This paper is focusing on the data mining solutions for the WWW, specifically how it can be used for the hyperlinks evaluation. We are focusing on the hyperlinks used in the web sites systems and on the problem which consider evaluation of its utility. Since hyperlinks reflect relation to other webpage one can expect that there exist way to verify if users follow desired navigation paths. The Challenge is to use available techniques to discover usage behavior patterns and interpret them. We have evaluated hyperlinks of the selected pages from www.bth.se web site. By using web expert’s help the usefulness of the data mining as the assessment basis was validated. The outcome of the research shows that data mining gives decision support for the changes in the web site navigational structure. / akasha.kate@gmail.com

Syftet med studien var att undersöka om digitala spel skapade för underhållning kan erbjuda spelaren färdighetsträning inom området taluppfattning i ämnet matematik. Studien genomfördes på 11 spel som valdes med hjälp av barn i årskurs 4–6 och ramverket baseras på McIntosh tolkning av vad taluppfattning innebär och sex aspekter framarbetades. Ett kodningsschema användes för att undersöka om spelen omfattar situationer som innehåller taluppfattning samt hur spelaren kan använda sig av taluppfattning i dessa situationer. Studien visar att möjligheterna för färdighetsträning finns i spelen men vissa spel särskiljer sig då de erbjuder mer komplexa beräkningssituationer än de andra spelen. Aspekten representationer för olika tal skilde sig från de andra då alla analysenheter inte omfattar denna aspekt. Resultatet av studien innebär att lärare kan använda sig av dessa spel och själva analysera spel för att använda dem i matematiska lärandesituationer. / The purpose of this study was to examine if digital games made for entertainment can offer the player skill training in the area of number sense in mathematics. The study took place on 11 games chosen after talking to student in class 4–6 and the framework was based on McIntosh interputation of number sense and six aspects was created. A coding scheme was used to examine if the games included situations where number sense could be used and how the player could practice their number sense in these situations. The study shows that the possibilities for practice is in the games but some games differentiate from others by offering the player more complex calculating situations than the other games. The aspect of multiple representations for numbers was separated from the others because all analyzed situations did not contain this aspect. The result of the study shows that teachers can use these games and themselves analyze other games to use in mathematic learning situations.

Matrices whose rows (or columns) consists of monomials of sequential powers are called Vandermonde matrices and can be used to describe several useful concepts and have properties that can be helpful for solving many kinds of problems. In this thesis we will discuss this matrix and some of its properties as well as a generalization of it and how it can be applied to curve fitting discharge current for the purpose of ensuring electromagnetic compatibility. In the first chapter the basic theory for later chapters is introduced. This includes the Vandermonde matrix and some of its properties, history, applications and generalizations, interpolation and regression problems, optimal experiment design and modelling of electrostatic discharge currents with the purpose to ensure electromagnetic compatibility. The second chapter focuses on finding the extreme points for the determinant for the Vandermonde matrix on various surfaces including spheres, ellipsoids, cylinders and tori. The extreme points are analysed in three dimensions or more. The third chapter discusses fitting a particular model called the p-peaked Analytically Extended Function (AEF) to data taken either from a standard for electromagnetic compatibility or experimental measurements. More specifically the AEF will be fitted to discharge currents from the IEC 62305-1 and IEC 61000-4-2 standards for lightning protection and electrostatic discharge immunity as well as some experimentally measured data of similar phenomena.

We give a proof of the Oka-Weil theorem which states that on compact, polynomially convex subsets of Cn, holomorphic functions can be approximated uniformly by holomorphic polynomials. / Vi ger ett bevis av Oka-Weil sats som säger att på kompakta och polynomkonvexa delmängder av Cn kan holomorfa funktioner approximeras likformigt med holomorfa polynom.

Financial engineering problems are of great importance in the academic community and BlackScholes equation is a revolutionary concept in the modern financial theory. Financial instruments such as stocks and derivatives can be evaluated using this model. Option evaluation, is extremely important to trade in the stocks. The numerical solutions of the Black-Scholes equation are used to simulate these options. In this thesis, the explicit and the implicit Euler methods are used for the approximation of Black-scholes partial differential equation and a second order finite difference scheme is used for the spatial derivatives. These temporal and spatial discretizations are used to gain an insight about the stability properties of the explicit and the implicit methods in general. The numerical results show that the explicit methods have some constraints on the stability, whereas, the implicit Euler method is unconditionally stable. It is also demostrated that both the explicit and the implicit Euler methods are only first order convergent in time and this implies too small step-sizes to achieve a good accuracy.

Syftet med denna läromedelsgranskning var att kartlägga hur olika läromedelbehandlar området taluppfattning, positionssystemet i årskurs 3 samt se vilka kritiskaaspekter som förekommer. Även se hur läromedlen ger möjlighet för eleverna attanvända olika representationsformer inom området. Två läromedel i årskurs 3 valdesut för analys. För att svara på frågeställningarna användes ett analysschema vid granskning avuppgifterna. Uppgifterna som undersöktes i respektive läromedel var de som berördepositionssystemet. I analysschemat användes begreppen kritiska aspekter, flerarepresentationsformer och Heddens teoretiska modell. Resultatet av studien visar att området positionssystemet i de två valda läromedleninte har en större del, det är få sidor i varje läromedel. Båda läromedel innehållermånga begrepp vilket gör att eleverna måste ha en begreppsförståelse om begreppenför att kunna lösa uppgifterna. En annan kritisk aspekt är att det inte finns mångaexempel till uppgifterna och i ett av läromedlen finns det inte heller något som visarpå vad positionssystemet är. När det gäller representationsformer visar resultatet attdet finns en spridning av representationsformer och att det förekommer i olika nivåerenligt Heddens teoretiska modell. Slutsatsen till studien var att positionssystemet bör ha en större roll och del iläromedlen och att de bör uppmuntra elever till användning av konkret material istörre utsträckning.

This thesis studies the relationship between the zeroes of complexpolynomials in one variable and the critical points of those polynomials. Our methods are both analytical and statistical in nature, usingtechniques from both complex analysis and probability theory. Wepresent an alternative proof for the famous Gauss-Lucas theorem aswell as proving that the distribution for the critical points of a randompolynomial with real zeroes will converge in probability to the distribution of the zeroes. A simulation of the case with complex zeroesis also presented, which gives statistical support that this holds forrandom polynomials with complex zeroes as well. Lastly, the previous results are then applied to Sendov’s conjecture where we take aprobabilistic approach to this problem.

The famous Black-Scholes partial differential equation is one of the most widely used and researched equations in modern financial engineering to address the complex evaluations in the financial markets. This thesis investigates a numerical technique, using a fourth-order discretization in time and space, to solve a generalized version of the classical Black-Scholes partial differential equation. The numerical discretization in space consists of a fourth order centered difference approximation in the interior points of the spatial domain along with a fourth order left and right sided approximation for the points near the boundary. On the other hand, the temporal discretization is made by implementing a Runge-Kutta order four (RK4) method. The designed approximations are analyzed numerically with respect to stability and convergence properties.

Abstract is not available.

The stock market is a place in which numerous entities interact, operate, andchange state based on the decisions they make. Further, the stock market itselfevolves and changes its dynamics over time as a consequence of the individualactions taking place in it. In this sense, the stock market can be viewed andtreated as a complex adaptive system. In this study, an agent-based model,simulating the trading of a single asset has been constructed with the purposeof investigating how the collective behaviour affects the dynamics of the stockmarket. For this purpose, the agent-based modelling program NetLogo wasused. Lastly, the conclusion of the study revealed that the dynamics of thestock market are clearly dependent on some specific factors of the collectivebehaviour, such as the information source of the investors.