Poetics of Subjectivity : Existence and Expressivity in Simone de Beauvoir's Philosophy

In the last thirty years, primarily feminist scholars have drawn attention to and re-evaluated the philosophy of Simone de Beauvoir (1908 1986). Her philosophical practice has been described as non-systematic, and her literary writing has been viewed as part of her non-systematic mode of philosophising. This dissertation radically deepens the question concerning Beauvoir s philosophical motivations for turning to literature as a mode to express subjectivity. It explicates the central concepts of Beauvoir s philosophy of existence, which are subjectivity, ambiguity, paradox and temporality, and their background in the modern traditions of existential philosophy and phenomenology. It also clarifies Beauvoir s main reason to turn to literature in order to express subjectivity as both singular and universal: as a specific mode of communication, literature is able to make the universality of existence manifest in the concrete, singular and temporal texture of life. In addition, the thesis gives examples of how Beauvoir s literary works contribute to an understanding of the complexity of subjectivity. I use the expression poetics of subjectivity to refer to the systematic relation between Beauvoir s existential and phenomenological notion of subjectivity and her literary works, and to her articulations of a creative mode of using language, especially in the novel. The thesis is divided into five chapters, of which the first three investigate Beauvoir s philosophy of existence at the intersection of the modern traditions of thought that began with René Descartes and Søren Kierkegaard s intuitions about subjectivity. Chapter 1 interprets Beauvoir s notion of ambiguity, as compared to paradox, and argues that both determine her notion of existence. Chapters 2 and 3 investigate the phenomenological side of Beauvoir s philosophy through a study of her response to early French interpretations of transcendental subjectivity, especially in the works of Jean-Paul Sartre and Maurice Merleau-Ponty. My analysis shows that Edmund Husserl s distinction between different levels of subjective experience is central to Beauvoir s understanding of subjectivity and to the different ego concepts she uses. Chapter 4 is a study of Beauvoir s reflections on the expression of subjective thought, and, more specifically, her philosophical conceptions of the metaphysical novel and the autobiography as two modes of indirect communication. Chapter 5, finally, compares two modes of investigating concrete subjectivity; Beauvoir s conceptual study of femininity in Le deuxième sexe and her literary expression of subjectivity in the novel L Invitée. My analysis reveals and explicates Beauvoir s original contribution to a comprehensive understanding of the becoming and paradox of human existence: the fundamental insight that these phenomena are sexed, historically as well as imaginatively.

On the Geometry of Infinite-Dimensional Grassmannian Manifolds and Gauge Theory

This PhD Thesis is about certain infinite-dimensional Grassmannian manifolds that arise naturally in geometry, representation theory and mathematical physics. From the physics point of view one encounters these infinite-dimensional manifolds when trying to understand the second quantization of fermions. The many particle Hilbert space of the second quantized fermions is called the fermionic Fock space. A typical element of the fermionic Fock space can be thought to be a linear combination of the configurations m particles and n anti-particles . Geometrically the fermionic Fock space can be constructed as holomorphic sections of a certain (dual)determinant line bundle lying over the so called restricted Grassmannian manifold, which is a typical example of an infinite-dimensional Grassmannian manifold one encounters in QFT. The construction should be compared with its well-known finite-dimensional analogue, where one realizes an exterior power of a finite-dimensional vector space as the space of holomorphic sections of a determinant line bundle lying over a finite-dimensional Grassmannian manifold. The connection with infinite-dimensional representation theory stems from the fact that the restricted Grassmannian manifold is an infinite-dimensional homogeneous (Kähler) manifold, i.e. it is of the form G/H where G is a certain infinite-dimensional Lie group and H its subgroup. A central extension of G acts on the total space of the dual determinant line bundle and also on the space its holomorphic sections; thus G admits a (projective) representation on the fermionic Fock space. This construction also induces the so called basic representation for loop groups (of compact groups), which in turn are vitally important in string theory / conformal field theory. The Thesis consists of three chapters: the first chapter is an introduction to the backround material and the other two chapters are individually written research articles. The first article deals in a new way with the well-known question in Yang-Mills theory, when can one lift the action of the gauge transformation group on the space of connection one forms to the total space of the Fock bundle in a compatible way with the second quantized Dirac operator. In general there is an obstruction to this (called the Mickelsson-Faddeev anomaly) and various geometric interpretations for this anomaly, using such things as group extensions and bundle gerbes, have been given earlier. In this work we give a new geometric interpretation for the Faddeev-Mickelsson anomaly in terms of differentiable gerbes (certain sheaves of categories) and central extensions of Lie groupoids. The second research article deals with the question how to define a Dirac-like operator on the restricted Grassmannian manifold, which is an infinite-dimensional space and hence not in the landscape of standard Dirac operator theory. The construction relies heavily on infinite-dimensional representation theory and one of the most technically demanding challenges is to be able to introduce proper normal orderings for certain infinite sums of operators in such a way that all divergences will disappear and the infinite sum will make sense as a well-defined operator acting on a suitable Hilbert space of spinors. This research article was motivated by a more extensive ongoing project to construct twisted K-theory classes in Yang-Mills theory via a Dirac-like operator on the restricted Grassmannian manifold.

Stochastic Filtering

The stochastic filtering has been in general an estimation of indirectly observed states given observed data. This means that one is discussing conditional expected values as being one of the most accurate estimation, given the observations in the context of probability space. In my thesis, I have presented the theory of filtering using two different kind of observation process: the first one is a diffusion process which is discussed in the first chapter, while the third chapter introduces the latter which is a counting process. The majority of the fundamental results of the stochastic filtering is stated in form of interesting equations, such the unnormalized Zakai equation that leads to the Kushner-Stratonovich equation. The latter one which is known also by the normalized Zakai equation or equally by Fujisaki-Kallianpur-Kunita (FKK) equation, shows the divergence between the estimate using a diffusion process and a counting process. I have also introduced an example for the linear gaussian case, which is mainly the concept to build the so-called Kalman-Bucy filter. As the unnormalized and the normalized Zakai equations are in terms of the conditional distribution, a density of these distributions will be developed through these equations and stated by Kushner Theorem. However, Kushner Theorem has a form of a stochastic partial differential equation that needs to be verify in the sense of the existence and uniqueness of its solution, which is covered in the second chapter.

Climate change and agriculture: theory and application of mitigation policies

Agriculture’s contribution to climate change is controversial as it is a significant source of greenhouse gases but also a sink of carbon. Hence its economic and technological potential to mitigate climate change have been argued to be noteworthy. However, social profitability of emission mitigation is a result from factors among emission reductions such as surface water quality impact or profit from production. Consequently, to value comprehensive results of agricultural climate emission mitigation practices, these co-effects to environment and economics should be taken into account. The objective of this thesis was to develop an integrated economic and ecological model to analyse the social welfare of crop cultivation in Finland on distinctive cultivation technologies, conventional tillage and conservation tillage (no-till). Further, we ask whether it would be privately or socially profitable to allocate some of barley cultivation for alternative land use, such as green set-aside or afforestation, when production costs, GHG’s and water quality impacts are taken into account. In the theoretical framework we depict the optimal input use and land allocation choices in terms of environmental impacts and profit from production and derive the optimal tax and payment policies for climate and water quality friendly land allocation. The empirical application of the model uses Finnish data about production cost and profit structure and environmental impacts. According to our results, given emission mitigation practices are not self-evidently beneficial for farmers or society. On the contrary, in some cases alternative land allocation could even reduce social welfare, profiting conventional crop cultivation. This is the case regarding mineral soils such as clay and silt soils. On organic agricultural soils, climate mitigation practices, in this case afforestation and green fallow give more promising results, decreasing climate emissions and nutrient runoff to water systems. No-till technology does not seem to profit climate mitigation although it does decrease other environmental impacts. Nevertheless, the data behind climate emission mitigation practices impact to production and climate is limited and partly contradictory. More specific experiment studies on interaction of emission mitigation practices and environment would be needed. Further study would be important. Particularly area specific production and environmental factors and also food security and safety and socio-economic impacts should be taken into account.

Dirichlet problem at infinity for p-harmonic functions on negatively curved spaces

The object of this dissertation is to study globally defined bounded p-harmonic functions on Cartan-Hadamard manifolds and Gromov hyperbolic metric measure spaces. Such functions are constructed by solving the so called Dirichlet problem at infinity. This problem is to find a p-harmonic function on the space that extends continuously to the boundary at inifinity and obtains given boundary values there. The dissertation consists of an overview and three published research articles. In the first article the Dirichlet problem at infinity is considered for more general A-harmonic functions on Cartan-Hadamard manifolds. In the special case of two dimensions the Dirichlet problem at infinity is solved by only assuming that the sectional curvature has a certain upper bound. A sharpness result is proved for this upper bound. In the second article the Dirichlet problem at infinity is solved for p-harmonic functions on Cartan-Hadamard manifolds under the assumption that the sectional curvature is bounded outside a compact set from above and from below by functions that depend on the distance to a fixed point. The curvature bounds allow examples of quadratic decay and examples of exponential growth. In the final article a generalization of the Dirichlet problem at infinity for p-harmonic functions is considered on Gromov hyperbolic metric measure spaces. Existence and uniqueness results are proved and Cartan-Hadamard manifolds are considered as an application.

Reading the Texture of Reality : Chaos Theory, Literature and the Humanist Perspective

Tutkimuksessa analysoidaan kaaosteorian vaikutusta kaunokirjallisuudessa ja kirjallisuudentutkimuksessa ja esitetään, että kaaosteorian roolia kirjallisuuden kentällä voidaan parhaiten ymmärtää sen avaamien käsitteiden kautta. Suoran soveltamisen sijaan kaaosteorian avulla on käyty uudenlaisia keskusteluja vanhoista aiheista ja luonnontieteestä ammennetut käsitteet ovat johtaneet aiemmin tukkeutuneiden argumenttien avaamiseen uudesta näkökulmasta käsin. Väitöskirjassa keskitytään kolmeen osa-alueeseen: kaunokirjallisen teoksen rakenteen teoretisointiin, ihmisen (erityisesti tekijän) identiteetin hahmottamiseen ja kuvailemiseen sekä fiktion ja todellisuuden suhteen pohdintaan. Tutkimuksen tarkoituksena on osoittaa, kuinka kaaosteorian kautta näitä aiheita on lähestytty niin kirjallisuustieteessä kuin kaunokirjallisissa teoksissakin. Väitöskirjan keskiössä ovat romaanikirjailija John Barthin, dramatisti Tom Stoppardin ja runoilija Jorie Grahamin teosten analyysit. Nämä kirjailijat ammentavat kaaosteoriasta keinoja käsitteellistää rakenteita, jotka ovat yhtä aikaa dynaamisia prosesseja ja hahmotettavia muotoja. Kaunokirjallisina teemoina nousevat esiin myös ihmisen paradoksaalisesti tunnistettava ja aina muuttuva identiteetti sekä lopullista haltuunottoa pakeneva, mutta silti kiehtova ja tavoiteltava todellisuus. Näiden kirjailijoiden teosten analyysin sekä teoreettisen keskustelun kautta väitöskirjassa tuodaan esiin aiemmassa tutkimuksessa varjoon jäänyt, koherenssia, ymmärrettävyyttä ja realismia painottava humanistinen näkökulma kaaosteorian merkityksestä kirjallisuudessa.

Convex-transitive Banach spaces and their hyperplanes

The topic of this dissertation is the geometric and isometric theory of Banach spaces. This work is motivated by the known Banach-Mazur rotation problem, which asks whether each transitive separable Banach space is isometrically a Hilbert space. A Banach space X is said to be transitive if the isometry group of X acts transitively on the unit sphere of X. In fact, some weaker symmetry conditions than transitivity are studied in the dissertation. One such condition is an almost isometric version of transitivity. Another investigated condition is convex-transitivity, which requires that the closed convex hull of the orbit of any point of the unit sphere under the rotation group is the whole unit ball. Following the tradition developed around the rotation problem, some contemporary problems are studied. Namely, we attempt to characterize Hilbert spaces by using convex-transitivity together with the existence of a 1-dimensional bicontractive projection on the space, and some mild geometric assumptions. The convex-transitivity of some vector-valued function spaces is studied as well. The thesis also touches convex-transitivity of Banach lattices and resembling geometric cases.

Conrad Summenhart's theory of individual rights and its medieval background

This study focuses on the theory of individual rights that the German theologian Conrad Summenhart (1455-1502) explicated in his massive work Opus septipartitum de contractibus pro foro conscientiae et theologico. The central question to be studied is: How does Summenhart understand the concept of an individual right and its immediate implications? The basic premiss of this study is that in Opus septipartitum Summenhart composed a comprehensive theory of individual rights as a contribution to the on-going medieval discourse on rights. With this rationale, the first part of the study concentrates on earlier discussions on rights as the background for Summenhart s theory. Special attention is paid to language in which right was defined in terms of power . In the fourteenth century writers like Hervaeus Natalis and William Ockham maintained that right signifies power by which the right-holder can to use material things licitly. It will also be shown how the attempts to describe what is meant by the term right became more specified and cultivated. Gerson followed the implications that the term power had in natural philosophy and attributed rights to animals and other creatures. To secure right as a normative concept, Gerson utilized the ancient ius suum cuique-principle of justice and introduced a definition in which right was seen as derived from justice. The latter part of this study makes effort to reconstructing Summenhart s theory of individual rights in three sections. The first section clarifies Summenhart s discussion of the right of the individual or the concept of an individual right. Summenhart specified Gerson s description of right as power, taking further use of the language of natural philosophy. In this respect, Summenhart s theory managed to bring an end to a particular continuity of thought that was centered upon a view in which right was understood to signify power to licit action. Perhaps the most significant feature of Summenhart s discussion was the way he explicated the implication of liberty that was present in Gerson s language of rights. Summenhart assimilated libertas with the self-mastery or dominion that in the economic context of discussion took the form of (a moderate) self-ownership. Summenhart discussion also introduced two apparent extensions to Gerson s terminology. First, Summenhart classified right as relation, and second, he equated right with dominion. It is distinctive of Summenhart s view that he took action as the primary determinant of right: Everyone has as much rights or dominion in regard to a thing, as much actions it is licit for him to exercise in regard to the thing. The second section elaborates Summenhart s discussion of the species dominion, which delivered an answer to the question of what kind of rights exist, and clarified thereby the implications of the concept of an individual right. The central feature in Summenhart s discussion was his conscious effort to systematize Gerson s language by combining classifications of dominion into a coherent whole. In this respect, his treatement of the natural dominion is emblematic. Summenhart constructed the concept of natural dominion by making use of the concepts of foundation (founded on a natural gift) and law (according to the natural law). In defining natural dominion as dominion founded on a natural gift, Summenhart attributed natural dominion to animals and even to heavenly bodies. In discussing man s natural dominion, Summenhart pointed out that the natural dominion is not sufficiently identified by its foundation, but requires further specification, which Summenhart finds in the idea that natural dominion is appropriate to the subject according to the natural law. This characterization lead him to treat God s dominion as natural dominion. Partly, this was due to Summenhart s specific understanding of the natural law, which made reasonableness as the primary criterion for the natural dominion at the expense of any metaphysical considerations. The third section clarifies Summenhart s discussion of the property rights defined by the positive human law. By delivering an account on juridical property rights Summenhart connected his philosophical and theological theory on rights to the juridical language of his times, and demonstrated that his own language of rights was compatible with current juridical terminology. Summenhart prepared his discussion of property rights with an account of the justification for private property, which gave private property a direct and strong natural law-based justification. Summenhart s discussion of the four property rights usus, usufructus, proprietas, and possession aimed at delivering a detailed report of the usage of these concepts in juridical discourse. His discussion was characterized by extensive use of the juridical source texts, which was more direct and verbal the more his discussion became entangled with the details of juridical doctrine. At the same time he promoted his own language on rights, especially by applying the idea of right as relation. He also showed recognizable effort towards systematizing juridical language related to property rights.

Abductive translation studies : The art of marshalling signs

This dissertation contributes to the fields of theoretical translation studies, semiotic translation theory, and the semiotics of translation. The aim of this work is to explore the alternative and potential which the semiotic approaches to translation entail from the viewpoint of contemporary translation studies. The overall objective is thus to show that a general semiotic translation theory, and in particular, a Peircean translation theory, are possible and indispensable. Furthermore, this study contributes to the semiotranslational approach and to its theory-building by developing the concept of abductive translation (studies). The specific theoretical frame of reference adopted in this study is provided by the semiotranslation introduced by Dinda L. Gorlée. This approach is primarily based on the semeiotic of Charles Sanders Peirce (1839 1914), and aims at a fusion of semiotics and translation studies. A more general framework is provided by the threefold background and material: the published and unpublished writings of Peirce, Peirce scholarship and Peircean-semiotic publications, as well as the translation-theoretical literature. Part One of this study concentrates on the justification, existence, and nature of the semiotic approaches to translation. This part provides a historical survey, a status report, and a discussion of this area of research, by employing the findings in a boundary-clearing that is multilayered both conceptually and terminologically. Part Two deals with Peircean semiotranslation. Here Gorlée s semiotranslational research is examined by focusing on the starting points, features, and development of semiotranslation. Attention is also paid to the state-of-the-art of semiotranslation theory and to the possibilities for future elaborations. Part Three focuses on the semiotranslational claim that translation is an abductive activity. The concept of abductive translation is based on abduction, one of Peirce s three modes of reasoning; at the same time Firstness, the category of abduction, becomes foregrounded. So abductive translation as a form of possibilistic translation receives here an extensive theoretical discussion by citing examples in which abduction manifests itself as (scientific) reasoning and as everyday contemplation. During this treatise, translation is first equated with sign action, then with interpretation and finally with reasoning. All these approaches appear to embody different facets of the same phenomenon Peirce s ubiquitous semiosis, and they all suggest that translation is inherently an intersemiotic activity in which a sign is inferred from another sign. Translation is therefore semiosis, semiosis is translation and interpretation, interpretation is reasoning, and so on ad infinitum all being manifestations of the art of marshalling signs. The three parts of this study are linked by the overall goal of abductive translation studies: investigation into abductive translation develops the theory of semiotranslation, and this enrichment of semiotranslation in turn constructs a semiotic paradigm within translation studies.

Karl Popper's Philosophy of Science - And the Evolution of the Popperian Worlds

This doctoral thesis in theoretical philosophy is a systematic analysis of Karl Popper's philosophy of science and its relation to his theory of three worlds. The general aim is to study Popper's philosophy of science and to show that Popper's theory of three worlds was a restatement of his earlier positions. As a result, a new reading of Popper's philosophy and development is offered and the theory of three worlds is analysed in a new manner. It is suggested that the theory of three worlds is not purely an ontological theory, but has a profound epistemological motivation. In Part One, Popper's epistemology and philosophy of science is analysed. It is claimed that Popper's thinking was bifurcated: he held two profound positions without noticing the tension between them. Popper adopted the position called the theorist around 1930 and focused on the logical structure of scientific theories. In Logik der Forschung (1935), he attempted to build a logic of science on the grounds that scientific theories may be regarded as universal statements which are not verifiable but can be falsified. Later, Popper emphasized another position, called here the processionalist. Popper focused on the study of science as a process and held that a) philosophy of science should study the growth of knowledge and that b) all cognitive processes are constitutive. Moreover, the constitutive idea that we see the world in the searchlight of our theories was combined with the biological insight that knowledge grows by trial and error. In Part Two, the theory of three worlds is analysed systematically. The theory is discussed as a cluster of theories which originate from Popper's attempt to solve some internal problems in his thinking. Popper adhered to realism and wished to reconcile the theorist and the processionalist. He also stressed the real and active nature of the human mind, and the possibility of objective knowledge. Finally, he wished to create a scientific world view.

Minimalistinen yhdyssanateoria ja käsitteiden yhdistely

The thesis aims to link the biolinguistic research program and the results of studies in comceptual combination from cognitive psychology. The thesis derives a theory of syntactic structure of noun and adjectival compounds from the Empty Lexicon Hypothesis. Two compound-forming operations are described: root-compounding and word-compounding. The aptness of theory is tested with finnish and greek compounds. From the syntactic theory semantic requirements for conceptual system are derived, especially requirements for handling morphosyntactic features. These requirements are compared to three formidable theories of conceptual combination: relation theory CARIN, Dual-Process theory and C3-theory. The claims of explanatory power of relational distributions of modifier in CARIN-theory ared discarded, as the method for sampling and building relational distributions is not reliable and the algorithmic instantiation of theory does not compute what it claims to compute. From relational theory there still remains results supporting existence of 'easy' relations for certain concepts. Dual-Process theory is found to provide results that cannot in theory be affected by linguistic system, but the basic idea of property compounds is kept. C3-theory is found to be not computationally realistic, but the basic results of diagnosticity and local properties (domains) of conceptual system are solid. The three conceptual combination models are rethought as a problem of finding the shortest route between the two concepts. The new basis for modeling is suggested to be bare conceptual landscape with morphosyntactiic or semantic features working as guidance and structural features of landscape basically unknown, but such as they react to features from linguistic system. Minimalistic principles to conceptual modeling are suggested.

Self-Concept and School Achievement of Pupils with Cleft Lip, Cleft Palate or Both : A longitudinal study

The goal of this research was to survey the self-concept and school achievement of pupils with cleft lip, cleft palate or both from juvenile age to adolescence. Longitudinal researches of self-concept and school achievement among pupils with cleft lip, cleft palate or both are uncommon. This research was the first longitudinal research ever conducted in Finland among this population. This research can be considered to be a special educational study because of the target group involved. Self-concept consists of the person s entire personality. Personality is biological and deterministic. Self-concept includes concepts, attitudes and feelings that the person has about him or her qualities, abilities and relations to the environment. The individual associates experiences to this personality with earlier observations through the social interaction. The individual will have the consciousness of the person s existence and action. The target group in this study consisted of Finnish children with clefts, who were comprised of four different age groups. The questionnaire was sent to all subjects (N1 = 419) both times. A total of 74 % of children returned the questionnaire in 1988 (N2=305). 48 % of children returned the questionnaire in 1993 (N3=203). 42% of children returned the questionnaire both times (N4=175) . These 175 children formed the research subjects. The survey was conducted in 1988, and again in 1993. In 1988, the pupils surveyed were 9 to 12 years of age, while in 1993 they were between 14 and 17 years old. The data was collected through the use of a questionnaire, which consisted of common questions and a personality inventory test that was developed for Finnish students by professor Maija-Liisa Rauste-von Wright. Quantitative analysis methods were used to examine the structure of self-concept and school achievement. Structures found in this research were observed in relation to disorder, gender and maturation. According to these results, structures of self-concepts and school achievement are in fact stable. Basic self-concept elements are seen to be formed at an early age. The developmental aspects of self-concept following puberty are observed as the stability of self-concept and as the forming of a general self. The level of school achievement is stable, but the structure of school achievement changes. From these results, it is possible to state that the gender of the child has a statistical significance regarding self-concept and school achievement. However, the experienced disorder does not have statistical significance as regards to self-concept and school achievement. Results of self-concept support the research of self-concept conducted earlier in Finland.

Composition operators on vector-valued BMOA and related function spaces

A composition operator is a linear operator between spaces of analytic or harmonic functions on the unit disk, which precomposes a function with a fixed self-map of the disk. A fundamental problem is to relate properties of a composition operator to the function-theoretic properties of the self-map. During the recent decades these operators have been very actively studied in connection with various function spaces. The study of composition operators lies in the intersection of two central fields of mathematical analysis; function theory and operator theory. This thesis consists of four research articles and an overview. In the first three articles the weak compactness of composition operators is studied on certain vector-valued function spaces. A vector-valued function takes its values in some complex Banach space. In the first and third article sufficient conditions are given for a composition operator to be weakly compact on different versions of vector-valued BMOA spaces. In the second article characterizations are given for the weak compactness of a composition operator on harmonic Hardy spaces and spaces of Cauchy transforms, provided the functions take values in a reflexive Banach space. Composition operators are also considered on certain weak versions of the above function spaces. In addition, the relationship of different vector-valued function spaces is analyzed. In the fourth article weighted composition operators are studied on the scalar-valued BMOA space and its subspace VMOA. A weighted composition operator is obtained by first applying a composition operator and then a pointwise multiplier. A complete characterization is given for the boundedness and compactness of a weighted composition operator on BMOA and VMOA. Moreover, the essential norm of a weighted composition operator on VMOA is estimated. These results generalize many previously known results about composition operators and pointwise multipliers on these spaces.

Composition operators, Aleksandrov measures and value distribution of analytic maps in the unit disc

A composition operator is a linear operator that precomposes any given function with another function, which is held fixed and called the symbol of the composition operator. This dissertation studies such operators and questions related to their theory in the case when the functions to be composed are analytic in the unit disc of the complex plane. Thus the subject of the dissertation lies at the intersection of analytic function theory and operator theory. The work contains three research articles. The first article is concerned with the value distribution of analytic functions. In the literature there are two different conditions which characterize when a composition operator is compact on the Hardy spaces of the unit disc. One condition is in terms of the classical Nevanlinna counting function, defined inside the disc, and the other condition involves a family of certain measures called the Aleksandrov (or Clark) measures and supported on the boundary of the disc. The article explains the connection between these two approaches from a function-theoretic point of view. It is shown that the Aleksandrov measures can be interpreted as kinds of boundary limits of the Nevanlinna counting function as one approaches the boundary from within the disc. The other two articles investigate the compactness properties of the difference of two composition operators, which is beneficial for understanding the structure of the set of all composition operators. The second article considers this question on the Hardy and related spaces of the disc, and employs Aleksandrov measures as its main tool. The results obtained generalize those existing for the case of a single composition operator. However, there are some peculiarities which do not occur in the theory of a single operator. The third article studies the compactness of the difference operator on the Bloch and Lipschitz spaces, improving and extending results given in the previous literature. Moreover, in this connection one obtains a general result which characterizes the compactness and weak compactness of the difference of two weighted composition operators on certain weighted Hardy-type spaces.

Variation in the Understanding of Lutheranism and Its Implications for Religious Education : Meaning Discernment of Students and Teachers in Finnish Upper Secondary Schools

The study investigated variation in the ways in which a group of students and teachers of Evangelical Lutheran religious education in Finnish upper secondary schools understand Lutheranism and searched for educational implications for learning in religious education. The aim of understanding the qualitative variation in understanding Lutheranism was explored through the relationship between the following questions, which correspond to the results reported in the following original refereed publications: 1) How do Finnish students understand Lutheranism? 2) How do Finnish teachers of religious education constitute the meaning of Lutheranism? 3) How could phenomenography and the Variation Theory of Learning contribute to learning about and from religion in the context of Finnish Lutheran Religious Education as compared to religious education in the UK? Two empirical studies (Hella, 2007; Hella, 2008) were undertaken from a phenomenographic research perspective (e.g., Marton, 1981) and the Variation Theory of Learning (e.g., Marton & Tsui et al. 2004) that developed from it. Data was collected from 63 upper secondary students and 40 teachers of religious education through written tasks with open questions and complementary interviews with 11 students and 20 teachers for clarification of meanings. The two studies focused on the content and structure of meaning discernment in students and teachers expressed understandings of Lutheranism. Differences in understandings are due to differences in the meanings that are discerned and focused on. The key differences between the ways students understand varied from understanding Lutheranism as a religion to personal faith with its core in mercy. The logical relationships between the categories that describe variation in understanding express a hierarchy of ascending complexity, according to which more developed understandings are inclusive of less developed ones. The ways the teachers understand relate to student s understandings in a sequential manner. Phenomenography and Variation Theory were discussed in the context of religious education in Finland and the UK in relation to the theoretical notion of learning about and from religion (Hella & Wright, 2008). The thesis suggests that variation theory enables religious educators to recognise the unity of learning about and from religion, as learning is always learning about something and involves simultaneous engagement with the object of learning and development as a person. The study also suggests that phenomenography and variation theory offer a means by which it is possible for academics, policy makers, curriculum designers, teachers and students to learn to discern different ways of understanding the contested nature of religions. Keywords: Lutheranism, understanding, variation, teaching, learning, phenomenography, religious education