To be successful in today's competitive market, service providers should look at user's satisfaction as a critical key. In order to gain a better understanding of customers' 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' 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.

Hur får matematiklärare tillsammans med specialläraren, ungdomar att efter upprepade misslyckanden med matematik att fortsätta kämpa. Svaret på den frågan kan vara matematisk elasticitet. Matematisk elasticitet är något som skulle vara värt att utveckla hos ungdomar i Sverige. De fyra grundpelarna matematisk elasticitet står på är att eleven har vetskap om: Tro på att hen kan lära sig matematik, värdet av kunskap i sitt framtida liv, för att utvecklas i matematik behöver eleven lägga ner tid på träning i matematik, och att våga bege sig in i utvecklingszonen och att stanna kvar där med hjälp av stöttning från läraren är viktigt. I den semistrukturerade intervjustudien ingick sju personer. Från intervjuerna sorterades citat in i sju kategorier enligt följande: tid, negativa känslor, positiva känslor, motivation, externmiljö, internmiljö och förhållningssätt. Studien visade att trots upprepade misslyckanden så går det att övervinna svårigheter. Ingenting är omöjligt. Det fanns elever med en inre motivation som tack vare det lyckades att klara matematiken trots tidigare misslyckanden. Mycket tack vare matematisk elasticitet. Som speciallärare i matematik är det lätt att fokusera på enstaka saker i matematik som måste läras ut, och att se helheten är lätt att glömma bort. Att istället fokusera på matematisk elasticitet är ett sätt att lära eleven självhjälp och inte bli beroende av vilken lärare som hen har. Komvuxlärarna jobbade med matematisk elasticitet fast de inte var medvetna om begreppet och vad det innebär, instinktivt gjorde de det ändå. / How do the mathematics teacher together with the special teacher get pupils to struggle after repeated failures? Mathematical resilience could be the answer. In a Swedish context this is something needed to develop pupils in mathematics. One way out of this is to focus on three important themes: value, struggle and growth. From this it develops four different knowledges such as having a growth mindset, mathematics can be valuable, struggle and support to stay in the growth zone. Seven persons were interviewed using semi structured interviews. Selected quotes were sorted in seven categories as follows: time, negative feelings, positive feelings, motivation, extern-, intern-environment and treatment. The study shows that if a pupil has difficulties with mathematics things are not hopeless. There were pupils with intrinsic motivation who succeeded after several failures with the help of mathematical resilience. This is valuable to know for special teachers. The math teachers at the adult-school was not aware of that they worked with mathematic resilience, but instinctively they did.

Det finns flera faktorer som påverkar elevers prestation inom matematik, bland annat elevers matematiska självkänsla. Denna pilotstudie utvecklar och diskuterar ett verktyg för att undersöka hur väl matematiklärare uppfattar sina elevers matematiska självkänsla. Frågeställningen som avsågs att försöka besvaras var följande: Hur väl stämmer matematiklärares uppfattningar om sina elevers matematiska självkänsla överens med elevens matematiska självkänsla?  Genom att granska elev-lärarsvarskombinationer undersöktes hur väl individuella elevers matematiska självkänsla uppfattades av sin matematiklärare. Resultatet påvisar att lärare summativt överskattar elevers matematiska självkänsla. Nollhypotesgranskning visar ej på någon tydlig trend då hälften av de undersökta elev-lärarsvarskombinationerna styrker nollhypotesen och hälften motsäger nollhypotesen. / There are several factors which affect students' performance in mathematics, including the students’ mathematical self-esteem. This pilot study tests a tool to examine mathematics teachers' perception of their students’ mathematical self esteem. The research question that was intended to be answered was the following:  How well do mathematics teachers' perceptions of their students' mathematical self-esteem agree with the students mathematical self-esteem?  By examining student-teacher response combinations through a null hypothesis, it was investigated how well individual students' mathematical self-esteem was perceived by their mathematics teacher. The results show that teachers summatively overestimate students' mathematical self-esteem. Null hypothesis review does not show any clear trend since half of the student-teacher response combinations examined confirmed the null hypothesis and half rejects the null hypothesis.

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.

The purpose of this qualitative study is to increase the knowledge of how Montessori teachers include mathematically gifted pupils through differentiated teaching. This was accomplished through semi-structured interviews with nine Montessori teachers from all over Sweden. The teachers were asked to describe how they plan their teaching, how they execute it and to share their thoughts and attitudes regarding this part of their job.    The results show that the Montessori teachers in this study use differentiated teaching based on the Montessori principles of individualisation. They make individual lesson plans for every pupil, based on the pupil’s level of knowledge, interests and needs. These plans are made together with the pupils, who thus have an impact on their own education. As the lesson plans are put into practice the pupils get to choose what to do when, during three hour work cycles. This means there are many different activities happening at the same time in the Montessori classroom. This seems to be beneficial to mathematically gifted pupils, as they appear to be offered an education at their individual level of knowledge. They are also able to set their own work pace and thus advance at their own speed. The Montessori manipulatives are important to the teachers, but the mathematically gifted pupils are able to leave them behind quickly and instead work with more abstract mathematics.    The study also shows that the teachers consider it exceedingly important that the mathematically gifted pupils are challenged and stimulated. For that reason, the teachers do not limit the pupils’ knowledge acquisition. The pupils are allowed to advance much further than what is expected at their age. In addition, the results of this study show that the Montessori teachers view working with gifted pupils as a positive and fun challenge and they consider it important to include these pupils in their teaching, instead of letting them work on their own.    The results of this study may also suggest that Montessori schools can be beneficial to mathematically gifted pupils. / Syftet med denna kvalitativa studie är att öka kunskapen om hur montessorilärare inkluderar matematiskt särbegåvade elever genom en differentierad undervisning. Detta gjordes genom semistrukturerade intervjuer med nio montessorilärare från hela Sverige. Samtliga undervisar, eller har undervisat, i matematik i årskurs f-3 och de har alla erfarenhet av matematiskt särbegåvade elever. Montessorilärarna ombads beskriva hur de planerar sin undervisning, hur de genomför den rent praktiskt samt att reflektera kring den här aspekten av deras jobb.    Resultatet visar att montessorilärarna differentierar undervisningen utifrån montessoripedagogikens principer om individualisering. De gör i stort sett helt individuella planeringar för varje elev som baseras på individens nivå, intressen och behov. Denna planering görs tillsammans med eleverna, som alltså kan påverka sin undervisning. När undervisningen sedan omsätts i praktik görs detta under arbetspass som är tre timmar långa. Där får eleverna själva välja vad de vill arbeta med och när. Detta innebär att det pågår en mängd olika aktiviteter samtidigt. Detta tycks vara gynnsamt för de matematiskt särbegåvade eleverna, då de tycks få en undervisning på just deras nivå. De kan också själva välja arbetstempo och därmed avancera i sin takt. Montessorimaterielen har en stor plats i lärarnas undervisning, men de särbegåvade eleverna kan, enligt de intervjuade lärarna, snabbt övergå till en abstrakt matematik.   Resultatet visar också att lärarna anser att det är av stor vikt att de matematiskt särbegåvade eleverna får utmaning och stimulans och begränsar dem därför inte i deras kunskapsinhämtning. Eleverna tillåts avancera långt över sin årskurstillhörighet. Studien visar dessutom att lärarna ser de särbegåvade eleverna som en positiv och rolig utmaning och att de tycker att det är viktigt att dessa elever inkluderas i undervisningen, istället för att lämnas ensamma i sin inlärning.    Sammantaget kan studien tyda på att montessoripedagogiken kan vara gynnsam för matematiskt särbegåvade elever.

Elever med särskild matematisk begåvning är i lika stort behov av att bli utmanade, hjälpta och sedda som alla andra elever. Dessa elever hamnar ibland i situationer då de behöver klara sig själva för att det finns andra elever som är i ”större” behov av lärarens uppmärksamhet. Syftet med denna studie är att få ökad kunskap om hur matematiklärare i årskurs 4–6 arbetar, utmanar och uppmärksammar elever med särskild matematisk begåvning. Metoden som använts är semistrukturerade intervjuer för att intervjua fyra aktivt undervisande matematiklärare i årskurs 4–6.  I samtliga intervjuer framkom teman som indikerade att kunskapen om dessa elevers behov av uppmärksamhet är hög men resurserna att ge dem det de behöver är bristfälliga vilket resulterar i att de ofta får klara sig själva. / Pupils with special mathematical talent are in the same need of being challenged, helped and seen as all other pupils. These students sometimes end up in situations where they need to cope themselves with parts of their learning, because there are other students who are in "greater" need of the teacher's attention. The purpose of this study is to gain a greater understanding of how teachers currently teaching mathematically talented students in grades 4-6, work with these students, the challenges the teachers face and how the teachers’ pay attention to pupils. The method used is semi-structured interviews for interviewing four teachers currently teaching mathematically talented students in grades 4–6. In all interviews the  emerging themes indicated that the knowledge of these pupils' need for attention is high, but the resources to give them what they need are inadequate, which results in them often having to cope with their own learning on their own.

I den här studien undersöks om och vilken typ av lärarstöd avseende Mathematical Knowledge of Teaching (MKT) lärarhandledningar till Favorit matematik 3A och Rik matematik 3A. Vi analyserar vilket stöd som lärarhandledningarna ger till lärare i områdena addition och subtraktion för årskurs 3. Analysen utgår från MKT:s analysmodell med stöd av fyra utvalda kategorier: Common Content Knowledge, Subject Matter Knowledge, Knowledge of Content and Students, Knowledge of Content and Teaching och Knowledge of Content and Curriculum. En komparativ analys genomfördes med MKT som teoretiskt ramverk. Resultatet visar på att lärarhandledningarna innehåller stöd till läraren i addition och subtraktion och delar av MKT. Lärarhandledningarna ger stöd till lärarna vid planering av undervisning, begreppsanvändning i undervisning, olika undervisningsmetoder, nivåökning av kapitel och hur läraren ges kunskap om materialet. Lärarhandledningarnas struktur förmedlar stödet på ett varierande sätt vilket också synliggör likheter och skillnader om de delar av MKT som lärarhandledningarna inte innehåller. / This study examines whether and what type of teacher support regarding Mathematical knowledge of teaching (MKT) contains teacher guides for Favorite Mathematics 3A and Rich Mathematics 3A. We analyze the support of teacher guides provide to teachers in the areas of addition and subtraction for year 3. The analysis is based on MKT's analysis model with the support of four selected categories; Common Content Knowledge, Subject Matter Knowledge, Knowledge of Content and Students, Knowledge of Content and Teaching and Knowledge of Content and Curriculum. A comparative analysis was performed with MKT as the theoretical framework. The results prove that the teacher guides contain support for the teacher in addition and subtraction and parts of MKT. The teacher guides provide support to the teachers when planning teaching, use of concepts in teaching, different teaching methods, level increase of chapters and how the teacher is given knowledge of the material. The structure of the teacher guides the support in a varying way, which also highlights similarities and differences about the parts of MKT that the teacher guides do not contain.