This thesis is devoted to an investigation of boundedness of a general convolution operator between certain weighted Lorentz-type spaces with the aim of proving analogues of the Young convolution inequality for these spaces. Necessary and sufficient conditions on the kernel function are given, for which the convolution operator with the fixed kernel is bounded between a certain domain space and the weighted Lorentz space of type Gamma. The considered domain spaces are the weighted Lorentz-type spaces defined in terms of the nondecreasing rearrangement of a function, the maximal function or the difference of these two quantities. In each case of the domain space, the corresponding Young-type convolution inequality is proved and the optimality of involved rearrangement-invariant spaces in shown. Furthermore, covering of the previously existing results is also discussed and some properties of the new rearrangement-invariant function spaces obtained during the process are studied. / <p>Paper II was a manuscript at the time of the defense.</p>

In this thesis, which consists of five papers (A,B,C,D,E), we are interested in questions related to quadrature domains. Among the problems studied are the possibility of changing the type of measure in a quadrature identity (from complex to real and from real signed to positive), properties of partial balayage, which in a sense can be used to generate quadrature domains, and mother bodies which are closely related to inversion of partial balayage. These three questions are discussed in papers A,D respectively B. The first of these questions (when trying to go from real signed to positive measures) leads to the study of approximation in the cone of positive harmonic functions. These questions are closely related to properties of the harmonic measure on the Martin boundary, and this relationship leads to the study of harmonic measures on ideal boundaries in paper E. Some other approaches to the same problem also lead to some extent to the study of properties of classical balayage in paper C. / QC 20101007

In this thesis we study the spaces of Gevrey functions and ultradistributions, focusing primarily on the properties reflected on their Fourier-Laplace transforms. In particular, we study the Paley-Wiener Theorems for compactly supported Gevrey functions and compactly supported Gevrey ultradistributions.

From the beginning of the study of spaces in functional analysis, bases have been an indispensable tool for operating with vectors and functions over a concrete space. Bases can be organized by types, depending on their properties. This thesis is intended to give an overview of some bases and their relations. We study Hamel basis, Schauder basis and Orthonormal basis; we give some properties and compare them in different spaces, explaining the results. For example, an infinite dimensional Hilbert space will never have a basis which is a Schauder basis and a Hamel basis at the same time, but if this space is separable it has an orthonormal basis, which is also a Schauder basis. The project deals mainly with Banach spaces, but we also talk about the case when the space is a pre Hilbert space.

In this thesis, we investigate two stock price models, the Black-Scholes (BS) model and the Merton Jump-Diffusion (MJD) model. Comparing the logarithmic return of the BS model and the MJD model with empirical stock price data, we conclude that the Merton Jump-Diffusion Model is substantially more suitable for the stock market. This is concluded visually not only by comparing the density functions but also by analyzing mean, variance, skewness and kurtosis of the log-returns. One technical contribution to the thesis is a suggested decision rule for initial guess of a maximum likelihood estimation of the MJD-modeled parameters.

Cost overruns in projects have historically been a problem spread over different sectors. Generating accurate estimates early in the project life cycle is difficult. However, uncertainty in cost estimates can be assessed. This report sought to analyze the consequences of neglecting correlation between cost estimates in the uncertainty analysis performed at WSP Management Stockholm. The uncertainty analysis consisted of a model using Monte Carlo simulation with PERT-distributed three-point estimates from expert judgement as input. 7 Swedish projects, 4 in infrastructure and 3 in construction, with a total expected cost of 7.1 billion SEK were analyzed; all in early stages of the project life cycle. Estimated costs were correlated successively in 3 different correlation scenarios with correlation coefficients 0.3, 0.7 and 1; later compared with the uncorrelated scenario. Results showed that: Each scenario led to an increase in the result’s standard deviation of 68%, 129% and 168% in average for correlation coefficients 0.3, 0.7 and 1 respectively. Furthermore, if the 85th percentile in the resulting cumulative distribution was to be used to determine the cost frame of the project, assuming no correlation in a scenario with the 10 most uncertain cost estimates correlated would lead to an underestimation of the final cost with 3%, 6% and 8% for correlation coefficients 0.3, 0.7 and 1 respectively. Lastly, if standard deviation in the results is low there is a reason to question the results. Estimating correlation in the model accounts for a wider range of outcomes and may be more realistic in an uncertain reality. Furthermore, correlation can compensate for the uncertainty that is lost in calculations as estimates are broken down into more detail.

With an upsurge in number of available smart phones, tablet PCs etc. most users find it easy to access Internet services using mobile applications. It has been a challenging task for mobile application developers to choose suitable security types (types of authentication, authorization, security protocols, cryptographic algorithms etc.) for mobile applications. Choosing an inappropriate security type for a mobile application may lead to performance degradation and vulnerable issues in applications. The choice of the security type can be done by decision making. Decision making is a challenging task for humans. When choosing a single alternative among a set of alternatives with multiple criteria, it is hard to know which one is the better decision. Mobile application developers need to incorporate Multi-Criteria Decision Making (MCDM) Models to choose a suitable security type for mobile application. A decision model for application security enhances decision making for mobile application developers to decide and set the required security types for the application. In this thesis, we discuss different types of MCDM models that have been applied in an IT security area and scope of applying MCDM models in application security area. Literature review and evaluation of the selected decision models gives a detailed overview on how to use them to provide application security. / The first chapter introduces the thesis work. The second chapter presents the background of decision making models, their process, and the classification of decision making models. The third chapter presents the research methodology we have used in different phases which aims to answer the research questions. The fourth chapter gives a detailed literature study of how decision models can be used in application security. The fifth chapter evaluates selected decision models. The sixth chapter concludes the thesis and presents future work.

The demand of wireless spectrum is increasing very fast as the field of telecommunication is advancing rapidly. The spectrum was underutilized because of fixed spectrum assignment policy and this valuable spectrum can be utilized efficiently by cognitive radio technology. In this thesis we have studied spectrum selection problems in cognitive radio network. Channel sharing and channel contention problems arise when multiple secondary users tend to select same channel. The thesis work is focused on spectrum selection issue with the aim to minimize the overall system time and to solve the problem of channel contention and channel sharing. The overall system time of secondary connection is an important performance measure to provide quality of service for secondary users in cognitive radio network. We studied two spectrum selection schemes that considerably reduce the overall system time and resolve the problems of channel sharing and channel contention. An analytical model associated with Preemptive Resume Priority (PRP) M/G/1 queuing model has been provided to evaluate the studied spectrum selection scheme. This model also analyzes the effect of multiple handoffs due to arrival of primary users. According to this scheme, the traffic load is distributed among multiple channels to balance the traffic load. Secondary users select the operating channels based on the spectrum selection algorithm. They can intelligently adopt better channel selection scheme by considering traffic statistics and overall transmission time. All simulation scenarios are developed in MATLAB. Based on our result we can conclude that both channel selection schemes considerably reduce the overall transmission time of secondary users in cognitive radio network. The overall transmission time increase with the rise of arrival rate of secondary user. The probability based channel selection scheme perform better with lower arrival rate and sensing based channel selection scheme perform better with higher arrival rate of secondary users. These channel selection schemes help distribute the traffic load of secondary users evenly among multiple channels. Hence, increase the channel utilization and resolve the channel contention problem.

We consider mathematical modeling of thin film flow between two rough surfaces which are in relative motion. For example such flows take place in different kinds of bearings and gears when a lubricant is used to reduce friction and wear between the surfaces. The mathematical foundations of lubrication theory is given by the Navier--Stokes equation, which describes the motion of viscous fluids. In thin domains several approximations are possible which lead to the so called Reynolds equation. This equation is crucial to describe the pressure in the lubricant film. When the pressure is found it is possible to predict vorous important physical quantities such as friction (stresses on the bounding surfaces), load carrying capacity and velocity field. In hydrodynamic lubrication the effect of surface roughness is not negligible, because in practical situations the amplitude of the surface roughness are of the same order as the film thickness. Moreover, a perfectly smooth surface does not exist in reality due to imperfections in the manufacturing process. Therefore, any realistic lubrication model should account for the effects of surface roughness. This implies that the mathematical modeling leads to partial differential equations with coefficients that will oscillate rapidly in space and time. A direct numerical computation is therefore very difficult, since an extremely dense mesh is needed to resolve the oscillations due to the surface roughness. A natural approach is to do some type of averaging. In this PhD thesis we use and develop modern homogenization theory to be able to handle the questions above. Especially, we use, develop and apply the method based on the multiple scale expansions and two-scale convergence. The thesis is based on five papers (A-E), with an appendix to paper A, and an extensive introduction, which puts these publications in a larger context. In Paper A the connection between the Stokes equation and the Reynolds equation is investigated. More precisely, the asymptotic behavior as both the film thickness <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cepsilon" /> and wavelength <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cmu" /> of the roughness tend to zero is analyzed and described. Three different limit equations are derived. Time-dependent equations of Reynolds type are obtained in all three cases (Stokes roughness, Reynolds roughness and high frequency roughness regime). In paper C we extend the work done in Paper A where we compare the roughness regimes by numeric computations for the stationary case. In paper B we present a mathematical model that takes into account cavitation, surfaces roughness and compressibility of the fluid. We compute the homogenized coefficients in the case of unidirectional roughness.In the paper D we derive a mathematical model of thin film flow between two close rough surfaces, which takes into account cavitation, surface roughness and pressure dependent density. Moreover, we use two-scale convergence to homogenize the model. Finally, in paper E we prove the existence of solutions to a frequently used mathematical model of thin film flow, which takes cavitation into account.

In this thesis we consider errors arising from finite difference operators on summation-by-parts (SBP) form, used in the discretisation of partial differential equations. The SBP operators are augmented with simultaneous-approximation-terms (SATs) to weakly impose boundary conditions. The SBP-SAT framework combines high order of accuracy with a systematic construction of provably stable boundary procedures, which renders it suitable for a wide range of problems. The first part of the thesis treats wave propagation problems discretised using SBP operators on coarse grids. Unless special care is taken, inaccurate approximations of the underlying dispersion relation materialises in the form of an incorrect propagation speed. We present a procedure for constructing SBP operators with minimal dispersion error. Experiments indicate that they outperform higher order non-optimal SBP operators for flow problems involving high frequencies and long simulation times. In the second part of the thesis, the formal order of accuracy of SBP operators near boundaries is analysed. We prove that the order in the interior of a diagonal norm based SBP operator must be at least twice that of the boundary stencil, irrespective of the grid point distribution near the boundary. This generalises the classical theory posed on uniform and conforming grids. We further show that for a common class of SBP operators, the diagonal norm defines a quadrature rule of the same order as the interior stencil. Again, this result is independent of the grid. In the final contribution if the thesis, we introduce the notion of a transmission problem to describe a general class of problems where different dynamics are coupled in time. Well-posedness and stability analyses are performed for continuous and discrete problems. A general condition is obtained that is necessary and sufficient for the transmission problem to satisfy an energy estimate. The theory provides insights into the coupling of fluid flow models, multi-block formulations, numerical filters, interpolation and multi-grid implementations.