This thesis consists of four papers on the topics of free loop spaces, Koszul duality and A∞-algebras.  In Paper I we consider a definition of differential operators for noncommutative algebras. This definition is inspired by the connections between differential operators of commutative algebras, L∞-algebras and BV-algebras. We show that the definition is reasonable by establishing results that are analoguous to results in the commutative case. As a by-product of this definition we also obtain definitions for noncommutative versions of Gerstenhaber and BV-algebras.  In Paper II we calculate the free loop space homology of (n-1)-connected manifolds of dimension of at least 3n-2. The Chas-Sullivan loop product and the loop bracket are calculated. Over a field of characteristic zero the BV-operator is determined as well. Explicit expressions for the Betti numbers are also established, showing that they grow exponentially.  In Paper III we restrict our coefficients to a field of characteristic 2. We study the Dyer-Lashof operations that exist on free loop space homology in this case. Explicit calculations are carried out for manifolds that are connected sums of products of spheres.  In Paper IV we extend the Koszul duality methods used in Paper II by incorporating A∞-algebras and A∞-coalgebras. This extension of Koszul duality enables us to compute free loop space homology of manifolds that are not necessarily formal and coformal. As an example we carry out the computations for a non-formal simply connected 7-manifold. / Denna avhandling består av fyra artiklar inom ämnena fria öglerum, Koszuldualitet och A∞-algebror. I Artikel I behandlar vi en definition av differentialoperatorer för ickekommutativa algebror. Denna definition är inspirerad av kopplingar mellan differentialoperatorer för kommutativa algebror, L∞-algebror och BV-algebror. Vi visar att definitionen är rimlig genom att etablera resultat som är analoga med resultat i det kommutativa fallet. Som en biprodukt får vi också definitioner för ickekommutativa varianter av Gerstenhaber och BV-algebror. I Artikel II beräknar vi den fria öglerumshomologin av (n-1)-sammanhängande mångfalder av dimension minst 3n-2. Chas-Sullivans ögleprodukt och öglehake beräknas. Över en kropp av karakteristik noll beräknas även BV-operatorn. Explicita uttryck för Bettitalen fastställs också, vilka visar att de växer exponentiellt. I Artikel III begränsar vi koefficienterna till en kropp av karakteristik 2. Vi studerar Dyer- Lashofoperationer som existerar på den fria öglerumshomologin i detta fall. Explicita beräkningar görs för mångfalder som är sammanhängande summor av produkter av sfärer. I Artikel IV utvidgar vi Koszuldualitetmetoden som används i Artikel II genom att inkorporera A∞-algebror och A∞-koalgebror. Denna utvidgning av Koszuldualitet gör det möjligt att beräkna fri öglerumshomologi för mångfalder som inte nödvändigtvis är formella och koformella. Som ett exempel utför vi beräkningar för en ickeformell enkelt sammanhängande 7-mångfald. / <p>At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 3: Manuscript. Paper 4: Manuscript.</p>

This research considers the role of those who support voluntary youth leaders in their responsibility to nurture spiritual development in children and young people. It discusses particularly those who work in organisations with an ethos of supporting such spiritual development and at the same time of welcoming members of many faiths and encouraging their full participation in their various faith traditions. The specific context of the research is the work of the Guide Movement and, in particular, of Girlguiding in the United Kingdom. The research addresses the current challenges but also the enormous value of providing for young people a multi-faith space in which it is genuinely ‘OK to do God’. It discusses the issues which leaders are raising and some suggestions which trainers have made for addressing these.

Abstract Background: The popularity of stocks in Sweden is high and with the prevailing low interest climate investors must invest in stocks to earn return on their investment. Achieving a higher return than the market has been a continuous struggle for professional as well as private investors. Having an investment strategy is of great importance because it helps the investor make rational decisions, avoid psychological traps, and prevents them from losing out on possible return. Investing in securities with different characteristics diversifies the portfolio and reduces the total risk taken. Therefore, an interest among investors in examining whether multiple valuation is a fitting investment strategy should exist. Further to examine if there are any multiples that are especially suited for specific branches. Purpose: The purpose of the study is to analyze which multiple of P/E, P/BV, EV/S and EV/EBITDA generates the highest risk-adjusted return through relative valuation within six branches on the Stockholm Stock Exchange. The study also aims to analyze whether high or low multiples generates the highest risk adjusted return in a Bull Market and try to explain why. Method: Too achieve the purpose, a quantitative study with an abductive approach has been used. An analysis of historical stock prices and multiples has been made. A total of 48 portfolios have been constructed including high respectively low P/E, P/BV, EV/S and EV/EBITDA multiples. The portfolios have been weighted on a yearly basis and afterwards compared with several risk-adjustment tools. The risk-adjusted return has thereafter been compared to a general index too make it possible to draw conclusions. Result: The result implies that it is statistically assured that investors can achieve a higher return than index by using multiple valuation as an investment strategy in four out of six examined branches. A difference in return among the branches and portfolios can be concluded and there were in total 18 out of 48 portfolios that showed a higher risk-adjusted return in which twelve were statistically assured. statistically assured higher return than the chosen index. Keywords: Multiple Valuation, Relative Valuation, Branches, P/E, P/BV, EV/S, EV/EBITDA, Stock Market Psychology, Bull Market.

Nonlinear sigma-models in physics have been a source of interesting and important ideas in geometry, topology, and algebra. One such model is the curved beta gamma system. This purely bosonic model studies maps from a Riemann surface to a target complex manifold X. The solutions to the classical equations of motion are holomorphic maps. An extension of this model - the so-called heterotic model, incorporates fermionic fields valued in a holomorphic vector bundle E on the complex manifold. In this thesis, I study this extended model within the framework of effective field theory and BV quantization developed by Kevin Costello. Building on earlier work of Gorbounov-Gwilliam-Williams in the purely bosonic case, my approach uses tools of Gelfand-Kazhdan formal geometry and derived deformation theory to extract obstructions to quantization (anomalies) and identify these with characteristic classes of the target manifold. Specifically, I show that the obstruction to solving the Quantum Master Equation can be identified with the class ch_2 (TX)-ch_2(E), and the obstruction to the quantizing equivariantly with respect to holomorphic vector fields on the source Riemann surface can be identified with c_1 (TX) - c_1(E). By analyzing the theory where the source is an elliptic curve, an explicit geometric construction of the partition function is given.

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We live in a time of Globalization, where we find ourselves rubbing shoulders and working together in one place with all kinds of people belonging to different races and different creeds. We live in a world which now finds itself immersed in deep global conflicts (terrorism, suicide bombings, political retaliations) which many attribute to religious fanaticism. Thus we can only continue to live peacefully if we maintain that respect for each others beliefs. This is the global dimension this paper wishes to bring forth.In our present situation, if many of us expatriates (in Cambodia) live far from our own native land and we live with people of another culture, understanding their milieu will certainly help us understand the people of that place. And since religion is tied up to a particular language and culture, particularly here in Cambodia, it would be worthwhile to study the different religious influences brought about through the centuries upon Cambodian culture. Hence the social dimension of the paper.The third dimension would be a practical one. Understanding the differences between religions, we could focus more on the bridges that unite rather than the walls that separate us. In this way we realize that being different does not lessen our humanity but rather enriches it.The paper will present a historical overview of the religious history of Cambodia. The literary survey used in this paper will then attempt to list and describe some particular influences of each of these religions (Animism, Brahmanism, Buddhism) to the Cambodian way of living at the present. Then the paper will try to infer some insights on the observations made focusing on how to build bridges for dialogue between Christians and Khmer Buddhists. The paper searches into the intertwining of Animism, Brahmanism and Buddhism into what is now uniquely Cambodia’s national religion and how this would impact other religions now entering Cambodia specifically Christianity.

This thesis reviewed literature exploring the factors contributing to spirituality and their effects on the development of self-concept in girls and women. Self-esteem, self-concept, and self-image, although closely related, were distinct constituents of mental health. Although religiousness and spirituality appeared to describe different concepts, they also were not fully independent. Christian spiritual formation was identified by the practice of spiritual disciplines and acts of faith with others. Spiritual and religious involvement were consistently and positively related to health and inversely related to disorders. However, there was inadequate conceptualization of Christian spirituality in the literature as an explanation effecting self-concept. Review of the evidence indicated that continued research is needed regarding the integration of spiritual disciplines as predictors for a distinct spiritual formation in women. Further research may provide evidence that healthy self-concept in women increases as a function of Christian spiritual formation.

Cette thèse est consacrée dans un premier temps à l’élaboration d’un modèle variationnel dedébruitage d’ordre deux, faisant intervenir l’espace BV 2 des fonctions à hessien borné. Nous nous inspirons ici directement du célèbre modèle de Rudin, Osher et Fatemi (ROF), remplaçant la minimisation de la variation totale de la fonction par la minimisation de la variation totale seconde, c’est à dire la variation totale de ses dérivées. Le but est ici d’obtenir un modèle aussi performant que le modèle ROF, permettant de plus de résoudre le problème de l’effet staircasing que celui-ci engendre. Le modèle que nous étudions ici semble efficace, entraînant toutefois l’apparition d’un léger effet de flou. C’est afin de réduire cet effet que nous introduisons finalement un modèle mixte, permettant d’obtenir des solutions à la fois non constantes par morceaux et sans effet de flou au niveau des détails. Dans une seconde partie, nous nous intéressons au problème d’extraction de texture. Un modèle reconnu comme étant l’un des plus performants est le modèle T V -L1, qui consiste simplement à remplacer dans le modèle ROF la norme L2 du terme d’attache aux données par la norme L1. Nous proposons ici une méthode originale permettant de résoudre ce problème utilisant des méthodes de Lagrangien augmenté. Pour les mêmes raisons que dans le cas du débruitage, nous introduisons également le modèle T V 2-L1, consistant encore une fois à remplacer la variation totale par la variation totale seconde. Un modèle d’extraction de texture mixte est enfin très brièvement introduit. Ce manuscrit est ponctué d’un vaste chapitre dédié aux tests numériques. / This thesis is devoted in a first part to the elaboration of a second order variational modelfor image denoising, using the BV 2 space of bounded hessian functions. We here take a leaf out of the well known Rudin, Osher and Fatemi (ROF) model, where we replace the minimization of the total variation of the function with the minimization of the second order total variation of the function, that is to say the total variation of its partial derivatives. The goal is to get a competitive model with no staircasing effect that generates the ROF model anymore. The model we study seems to be efficient, but generates a blurry effect. In order to deal with it, we introduce a mixed model that permits to get solutions with no staircasing and without blurry effect on details. In a second part, we take an interset to the texture extraction problem. A model known as one of the most efficient is the T V -L1 model. It just consits in replacing the L2 norm of the fitting data term with the L1 norm.We propose here an original way to solve this problem by the use of augmented Lagrangian methods. For the same reason than for the denoising case, we also take an interest to the T V 2-L1 model, replacing again the total variation of the function by the second order total variation. A mixed model for texture extraction is finally briefly introduced. This manuscript ends with a huge chapter of numerical tests.

This essay examines the Swedish missionary association Bible Faithful Friends’ (Bibeltrogna Vänner, BV) ecclesiological development between the years 1911 – 1986 and their relation to the Church of Sweden. This essay’s three main questions are: - How did the ecclesiology of BV develop during the years 1911 – 1986, with certain focus on 1967-1986? - In what way was this ecclesiology imprinted by a) the structure of the missionary association? b) and the ecclesiological standpoint of the leader Axel B. Svensson? As regards the first question, the study shows that BV's ecclesiology, particularly in the years 1967 – 1986, is characterized by a church debate between BV's board and the promoters and founders of the Lutheran Confessional Church (Lutherska Bekännelsekyrkan, LBK). The latter was founded due to what they identified as confessional deviations in the Church of Sweden. Their view of church fellowship was that the invisible and the visible church should be uniform in doctrine, faith and confession. Accordingly, they argued that the lack of church discipline had led the Church of Sweden to deviate from the word of God and the apostles' doctrine. In the 1980’s, a proposal to allow Evangelical Lutheran congregations to form within BV, initiated a theological work by the board. The annual meeting of 1986 resolves not only to permit the emergence of free Evangelical Lutheran congregations within BV, but rather to encourage such a transition. In the second question, this study shows that the varying local church conditions among missionaries in northern Skåne in the 1870’s, resulted in the formation of "Communion fellowships". The historical explanations to the formation of these fellowships vary. However, essential to this study is the explanation given in BV’s internal historiography. This reveals that these fellowships were founded out of a need to receive Holy Communion as they had been excommunicated from the parish church. In other areas, missionaries were welcomed and encouraged by the church; hence Holy Communion was not here an issue. These varying local conditions in the grassroots movement BV contributed most likely to the association's pragmatic position in the church issue. Furthermore, one was united in the focus of mission, both near and abroad. In the third question, the study shows that Axel B. Svensson's ecclesiology had an essential impact on BV's official position in the church issue. Moreover, the absence of his voice after his death in 1967 makes clear that his ecclesiology was considered indicative to both BV and LBK. Both used him as legitimizing their own position but perceived him quite differently. However the dominating position among BV members was to remain within the Church of Sweden by working for spiritual revival in her midst. Being an ecclesiola in ecclesian, and thereby promote revival. At the same time one was open towards a relationship change towards the Church of Sweden if this would be considered necessary. 1986 is the year when one could regard this statement to be put to test: through encouraging the formation of Evangelical Lutheran congregations within BV, the association proves to stay true to its pragmatic ecclesiological standpoint were collaboration on the mission field, home and abroad, is superior to union in church issues. My analysis of these results comes to the conclusion that BV was once and is still founded in the identity of being "ecclesiola in ecclesia". Therefore, during the 1967 – 1986 debate, this identity is challenged by certain BV members wanting to be ecclesia instead of ecclesiola. The pragmatic ecclesiological standpoint, which has long been practiced in the northern Skåne example, in the work of Axel B. Svensson and in the decision of 1986, was hence the reason to why BV was able to stay true to their particular mission: being ecclesiola in ecclesia.