, the dependence of the spectral parameter is in general non-linear and the operators are not selfadjoint. In this thesis non-selfadjoint operator functions are studied and several methods for obtaining properties of unbounded non-selfadjoint operator functions are presented. Equivalence is used to characterize operator functions since two equivalent operators share many significant characteristics such as the spectrum and closeness. Methods of linearization and other types of equivalences are presented for a class of unbounded operator matrix functions. To study properties of the spectrum for non-selfadjoint operator functions, the numerical range is a powerful tool. The thesis introduces an optimal enclosure of the numerical range of a class of unbounded operator functions. The new enclosure can be computed explicitly, and it is investigated in detail. Many properties of the numerical range such as the number of components can be deduced from the enclosure. Furthermore, it is utilized to prove the existence of an infinite number of eigenvalues accumulating to specific points in the complex plane. Among the results are proofs of accumulation of eigenvalues to the singularities of a class of unbounded rational operator functions. The enclosure of the numerical range is also used to find optimal and computable estimates of the norm of resolvent and a corresponding enclosure of the ε-pseudospectrum.

In this paper we derive the eigenfunctions to the Hamiltonian operator associated with the Harmonic Oscillator, and show that they are given by the Hermite functions. Then we prove that the Hermite functions form an orthonormal basis in the underlying Hilbert space. We also classify the inverse to the Hamiltonian operator as a Schatten-von Neumann operator. Finally, we derive the fundamental solution to the Schrödinger Equation corresponding to the Harmonic Oscillator using Mehler’s formula.