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We consider the Cauchy problem for the Helmholtz equation with a domain in R^d, d>2 with N cylindrical outlets to infinity with bounded inclusions in R^{d-1}. Cauchy data are prescribed on the boundary of the bounded domains and the aim is to find solution on the unbounded part of the boundary. In 1989, Kozlov and Maz'ya proposed an alternating iterative method for solving Cauchy problems associated with elliptic,self-adjoint and positive-definite operators in bounded domains. Different variants of this method for solving Cauchy problems associated with Helmholtz-type operators exists. We consider the variant proposed by Mpinganzima et al. for bounded domains and derive the necessary conditions for the convergence of the procedure in unbounded domains. For the numerical implementation, a finite difference method is used to solve the problem in a simple rectangular domain in R^2 that represent a truncated infinite strip. The numerical results shows that by appropriate truncation of the domain and with appropriate choice of the Robin parameters, the Robin-Dirichlet alternating iterative procedure is convergent., 7 figures,3 tables

Sammanfattning Kapaciteten i litiumjonbatterier minskar över tid och användning. Faktorer såsom temperatur,laddningsnivå och djupet av laddningscykeln bidrar till en snabbare degradering. I vissa fall är detomöjligt att kontrollera dessa faktorer, till exempel om användaren lämnar sin telefon på laddningöver natten. Examensarbetets hypotes är att automatisk styrning av batteriladdningen kan reduceralånga perioder av hög laddning och därmed förlänga batteriets livslängd med en liten ansträngningför användaren. Efter en studie och analys om batteridegradering och dess miljöaspekter utformades ochkonstruerades en prototyplösning som proof-of-concept där laddningen styrs automatiskt. Enmobilapplikation skapades för att samla information om batterikonsumtion över dagen. Med hjälpav volontärer genomfördes en fältstudie som pågick under fyra veckor, där syftet var att presenterahur mobiltelefonägare laddar och laddar ur sina mobiltelefoner. Resultaten visade att prototypen skulle ge en försumbar till liten förlängning av batterilivslängden,starkt beroende på användarens tidigare laddningsmönster. Vidare arbete krävs för att uppskattapåverkan av batteridegradering vid alternativa prototyplösningar. Nyckelord Litiumjonbatteri, batteridegradering, mobiltelefon, simulering, automation, android, bluetooth,mikrokontroller

In this paper we consider two different linear covariance structures, e.g., banded and bended Toeplitz, and how to estimate them using different methods, e.g., by minimizing different norms. One way to estimate the parameters in a linear covariance structure is to use tapering, which has been shown to be the solution to a universal least squares problem. We know that tapering not always guarantee the positive definite constraints on the estimated covariance matrix and may not be a suitable method. We propose some new methods which preserves the positive definiteness and still give the correct structure. More specific we consider the problem of estimating parameters of a multivariate normal p–dimensional random vector for (i) a banded covariance structure reflecting m–dependence, and (ii) a banded Toeplitz covariance structure.

A false aneurysm is a hematoma, i.e. collection ofblood outside of a blood vessel, that forms due to a hole in the wall of an artery . This represents a serious medical condition that needs to be monitored and, under certain conditions, treatedurgently. In this work a one-dimensional model of a false aneurysm isproposed. The new model is based on a one-dimensional model of anartery previously presented by the authors and it takes into accountthe interaction between the hematoma and the surrounding musclematerial. The model equations are derived using rigorous asymptoticanalysis for the case of a simplified geometry. Even though the model is simple it still supports a realisticbehavior for the system consisting of the vessel and the hematoma. Using numerical simulations we illustrate the behavior ofthe model. We also investigate the effect of changing the size of the hematoma. The simulations show that ourmodel can reproduce realistic solutions. For instance we show thetypical strong pulsation of an aneurysm by blood entering the hematoma during the work phase of the cardiac cycle, and the blood returning tothe vessel during the resting phase. Also we show that the aneurysmgrows if the pulse rate is increased due to, e.g., a higher work load.

In this study we discuss the pricing of weather derivatives whose underlying weather variable is temperature. The dynamics of temperature in this study follows a two state regime switching model with a heteroskedastic mean reverting process as the base regime and a shifted regime defined by Brownian motion with mean different from zero. We develop the mathematical formulas for pricing futures contract on heating degree days (HDDs), cooling degree days (CDDs) and cumulative average temperature (CAT) indices. We also present the mathematical expressions for pricing the corresponding options on futures contracts for the same temperature indices. The local volatility nature of the model in the base regime captures very well the dynamics of the underlying process, thus leading to a better pricing processes for temperature derivatives contracts written on various index variables. We provide the description of Montecarlo simulation method for pricing weather derivatives under this model and use it to price a few weather derivatives call option contracts.

Engine oils fill important functions in the operation of modern internal combustion engines. Many essential functions are provided by compounds that are either sacrificial or susceptible to degradation. The engine oil will eventually fail to provide these functions with possibly unrepairable damages as a result. To decide how often the oil should be changed, there are several laboratory tests to monitor the oil condition, e.g. FTIR (oxidation, nitration, soot, water), viscosity, TAN (acidity), TBN (alkalinity), ICP (elemental analysis) and GC (fuel dilution). These oil tests are however often labor intensive and costly and it would be desirable to supplement and/or replace some of them with simpler and faster methods. One way, is to utilise the whole spectrum of the FTIR-measurements already performed. FTIR is traditionally used to monitor chemical properties at specific wave lengths, but also provides information, in a more multivariate way though, relevant for viscosity, TAN, and TBN. In order to make use of the whole FTIR-spectrum, methods capable of handling high dimensional data have to be used. Partial Least Squares Regression (PLSR) will be used in order to predict the relevant chemical properties. This survey also considers feature selection methods based on the second order statistic Higher Criticism as well as Hierarchical Clustering. The Feature Selection methods are used in order to ease further research on how infrared data may be put into usage as a tool for more automated oil analyses. Results show that PLSR may be utilised to provide reliable estimates of mentioned chemical quantities. In addition may mentioned feature selection methods be applied without losing prediction power. The feature selection methods considered may also aid analysis of the engine oil itself and feature work on how to utilise infrared properties in the analysis of engine oil in other situations. Motoroljor fyller viktiga funktioner i en modern förbränningsmotor. Många viktiga funktioner tillgodoses av ämnen som antingen förbrukas över tid eller är sårbara mot nedbrytning. Efter tillräckligt lång tid kommer motoroljan inte längre kunna tillgodose motorn med dessa funktioner. För att ta reda på hur snabbt en olja bryts ned under körning och hur ofta den behöver bytas ut, finns det flera laborativa analysmetoder. De vanligaste är FTIR (oxidation, nitrering, sot, vatten), viskositet (smörjförmåga), TAN (surhet), TBN (basisk buffert), ICP (grundämnesanalys) and GC (bränsleutspädning). Dessa oljetester är ofta arbetsintensiva och kostsamma och det vore önskvärt att ersätta eller komplettera dessa med mätningar från en FTIR-spektrometer. För att kunna använda hela det spektrumet krävs att statistiska metoder kapabla till att hantera högdimensionella data används. Partial Least Squares Regression används för att prediktera relevanta test från kemisk oljeanalys. Den här studien betraktar också variabelselektionsmetoder baserade på andra ordningens statistik Higher Criticism såväl som hierarkisk klustring. Variabelselektionsmetoderna används för att bidra till framtida utveckling mot hur data från det infraröda spektrumet ska användas för att kunna automatisera oljeanalyser. Resultaten visar att PLSR kan användas för att tillhandahålla exakta prediktioner av ovan nämnda kvantiteter. Vidare kan variabelselektionsmetoderna i undersökningen användas för att reducera antalet variabler och fortfarande bibehålla prediktionsförmågan. Variabelselektionsmetoderna kan också användas som verktyg för att i framtiden bidra med kunskap hur oljans egenskaper i det infraröda spektrumet kan utnyttjas för analys av motorolja i andra situationer.

Two regime switching models for predicting temperature dynamics are presented in this study for the purpose to be used for weather derivatives pricing. One is an existing model in the literature (Elias model) and the other is presented in this paper. The new model we propose in this study has a mean reverting heteroskedastic process in the base regime and a Brownian motion in the shifted regime. The parameter estimation of the two models is done by the use expectation-maximization (EM) method using historical temperature data. The performance of the two models on prediction of temperature dynamics is compared using historical daily average temperature data from five weather stations across Sweden. The comparison is based on the heating degree days (HDDs), cooling degree days (CDDs) and cumulative average temperature (CAT) indices. The expected HDDs, CDDs and CAT of the models are compared to the true indices from the real data. Results from the expected HDDs, CDDs and CAT together with their corresponding daily average plots demonstrate that, our model captures temperature dynamics relatively better than Elias model.

With this thesis we aim to create an efficient scheduling algorithm for elevators that can move in multiple directions and establish if and when the algorithm is efficient in comparison to algorithms constructed for traditional elevator algorithms. To measure efficiency, a simulator is constructed to simulate an elevator system implementing different algorithms. Because of the challenge of constructing a simulator and since we did not find either a simulator nor any algorithms for use in multidirectional elevator systems publicly, we decided to focus on these subjects. The results in this thesis leads us to the conclusion that a multidirectional elevator algorithm is efficient to use under certain circumstances. If the traffic is concentrated to one floor in the building the multidirectional elevator system performs poorly but when the traffic is spread out it outperforms traditional elevators algorithms. We hope that this research will inspire to further research in the area of multidirectional elevator systems.

The Cauchy problem for the Helmholtz equation appears in applications related to acoustic or electromagnetic wave phenomena. The problem is ill–posed in the sense that the solution does not depend on the data in a stable way. In this paper we give a detailed study of the problem. Specifically we investigate how the ill–posedness depends on the shape of the computational domain and also on the wave number. Furthermore, we give an overview over standard techniques for dealing with ill–posed problems and apply them to the problem.

In the modern society it is well known that an individual’s background matters in his career, but should it be taken into consideration in a recruiting process in general and a recruiting process of NBA-players in particular? Previous research shows that white basketball players from high-income families have a 75% higher chance of becoming an NBA player compared to a white basketball player from a low-income family. In this paper, we have examined whether there is a connection between NBA-player background and the chances of succeeding in the NBA given that the player has been picked in the NBA-draft. The results have been carried out using machine learning algorithms based on Gaussian Processes. The results show that draft decisions will not be improved by taking socio-economic background into consideration.

Denna uppsats klargör vad Schengensamarbetet är för något, varför det finns och hur det fungerar. Uppsatsen går igenom alla delar av samarbetet som till synes största del består av att avskaffa personkontrollerna mellan medlemsländerna.

The thermal conductivity properties of a material can be determined experimentally by using temperature measurements taken at specified locations inside the material. We examine a situation where the properties of a (previously known) material changed locally. Mathematically we aim to find the coefficient k(x) in the stationary heat equation (kTx)x = 0;under the assumption that the function k(x) can be parametrized using only a few degrees of freedom. The coefficient identification problem is solved using a least squares approach; where the (non-linear) control functional is weighted according to the distribution of the measurement locations. Though we only discuss the 1D case the ideas extend naturally to 2D or 3D. Experimentsdemonstrate that the proposed method works well.

We consider two dimensional inverse steady state heat conductionproblems in complex geometries. The coefficients of the elliptic equation are assumed to be non-constant. Cauchy data are given on onepart of the boundary and we want to find the solution in the wholedomain. The problem is ill--posed in the sense that the solution doesnot depend continuously on the data. Using an orthogonal coordinate transformation the domain is mappedonto a rectangle. The Cauchy problem can then be solved by replacing one derivative by a bounded approximation. The resulting well--posed problem can then be solved by a method of lines. A bounded approximation of the derivative can be obtained by differentiating a cubic spline, that approximate the function in theleast squares sense. This particular approximation of the derivativeis computationally efficient and flexible in the sense that its easy to handle different kinds of boundary conditions.This inverse problem arises in iron production, where the walls of amelting furnace are subject to physical and chemical wear. Temperature and heat--flux data are collected by several thermocouples locatedinside the walls. The shape of the interface between the molten ironand the walls can then be determined by solving an inverse heatconduction problem. In our work we make extensive use of Femlab for creating testproblems. By using FEMLAB we solve relatively complex model problems for the purpose of creating numerical test data used for validating our methods. For the types of problems we are intressted in numerical artefacts appear, near corners in the domain, in the gradients that Femlab calculates. We demonstrate why this happen and also how we deal with the problem.