92 resultados para sovellettu matematiikka


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This is a case-study of students well-being studying in Sibelius Upper Secondary School which has got a special educational task in dance and music. The first purpose of this study is to analyse the students well-being, motivation, studying satisfaction and try to find out what kind of problems the students meet when studying in Upper Secondary School. The second purpose of this study is to try find means in counselling to help students in their Upper Secondary School Studies. The data were gathered in three parts. The first questioning was based on Allardt s (1976; 1998) well-being theory. In this questioning (N = 187) the students described their satisfaction in having (material things), loving (social relationships) and being (free time). The second data was collected by interviews (N = 19). The third data is a follow-up questioning (N = 10) for graduated students. The whole data was analysed with qualitative methods. The gathered qualitative data were compared with the quantitative data gathered by the National Institute for Health and Welfare. Results of this study indicate that the students in this case-study are mainly satisfied with their well-being, social and material things in their studying environment including counselling and teaching. The research results show that some of the students are exhausted due too muchtime spent in studying. This was verified also in the quantitative data gathered by the National Institute for Health and Welfare. These students suffer for the lack of free time and rest. Students who are motivated and have reached the autonomous way of studying do better in their Upper Secondary School Studies than those who study in unautonomous way.A quite wide range of students tend to make individual studying programmes and spend four or more years in Upper Secondary School instead of the three year programme. The individual programme gives them more time for practicing their special skills in the field of the school s special educational task and to give themselves more time for studying the basic subjects of the Upper Secondary School. Some of the students who tend to take extra years in Upper Secondary School have difficulties in their studying skills and are unsure of their studying motivation. The competition among students in Upper Secondary School with the special educational task causes stress and exhaustion for some of the studied students. These students have difficulties with integrating themselves into the social environment. For the other students the school s social environment works as a motivator for their studies and increases their well-being in their studies. According to the results of the follow-up questioning in this study the students value most the network with the other students they made while studying at the Sibelius Upper Secondary School. According to this study the students would need more counselling in all stages of their Upper Secondary School Studies. The autonomous students do quite well in their studies despite of the small amount of given counselling. They would also need more counselling in planning their further studies after Upper Secondary School. The biggest challenges to student counselling in Sibelius Upper Secondary School are helping the students to find their individual ways of studying and helping them to learn the ways of autonomous studying skills. Keywords: Upper Secondary School with a special educational task, well-being, talent, Upper Secondary School, Young person in Upper Secondary School, motivation, counselling, studying

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The aim of this work was to study, whether international fashion trends show in knit designs in Finnish craft magazines and how trends are modified. Women s knitted clothes and accessories in autumn winter season 2005 2006 were analyzed. Future research, trends, fashion, designing and knitting provides theoretical basis for this study. The trend material of this study came from Carlin Women s knitwear winter 2005 2006, which is fashion forecast for Women s knitwear. In addition to the trend book, I selected two international fashion magazines to reinforce this study. Fashion magazines were L´Officiel, 1000 models, Milan New York winter 05/06, No 52, April 2005 and Collezioni Donna, Prêt-à-porter autumn-winter 2005 2006, No 107. Finnish craft magazines in this study were MODA s issues 4/2005, 5/2005, 6/2005 and Novita s issues autumn 2005, winter 2005 and Suuri Käsityölehti s issues 8/2005, 9/2005, 10/2005. For the base of the analyze I took themes from the trend book. From fashion magazines I searched knitwear designs and these designs were sorted out by themes of trend book. To this trend and fashion material I compared knit designs from craft magazines. I analyzed how fashion trends show in knit designs and how they are modified. I also studied what features of trends were shown and which did not appear in knit designs of the craft magazines. For analyzing trend pictures and knit designs in craft magazines I applied qualitative content analysis and image analysis. According to the results of this research, effects of trend can be recognized in knit designs of craft maga-zines, although the fashion trends have been applied very discreetly. Knit designs were very similar re-gardless of magazine. The craft magazine data included approximately as many designs from Novita and MODA. In Suuri Käsityölehti provided only fifth of the designs data. There were also designs in MODA and Suuri Käsityölehti, which were made of Novita s yarns. This research material includes yarns of 15 different yarn manufacturers. Although half of all knit designs were knitted from Novita s yarn. There were 10 different yarns from Novita. Nevertheless Novita s yarn called Aino was the most popular. Finnish craft magazines have not respond to popularity of knitting. Magazines do not provide any novelty designs for knitters. Knit designs in Finnish craft magazines are usually practical basic designs without any innovativeness.

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Objectives. In this research I analyzed the learning process of teacher students in a planning meeting using the expansive learning cycle and types of interaction approaches. In activity theory framework the expansive learning cycle has been applied widely in analyzing learning processes taking several years. However, few studies exist utilizing expansive cycles in analyzing short single meetings. In the activity theory framework talk and interaction have been analyzed using following types of interaction: coordination, cooperation and communication. In these studies single interaction situations have been analyzed, in which the status and power positions of participants has been very different. Interactions of self-directed teams, in which the participants are equal, have been examined very little. I am not aware of any studies, in which both learning actions of the expansive cycle and types of interaction by analyzing the same data would have been utilized. The aim of my study was to describe the process of collaborative innovative learning in a situation where the student group tries to accomplish a broad and ill-defined learning task. I aim to describe, how this planning process proceeds through different phases of learning actions of the expansive cycle. My goal is to understand and describe the transformations in the quality of interaction and transitions which are related to it. Another goal of this study is to specify the possible similarities and differences between expansive learning and types of interactions. Methods. Data of this study consisted of videotaped meetings, which were part of the study module for class teacher degree. The first meeting of the study module was chosen to be the primary research material. Five students were present in the group meeting. Transcription of the conversation was analyzed by classifying the turns of conversation following phases of the expansive cycle. After that the material was categorized again by using types of interaction. Results and conclusions. As a result of this study I was able to trace all the phases of the expansive cycle except one. Also, I was able to identify all interaction types. When I compared the two modes of analysis side by side I was able to find connecting main phases. Thus I was able to identify the interdependence between the two ways of analysis on a higher level, although I was not able to notice correlation on the level of individual phases. Based on this, I conclude that learning of the group was simultaneously specification and formulation of the object at the different phases of expansive learning and transformation of the quality of the interaction while searching for the common object.

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Integrating biodiversity conservation into forest management in non-industrial private forests requires changes in the practices of those public and private actors that have implementing responsibilities and whose strategic and operational opportunities are at stake. Understanding this kind of context-dependent institutional adaptation requires bridging between two analytical approaches: policy implementation and organizational adaptation, backed up with empirical analysis. The empirical analyses recapitulated in this thesis summary address organizational competences, specialization, professional judgment, and organizational networks. The analyses utilize qualitative and quantitative data from public and private sector organizations as well as associations. The empirical analyses produced stronger signals of policy implementation than of organizational adaptation. The organizations recognized the policy and social demand for integrating biodiversity conservation into forest management and their professionals were in favor of conserving biodiversity. However, conservation was integrated to forest management so tightly that it could be said to be subsumed by mainstream forestry. The organizations had developed some competences for conservation but the competences did not differentiate among the organizations other than illustrating the functional differences between industry, administration and associations. The networks that organizations depended on consisted of traditional forestry actors and peers both in planning policy and at the operational level. The results show that he demand for biodiversity conservation has triggered incremental changes in organizations. They can be considered inert regarding this challenge. Isomorphism is advanced by hierarchical guidance and standardization, and by professional norms. Analytically, this thesis contributes to the understanding of organizational behavior across the public and private sector boundaries. The combination of a policy implementation approach inherent in analysis of public policies in hierarchical administration settings, and organizational adaptation typically applied to private sector organizations, highlights the importance of institutional interpretation. Institutional interpretation serves the understanding of the empirically identified diversions from the basic tenets of the two approaches. Attention to institutions allows identification of the overlap of the traditionally segregated approaches.

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Tutkimuksen tavoitteena on historiantutkimuksen menetelmiä käyttäen selvittää metsänhoidon teorian sekä käytännön metsänhoidon kehitysvaiheet ja näihin vaikuttaneet tekijät, keskiajalta lähtien 1870-luvulla tapahtuneeseen metsäteollisuuden läpimurtoon saakka. Tutkimus tarkastelee Suomen metsiä, niiden käyttöä ja metsänhoidon alkuvaiheita Ruotsin ja Venäjän vallan aikoina. Vastauksia haetaan erityisesti seuraaviin pääkysymyksiin: - miten eri metsänkäyttömuodot ja -käyttäjät vaikuttivat metsiin ja metsänhoidon edistymiseen? - millä tavoin maanomistuksen kehitys vaikutti metsien käyttöön ja hoitoon? - millaisiin päämääriin ja yhteiskunnallisiin taustatekijöihin metsien käytön julkinen ohjaus perustui? - mitä käytännön vaikutuksia valtion metsäpolitiikalla ja ohjauksella oli metsänhoidon kehitykseen? - missä ja miten kehittyivät Suomessa sovellettu metsänhoidon teoria ja käytännön menetelmät? - mitkä tekijät säätelivät metsänhoidon teorioiden soveltamista käytäntöön? - mikä oli naapurimaiden metsänhoidon sekä kansainvälisten yhteyksien merkitys metsänhoidon kehitykselle Suomessa? - miten vuosisatainen pelko metsien ja puun loppumisesta vaikutti metsänhoidon kehitykseen? - millainen merkitys puun arvon kehityksellä oli metsänhoidon alkuun saattamiselle ja edistymiselle? Suomessa harjoitettiin 1870-luvulle saakka pääasiassa talonpoikaista metsänkäyttöä. Maaseudun väestö hankki toimeentulonsa metsistä eränkäynnin, kaskiviljelyn, laiduntamisen, rakennushirsien valmistamisen, tervantuotannon ja paikoin myös potaskan tai sysien valmistamisen avulla. Erityisesti rannikkoseuduilla tuotettiin "isorakennuksen puita", lehtereitä, mastopuita ja muuta erikoispuutavaraa. Lautojen ja lankkujen sahaus laajeni vähitellen, saavuttaen 1800-luvun lopulla hallitsevan aseman myyntiin tarkoitettujen metsäntuotteiden tuotannossa. Polttopuun sekä muun kotitarvepuun kulutus säilyi suurimpana puunkäytön ryhmänä pitkälle 1900-luvulle saakka. Mainituista metsänkäyttömuodoista erityisesti kaskeaminen ja sitä seuraava laiduntamisvaihe sekä tervaspuiden koloaminen "autioittivat" laajoja metsäalueita. Tiheimmin asutuilla seuduilla esiintyi pulaa poltto- ja rakennuspuusta myöhäiskeskiajalta alkaen. Nämä ongelmat sekä laivanrakennuksen ja vuoriteollisuuden puunsaannin turvaamisen tarve johtivat 1600-luvun puolivälissä pysyvään metsänkäytön julkiseen ohjaukseen. Tuolloin Ruotsin valtakunnan metsälainsäädännön kivijalaksi tuli kestävyyden periaate, josta kruunu kylläkin joutui tinkimään moneen otteeseen. Valtion jatkuva rahantarve oli käytännössä metsäpolitiikan tärkein taustavoima sekä Ruotsin vallan että autonomian aikana. Jo 1600-luvulla ruvettiin vaatimaan talonpoikien yhteismaiden jakamista omistajilleen vastuullisemman metsänkäytön nimissä. Isoajakoa saatiin Suomessa odottaa 1770-luvulle saakka. Etelä-Suomessa se valmistui melko nopeasti, 1800-luvun puoliväliin mennessä. Sillä olikin myönteinen, metsien säästävämpään käsittelyyn johtava vaikutus. Valtiosta tuli isonjaon myötä erityisesti Pohjois-Suomessa merkittävä metsänomistaja 1800-luvun jälkipuoliskolla. Valtion metsähallinto, jota maaherrat ja sivistyneistö vaativat perustettavaksi jo 1700-luvun puolivälissä, aloitti toimintansa maanlaajuisesti 1860-luvulla. Se oli ensimmäinen merkittävä metsänhoidon organisaatio, ja vasta sen myötä metsänkäyttöä ohjaavilla säädöksillä ja ohjeilla alkoi olla käytännön merkitystä. Yksityismetsiä varten ei tällaista organisaatiota vielä perustettu, niitä rasittivat pahoin nousevan sahateollisuuden määrämittahakkuut pitkälle 1900-luvun puolelle. Turun Akatemiassa tehtiin mittavaa metsänhoidon menetelmiä koskevaa sekä myös metsäpoliittista tutkimustyötä 1700-luvun jälkipuoliskolla. Tulokset eivät vielä sanottavasti siirtyneet käytäntöön, lähinnä puun alhaisen arvon ja tarvittavien organisaatioiden puuttumisen takia. Kun valtion metsähallintoa ja Suomen omaa metsäopetusta ryhdyttiin perustamaan 1800-luvun puolivälissä, haettiin metsänhoidon mallia alan johtavaksi maaksi kehittyneestä Saksasta. Tultaessa 1870-luvulle, oli Evolla jo käynnissä voimakas kehitystyö maamme olosuhteisiin soveltuvien menetelmien luomiseksi saksalaisen teorian pohjalta. Metsänhoidon tiedot ja taidot olisivat jo tässä vaiheessa riittäneet kestävän metsätalouden harjoittamiseen kaikkien omistajaryhmien metsissä, jos tarvittavat organisaatiot olisi kyetty perustamaan ja metsäammattilaisia olisi koulutettu tarpeeksi. Metsänhoidon kehitystä hidastivat 1800-luvun lopulla lähinnä valtion heikko talous ja poliittiset näkemyserot. Metsäteollisuuden 1870-luvulta alkanut voimakas kasvu ja lisääntyvä puuntarve pakottivat kuitenkin valtiovallan pitämään huolta puuntuotannon jatkuvuudesta. Metsäteollisuuden kasvavan viennin kautta lisääntyvät verotulot ja kan-santalouden myönteinen kehitys antoivat vähitellen mahdollisuuden metsänhoidon edistämiseen ammattilaisten koulutuksen, kansalaisten neuvonnan, lainsäädännön ja viranomaisten toiminnan kautta. Tämä tutkimus lähestyy aihettaan metsähistorian, taloushistorian, yhteiskuntahistorian ja ympäristöhistorian näkökulmista. Ajankohtaista merkitystä sillä on kehitysmaiden sekä Itä-Euroopan siirtymätalouksien metsänhoidon edistämiselle, missä suomalaiset metsäammattilaiset ovat mukana lukuisten kehityshankkeiden asiantuntijoina. Kymmenissä maissa metsätalous kamppailee samanlaisten ongelmien kanssa kuin Suomessa ja naapurimaissa 100 - 300 vuotta sitten. Meidän kokemuksistamme on näille kansantalouksille hyötyä valtion- ja yksityismetsätalouden metsänhoito-organisaatioita sekä metsälainsäädäntöä kehitettäessä.

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This thesis examines the feasibility of a forest inventory method based on two-phase sampling in estimating forest attributes at the stand or substand levels for forest management purposes. The method is based on multi-source forest inventory combining auxiliary data consisting of remote sensing imagery or other geographic information and field measurements. Auxiliary data are utilized as first-phase data for covering all inventory units. Various methods were examined for improving the accuracy of the forest estimates. Pre-processing of auxiliary data in the form of correcting the spectral properties of aerial imagery was examined (I), as was the selection of aerial image features for estimating forest attributes (II). Various spatial units were compared for extracting image features in a remote sensing aided forest inventory utilizing very high resolution imagery (III). A number of data sources were combined and different weighting procedures were tested in estimating forest attributes (IV, V). Correction of the spectral properties of aerial images proved to be a straightforward and advantageous method for improving the correlation between the image features and the measured forest attributes. Testing different image features that can be extracted from aerial photographs (and other very high resolution images) showed that the images contain a wealth of relevant information that can be extracted only by utilizing the spatial organization of the image pixel values. Furthermore, careful selection of image features for the inventory task generally gives better results than inputting all extractable features to the estimation procedure. When the spatial units for extracting very high resolution image features were examined, an approach based on image segmentation generally showed advantages compared with a traditional sample plot-based approach. Combining several data sources resulted in more accurate estimates than any of the individual data sources alone. The best combined estimate can be derived by weighting the estimates produced by the individual data sources by the inverse values of their mean square errors. Despite the fact that the plot-level estimation accuracy in two-phase sampling inventory can be improved in many ways, the accuracy of forest estimates based mainly on single-view satellite and aerial imagery is a relatively poor basis for making stand-level management decisions.

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African indigenous foods have received limited research. Most of these indigenous foods are fermented and they form part of the rich nutritional culture of many groups in African countries. The industrialization and commercialisation of these indigenous African fermented foods should be preceded by a thorough scientific knowledge of their processing which can be vital in the elimination of hunger and poverty. This study highlighted emerging developments and the microbiology of cereal-based and cassava-based food products that constitute a major part of the human diet in most African countries. In addition, investigations were also carried out on the coagulant of the Calotropis procera plant used in traditional production of Nigerian Wara cheese and on the effects of adding a nisin producing Lactococcus lactis strain originating from human milk to Nigerian Wara cheese. Fermented cereal-based food such as ogi utilize popular African and readily available grains maize, millet or sorghum as substrates and is popular as a weaning diet in infants. In this study, the bulkiness caused by starch gelatinization was solved by amylase treatments in the investigation on cooked and fermented oat bran porridge. A similar treatment could reduce the viscosity of any cereal porridge. The properties of the Sodom apple leaves (Calotropis procera) extract in cheesemaking were studied. C. procera was affected by monovalent (K+ and Na+) and divalent (Mg2+ and Ca2+) cations during coagulation. The rennet strength of this coagulant was found to be 7 % compared to animal rennet at 35 °C. Increasing the incubation temperature to 70 °C increased the rennet strength 28-fold. The molecular weight of the partially purified protease was determined by SDS-PAGE and was confirmed by Zymography to be approximately 60 kilodaltons. The high proteolytic activity at 70 °C supported the suitability of the protease enzyme as a coagulant in future commercial production of Nigerian Wara cheese. It was also possible to extend the shelf life of Wara cheese by a nisin producing lactic acid bacteria Lactococcus lactis LAC309. The levels of nisin in both whey and curd fractions of Wara were investigated, results showed a 3 log reduction of toxicogenic Bacillus licheniformis spiked on Wara after 3 days. These studies are the first in Finland to promote the advancement of scientific knowledge in African foods. Recognizing these indigenous food products and an efficient transfer of technology from the developed countries to industrialize them are necessary towards a successful realization of the United Nations Millenium Development Program.

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Determination of testosterone and related compounds in body fluids is of utmost importance in doping control and the diagnosis of many diseases. Capillary electromigration techniques are a relatively new approach for steroid research. Owing to their electrical neutrality, however, separation of steroids by capillary electromigration techniques requires the use of charged electrolyte additives that interact with the steroids either specifically or non-specifically. The analysis of testosterone and related steroids by non-specific micellar electrokinetic chromatography (MEKC) was investigated in this study. The partial filling (PF) technique was employed, being suitable for detection by both ultraviolet spectrophotometry (UV) and electrospray ionization mass spectrometry (ESI-MS). Efficient, quantitative PF-MEKC UV methods for steroid standards were developed through the use of optimized pseudostationary phases comprising surfactants and cyclodextrins. PF-MEKC UV proved to be a more sensitive, efficient and repeatable method for the steroids than PF-MEKC ESI-MS. It was discovered that in PF-MEKC analyses of electrically neutral steroids, ESI-MS interfacing sets significant limitations not only on the chemistry affecting the ionization and detection processes, but also on the separation. The new PF-MEKC UV method was successfully employed in the determination of testosterone in male urine samples after microscale immunoaffinity solid-phase extraction (IA-SPE). The IA-SPE method, relying on specific interactions between testosterone and a recombinant anti-testosterone Fab fragment, is the first such method described for testosterone. Finally, new data for interactions between steroids and human and bovine serum albumins were obtained through the use of affinity capillary electrophoresis. A new algorithm for the calculation of association constants between proteins and neutral ligands is introduced.

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This thesis contains five experimental spectroscopic studies that probe the vibration-rotation energy level structure of acetylene and some of its isotopologues. The emphasis is on the development of laser spectroscopic methods for high-resolution molecular spectroscopy. Three of the experiments use cavity ringdown spectroscopy. One is a standard setup that employs a non-frequency stabilised continuous wave laser as a source. In the other two experiments, the same laser is actively frequency stabilised to the ringdown cavity. This development allows for increased repetition rate of the experimental signal and thus the spectroscopic sensitivity of the method is improved. These setups are applied to the recording of several vibration-rotation overtone bands of both H(12)C(12)CH and H(13)C(13)CH. An intra-cavity laser absorption spectroscopy setup that uses a commercial continuous wave ring laser and a Fourier transform interferometer is presented. The configuration of the laser is found to be sub-optimal for high-sensitivity work but the spectroscopic results are good and show the viability of this type of approach. Several ro-vibrational bands of carbon-13 substituted acetylenes are recorded and analysed. Compared with earlier work, the signal-to-noise ratio of a laser-induced dispersed infrared fluorescence experiment is enhanced by more than one order of magnitude by exploiting the geometric characteristics of the setup. The higher sensitivity of the spectrometer leads to the observation of two new symmetric vibrational states of H(12)C(12)CH. The precision of the spectroscopic parameters of some previously published symmetric states is also improved. An interesting collisional energy transfer process is observed for the excited vibrational states and this phenomenon is explained by a simple step-down model.

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Digital elevation models (DEMs) have been an important topic in geography and surveying sciences for decades due to their geomorphological importance as the reference surface for gravita-tion-driven material flow, as well as the wide range of uses and applications. When DEM is used in terrain analysis, for example in automatic drainage basin delineation, errors of the model collect in the analysis results. Investigation of this phenomenon is known as error propagation analysis, which has a direct influence on the decision-making process based on interpretations and applications of terrain analysis. Additionally, it may have an indirect influence on data acquisition and the DEM generation. The focus of the thesis was on the fine toposcale DEMs, which are typically represented in a 5-50m grid and used in the application scale 1:10 000-1:50 000. The thesis presents a three-step framework for investigating error propagation in DEM-based terrain analysis. The framework includes methods for visualising the morphological gross errors of DEMs, exploring the statistical and spatial characteristics of the DEM error, making analytical and simulation-based error propagation analysis and interpreting the error propagation analysis results. The DEM error model was built using geostatistical methods. The results show that appropriate and exhaustive reporting of various aspects of fine toposcale DEM error is a complex task. This is due to the high number of outliers in the error distribution and morphological gross errors, which are detectable with presented visualisation methods. In ad-dition, the use of global characterisation of DEM error is a gross generalisation of reality due to the small extent of the areas in which the decision of stationarity is not violated. This was shown using exhaustive high-quality reference DEM based on airborne laser scanning and local semivariogram analysis. The error propagation analysis revealed that, as expected, an increase in the DEM vertical error will increase the error in surface derivatives. However, contrary to expectations, the spatial au-tocorrelation of the model appears to have varying effects on the error propagation analysis depend-ing on the application. The use of a spatially uncorrelated DEM error model has been considered as a 'worst-case scenario', but this opinion is now challenged because none of the DEM derivatives investigated in the study had maximum variation with spatially uncorrelated random error. Sig-nificant performance improvement was achieved in simulation-based error propagation analysis by applying process convolution in generating realisations of the DEM error model. In addition, typology of uncertainty in drainage basin delineations is presented.

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Individual movement is very versatile and inevitable in ecology. In this thesis, I investigate two kinds of movement body condition dependent dispersal and small-range foraging movements resulting in quasi-local competition and their causes and consequences on the individual, population and metapopulation level. Body condition dependent dispersal is a widely evident but barely understood phenomenon. In nature, diverse relationships between body condition and dispersal are observed. I develop the first models that study the evolution of dispersal strategies that depend on individual body condition. In a patchy environment where patches differ in environmental conditions, individuals born in rich (e.g. nutritious) patches are on average stronger than their conspecifics that are born in poorer patches. Body condition (strength) determines competitive ability such that stronger individuals win competition with higher probability than weak individuals. Individuals compete for patches such that kin competition selects for dispersal. I determine the evolutionarily stable strategy (ESS) for different ecological scenarios. My models offer explanations for both dispersal of strong individuals and dispersal of weak individuals. Moreover, I find that within-family dispersal behaviour is not always reflected on the population level. This supports the fact that no consistent pattern is detected in data on body condition dependent dispersal. It also encourages the refining of empirical investigations. Quasi-local competition defines interactions between adjacent populations where one population negatively affects the growth of the other population. I model a metapopulation in a homogeneous environment where adults of different subpopulations compete for resources by spending part of their foraging time in the neighbouring patches, while their juveniles only feed on the resource in their natal patch. I show that spatial patterns (different population densities in the patches) are stable only if one age class depletes the resource very much but mainly the other age group depends on it.

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The topic of this dissertation lies in the intersection of harmonic analysis and fractal geometry. We particulary consider singular integrals in Euclidean spaces with respect to general measures, and we study how the geometric structure of the measures affects certain analytic properties of the operators. The thesis consists of three research articles and an overview. In the first article we construct singular integral operators on lower dimensional Sierpinski gaskets associated with homogeneous Calderón-Zygmund kernels. While these operators are bounded their principal values fail to exist almost everywhere. Conformal iterated function systems generate a broad range of fractal sets. In the second article we prove that many of these limit sets are porous in a very strong sense, by showing that they contain holes spread in every direction. In the following we connect these results with singular integrals. We exploit the fractal structure of these limit sets, in order to establish that singular integrals associated with very general kernels converge weakly. Boundedness questions consist a central topic of investigation in the theory of singular integrals. In the third article we study singular integrals of different measures. We prove a very general boundedness result in the case where the two underlying measures are separated by a Lipshitz graph. As a consequence we show that a certain weak convergence holds for a large class of singular integrals.

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A composition operator is a linear operator between spaces of analytic or harmonic functions on the unit disk, which precomposes a function with a fixed self-map of the disk. A fundamental problem is to relate properties of a composition operator to the function-theoretic properties of the self-map. During the recent decades these operators have been very actively studied in connection with various function spaces. The study of composition operators lies in the intersection of two central fields of mathematical analysis; function theory and operator theory. This thesis consists of four research articles and an overview. In the first three articles the weak compactness of composition operators is studied on certain vector-valued function spaces. A vector-valued function takes its values in some complex Banach space. In the first and third article sufficient conditions are given for a composition operator to be weakly compact on different versions of vector-valued BMOA spaces. In the second article characterizations are given for the weak compactness of a composition operator on harmonic Hardy spaces and spaces of Cauchy transforms, provided the functions take values in a reflexive Banach space. Composition operators are also considered on certain weak versions of the above function spaces. In addition, the relationship of different vector-valued function spaces is analyzed. In the fourth article weighted composition operators are studied on the scalar-valued BMOA space and its subspace VMOA. A weighted composition operator is obtained by first applying a composition operator and then a pointwise multiplier. A complete characterization is given for the boundedness and compactness of a weighted composition operator on BMOA and VMOA. Moreover, the essential norm of a weighted composition operator on VMOA is estimated. These results generalize many previously known results about composition operators and pointwise multipliers on these spaces.

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This thesis is a study of a rather new logic called dependence logic and its closure under classical negation, team logic. In this thesis, dependence logic is investigated from several aspects. Some rules are presented for quantifier swapping in dependence logic and team logic. Such rules are among the basic tools one must be familiar with in order to gain the required intuition for using the logic for practical purposes. The thesis compares Ehrenfeucht-Fraïssé (EF) games of first order logic and dependence logic and defines a third EF game that characterises a mixed case where first order formulas are measured in the formula rank of dependence logic. The thesis contains detailed proofs of several translations between dependence logic, team logic, second order logic and its existential fragment. Translations are useful for showing relationships between the expressive powers of logics. Also, by inspecting the form of the translated formulas, one can see how an aspect of one logic can be expressed in the other logic. The thesis makes preliminary investigations into proof theory of dependence logic. Attempts focus on finding a complete proof system for a modest yet nontrivial fragment of dependence logic. A key problem is identified and addressed in adapting a known proof system of classical propositional logic to become a proof system for the fragment, namely that the rule of contraction is needed but is unsound in its unrestricted form. A proof system is suggested for the fragment and its completeness conjectured. Finally, the thesis investigates the very foundation of dependence logic. An alternative semantics called 1-semantics is suggested for the syntax of dependence logic. There are several key differences between 1-semantics and other semantics of dependence logic. 1-semantics is derived from first order semantics by a natural type shift. Therefore 1-semantics reflects an established semantics in a coherent manner. Negation in 1-semantics is a semantic operation and satisfies the law of excluded middle. A translation is provided from unrestricted formulas of existential second order logic into 1-semantics. Also game theoretic semantics are considerd in the light of 1-semantics.

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This thesis consists of an introduction, four research articles and an appendix. The thesis studies relations between two different approaches to continuum limit of models of two dimensional statistical mechanics at criticality. The approach of conformal field theory (CFT) could be thought of as the algebraic classification of some basic objects in these models. It has been succesfully used by physicists since 1980's. The other approach, Schramm-Loewner evolutions (SLEs), is a recently introduced set of mathematical methods to study random curves or interfaces occurring in the continuum limit of the models. The first and second included articles argue on basis of statistical mechanics what would be a plausible relation between SLEs and conformal field theory. The first article studies multiple SLEs, several random curves simultaneously in a domain. The proposed definition is compatible with a natural commutation requirement suggested by Dubédat. The curves of multiple SLE may form different topological configurations, ``pure geometries''. We conjecture a relation between the topological configurations and CFT concepts of conformal blocks and operator product expansions. Example applications of multiple SLEs include crossing probabilities for percolation and Ising model. The second article studies SLE variants that represent models with boundary conditions implemented by primary fields. The most well known of these, SLE(kappa, rho), is shown to be simple in terms of the Coulomb gas formalism of CFT. In the third article the space of local martingales for variants of SLE is shown to carry a representation of Virasoro algebra. Finding this structure is guided by the relation of SLEs and CFTs in general, but the result is established in a straightforward fashion. This article, too, emphasizes multiple SLEs and proposes a possible way of treating pure geometries in terms of Coulomb gas. The fourth article states results of applications of the Virasoro structure to the open questions of SLE reversibility and duality. Proofs of the stated results are provided in the appendix. The objective is an indirect computation of certain polynomial expected values. Provided that these expected values exist, in generic cases they are shown to possess the desired properties, thus giving support for both reversibility and duality.