In this work we take interest in frames and modulation spaces. On the basis of their properties, we show how frame expansions can be used to prove the boundedness of a particular class of Hilbert operators on modulation spaces taking advantage of the special category of piece-wise polynomial functions known as B-splines.

This thesis concerns the Wiener algebra of periodic functions with absolutely convergent Fourier series, and the "Wiener-Lévy functions", meaning functions that preserve absolute convergence of Fourier series under composition. Results regarding the properties of functions in the Wiener algebra are established, as well as properties of Wiener-Lévy functions. By the Wiener-Lévy Theorem, analyticity is a sufficient condition for a function to be a Wiener-Lévy function, and in this paper, we find the necessary condition of being real analytic in the real and imaginary variable, separately.

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<p>In this thesis a new method for the option pricing will be introduced with</p><p>the help of the Mellin transforms. Firstly, the Mellin transform techniques for</p><p>options on a single underlying stock is presented. After that basket options</p><p>will be considered. Finally, an improvement of existing numerical results</p><p>applied to Mellin transforms for 1-basket and 2-basket American Put Option</p><p>will be discussed concisely. Our approach does not require either variable</p><p>transformations or solving diusion equations.</p>

<p>The environmental debate is more intensive than ever before and the demands on companies increase. There are a number of methods to make it easier for the companies to fulfil the demands. Life Cycle Assessment (LCA) end ecodesign are some of the methods that can be used.</p><p> </p><p>Syntronic AB has the possibility to reduce the products´ environmental impact in the design phase. Therefore it is important for the company to make it possible to visualize the negative environmental impacts a product can cause in an easy way. It is also important to visualize for there clients if any improvement is possible.</p><p> </p><p>The purpose of this thesis is to develop a simplified model. The purpose of the model is to illustrate the environmental impact in the design phase of the product. To develop the model we have used previous research about environmental impact, legislation and methods. With that as a base we have develop a simplified model which Syntronic AB can use in their communication with their clients.</p><p> </p><p>The model is built up so that different parameters can be used. That means that the model can be applied so it makes it possible to compare compatible material and components to already existing materials and components.</p><p> </p><p>The problem in doing a LCA is to get data that is up to date and trustworthy. It limits the models trustworthiness if you are forced to use stencil data. Therefore the result that the model generates should be considered as an image to used in decision making when the company communicates environmental adapt in product development.</p>

This thesis concerns numerical techniques for two phase flowsimulations; the two phases are immiscible and incompressible fluids. Strategies for accurate simulations are suggested. In particular, accurate approximations of the weakly discontinuousvelocity field, the discontinuous pressure, and the surface tension force and a new model for simulations of contact line dynamics are proposed. In two phase flow problems discontinuities arise in the pressure and the gradient of the velocity field due to surface tension forces and differences in the fluids' viscosity. In this thesis, a new finite element method which allows for discontinuities along an interface that can be arbitrarily located with respect to the mesh is presented. Using standard linear finite elements, the method is for an elliptic PDE proven to have optimal convergence order and a system matrix with condition number bounded independently of the position of the interface.The new finite element method is extended to the incompressible Stokes equations for two fluid systemsand enables accurate approximations of the weakly discontinuous velocity field and the discontinuous pressure. An alternative way to handle discontinuities is regularization. In this thesis, consistent regularizations of Dirac delta functions with support on interfaces are proposed. These regularized delta functions make it easy to approximate surface tension forces in level set methods. A new model for simulating contact line dynamics is also proposed. Capillary dominated flows are considered and it is assumed that contact line movement is driven by the deviation of the contact angle from its static value. This idea is used together with the conservative level set method. The need for fluid slip at the boundary is eliminated by providing a diffusive mechanism for contact line movement. Numerical experiments in two space dimensions show that the method is able to qualitatively correctly capture contact line dynamics. / QC 20110503

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