Homogeneous model theory of metric structures

This thesis studies homogeneous classes of complete metric spaces. Over the past few decades model theory has been extended to cover a variety of nonelementary frameworks. Shelah introduced the abstact elementary classes (AEC) in the 1980s as a common framework for the study of nonelementary classes. Another direction of extension has been the development of model theory for metric structures. This thesis takes a step in the direction of combining these two by introducing an AEC-like setting for studying metric structures. To find balance between generality and the possibility to develop stability theoretic tools, we work in a homogeneous context, thus extending the usual compact approach. The homogeneous context enables the application of stability theoretic tools developed in discrete homogeneous model theory. Using these we prove categoricity transfer theorems for homogeneous metric structures with respect to isometric isomorphisms. We also show how generalized isomorphisms can be added to the class, giving a model theoretic approach to, e.g., Banach space isomorphisms or operator approximations. The novelty is the built-in treatment of these generalized isomorphisms making, e.g., stability up to perturbation the natural stability notion. With respect to these generalized isomorphisms we develop a notion of independence. It behaves well already for structures which are omega-stable up to perturbation and coincides with the one from classical homogeneous model theory over saturated enough models. We also introduce a notion of isolation and prove dominance for it.

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.

An inhomogeneity problem in couple stress theory

Using Hilbert theory and Mindlin's couple stress theory, the problem of two-dimensional circular inhomogeneity (when the inserted material is of different size than the size of the cavity and having different elastic constants) is studiedin this paper. Stress could be bounded at infinity. The formulation is valid also for regions other then the circular ones when the matrix is finite has also been tackled. Numerical results are in conformity with the fact that the effect of couple stresses is negligible when the ratio of the smallest dimension of the body to the cahracteristic length is large.

Self-consistent theory of localization in weakly disordered systems

An analytic treatment of localization in a weakly disordered system is presented for the case where the real lattice is approximated by a Cayley tree. Contrary to a recent assertion we find that the mobility edge moves inwards into the band as disorder increases from zero.

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.

Spirituality of Finnish peacekeepers

The previous academic research on Finnish peacekeeping has clarified the operative and historical aspects of Finnish peacekeeping lacking the view of an individual who does the actual peacekeeping work. This research is based on the underlying theoretical assumption of human beings possessing different kinds of talents and intelligences creating a holistic entity. In this broad perspective spirituality was explored as an umbrella concept, as a holistic ability or talent, that can be explored as the deepest aspect of defining what it means to be human. The theoretical framework incorporated the concept of an intelligence, which is defined in Gardner's theory of multiple intelligences as the ability to solve problems, or to create products, that are valued within one or more cultural settings (Gardner, 1993, x). The viability of this theory was studied in the sample of Finnish peacekeepers. Spirituality in the theoretical and conceptual horizon was viewed as an extension of Gardner's theory of intelligences as one potential Gardnerian intelligence candidate. In addition to Gardner's theory, spirituality was explored as sensitivity which includes capacities such as sensing awareness, sensing mystery and sensing value (Hay, 1998). Also the practical aspects of spirituality were taken in account as shown in our everyday lives giving us the direction and influencing our social responsibilities and concerns (Bradford, 1995). Spirituality was explored also involving the element of the peacekeepers' community, the element of personal moral orientations and in the domain of religion and coping. The purpose of this research aimed in two dimensions. First, the aim was to outline the intelligence profile and the spiritual sensitivity profile of peacekeepers. Second, the aim was to understand qualitatively the nature of peacekeepers' spirituality The research interests were studied with different kinds of peacekeepers. Applying the mixed methods approach the research was conducted in two phases: first the former SFOR peacekeepers (N=6) were interviewed and the data was analysed. Inspired by the primary findings of these interviews, the data for the case-study of one peacekeeper was collected in co-operation with one former SFOR peacekeeper (N=1). In the second phase the data was collected from KFOR peacekeepers through the quantitative MI-Survey and the spiritual sensitivity survey (N=195). The quantitative method was used to outline the intelligence profile and the spiritual sensitivity profile of peacekeepers (N=195). In the mixed methods approach this method highlighted the general overview of intelligence traits and spiritual sensitivity of peacekeepers. In the mixed methods approach the qualitative method including interviews (N=6) and a case-study of one peacekeeper (N=1) increased subjective, qualitative information of spirituality of peacekeepers. The intelligence profile of peacekeepers highlighted the bodily-kinesthetic and interpersonal dimensions as the practical and social aspects of peacekeepers. Strong inter-item dependencies in the intrapersonal intelligence profile meant that peacekeepers possess a self-reflection and self-knowledge component and they reflect on deep psychological and philosophical issues. Regarding the spiritual sensitivity, peacekeepers found awareness-sensing, mystery-sensing, value-sensing and community-sensing important. The community-sensing emphasised a strong will to advance peace and to help people who are in need: things that are close to the heart of the peacekeepers. These results depicted practicality, being socially capable, and reflecting one's inner world as essential to peacekeepers. Moreover, spirituality as peacekeepers' moral endeavour became clearer because the sub-model of their community-sensing described morally charged destinations: advancing peace and helping people in need. In the qualitative findings peacekeepers articulated justice orientation and rule-following characterising the nature of peacekeepers' moral attitude and moral call (Kohlberg, 1969). An ethic of care (Gilligan, 1982) describes mainly female moral orientation, but the findings revealed that an ethic of care is also an important agent supporting strongly male peacekeepers in their aim to carry out qualitatively good peacekeeping work. The moral endeavour was voiced, when the role of religion in coping meant the assessment of the a way of life, a way of conduct, a way of being truthful to one's own values in confusing surroundings. The practical level of spiritual and religious contemplation was voiced as morally charged inner motivation to fulfil one's duties and at the same time to cope with various peacekeeping challenges. The results of different data sets were combined and interpreted as the moral endeavour, which characterises peacekeepers' spirituality. As the combining result, the perspective of peacekeepers' spirituality is considered moral or at least morally charged.

Pyhä Teresa ja keskiajan mystiikan teoriat

In my dissertation I have studied St Teresa (1515-1582) in the light of medieval mystical theories. I have two main levels in my research: historical and theological. On the historical level I study St Teresa s personal history in the context of her family and the Spanish society. On the theological level I study both St Teresa s mysticism and her religious experience in the light of medieval mysticism. St Teresa wrote a book called Life , which is her narrative autobiography and story about her mystical spiritual formation. She reflected herself through biblical texts interpreting them in the course of the biblical hermeneutics like allegory, typology, tropology and anagogy. In addition to that she read others life stories from her period of time, but reflected herself only slightly through the sociological point of view. She used irony as a means to gain acceptance to her authority and motive to write. Her position has been described as a double bind because of writing at the request of educated men and to the non-educated women as she herself was uneducated. She used irony as a means to achieve valuation to women, to gain negative attributes connected to them and to gain authority to teach them mystical spirituality, the Bible and prayer. In this ironic tendency she was a feminist writer. In order to understand medieval mysticism I have written in the first chapter a review of the main trends in medieval mysticism in connection with the classical emotional theories. Two medieval mystical theories show an important role in St Teresa s mysticism. One is love mysticism and the other is the three partite way of mysticism (purification, illumination and union). The classic-philosophical emotional theories play a role in both patterns. The theory of love mysticism St Teresa interpreted in the traditional way stressing the spiritual meaning of love in connexion with God and neighbors. Love is an emotion, which is bound with other emotions, but all objects of love don t strengthen spiritual love. In the three partite way of mysticism purification means to find biblical values in life and to practice meditative self-knowledge theologically interpreted. In illumination human understanding has to be illuminated by God and united to mystical knowledge from God. St Teresa considered illumination a way to learn things. Illumination has also psychological aspects like recognition of many trials and pains, which come from life on earth. Theologically interpreted in illumination one should die to oneself, let oneself be transformed and renewed by God. I have also written a review of the modern philosophical discussion on personal identity where memory and mental experiences are important creators of personal identity. St Teresa bound medieval mystical teaching together with her personal religious experience. Her personal identity is by its character based on her narrative life story where mental experiences play important role. Previous researchers have labelled St Teresa as an ecstatic person whose experiences produced ecstatic phenomena to the mysticism. These phenomena combined with visions have in one respect made of her a person who has brought physical and visionary tendencies to theology. In spite of that she also represents a modern tendency trying to give words to experiences, which at first seem to be exceptional and extreme and which are easily interpreted as one-sided either physical or sexual or unsaid. In other respect I have stressed the personality of St Teresa that was represented as both strong and weak. The strong personality for her is demonstrated by religious faith and in its practice. The weak personality was for her a natural personal identity. St Teresa saw a unifying aspect in almost all. Firstly, her mysticism was aimed towards union with God and secondly, the unifying aspects and common rules in human relations in community life were central. Union with God is based on the fact that in a soul God is living in its centre, where God is present in the Trinitarian way. The picture of God in ourselves is a mirror but to get to know God better is to recognize his/her presence in us. When the soul recognizes itself as a dwelling place of God, it knows itself as God knows him/herself. There is equality between God and the soul. To be a Christian means to participate in God in his Trinitarian being. The participation to God is a process of divinization that puts a person into transformation, change and renewal. The unitive aspect concludes also knowledge of opposites between experience of community and solitude as well as community and separateness. As a founder of monasteries St Teresa practiced theology of poverty. She renewed the monastic life founding a rule called discalced that stressed ascetic tendencies. Supporters of her work were after the difficulties in the beginning both society and churchly leaders. She wrote about the monasteries including in her description at times seriousness at times humor and irony. Her stories are said to be picaresque histories that contain stories of ordinary laymen and many unexpected occasions. She exercised a kind of Bakhtinian dialogue in her letters. St Teresa stressed the virtues like sacrifice, determination and courage in the monastic life. Most of what she taught of virtues is based on biblical spirituality but there are also psychological tendencies in her writings. The theological pedagogical advice is mixed with psychology, but she herself made no distinction between different aspects in her teaching. To understand St Teresa and her mysticism is to recognize that she mixes her personal religious experience and mysticism, which widens mysticism to religious experience in a new way, although this corresponds also the very definition of mysticism. St Teresa concentrated on mental-spiritual experiences and the aim of her mystical teaching was to produce a human mind well cured like a garden that has God as its gardener.

On the theory of polarographic maxima

The theory of polarographic maxima is presented taking into account the interaction of momentum transport, the electrostatic potential field, the adsorption—desorption and the faradaic processes. Several earlier results are generalised. The systems approach employed here is also extended to quasi-linear situations.

Optimal maintenance policy for equipment subject to random deterioration and random failure A modern control theory approach.

The stochastic version of Pontryagin's maximum principle is applied to determine an optimal maintenance policy of equipment subject to random deterioration. The deterioration of the equipment with age is modelled as a random process. Next the model is generalized to include random catastrophic failure of the equipment. The optimal maintenance policy is derived for two special probability distributions of time to failure of the equipment, namely, exponential and Weibull distributions Both the salvage value and deterioration rate of the equipment are treated as state variables and the maintenance as a control variable. The result is illustrated by an example

Imagination and diversity in the philosophy of Hobbes

This dissertation is a study of some aspects of theoretical philosophy of the early modern thinker Thomas Hobbes (1588-1679). The focal point of the work is Hobbes s conception of imagination, which is discussed from both a systematic and a historical point of view, as well as in the light of contemporary scholarship. I argue that though there are significant similarities between the view of Hobbes and that of his predecessors, he gives a novel theory of imagination, which clarifies not only early modern discussions on human nature, knowledge, science, and literary criticism, but above all his own versatile philosophy. The prologue of the dissertation introduces methodological principles and gives critical remarks on the standard view of Hobbes. In Chapter II, I discuss the prominent theories of imagination before Hobbes and link them to his account. I argue that though Hobbes adopted the Aristotelian framework, his view is not reduced to it, as he borrows from various sources, for instance, from the Stoics and from Renaissance thought. Chapters III and IV form the psychological part of the work. In the Chapter III I argue that imagination, not sense, is central in the basic cognitive operations of the mind and that imagination has a decisive role in Hobbes s theory of motivation. The Chapter IV concentrates on various questions of Hobbes s philosophy of language. The chapter ends with a defence of a less naturalistic reading of Hobbes s theory of human nature. Chapters V and VI form the epistemological part of the work. I suggest, contrary to what has been recently claimed, that though Hobbes s ideas of good literary style do have a point of contact with his philosophy (e.g. the psychology of creative process), his ideas in the field are independent of his project of demonstrative political science. Instead I argue that the novelty of his major political work, Leviathan (1651), is based on a new theory of knowledge which he continued to develop in the post-Leviathan works. Chapter VII seeks to connect the more theoretical conclusions of Chapters V and VI to Hobbes's idea(l) of science as well as to his philosophical practice. On the basis of Hobbes s own writings as well as some historical examinations, I argue that method is not an apt way to conceptualise Hobbes s philosophical practice. Contemporary readings of Hobbes s theory of science are critically discussed and the chapter ends with an analysis of Hobbes s actual argumentation. In addition to the concluding remarks, the epilogue suggest three things: first, imagination is central when trying to understand Hobbes s versatile philosophy; second, that it is misleading to depict Hobbes as a simple materialist, mechanist, and empiricist; and, third, that in terms of imagination his influence on early modern thought has not been fully appreciated.

Can moral potency and psychological risk close the gap between ethical beliefs and unacceptable consumer behavior?

Depending on how they perceive risk, consumers may not always act according to their ethical beliefs, exposing a gap between beliefs and behavior. We investigate the effect of moral potency on perceived psychological risk of committing an unacceptable behavior. The results suggest that perceived risk is triggered by moral ownership.

Orbit perturbation theory of beam-plasma instability

The nonlinear theory of the instability caused by an electron beam-plasma interaction is studied. A nonlinear analysis has been carried out using many-body methods. A general formula for a neutral collisionless plasma, without external fields, is derived. This could be used for calculating the saturation levels of other instabilities. The effect of orbit perturbation theory on the beam-plasma instability is briefly reviewed.