Renormalization methods in KAM theory

It is well known that an integrable (in the sense of Arnold-Jost) Hamiltonian system gives rise to quasi-periodic motion with trajectories running on invariant tori. These tori foliate the whole phase space. If we perturb an integrable system, the Kolmogorow-Arnold-Moser (KAM) theorem states that, provided some non-degeneracy condition and that the perturbation is sufficiently small, most of the invariant tori carrying quasi-periodic motion persist, getting only slightly deformed. The measure of the persisting invariant tori is large together with the inverse of the size of the perturbation. In the first part of the thesis we shall use a Renormalization Group (RG) scheme in order to prove the classical KAM result in the case of a non analytic perturbation (the latter will only be assumed to have continuous derivatives up to a sufficiently large order). We shall proceed by solving a sequence of problems in which theperturbations are analytic approximations of the original one. We will finally show that the approximate solutions will converge to a differentiable solution of our original problem. In the second part we will use an RG scheme using continuous scales, so that instead of solving an iterative equation as in the classical RG KAM, we will end up solving a partial differential equation. This will allow us to reduce the complications of treating a sequence of iterative equations to the use of the Banach fixed point theorem in a suitable Banach space.

Novel Mass Spectrometric Analysis Methods for Anabolic Androgenic Steroids in Sports Drug Testing

The feasibility of different modern analytical techniques for the mass spectrometric detection of anabolic androgenic steroids (AAS) in human urine was examined in order to enhance the prevalent analytics and to find reasonable strategies for effective sports drug testing. A comparative study of the sensitivity and specificity between gas chromatography (GC) combined with low (LRMS) and high resolution mass spectrometry (HRMS) in screening of AAS was carried out with four metabolites of methandienone. Measurements were done in selected ion monitoring mode with HRMS using a mass resolution of 5000. With HRMS the detection limits were considerably lower than with LRMS, enabling detection of steroids at low 0.2-0.5 ng/ml levels. However, also with HRMS, the biological background hampered the detection of some steroids. The applicability of liquid-phase microextraction (LPME) was studied with metabolites of fluoxymesterone, 4-chlorodehydromethyltestosterone, stanozolol and danazol. Factors affecting the extraction process were studied and a novel LPME method with in-fiber silylation was developed and validated for GC/MS analysis of the danazol metabolite. The method allowed precise, selective and sensitive analysis of the metabolite and enabled simultaneous filtration, extraction, enrichment and derivatization of the analyte from urine without any other steps in sample preparation. Liquid chromatographic/tandem mass spectrometric (LC/MS/MS) methods utilizing electrospray ionization (ESI), atmospheric pressure chemical ionization (APCI) and atmospheric pressure photoionization (APPI) were developed and applied for detection of oxandrolone and metabolites of stanozolol and 4-chlorodehydromethyltestosterone in urine. All methods exhibited high sensitivity and specificity. ESI showed, however, the best applicability, and a LC/ESI-MS/MS method for routine screening of nine 17-alkyl-substituted AAS was thus developed enabling fast and precise measurement of all analytes with detection limits below 2 ng/ml. The potential of chemometrics to resolve complex GC/MS data was demonstrated with samples prepared for AAS screening. Acquired full scan spectral data (m/z 40-700) were processed by the OSCAR algorithm (Optimization by Stepwise Constraints of Alternating Regression). The deconvolution process was able to dig out from a GC/MS run more than the double number of components as compared with the number of visible chromatographic peaks. Severely overlapping components, as well as components hidden in the chromatographic background could be isolated successfully. All studied techniques proved to be useful analytical tools to improve detection of AAS in urine. Superiority of different procedures is, however, compound-dependent and different techniques complement each other.

Thin-Layer Chromatography with Ultraviolet and Mass Spectrometric Detection: From Preparative-Layer to Miniaturized Ultra-Thin-Layer Technique

The present challenge in drug discovery is to synthesize new compounds efficiently in minimal time. The trend is towards carefully designed and well-characterized compound libraries because fast and effective synthesis methods easily produce thousands of new compounds. The need for rapid and reliable analysis methods is increased at the same time. Quality assessment, including the identification and purity tests, is highly important since false (negative or positive) results, for instance in tests of biological activity or determination of early-ADME parameters in vitro (the pharmacokinetic study of drug absorption, distribution, metabolism, and excretion), must be avoided. This thesis summarizes the principles of classical planar chromatographic separation combined with ultraviolet (UV) and mass spectrometric (MS) detection, and introduces powerful, rapid, easy, low-cost, and alternative tools and techniques for qualitative and quantitative analysis of small drug or drug-like molecules. High performance thin-layer chromatography (HPTLC) was introduced and evaluated for fast semi-quantitative assessment of the purity of synthesis target compounds. HPTLC methods were compared with the liquid chromatography (LC) methods. Electrospray ionization mass spectrometry (ESI MS) and atmospheric pressure matrix-assisted laser desorption/ionization MS (AP MALDI MS) were used to identify and confirm the product zones on the plate. AP MALDI MS was rapid, and easy to carry out directly on the plate without scraping. The PLC method was used to isolate target compounds from crude synthesized products and purify them for bioactivity and preliminary ADME tests. Ultra-thin-layer chromatography (UTLC) with AP MALDI MS and desorption electrospray ionization mass spectrometry (DESI MS) was introduced and studied for the first time. Because of the thinner adsorbent layer, the monolithic UTLC plate provided 10 100 times better sensitivity in MALDI analysis than did HPTLC plates. The limits of detection (LODs) down to low picomole range were demonstrated for UTLC AP MALDI and UTLC DESI MS. In a comparison of AP and vacuum MALDI MS detection for UTLC plates, desorption from the irregular surface of the plates with the combination of an external AP MALDI ion source and an ion trap instrument provided clearly less variation in mass accuracy than the vacuum MALDI time-of-flight (TOF) instrument. The performance of the two-dimensional (2D) UTLC separation with AP MALDI MS method was studied for the first time. The influence of the urine matrix on the separation and the repeatability was evaluated with benzodiazepines as model substances in human urine. The applicability of 2D UTLC AP MALDI MS was demonstrated in the detection of metabolites in an authentic urine sample.

The non-literary Latin letters. A study of their syntax and pragmatics

This dissertation studies the language of Latin letters that were written in Egypt and Vindolanda (in northern Britain) during the period 1st century BC 3rd century AD on papyri, ostraca, and wooden tablets. The majority of the texts is, in one way or another, connected with the Roman army. The focus of the study is on syntax and pragmatics. Besides traditional philological methods, modern syntactic theory is used as well, especially in the pragmatic analysis. The study begins with a critical survey of certain concepts that are current in the research on the Latin language, most importantly the concept of vulgar Latin , which, it is argued, seems to be used as an abstract noun for variation and change in Latin . Further, it is necessary to treat even the non-literary material primarily as written texts and not as straightforward reflections of spoken language. An examination of letter phraseology shows that there is considerable variation between the two major geographical areas of provenance. Latin letter writing in Egypt was influenced by Greek. The study highlights the importance of seeing the letters as a text type, with recurring phraseological elements appearing in the body text as well. It is argued that recognising these elements is essential for the correct analysis of the syntax. Three areas of syntax are discussed in detail: sentence connection (mainly parataxis), syntactically incoherent structures and word order (the order of the object and the verb). For certain types of sentence connection we may plausibly posit an origin in spoken Latin, but for many other linguistic phenomena attested in this material the issue of spoken Latin is anything but simple. Concerning the study of historical syntax, the letters offer information about the changing status of the accusative case. Incoherent structures may reflect contaminations in spoken language but usually the reason for them is the inability of the writer to put his thoughts into writing, especially when there is something more complicated to be expressed. Many incoherent expressions reflect the need to start the predication with a thematic constituent. Latin word order is seen as resulting from an interaction of syntactic and pragmatic factors. The preference for an order where the topic is placed sentence-initially can be seen in word order more generally as well. Furthermore, there appears a difference between Egypt and Vindolanda. The letters from Vindolanda show the order O(bject) V(erb) clearly more often than the letters from Egypt. Interestingly, this difference correlates with another, namely the use of the anaphoric pronoun is. This is an interesting observation in view of the fact that both of these are traditional Latin features, as opposed to those that foreshadow the Romance development (VO order and use of the anaphoric ille). However, it is difficult to say whether this is an indication of social or regional variation.

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.

Rhetoric and Representation : Exploring the Cultural Meaning of the Natural Sciences in Contemporary Popular Science Writing and Literature

Kirjallisuuden- ja kulttuurintutkimus on viimeisten kolmen vuosikymmenen aikana tullut yhä enenevässä määrin tietoiseksi tieteen ja taiteen suhteen monimutkaisesta luonteesta. Nykyään näiden kahden kulttuurin tutkimus muodostaa oman kenttänsä, jolla niiden suhdetta tarkastellaan ennen kaikkea dynaamisena vuorovaikutuksena, joka heijastaa kulttuurimme kieltä, arvoja ja ideologisia sisältöjä. Toisin kuin aiemmat näkemykset, jotka pitävät tiedettä ja taidetta toisilleen enemmän tai vähemmän vastakkaisina pyrkimyksinä, nykytutkimus lähtee oletuksesta, jonka mukaan ne ovat kulttuurillisesti rakentuneita diskursseja, jotka kohtaavat usein samankaltaisia todellisuuden mallintamiseen liittyviä ongelmia, vaikka niiden käyttämät metodit eroavatkin toisistaan. Väitöskirjani keskittyy yllä mainitun suhteen osa-alueista popularisoidun tietokirjallisuuden (muun muassa Paul Davies, James Gleick ja Richard Dawkins) käyttämän kielen ja luonnontieteistä ideoita ammentavan kaunokirjallisuuden (muun muassa Jeanette Winterson, Tom Stoppard ja Richard Powers) hyödyntämien keinojen tarkasteluun nojautuen yli 30 teoksen kattavaa aineistoa koskevaan tyylin ja teemojen tekstianalyysiin. Populaarin tietokirjallisuuden osalta tarkoituksenani on osoittaa, että sen käyttämä kieli rakentuu huomattavassa määrin sellaisille rakenteille, jotka tarjoavat mahdollisuuden esittää todellisuutta koskevia argumentteja mahdollisimman vakuuttavalla tavalla. Tässä tehtävässä monilla klassisen retoriikan määrittelemillä kuvioilla on tärkeä rooli, koska ne auttavat liittämään sanotun sisällön ja muodon tiukasti toisiinsa: retoristen kuvioiden käyttö ei näin ollen edusta pelkkää tyylikeinoa, vaan se myös usein kiteyttää argumenttien taustalla olevat tieteenfilosofiset olettamukset ja auttaa vakiinnuttamaan argumentoinnin logiikan. Koska monet aikaisemmin ilmestyneistä tutkimuksista ovat keskittyneet pelkästään metaforan rooliin tieteellisissä argumenteissa, tämä väitöskirja pyrkii laajentamaan tutkimuskenttää analysoimalla myös toisenlaisten kuvioiden käyttöä. Osoitan myös, että retoristen kuvioiden käyttö muodostaa yhtymäkohdan tieteellisiä ideoita hyödyntävään kaunokirjallisuuteen. Siinä missä popularisoitu tiede käyttää retoriikkaa vahvistaakseen sekä argumentatiivisia että kaunokirjallisia ominaisuuksiaan, kuvaa tällainen sanataide tiedettä tavoilla, jotka usein heijastelevat tietokirjallisuuden kielellisiä rakenteita. Toisaalta on myös mahdollista nähdä, miten kaunokirjallisuuden keinot heijastuvat popularisoidun tieteen kerrontatapoihin ja kieleen todistaen kahden kulttuurin dynaamisesta vuorovaikutuksesta. Nykyaikaisen populaaritieteen retoristen elementtien ja kaunokirjallisuuden keinojen vertailu näyttää lisäksi, kuinka tiede ja taide osallistuvat keskusteluun kulttuurimme tiettyjen peruskäsitteiden kuten identiteetin, tiedon ja ajan merkityksestä. Tällä tavoin on mahdollista nähdä, että molemmat ovat perustavanlaatuisia osia merkityksenantoprosessissa, jonka kautta niin tieteelliset ideat kuin ihmiselämän suuret kysymyksetkin saavat kulttuurillisesti rakentuneen merkityksensä.

Univariate, bivariate, and multivariate methods in corpus-based lexicography : A study of synonymy

In this dissertation, I present an overall methodological framework for studying linguistic alternations, focusing specifically on lexical variation in denoting a single meaning, that is, synonymy. As the practical example, I employ the synonymous set of the four most common Finnish verbs denoting THINK, namely ajatella, miettiä, pohtia and harkita ‘think, reflect, ponder, consider’. As a continuation to previous work, I describe in considerable detail the extension of statistical methods from dichotomous linguistic settings (e.g., Gries 2003; Bresnan et al. 2007) to polytomous ones, that is, concerning more than two possible alternative outcomes. The applied statistical methods are arranged into a succession of stages with increasing complexity, proceeding from univariate via bivariate to multivariate techniques in the end. As the central multivariate method, I argue for the use of polytomous logistic regression and demonstrate its practical implementation to the studied phenomenon, thus extending the work by Bresnan et al. (2007), who applied simple (binary) logistic regression to a dichotomous structural alternation in English. The results of the various statistical analyses confirm that a wide range of contextual features across different categories are indeed associated with the use and selection of the selected think lexemes; however, a substantial part of these features are not exemplified in current Finnish lexicographical descriptions. The multivariate analysis results indicate that the semantic classifications of syntactic argument types are on the average the most distinctive feature category, followed by overall semantic characterizations of the verb chains, and then syntactic argument types alone, with morphological features pertaining to the verb chain and extra-linguistic features relegated to the last position. In terms of overall performance of the multivariate analysis and modeling, the prediction accuracy seems to reach a ceiling at a Recall rate of roughly two-thirds of the sentences in the research corpus. The analysis of these results suggests a limit to what can be explained and determined within the immediate sentential context and applying the conventional descriptive and analytical apparatus based on currently available linguistic theories and models. The results also support Bresnan’s (2007) and others’ (e.g., Bod et al. 2003) probabilistic view of the relationship between linguistic usage and the underlying linguistic system, in which only a minority of linguistic choices are categorical, given the known context – represented as a feature cluster – that can be analytically grasped and identified. Instead, most contexts exhibit degrees of variation as to their outcomes, resulting in proportionate choices over longer stretches of usage in texts or speech.

Patterns of Transcendence : Classical Myth in Marina Tsvetaeva's Poetry of the 1920s

This study examines the position and meaning of Classical mythological plots, themes and characters in the oeuvre of the Russian Modernist poet Marina Tsvetaeva (1892-1941). The material consists of lyric poems from the collection Posle Rossii (1928) and two longer lyrical tragedies, Ariadna (1924) and Fedra (1927). These works are examined in the context of Russian Modernism and Tsvetaeva s own poetic development, also taking into account the author s biography, namely, her correspondence with Boris Pasternak. Tsvetaeva s appropriations of the myths enter into a dialogue with the Classical tradition and with the earlier Russian and Western literary manifestations of the source material. Her Classical texts are inextricably linked with her own authorial myth, they are used to project both her ideas about poetry as well as the authored self of her poems. An important context for Tsvetaeva s application of the Classical myths is the concept of the Platonic ladder of Eros. This plot evokes the process of transcendence of the mortal subject into the immaterial realm and is applied by the author as an extended metaphor of the poet s birth. Emphasizing the dialectical movement between the earthly and the divine, Tsvetaeva s Classical personae foreground various positions of the individual between these two realms. By means of kaleidoscopic reformulations of similar metaphors and concepts, Tsvetaeva s mythological poems illustrate the poet s position between the material and the immaterial and the various consequences of this dichotomy on the creative mission. At the heart of Tsvetaeva s appropriation of the Sibyl, Phaedra, Eurydice and Ariadne is the tension between the body and disembodiment. The two lyrical tragedies develop the dichotomous worldview further, nevertheless emphasizing the dual perspective of the divine and the earthly realms: immaterial existence is often evaluated from a material perspective and vice versa. The Platonic subtext is central for Ariadna, focussing on Theseus development from an earthly hero to a spiritual one. Fedra concentrates on Phaedra s divinely induced physical passion, which is nevertheless evoked in a creative light.

Olla elävän sanat : Roolirunon laji Maila Pylkkösen teoksessa Arvo. Vanhaäiti puhuu runonsa

Maila Pylkkönen (1931 1986) was one of the most important modernist poets in Finland and a central figure in developing the dramatic monologue in Finnish literature. The study examines Pylkkönen s poetic work Arvo. Vanhaäiti puhuu runonsa (Value. An old woman speaks her poem, 1959) as an example of the dramatic monologue, approaching it from three perspectives: its generic features and background, and the poetic framework to which it connects in the context of Pylkkönen s poetry. In addition to methods of literary scholarship, the poetic analysis benefits from a linguistic approach. The study shows that the dramatic monologue genre drives Pylkkönen s first work, Klassilliset tunteet (Classical feelings, 1957), in a context of finding poetic identity, characterised by the expression to be the words of a living creature . The study demonstrates that important generic features of the dramatic monologue, namely, a poem representing a speech-event and a hierarchical structure, are also Arvo s most significant generic features. Arvo s poems as speech-events are examined for their internal progressive, pragmatic unity constructed through single line units; for their function as narratives dealing with the life story of an old woman, Arvo s speaker; and from the perspective of the communication between the old woman and the poems other characters. Arvo s speech-events can also be seen as semantic shifts from one poem to another: the poems construct semantic stages representing different phases of the old woman s life. The study demonstrates that analysis of Arvo s hierarchical structure, that is, the relationship between the speaker and the rhetorical levels, reveals the work s structural and ideological wholeness by focusing on the old woman s emotions: longing, loneliness and alienation from the world. In other words, the contradictions between the explicit level of the speaker and an implied rhetorical level open up the tragedy of an old woman s daily life. Study of Arvo s hierarchical structure also highlights the special position of the reader in the framework of a dramatic monologue. The elements of a dramatic present in which the old woman s emotions are conveyed, an italicized opening poem, and the work s title Value invite the reader to consider Arvo as a structural and ideological whole. The function of Arvo s hierarchical structure is to ask the reader to recognise the hopelessness of the old woman s situation, understand it, and even identify with it.