Komplexa tal - vad är det?

Komplexa tal har traditionellt undervisats i de finländska gymnasierna som en valbar kurs. Denna situation har förändrats i och med de nya läroplanerna som tagits i bruk senast hösten 2005. Den nya, striktare läroplanen ger inte lika stora valmöjligheter för skolorna att bestämma undervisningsstoffet, inte ens för de valbara kurserna, och därför har många gymnasier varit tvungna att sluta undervisa om komplexa tal. För att fortsättningsvis ge en möjlighet för gymnasieelever att studera komplexa tal finns detta kompendium. Kompendiet fyller två syften. I de gymnasier där komplexa tal fortfarande finns med i läroplanen kan kompendiet användas som läromedel på ifrågavarande kurs. Kompendiet torde vara önskat eftersom det inte existerar något modernt, finlandssvenskt läromedel där de komplexa talen tas upp. Kompendiets andra, huvudsakliga syfte är att finnas till att ge en möjlighet för de elever, som inte går ett gymnasium där komplexa tal undervisas, att på egen hand lära sig grunder om komplexa tal. Kunskap om utvidgandet av talområdet från reella talen till komplexa hör till matematisk allmänbildning, och är till stor nytta om man är intresserad av att fortsätta studera matematik eller naturvetenskaper efter gymnasiet. Kompendiet kommer att läggas ut på nätet för att få det lättillgängligt. I det första kapitlet behandlas matematikens uppkomst. Det andra kapitlet är en introduktion till varför man behöver komplexa tal, där gås tal- och mängdlära igenom samtidigt som de i kompendiet använda beteckningarna introduceras. I det tredje kapitlet behandlas de komplexa talen; grundläggande räkneregler, absolutbelopp och argument, komplexa tal i polär form och lösning till högregradsekvationer är centrala begrepp. de Moivers formel är ett av de viktigare målen, även Eulers formel behandlas kort. Problematik med negativa kvadratrötter tas också upp. Det fjärde kapitlet handlar om de komplexa talens intressanta historia. I kompendiet finns rikligt med exempel och övningsuppgifter. Kapitel fem innehåller extra övningsuppgifter och i kapitel sex finns lösningarna till samtliga uppgifter. Trots att kompendiets omfång avsevärt ökas i och med dessa lösningar är det av värde att de finns med för att kompendiets huvudsakliga syfte skall uppfyllas: att eleverna på egen hand skall kunna lära sig stoffet.

Phylogenetic studies of cyanobacterial lichens

Phylogenetic studies of cyanobacterial lichens Lichens are symbiotic assemblages between fungi (mycobiont) and green algae (phycobiont) or/and cyanobacteria (cyanobiont). Fossil records show that lichen-like symbioses occurred already 600 million years ago. Lichen symbiosis has since then become an important life strategy for the Fungi, particularly for species in the phylum Ascomycota as approximately 98% of the lichenized fungal species are ascomycetes. The taxonomy of lichen associations is based on the mycobiont. We reconstructed, using DNA sequence data, hypotheses of phylogenetic relationships of lichen-forming fungi that include species associated with cyanobacteria. These hypotheses of phylogeny should form the basis for the taxonomy. They also allowed studies of the origin and the evolution of specific symbioses. Genetic diversity and phylogenetic relationships of symbiotic cyanobionts were also studied in order to examine selectivity of cyanobionts and mycobionts as well as possible co-evolution between partners involved in lichen associations. The suggested circumscription of the family Stereocaulaceae to include Stereocaulon and Lepraria is supported. The recently described crustose Stereocaulon species seem to be correctly placed in the genus, although Stereocaulon traditionally included only fruticose species. The monospecific crustose genus Muhria is also shown to be best placed in Stereocaulon. Family Lobariaceae as currently delimited is monophyletic. Within Lobariaceae genus Sticta including Dendriscocaulon dendroides form a monophyletic group while the genera Lobaria and Pseudocyphellaria are non-monophyletic. A new classification of Lobariaceae is obviously needed. Further studies are however required before a final proposal for a new classification can be made. Our results show that the cyanobacterial symbiotic state has been gained repeatedly in the Ascomycota while losses of symbiotic cyanobacteria appear to be rare. The symbiosis with green algae is confirmed to have been gained repeatedly in Ascomycota but also repeatedly lost. Cyanobacterial symbioses therefore seem to be more stable than green algal associations. Cyanobacteria are perhaps more beneficial for the lichen fungi and therefore maintained. The results indicate a dynamic association of the lichen symbiosis. This evolutionary instability will perhaps be important for the lichen fungi as the utilization of options will perhaps enable lichens to colonize new substrates and survive environmental changes. Some cyanobacterial lichen genera seem to be highly selective towards the cyanobiont while others form symbioses with a broad spectrum of cyanobacteria. No evidence of co-evolution between fungi and cyanobacteria in cyanolichens could be demonstrated.

Vaggvisor i Kvevlax : Språkliga strukturer och konstruktioner

Lullabies in Kvevlax. Linguistic structures and constructions. The study is a linguistic analysis of constructions that shape the texts used in lullabies in Kvevlax in Ostrobothnia in Finland. The empirical goal is to identify linguistic constructions in traditional lullabies that make use of the dialect of the region. The theoretical goal was to test the usability of Construction Grammar (CxG) in analyses of this type of material, and to further develop the formal description of Construction Grammar in such a way as to make it possible to analyze all kinds of linguistically complex texts. The material that I collected in the 1960s comprises approximately 600 lullabies and concomitant interviews with the singers on the use of lullabies. In 1991 I collected additional material in Kvevlax. The number of informants is close to 250. Supplementary material covering the Swedish-language regions in Finland was compiled from the archives of the Society of Swedish Literature in Finland. The first part of the study is mainly based on traditional grammar and gives general information about the language and the structures used in the lullabies. In the detailed study of the Kvevlax lullabies in the latter part of the study I use a version of Construction Grammar intended for the linguistic analysis of usage-based texts. The analysis focuses on the most salient constructions in the lullabies. The study shows that Construction Grammar as a method has more general applicability than traditional linguistic methods. The study identifies important constructions, including elements typical of this genre, that structure the text in different variants of the same lullabies. In addition, CxG made it possible to study pragmatic aspects of the interactional, cultural and contextual language that is used in communication with small children. The constructions found in lullabies are also used in language in general. In addition to being able to give detailed linguistic descriptions of the texts, Construction Grammar can also explain the multidimensionality of language and the variations in the texts. The use of CxG made it possible to show that variations are not random but follow prototypical linguistic patterns, constructions. Constructions are thus found to be linguistic resources with built-in variation potentials.

Conditionally One of 'Us' : A Study of Print Media, Minorities and Positioning Practices

This study deals with how ethnic minorities and immigrants are portrayed in the Finnish print media. The study also asks how media users of various ethnocultural backgrounds make sense of these mediated stories. A more general objective is to elucidate negotiations of belonging and positioning practices in an increasingly complex society. The empirical part of the study is based on content analysis and qualitative close reading of 1,782 articles in five newspapers (Hufvudstadsbladet, Vasabladet, Helsingin Sanomat, Iltalehti and Ilta-Sanomat) during various research periods between 1999 and 2007. Four case studies on print media content are followed up by a focus group study involving 33 newspaper readers of Bosnian, Somalian, Russian, and 'native' Finnish backgrounds. The study draws from different academic and intellectual traditions; mainly media and communication studies, sociology and social psychology. The main theoretical framework employed is positioning theory, as developed by Rom Harré and others. Building on this perspective, situational self-positioning, positioning by others, and media positioning are seen as central practices in the negotiation of belonging. In support of contemporary developments in social sciences, some of these negotiations are seen as occurring in a network type of communicative space. In this space, the media form one of the most powerful institutions in constructing, distributing and legitimising values and ideas of who belongs to 'us', and who does not. The notion of positioning always involves an exclusionary potential. This thesis joins scholars who assert that in order to understand inclusionary and exclusionary mechanisms, the theoretical starting point must be a recognition of a decent and non-humiliating society. When key insights are distilled from the five empirical cases and related to the main theories, one of the major arguments put forward is that the media were first and foremost concerned with a minority actor's rightful or unlawful belonging to the Finnish welfare system. However, in some cases persistent stereotypes concerning some immigrant groups' motivation to work, pay taxes and therefore contribute are so strong that a general idea of individualism is forgotten in favour of racialised and stagnated views. Discussants of immigrant background also claim that the positions provided for minority actors in the media are not easy to identify with; categories are too narrow, journalists are biased, the reporting is simplifying and carries labelling potential. Hence, although the will for the communicative space to be more diverse and inclusive exists — and has also in many cases been articulated in charters, acts and codes — the positioning of ethnic minorities and immigrants differs significantly from the ideal.

Magnetically induced currents and magnetic response properties of molecules

The magnetically induced currents in organic monoring and multiring molecules, in Möbius shaped molecules and in inorganic all-metal molecules have been investigated by means of the Gauge-including magnetically induced currents (GIMIC) method. With the GIMIC method, the ring-current strengths and the ring-current density distributions can be calculated. For open-shell molecules, also the spin current can be obtained. The ring-current pathways and ring-current strengths can be used to understand the magnetic resonance properties of the molecules, to indirectly identify the effect of non-bonded interactions on NMR chemical shifts, to design new molecules with tailored properties and to discuss molecular aromaticity. In the thesis, the magnetic criterion for aromaticity has been adopted. According to this, a molecule which has a net diatropic ring current might be aromatic. Similarly, a molecule which has a net paratropic current might be antiaromatic. If the net current is zero, the molecule is nonaromatic. The electronic structure of the investigated molecules has been resolved by quantum chemical methods. The magnetically induced currents have been calculated with the GIMIC method at the density-functional theory (DFT) level, as well as at the self-consistent field Hartree-Fock (SCF-HF), at the Møller-Plesset perturbation theory of the second order (MP2) and at the coupled-cluster singles and doubles (CCSD) levels of theory. For closed-shell molecules, accurate ring-current strengths can be obtained with a reasonable computational cost at the DFT level and with rather small basis sets. For open-shell molecules, it is shown that correlated methods such as MP2 and CCSD might be needed to obtain reliable charge and spin currents. The basis set convergence has to be checked for open-shell molecules by performing calculations with large enough basis sets. The results discussed in the thesis have been published in eight papers. In addition, some previously unpublished results on the ring currents in the endohedral fullerene Sc3C2@C80 and in coronene are presented. It is shown that dynamical effects should be taken into account when modelling magnetic resonance parameters of endohedral metallofullerenes such as Sc3C2@C80. The ring-current strengths in a series of nano-sized hydrocarbon rings are related to static polarizabilities and to H-1 nuclear magnetic resonance (NMR) shieldings. In a case study on the possible aromaticity of a Möbius-shaped [16]annulene we found that, according to the magnetic criterion, the molecule is nonaromatic. The applicability of the GIMIC method to assign the aromatic character of molecules was confirmed in a study on the ring currents in simple monocylic aromatic, homoaromatic, antiaromatic, and nonaromatic hydrocarbons. Case studies on nanorings, hexaphyrins and [n]cycloparaphenylenes show that explicit calculations are needed to unravel the ring-current delocalization pathways in complex multiring molecules. The open-shell implementation of GIMIC was applied in studies on the charge currents and the spin currents in single-ring and bi-ring molecules with open shells. The aromaticity predictions that are made based on the GIMIC results are compared to other aromaticity criteria such as H-1 NMR shieldings and shifts, electric polarizabilities, bond-length alternation, as well as to predictions provided by the traditional Hückel (4n+2) rule and its more recent extensions that account for Möbius twisted molecules and for molecules with open shells.

A metabolomic approach to studying mechanisms of polymeric gene delivery to retinal pigment epithelial cells

Tiivistelmä ReferatAbstract Metabolomics is a rapidly growing research field that studies the response of biological systems to environmental factors, disease states and genetic modifications. It aims at measuring the complete set of endogenous metabolites, i.e. the metabolome, in a biological sample such as plasma or cells. Because metabolites are the intermediates and end products of biochemical reactions, metabolite compositions and metabolite levels in biological samples can provide a wealth of information on on-going processes in a living system. Due to the complexity of the metabolome, metabolomic analysis poses a challenge to analytical chemistry. Adequate sample preparation is critical to accurate and reproducible analysis, and the analytical techniques must have high resolution and sensitivity to allow detection of as many metabolites as possible. Furthermore, as the information contained in the metabolome is immense, the data set collected from metabolomic studies is very large. In order to extract the relevant information from such large data sets, efficient data processing and multivariate data analysis methods are needed. In the research presented in this thesis, metabolomics was used to study mechanisms of polymeric gene delivery to retinal pigment epithelial (RPE) cells. The aim of the study was to detect differences in metabolomic fingerprints between transfected cells and non-transfected controls, and thereafter to identify metabolites responsible for the discrimination. The plasmid pCMV-β was introduced into RPE cells using the vector polyethyleneimine (PEI). The samples were analyzed using high performance liquid chromatography (HPLC) and ultra performance liquid chromatography (UPLC) coupled to a triple quadrupole (QqQ) mass spectrometer (MS). The software MZmine was used for raw data processing and principal component analysis (PCA) was used in statistical data analysis. The results revealed differences in metabolomic fingerprints between transfected cells and non-transfected controls. However, reliable fingerprinting data could not be obtained because of low analysis repeatability. Therefore, no attempts were made to identify metabolites responsible for discrimination between sample groups. Repeatability and accuracy of analyses can be influenced by protocol optimization. However, in this study, optimization of analytical methods was hindered by the very small number of samples available for analysis. In conclusion, this study demonstrates that obtaining reliable fingerprinting data is technically demanding, and the protocols need to be thoroughly optimized in order to approach the goals of gaining information on mechanisms of gene delivery.

Blue mussel beds as biodiversity hotspots on the rocky shores of the northern Baltic Sea

ABSTRACT The Baltic Sea is a vulnerable ecosystem currently undergoing a number of changes, both natural and human induced. The changes are likely to affect the species found on these shores, e.g. their distribution and interactions with other species. Blue mussels (Mytilus trossulus x Mytilus edulis) provide one of the main biogenic hard structures on the shallow shores of the Baltic Sea where they aggregate into dense beds and provide a number of resources for over 40 associated macrofaunal species, thus functioning as ecosystem engineers. The blue mussel, being a marine species, is highly likely to be affected by any changes in sea water salinity, circulation and/or water balance. These changes could trickle down also to affect the associated macrofaunal communities. The aims of this thesis were three-fold: first, I examined and described the macrofaunal communities found within blue mussel patches since the fauna associated with mussel patches had never been described in the study area prior to this thesis. Second, I explored how changes in mussel density, size as well as patch size and shape would affect the mussel communities. Finally, I tested how general landscape theories derived from terrestrial studies function in blue mussel systems. Theories included the structural heterogeneity hypothesis, species-area relationships, edge effects and patch isolation effects. The work shows that blue mussels in the northern Baltic Sea have an indisputable function as diversity hotspots and that the faunal assemblages found in mussel patches are extremely rich and unique. Further on, it shows that changes in mussel biomass, size, patch size and amount of edge have the potential to alter the faunal assemblages and diversity within patches. Finally, it shows that although some landscape theories, such as the structural heterogeneity hypothesis, seem to apply also in blue mussel communities, others cannot be directly applied due to the different prevailing conditions in the study system. This is a pioneering work looking at diversity shaping processes on the rocky shores of the Gulf of Finland, making up over 40% of the total water basin. A focus on niche construction, positive facilitation effects and ecosystem engineering could provide new insights and methods for conservation biology, but before this can be done, we need to fully understand the circumstances under which a species becomes an ecosystem engineer and recognize the systems in which it functions.