21 resultados para Hilbert symbol
em Helda - Digital Repository of University of Helsinki
Resumo:
The subject of the study is the classical Latin concept 'mundus muliebris', usually translated simply as women’s toiletry items. The task of the research is, on one hand, to find a more accurate and comprehensive literary definition for the concept as used in the early Imperial period, and on the other, to examine whether it is possible to find corresponding groupings of material objects among the finds from Pompeian houses destroyed by the eruption of Mount Vesuvius in AD 79. The study is based on two different bodies of evidence, literary and material, and consequently uses two independent methods of research. In the philological part of the study, all occurrences of the concept 'mundus muliebris' in classical Latin texts were identified and analysed in their proper literary context, paying special attention to information about the nature of the objects included (name, owner, quantity, value, location in the house). On the basis of this analysis, mirrors were chosen as the key elements of the archaeological research, being ̶ hypothetically ̶ the most probable objects to be found among any extant 'mundus muliebris' contexts in Pompeian houses. In the archaeological part of the study, all mirrors deposited in the Archaeological Storerooms of Pompeii, mostly unpublished, were examined, together with their original find contexts. For more detailed documentation, classification, as well as quantitative and functional analysis, the fifty-nine best preserved household or shop contexts were chosen. Among these contexts, only a few ‘ideal’ groups closely corresponding to the literary definitions were found. However, in most cases a functional artifact pattern of toiletry items could indeed be found grouped together with the mirror. The arrangement of the contexts in the domestic space also revealed a clear pattern. Firstly, the contexts consistently seem to be found in the place of storage, inside locked boxes, not in the place of use. Secondly, they show that for the storage of such objects small closed rooms flanking the main entrance of the house were preferred. Culturally, 'mundus muliebris' can be described as a very complex multi-layered concept intimately interrelated with the female gender, an instrument of its bodily creation and a symbol of its nature. Concretely, it has at its core mirrors and instruments for the care of skin and hair, and includes, in more technical definitions, washing equipment as well. In the Roman domus, lacking specific women’s quarters, this box containing toiletries and other personal objects could be defined as the true, although mobile, private space of the household’s female members.
Resumo:
Titled "An Essay on Antimetaphoric Resistance", the dissertation investigates what is here being called "Counter-figures": a term which has in this context a certain variety of applications. Any other-than-image or other-than-figure, anything that cannot be exhausted by figuration (and that is, more or less, anything at all, except perhaps the reproducible images and figures themselves) can be considered "counter-figurative" with regard to the formation of images and figures, ideas and schemas, "any graven image, or any likeness of any thing". Singularity and radical alterity, as well as temporality and its peculiar mode of uniqueness are key issues here, and an ethical dimension is implied by, or intertwined with, the aesthetic. In terms borrowed from Paul Celan's "Meridian" speech, poetry may "allow the most idiosyncratic quality of the Other, its time, to participate in the dialogue". This connection between singularity, alterity and temporality is one of the reasons why Celan so strongly objects to the application of the traditional concept of metaphor to poetry. As Celan says, "carrying over [übertragen]" by metaphor may imply an unwillingness to "bear with [mittragen]" and to "endure [ertragen]" the poem. The thesis is divided into two main parts. The first consists of five distinct prolegomena which all address the mentioned variety of applications of the term "counter-figures", and especially the rejection or critique of either metaphor (by Aristotle, for instance) or the concept of metaphor (defined by Aristotle, and sometimes deemed "anti-poetic" by both theorists and poets). Even if we restrict ourselves to the traditional rhetorico-poetical terms, we may see how, for instance, metonymy can be a counter-figure for metaphor, allegory for symbol, and irony for any single trope or for any piece of discourse at all. The limits of figurality may indeed be located at these points of intersection between different types of tropes or figures, and even between figures or tropes and the "non-figurative trope" or "pseudo-figure" called catachresis. The second part, following on from the open-ended prolegomena, concentrates on Paul Celan's poetry and poetics. According to Celan, true poetry is "essentially anti-metaphoric". I argue that inasmuch as we are willing to pay attention to the "will" of the poetic images themselves (the tropes and metaphors in a poem) to be "carried ad absurdum", as Celan invites us to do, we may find alternative ways of reading poetry and approaching its "secret of the encounter", precisely when the traditional rhetorical instruments, and especially the notion of metaphor, become inapplicable or suspicious — and even where they still seem to impose themselves.
Resumo:
The aim of this study is to define and analyse the symbolism hidden in the gamelan music of the Central Javanese, especially in the Yogyakartanese wayang kulit shadow theatre. This dissertation is divided into two parts. The first part deals with the theory, history and practice of Central Javanese shadow theatre. It also presents the tone symbol theory on which this study is based of B. Y. H. Sastrapustaka, the court servant and musician of the sultan s palace of Yogyakarta. For historical comparison, other theories and phenomena that seem to have some connections with the previously mentioned tone symbol theory are presented here as well as the equipment of the shadow theatre, its music, musical instruments and the shadow theatre in general in literature. The theoretic-methodological basis of the study is an enlarged model of research of cultural music, in which a person in the centre of the model with his/her concepts and by his/her behaviour creates a work of art and receives criticism through feedback, while the process of reciprocal action dynamically affects the whole development of the culture in question. In connection with the concepts of the work of art, the manner of approach of this study is also semiotic as the tone symbol theory gives a particular meaning to each musical note. Thus the purpose of this study is to find answers to how the tone symbol theory manifests itself in practical music making, what its origin is, if it is well known or not, and whether shadow theatre music supports this theory. The second part of this dissertation deals with material collected through interviews and observations as well as representative samples of musical pieces for shadow theatre and their analyses. In relation to this a special tool for analysing gamelan music, developed for the purpose of this study, is also presented. Sufficiently versatile material on the essence and meaning of the shadow theatre collected from many puppet masters of an older generation, many of whom are no longer with us, constitutes an important part of this study. This study proves that the tone symbol theory of Sastrapustaka is of tantristic tradition from the Hindu-Javanese period before the 16th century and before the appearance of Islam in Java. The variants of the previously mentioned theory can be found also in other fields of Javanese advanced civilization, such as architecture and dance. But it seems that knowledge about the tone symbolism connected to the shadow theatre especially has only been preserved in the sultan s palace of Yogyakarta and its intimate circles. The outsider puppet masters surely follow the theory, but they do not necessarily know its origin. As a result of the musical analysis, it is obvious that the musical pieces used for the shadow theatre bear different kinds of symbolic meanings which only an initiated person can feel and understand. These meanings are closely related to the plot of the play at the moment.
Resumo:
The study is an examination of how the distant national past has been conceived and constructed for Finland from the mid-sixteenth century to the Second World War. The author argues that the perception and need of a national 'Golden Age' has undergone several phases during this period, yet the perceived Greatness of the Ancient Finns has been of great importance for the growth and development of the fundamental concepts of Finnish nationalism. It is a question reaching deeper than simply discussing the Kalevala or the Karelianism of the 1890s. Despite early occurrences of most of the topics the image-makers could utilize for the construction of an Ancient Greatness, a truly national proto-history only became a necessity after 1809, when a new conceptual 'Finnishness' was both conceived and brought forth in reality. In this process of nation-building, ethnic myths of origin and descent provided the core of the nationalist cause - the defence of a primordial national character - and within a few decades the antiquarian issue became a standard element of the nationalist public enlightenment. The emerging, archaeologically substantiated, nationhood was more than a scholarly construction: it was a 'politically correct' form of ethnic self-imaging, continuously adapting its message to contemporary society and modern progress. Prehistoric and medieval Finnishness became even more relevant for the intellectual defence of the nation during the period of Russian administrative pressure 1890-1905. With independence the origins of Finnishness were militarized even further, although the 'hot' phase of antiquarian nationalism ended, as many considered the Finnish state reestablished after centuries of 'dependency'. Nevertheless, the distant past of tribal Finnishness and the conceived Golden Age of the Kalevala remained obligating. The decline of public archaeology is quite evident after 1918, even though the national message of the antiquarian pursuits remained present in the history culture of the public. The myths, symbols, images, and constructs of ancient Finnishness had already become embedded in society by the turn of the century, like the patalakki cap, which remains a symbol of Finnishness to this day. The method of approach is one of combining a broad spectrum of previously neglected primary sources, all related to history culture and the subtle banalization of the distant past: school books, postcards, illustrations, festive costumes, drama, satirical magazines, novels, jewellery, and calendars. Tracing the origins of the national myths to their original contexts enables a rather thorough deconstruction of the proto-historical imaginary in this Finnish case study. Considering Anthony D. Smith's idea of ancient 'ethnies' being the basis for nationalist causes, the author considers such an approach in the Finnish case totally misplaced.
Resumo:
The subject of doctoral thesis is the analysis and interpretation of instrumental pieces composed by Einojuhani Rautavaara (b. 1928) that have been given angelic titles: Archangel Michael Fighting the Antichrist from the suite Icons (1955)/Before the Icons (2006), Angels and Visitations (1978), the Double Bass Concerto Angel of Dusk (1980), Playgrounds for Angels (1981)and the Seventh Symphony Angel of Light (1994). The aim of the work is to find those musical elements common to these pieces that distinguish them from Rautavaara s other works and to determine if they could be thought of as a series. I prove that behind the common elements and titles stands the same extramusical idea the figure of an angel that the composer has described in his commentaries. The thesis is divided into three parts. Since all of the compositions possess titles that refer to the spiritual symbol of an angel, the first part offers a theoretical background to demonstrate the significant role played by angels in various religions and beliefs, and the means by which music has attempted to represent this symbol throughout history. This background traces also Rautavaara s aesthetic attitude as a spiritual composer whose output can be studied with reference to his extramusical interests including literature, psychology, painting, philosophy and myths. The second part focuses on the analysis of the instrumental compositions with angelic titles, without giving consideration to their commentaries and titles. The analyses concentrate in particular on those musical features that distinguish these pieces from Rautavaara s other compositions. In the third part these musical features are interpreted as symbols of the angel through comparison with vocal and instrumental pieces which contain references to the character of an angel, structures of mythical narration, special musical expressions, use of instruments and aspects of brightness. Finally I explore the composer s interpretative codes, drawing on Rilke s cycle of poems Ten Duino Elegies and Jung s theory of archetypes, and analyze the instrumental pieces with angelic titles in the light of the theory of musical ekphrasis.
Resumo:
Modern ryijys, fabric by the yard and handicrafts. Finnish textile art and modernizing applied art during the inter-war years Textile art was in the 1920s and 1930s in the front rank of Finnish applied art and design. Modern ryijys, tapestries and fabrics by the yard by contemporary textile artists were on show in Finland and abroad. Textile art had also become interesting commercially, especially in interior textiles of modern homes. The research uses sources of the Ornamo Association of Decorative Artists, for example the Ornamo year books published from 1927, the Finnish Society of Crafts and Design and the country s only school of applied arts, the Central School of Arts and Crafts and the Museum of Applied Arts maintained by the society and also the national specialist organisation the Friends of Finnish Handicraft. It also refers to the magazines Käsiteollisuus and Kotiliesi. The art historical dissertation studies the renaissance of weaving art of the inter-war years in Finland. It problematizes the relation of the succesfull and appreciated textile art to the concept of breakthrough of Modernism (Functionalism). With the material from textile artists activities it questions the prevailing idea of slow modernization of Finnish applied art and design and challenges the polarization of craft and industry in the discourses of Modernisms of design. The public discussions about modernization of design and applied art where textile art and especially the ryijy got sometimes into difficult positions are interpreted as power struggles. After taking independence in 1917 the Finnish tradition of ryijy rugs was set as a symbol of the original culture of the young nation. The research studies the development of the so called art ryijy and the notions and meanings of hand weaving in the national context and also in relation to contemporary events in international applied art and design. It highlights the continuity of hand crafted production of textiles and the strong position of textile artists working in this field. The research opens new perspectives to Finnish textile artists by showing their activities as entrepreneurs in their own weaving studios or design studios and referring to their many relations and functions as pattern designers and educators in the growing handicraft industries.
Resumo:
Vilho Helanen (1899 1952) was a right-wing opinion leader in interwar Finland. But following the Second World War, the political situation in the country changed dramatically, and Helanen lost his job as well as his influential social station. He began to write detective fiction, and between 1946 and 1952 published seven novels (one had already been published in 1941). The novels protagonist is Kaarlo Rauta, a lawyer who acts as a private investigator. This doctoral dissertation analyzes the Rauta series from three different points of view. It investigates the extent to which the author s life and his strong political background appears in the series. The study also situates the series within Finnish society during and after the war. Finally, the study examines the Rauta series in terms of the genre conventions of detective fiction, that is, the study compares the Rauta series with other Finnish crime fiction and international crime fiction written during the 1940s. The Iron and The Cross Spider uses the term citizenship education when analyzing how Helanen implicitly continued his political teaching when writing crime fiction. The series includes a didactic register, which instructs the middle class in appropriate behaviour and manners, and the social roles entailed by gender. A special area of focus in this didacticism are norms of correct masculinity and femininity. The study devotes specific attention to the status of character in the series. The masculine detective and his beautiful wife are prominent, as is the fictive community and the tensions that criss-cross it. After the war, the Rauta series takes on a positive tone. Men can earn their place in society by fighting at the front, and after the war a homosocial bond exists between all the former soldiers. Women are shut out of the war experience. The detective hero has served in the war, but he is physically and psychologically untouched by it. The community is threatened by artists and immoral bohemians, but not the working class. Artists have affairs outside of marriage and abnormal sexual habits. The members of the upper class are also described as immoral in the series. Sadistic sexuality is often characteristic of the criminals, who are mostly femme fatales in the fashion of hard-boiled detective stories and film noir. Also, strong feelings have a negative connotation in the series, and showing them is forbidden behaviour. Men become criminals when they are insufficiently masculine or when they have not carried out their duty by fighting in the war. Helanen portrayed the communists, his political opponents from the 1930s, as criminals in his post-war series, but they were not openly represented as Russians or communists. Instead, Helanen used the cross spider as their symbol, a symbol which the readers of the time would recognize.
Resumo:
I min avhandling diskuterar jag om och hur man kan läsa Eva Wichmans novell "Kärret" (ur Molnet såg mig, 1942) som en prosamodernistisk berättelse om ett kvinnligt subjekt, och om kvinnligtskapande. Jag vill mot en prosamodernistisk bakgrund visa min tolkning med en stilistisk och entematisk analys. I min inledning markerar jag att forskare har haft svårt att avgöra vad Eva Wichman egentligen vill säga med "Kärret". De flesta definierar "Kärret" som en fabel, en moralisk berättelse. I min tolkning betonar jag att novellen kan läsas som en prosamodernistisk fabel om det kvinnliga skapandet. Eva Wichman har i många av sina verk beskrivit en kvinnlig konstnärs svårigheter i massamhället och den manliga världen. Jag anser därför att denna tolkning inte är långsökt då det gäller en naturallegori som "Kärret". Jag redovisar kort för bakgrunden till prosamodernismen; definierar stilistiska grundbegrepp i lyrikoch prosa samt diskuterar med hjälp av Peter Luthersson och Gunilla Domellöf hur den modernistiska individualiteten konstituerar sig i förhållande till samhället ochmoderniseringsprocessen. Jag tar fasta på den kvinnliga författarens skapandeprocess och poängterar, med hjälp av bl.a. Dominique Head och Domellöf, att det kvinnliga skapandet ofta är svårt att erhålla i ett traditionellt manligt samhälle. Head, Domellöf och Rachel Blau DuPlessis menar att det modernistiska skapandet hos kvinnor i stor grad sker med hjälp av stilistiska brott och luckor. I synnerhet förhållandet mellan metafor och metonymi utgör en viktig metod för den kvinnliga modernisten. I mitt tredje kapitel analyserar jag "Kärret" stilistiskt. Modernismen i "Kärret" går ut sammanställa motsatser och sinnesanalogier. Jag tar upp det lyriska och metaforiska i "Kärret"; upprepningar,parallellismer, rytm och dynamik, samt förhållandet mellan metaforer och metonymier utgående från en artikel av David Lodge. Jag demonstrerar i stilanalysen hur Eva Wichman bygger upp ett cykliskt mytiskt berättande. Detta cirkelberättande kan, enligt Domellöf, ses som en kvinnlig utmaning mot det traditionella manliga berättandet. Förhållandet mellan metaforer och metonymier spelar en stor roll också i min tematiska analys. Jag läser kärret i novellen som en symbol för ett kvinnlig subjekt. Kärret är uppbyggt av motsatser. Dessamotsatser kan ses som metaforer i min tolkning av kärret som kvinnligt subjekt. Motsatsparen yta/djup läser jag som den medvetna respektive undermedvetna nivån i det kvinnliga subjektet. Djupet, den undermedvetna nivån, analyserar jag delvis med hjälp av Julia Kristevas begrepp abjektet. Metaforerna spegel/öga ser jag som subjekt/objekt och manligt/kvinnligt i förhållande till det kvinnliga subjektet. Med hjälp av abjektet, omnipotens/känslighet, rörelse/statis samt liv/död visar jag hur Eva Wichman beskriver det konstnärliga skapandet, och den konstnärliga alieneringen i kontrast till det förtryckandet massamhället. Här baserar jag mig på Lutherssons resonemang om den modernistiska individualiteten. På så sätt drar jag slutsatsen att kärret som kvinnligt subjekt kan läsas som ett kvinnligt författarjag. "Kärret" är en berättelse om kvinnlig skaparkraft, om ett kvinnligt subjekt som skapar och verkar isamhället. Eva Wichman gestaltar det kvinnliga berättandet både tematiskt och språkligt. Därför är "Kärret" enligt mig inte en pessimistisk berättelse om ett "säkert nederlag" som många påstår, utan en storslagen fabel om ett modernistiskt subjekt i process. Nyckelord: Eva Wichman, Molnet såg mig, prosamodernism, kvinnligt subjekt, abjekt, metafor, metonymi
Resumo:
The main purpose of the research was to illustrate chemistry matriculation examination questions as a summative assessment tool, and represent how the questions have evolved over the years. Summative assessment and its various test item classifications, Finnish goal-oriented curriculum model, and Bloom’s Revised Taxonomy of Cognitive Objectives formed the theoretical framework for the research. The research data consisted of 257 chemistry questions from 28 matriculation examinations between 1996 and 2009. The analysed test questions were formulated according to the national upper secondary school chemistry curricula 1994, and 2003. Qualitative approach and theory-driven content analysis method were employed in the research. Peer review was used to guarantee the reliability of the results. The research was guided by the following questions: (a) What kinds of test item formats are used in chemistry matriculation examinations? (b) How the fundamentals of chemistry are included in the chemistry matriculation examination questions? (c) What kinds of cognitive knowledge and skills do the chemistry matriculation examination questions require? The research indicates that summative assessment was used diversely in chemistry matriculation examinations. The tests included various test item formats, and their combinations. The majority of the test questions were constructed-response items that were either verbal, quantitative, or experimental questions, symbol questions, or combinations of the aforementioned. The studied chemistry matriculation examinations seldom included selected-response items that can be either multiple-choice, alternate choice, or matching items. The relative emphasis of the test item formats differed slightly depending on whether the test was a part of an extensive general studies battery of tests in sciences and humanities, or a subject-specific test. The classification framework developed in the research can be applied in chemistry and science education, and also in educational research. Chemistry matriculation examinations are based on the goal-oriented curriculum model, and cover relatively well the fundamentals of chemistry included in the national curriculum. Most of the test questions related to the symbolism of chemical equation, inorganic and organic reaction types and applications, the bonding and spatial structure in organic compounds, and stoichiometry problems. Only a few questions related to electrolysis, polymers, or buffer solutions. None of the test questions related to composites. There were not any significant differences in the emphasis between the tests formulated according to the national curriculum 1994 or 2003. Chemistry matriculation examinations are cognitively demanding. The research shows that the majority of the test questions require higher-order cognitive skills. Most of the questions required analysis of procedural knowledge. The questions that only required remembering or processing metacognitive knowledge, were not included in the research data. The required knowledge and skill level varied slightly between the test questions in the extensive general studies battery of tests in sciences and humanities, and subject-specific tests administered since 2006. The proportion of the Finnish chemistry matriculation examination questions requiring higher-order cognitive knowledge and skills is very large compared to what is discussed in the research literature.
Resumo:
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.
Composition operators, Aleksandrov measures and value distribution of analytic maps in the unit disc
Resumo:
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.
Resumo:
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.
Resumo:
For the first time the attempt of Denmark, Finland, Norway and Sweden to increase Nordic economic co-operation and integration (NORDEK 1968-1970) is analysed by using records from the four governments archives and interviews with central actors participating. A dominating argument has until now been that dynamics in Nordic economic integration is different from dynamics in European integration. This archive based study disproves the myth however of ideological Nordism and of short term political developments outside Norden as most important for the NORDEK initiative. The NORDEK initiative was actually more a consequence of a long term socioeconomic and socio-political path dependant process. The study also disproves the myth that the NORDEK plan was a political and ideological symbol without socioeconomic substance. The purpose with NORDEK was to create a better basis for generating economic growth and social welfare. The proposed NORDEK institutions were therefore developed to promote economic progress. The study finally shows that the NORDEK failure in 1970 was not a result of lacking economic rationale or incompatible economic interests. The failure was a result of a power struggle in Finnish domestic policy and lacking political will in the other Nordic countries to continue without Finland.