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.

Adaptive tree multigrids and simplified spherical harmonics approximation in deterministic neutral and charged particle transport

A new deterministic three-dimensional neutral and charged particle transport code, MultiTrans, has been developed. In the novel approach, the adaptive tree multigrid technique is used in conjunction with simplified spherical harmonics approximation of the Boltzmann transport equation. The development of the new radiation transport code started in the framework of the Finnish boron neutron capture therapy (BNCT) project. Since the application of the MultiTrans code to BNCT dose planning problems, the testing and development of the MultiTrans code has continued in conventional radiotherapy and reactor physics applications. In this thesis, an overview of different numerical radiation transport methods is first given. Special features of the simplified spherical harmonics method and the adaptive tree multigrid technique are then reviewed. The usefulness of the new MultiTrans code has been indicated by verifying and validating the code performance for different types of neutral and charged particle transport problems, reported in separate publications.

Reynolds stress and heat flux in spherical shell convection

Context. Turbulent fluxes of angular momentum and heat due to rotationally affected convection play a key role in determining differential rotation of stars. Aims. We compute turbulent angular momentum and heat transport as functions of the rotation rate from stratified convection. We compare results from spherical and Cartesian models in the same parameter regime in order to study whether restricted geometry introduces artefacts into the results. Methods. We employ direct numerical simulations of turbulent convection in spherical and Cartesian geometries. In order to alleviate the computational cost in the spherical runs and to reach as high spatial resolution as possible, we model only parts of the latitude and longitude. The rotational influence, measured by the Coriolis number or inverse Rossby number, is varied from zero to roughly seven, which is the regime that is likely to be realised in the solar convection zone. Cartesian simulations are performed in overlapping parameter regimes. Results. For slow rotation we find that the radial and latitudinal turbulent angular momentum fluxes are directed inward and equatorward, respectively. In the rapid rotation regime the radial flux changes sign in accordance with earlier numerical results, but in contradiction with theory. The latitudinal flux remains mostly equatorward and develops a maximum close to the equator. In Cartesian simulations this peak can be explained by the strong 'banana cells'. Their effect in the spherical case does not appear to be as large. The latitudinal heat flux is mostly equatorward for slow rotation but changes sign for rapid rotation. Longitudinal heat flux is always in the retrograde direction. The rotation profiles vary from anti-solar (slow equator) for slow and intermediate rotation to solar-like (fast equator) for rapid rotation. The solar-like profiles are dominated by the Taylor-Proudman balance.

Il mundus muliebris nelle fonti latine e nei contesti Pompeiani

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.

The North in the Old English Orosius : A Geographical Narrative in Context

This doctoral dissertation examines the description of the North as it appears in the Old English Orosius (OE Or.) in the form of the travel accounts by Ohthere and Wulfstan and a catalogue of peoples of Germania. The description is discussed in the context of ancient and early medieval textual and cartographic descriptions of the North, with a special emphasis on Anglo-Saxon sources and the intellectual context of the reign of King Alfred (871-899). This is the first time that these sources, a multidisciplinary approach and secondary literature, also from Scandinavia and Finland, have been brought together. The discussion is source-based, and archaeological theories and geographical ideas are used to support the primary evidence. This study belongs to the disciplines of early medieval literature and (cultural) history, Anglo-Saxon studies, English philology, and historical geography. The OE Or. was probably part of Alfred s educational campaign, which conveyed royal ideology to the contemporary elite. The accounts and catalogue are original interpolations which represent a unique historical source for the Viking Age. They contain unparalleled information about peoples and places in Fennoscandia and the southern Baltic and sailing voyages to the White Sea, the Danish lands, and the Lower Vistula. The historical-philological analysis reveals an emphasis on wealth and property, rank, luxury goods, settlement patterns, and territorial divisions. Trade is strongly implied by the mentions of central places and northern products, such as walrus ivory. The references to such peoples as the Finnas, the Cwenas, and the Beormas appear in connection with information about geography and subsistence in the far North. Many of the topics in the accounts relate to Anglo-Saxon aristocratic culture and interests. The accounts focus on the areas associated with the Northmen, the Danes and the Este. These areas resonated in the Anglo-Saxon geographical imagination: they were curious about the northern margin of the world, their own continental ancestry and the geography of their homeland of Angeln, and they had an interest in the Goths and their connection with the southern Baltic in mythogeography. The non-judgemental representation of the North as generally peaceful and relatively normal place is related to Alfredian and Orosian ideas about the unity and spreading of Christendom, and to desires for unity among the Germani and for peace with the Vikings, who were settling in England. These intellectual contexts reflect the innovative and organizational forces of Alfred s reign. The description of the North in the OE Or. can be located in the context of the Anglo-Saxon worldview and geographical mindset. It mirrors the geographical curiosity expressed in other Anglo-Saxon sources, such as the poem Widsith and the Anglo-Saxon mappa mundi. The northern section of this early eleventh-century world map is analyzed in detail here for the first time. It is suggested that the section depicts the North Atlantic and the Scandinavian Peninsula. The survey of ancient and early medieval sources provides a comparative context for the OE Or. In this material, produced by such authors as Strabo, Pliny, Tacitus, Jordanes, and Rimbert, the significance of the North was related to the search for and definition of the northern edge of the world, universal accounts of the world, the northern homeland in the origin stories of the gentes, and Carolingian expansion and missionary activity. These frameworks were transmitted to Anglo-Saxon literary culture, where the North occurs in the context of the definition of Britain s place in the world.

Arkeen pudonnut sibylla : Modernin naisen identiteetin rakentuminen Marja-Liisa Vartion romaanissa Kaikki naiset näkevät unia

A Sibyl fallen into everyday life. The enfolding of the identity of modern woman in Marja- Liisa Vartio s novel Kaikki naiset näkevät unia ( All Women Have Dreams ). --- Marja-Liisa Vartio played a remarkable part in renewing Finnish literature. My thesis examines her novel Kaikki naiset näkevät unia (1960), which describes the life of a middle-aged housewife, Mrs. Pyy ( Mrs. Hazel Hen ). She has moved from country to city and lives now in a suburb, in the Helsinki of the 1950 s. In Finnish literature, the novel is the first significant description of a modern city woman accomplished by modernistic means. My research examines the identity of a woman in the Finland of the 50 s, an epoch marked by the inevitable transition into modernity. My aim is to look into the ways in which the female identity enfolds in Kaikki naiset näkevät unia, how it takes its form, how it is described and commented. The primary method is contextual close reading; the novel is seen in the social, cultural and historical context of the time it was published. Essential elements in this study are literary motifs and images in the novel, and particularly transtextual relations as defined by Gérald Genette. The focus is on hypertextuality, intertextuality and paratextuality. Kaikki naiset näkevät unia emerges as a modern version of Madame Bovary by Gustave Flaubert. A woman s life spent in illusive dreaming is transferred from a 1900th century bourgeois town in France to a middle class Finnish suburb in the 1950 s. Vartio s novel is a variant of an ancient Finnish ballad I, a bird without a nest , making it into a modern narration of transition. The inner, mental journey from country to city is of great length, and the liminal life in a suburb does not make the passage any easier. Like the lyrical voices in the poetry of Edith Södergran, also Mrs. Pyy finds it hard to discover any values of sisterhood or those of ideal femininity in modern times. In earlier studies of Marja-Liisa Vartio s prose, stress has been laid on the discourse of her narrators and characters, as well as on its modern literary form. In this research, however, urgent allusions to paintings, old and new, are taken into account, since Mrs. Pyy mirrors herself against art, both classical and modern. Principal images in this context are Michelangelo s Sibyls in the ceiling of the Sistine Chapel, and a modern painting, which remains unidentified. Mrs. Pyy turns out to be a tragicomic character, who has magnanimous illusions about herself, but is compelled to accept the fact the she is only a mediocre person. She is nothing more than a first generation city dweller; she is not a modern, aloof outsider but a mere dilettante, who desperately tries to live out modern city life. Kaikki naiset näkevät unia is a striking picture of the 1950 s, a picture that is construed in the consciousness of Mrs. Pyy. We are shown everyday life growing more and more modern after the war and woman s role growing more and more subject to increasing pressure for change.

Truth, Proof and Gödelian Arguments : A Defence of Tarskian Truth in Mathematics

One of the most fundamental questions in the philosophy of mathematics concerns the relation between truth and formal proof. The position according to which the two concepts are the same is called deflationism, and the opposing viewpoint substantialism. In an important result of mathematical logic, Kurt Gödel proved in his first incompleteness theorem that all consistent formal systems containing arithmetic include sentences that can neither be proved nor disproved within that system. However, such undecidable Gödel sentences can be established to be true once we expand the formal system with Alfred Tarski s semantical theory of truth, as shown by Stewart Shapiro and Jeffrey Ketland in their semantical arguments for the substantiality of truth. According to them, in Gödel sentences we have an explicit case of true but unprovable sentences, and hence deflationism is refuted. Against that, Neil Tennant has shown that instead of Tarskian truth we can expand the formal system with a soundness principle, according to which all provable sentences are assertable, and the assertability of Gödel sentences follows. This way, the relevant question is not whether we can establish the truth of Gödel sentences, but whether Tarskian truth is a more plausible expansion than a soundness principle. In this work I will argue that this problem is best approached once we think of mathematics as the full human phenomenon, and not just consisting of formal systems. When pre-formal mathematical thinking is included in our account, we see that Tarskian truth is in fact not an expansion at all. I claim that what proof is to formal mathematics, truth is to pre-formal thinking, and the Tarskian account of semantical truth mirrors this relation accurately. However, the introduction of pre-formal mathematics is vulnerable to the deflationist counterargument that while existing in practice, pre-formal thinking could still be philosophically superfluous if it does not refer to anything objective. Against this, I argue that all truly deflationist philosophical theories lead to arbitrariness of mathematics. In all other philosophical accounts of mathematics there is room for a reference of the pre-formal mathematics, and the expansion of Tarkian truth can be made naturally. Hence, if we reject the arbitrariness of mathematics, I argue in this work, we must accept the substantiality of truth. Related subjects such as neo-Fregeanism will also be covered, and shown not to change the need for Tarskian truth. The only remaining route for the deflationist is to change the underlying logic so that our formal languages can include their own truth predicates, which Tarski showed to be impossible for classical first-order languages. With such logics we would have no need to expand the formal systems, and the above argument would fail. From the alternative approaches, in this work I focus mostly on the Independence Friendly (IF) logic of Jaakko Hintikka and Gabriel Sandu. Hintikka has claimed that an IF language can include its own adequate truth predicate. I argue that while this is indeed the case, we cannot recognize the truth predicate as such within the same IF language, and the need for Tarskian truth remains. In addition to IF logic, also second-order logic and Saul Kripke s approach using Kleenean logic will be shown to fail in a similar fashion.

Minästä toiseen : Lacanilaisen subjektin syntymä Anaïs Ninin House of Incestissä ja Hélène Cixous'n Dedans'issa

The study approaches two modern novels using the conceptual frame of Lacanian psychoanalysis, especially the Lacanian notion of subject. The novels can be described as subversive “Bildungsromans” (development novels) highly influenced by psychoanalytic thought. Anaïs Nin’s (1903—1977) “poetic novel” House of Incest (1936) is a story of sexual and artistic awakening while Hélène Cixous’s (b. 1937) first novel Dedans (1969) depicts the growth of a little girl whose father dies. Both are first novels and first person narratives. Concentrating in the narrator’s internal life the novels writings break with the realistic conventions of narrative, bringing forth the themes of anguish, alienation from the world and escape into the prison like realm of the self. The study follows roughly the Lacanian process of becoming a subject. Each chapter opens up with a quick introduction to the Lacanian concepts used in the following part that analyses the novels. The study can thus also be used as a brief introduction to Lacanian theory in finnish. The psychoanalytic narrative/story of the birth of the subject and the novels stories can be seen as mirroring each other. The method of the study is thus based on a dialogue between the theoretical concepts and the analyses. Novels are being approached as texts that break with the Cartesian notion of an autonomous subject making room for a dialectics of self and other, for a movement in which the “I” builds an identity mirroring itself with others. While both of the novels recount the birth of a character called I, they also have a first person narrator apart from the character “I”. Having constituted the self’s identity, the narrator finds from inside of the self also an other or “you” – this discovery is the final clue to the coffin of the autonomous self. From the Lacanian perspective man’s great Other is the order of language, Symbolic, which constitutes the individual, the speaking subject. Using this perspective the novels are interpreted as describing the process of becoming a subject of the Symbolic; subjected to Symbolic order. This “birth process” happens in particular in the Imaginary register, where the self’s identity is built. In the Imaginary or Mirror phase the “I” mirrors himself with different others (e.g. with his mirror image and the family members, the surrounding others) learning to see his body and his selfhood both as familiar and strange, other. In the Imaginary phase the novels’ characters are also trying to deal with the opposite realm of the Symcolic, the Real. The Lacanian Real is not the reality “before words” but a reality left over from the Symbolic, aside of it but constituted by the Symbolic, to be deducted only from within it. In the novels the Real is experienced as a womblike state where the self is immersed in the other’s body. The process of coming a subject of the Symbolic is depicted also as a process of renouncing the “dream of the womb”, which, if realized, could only mean the non-existence of the subject, i.e. death. The study concentrates on analysing the novels’ writing, where meanings are constantly changing: “I” becomes you, the father becomes a mother, inside becomes outside. This technique enables also the deconstruction of certain opposing notions in the novels. The Lacanian point of view exposes language as a constantly moving universe where the subject has no more stability than the momentary meanings language creates. The self’s identity depicted in the novels is a Lacanian fixed identity, whose growth is necessary but opposes the flux imminent to the Symbolic. The anguish experienced in the novels, in the “house of incest” or “inside”, is due to clinging on the unchanging “I”. However, the writing of the novels shows how the meaning of the “I” changes constantly and the fixity thus becomes movement. This way House of Incest and Dedans, despite their pessimistic stories, manage to create an image of a new, moving subject.

Lumometsän syli : Anni Swanin satusymbolismi 1896-1923

Lumometsän syli, Anni Swanin satusymbolismi 1896-1923 on suomenkielisen satukirjallisuuden poetiikkaa ja 1900-luvun alun modernia naiseutta selvittävä feministiseen tutkimustraditioon liittyvä tutkimus. Sen kohteena ovat lasten- ja nuortenkirjailija Anni Swanin (1875-1958) satukokoelmat vuosilta 1901-1923 ja Uusi Suometar -lehden sadunomaiset novellit vuosilta 1896-1904. Tutkimus tuo uutta tietoa lastenkirjallisuuden osalta 1900-luvun alun modernin ihmisen problematiikasta. Se sisältää naissubjektin kehityskaaren ja sisäisen kasvun kohti naistaiteilijuutta. Yksityiskohtaisen tarkastelun kohteina ovat sadut Veli ja sisar (1917), Ihmekukka (1905), Marjaanan helmikruunu (1912), Aaltojen salaisuus (1901), Jääkukka (1905), Tyttö ja kuolema (1917), Merenkuningatar ja hänen poikansa (1905), Lumolinna (1905) ja Tarina Kultasirkasta (1901). Tutkimuksessa tarkastellaan Swanin satujen poeettista kieltä ja naiseuden tematiikkaa ranskalaisen postmodernin ajan feministisen viitekehyksen valossa. Siinä keskeisiä ovat Julia Kristevan psykoanalyyttispohjaiset näkemykset ja Hélène Cixous´n sekä Luce Irigarayn ajatukset feminiinisestä kirjoituksesta. Sadut kontekstualisoidaan ajankohdan symbolistiseen taidevirtaukseen ja Suomen taiteen kultakauteen. Satuja tulkitaan naiskirjailijan lajina ja erityisenä naisen metaforisen ilmaisun muotona. Satujen feministinen lukutapa purkaa perinteisiä lukemiskonventioita ja merkitsee satutekstin lukemista "toisin". Se avaa varhaista modernia naiseutta ja sille ominaista naisen ilmaisukielen erityisyyttä sekä mykkää ei-kielellistä, melankolian ilmaisua. Tutkimus tuo esiin uudenlaisen naiskirjailijan aistimusvoimaisen kielen. Swanin satusymbolismi on luonnon kauneuden synesteettista ja aistimusvoimaista kerrontaa, jolle on luonteenomaista aistiestetiikka, metaforisuus, metonymisyys ja metamorfoosit. Swan vahvistaa osaltaan naisen sankaruutta, omaa ilmaisukieltä ja ääntä. Tuloksena paljastuu satuperinteeseen verrattuna uudenlaisia tyttöyden, äitiyden, naistaiteilijuuden ja perheen malleja ja niiden representaatioita. Satumallit osoittautuvat aikanaan moderneiksi tyttösankareiksi, osin ambivalenteiksi uudenlaista naiseutta ja suhteessa oloa heijastaviksi ja ovat siten varhaisia feministisen sadun tunnusmerkkejä. Tutkimus selvittää, miten Swan rakentaa omaperäisen satusymboliikan. Satumetsä on luonnonkauniin suomalaismetsän symbolinen mielenmaisema ja samanaikaisesti sadun myyttis-symbolinen topos. Swanin luontokäsitys sisältää luonnonsuojelun ja varhaisen ekokriittisen näkemyksen. Tutkimus osoittaa Swanin satujen kytkeytyvän 1900-luvun alun modernismiin ja Suomen taiteen kultakauteen. Swan on suomenkielisen symbolistisen taidesadun kehittäjä ja feministisen sadun aloittaja.