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The global energy consumption increases annually. Although the current supply of fossil and nuclear fuels is enough to meet the growing energy demand it is more sustainable for the society to rely more on renewable energy sources because of the environmental concerns of fossil fuel combustion and nuclear fission. One of the promising renewable energy sources is solar power. Currently the competitiveness of solar power with the conventional energy sources is limited by the expensiveness of the solar cells. The most successful solar cell technologies require expensive fabrication methods and materials. However, this situation can drastically change with the emergence of perovskite ternary halide solar cells. Perovskite ternary halides possess optical and electronic properties required for efficient light absorption in solar cells. In addition, they consist of abundant inexpensive elements and can be deposited using easy and low-cost sol-gel methods. During the last four years, the efficiency of perovskite solar cells was improved by a factor of 4 and the record holding devices now reach 16 % efficiency. Due to the novelty of perovskite solar cells there are formidable gaps in the knowledge of perovskite ternary halide properties and mechanisms of perovskite solar cell operation. Literature review in this thesis focuses on classifying known perovskite ternary halides, their properties and deposition methods as well as highlighting discrepancies and most important knowledge gaps. Special attention is also devoted to different types of perovskite solar cells and their working principles. The literature review is complemented by calculations on the existence and the optical properties of not yet studied perovskite ternary halides, and on lattice matching of different known perovskite halides in the context of multijunction perovskite solar cells. Conventional perovskite halide deposition methods are inexpensive but also limited to small area substrates. In order to reach economic feasibility the perovskite deposition methods must be scalable to large area substrates. In the experimental part of this thesis, an attempt is made to solve the scalability challenge by developing perovskite ternary halide deposition processes for techniques that have scalability as an inherent property. These techniques are atomic layer deposition and electrodeposition. Although an electrodeposition process for cesium tin(II) iodide was developed, the morphology and phase of the deposits along with the stability of the electrodeposition solutions were difficult to control. For atomic layer deposition processes the volatility of the halides presents a challenge, however encouraging preliminary results were obtained in the cases of binary iodide deposition such as cesium iodide and copper(I)iodide. These results can serve as a basis for the future research of both binary and ternary halide atomic layer deposition.

The topological data analysis studies the shape of a space at multiple scales. Its main tool is persistent homology, which is based on other homology theory, usually simplicial homology. Simplicial homology applies to finite data in real space, and thus it is mainly used in applications. This thesis aims to introduce the theories behind persistent homology and its application, image completion algorithm. Persistent homology is motivated by the question of which scale is the most essential to study data shape. A filtration contains all scales we want to explore, and thus it is an essential tool of persistent homology. The thesis focuses on forming a filtaration from a Delaunay triangulation and its subcomplexes, alpha-complexes. We will found that these provide sufficient tools to consider homology classes birth and deaths, but they are not particularly easy to use in practice. This observation motivates to define a regional complement of the dual alpha graph. We found that its components' and essential homology classes' birth and death times correspond. The algorithm utilize this observation to complete images. The results are good and mainly as could be expected. We discuss that algorithm has potential since it does need any training or other input parameters than data. However, future studies are needed to imply it, for example, in three-dimensional data.

Cold quark matter is matter consisting of free quarks in high energy density, and it can be formed when the energy density of ordinary hadronic matter increases to a region of 1 GeV/fm3. At such high energies, hadronic matter undergoes a phase transition and quarks that would normally be in color confinement break free to form a new phase. It is assumed that similar process happened in the very early universe, but in the opposite direction, when high temperature quark-gluon plasma cooled down significantly. With the cooling, the quark and gluon degrees of freedom switched to hadrons and ordinary matter began to form. Opposed to the hot quark-gluon plasma, there are no direct observations of cold quark matter and its existence is still speculative. Still, it is suspected that cold quark matter can be found in dense neutron star cores or even as stable quark matter in strange quark stars. Theoretically, cold quark matter and quark-gluon plasma can be studied in finite-temperature field theory. Finite-temperature field theory combines the field formalism of quantum field theory and the thermodynamical and statistical methods utilized in quantum statistics. The asymptotic freedom of the theory of strong interactions, quantum chromodynamics (QCD), provides an opportunity to expand the equation of state of high-energy quark matter in the limit of weak coupling, and thus opens a door to implement the tools of finite-temperature field theory perturbatively. Along with the perturbative analysis, it is useful to look at the possibilities offered by effective theories. Two of which are important in the study of finite-temperature QCD, dimensional reduction and hard thermal loop effective theory. Both effective theories address the issue of infrared divergences that arise in finite-temperature field theory efficiently compared to the naïve loop expansion. In dimensional reduction, scales that are defined as hard by the scale hierarchy are integrated out of the theory, after which the infrared problems of gluonic Matsubara zero-modes can be studied in a simpler three-dimensional setting. Hard thermal loop effective theory, on the other hand, examines the infrared divergences that appear in loop-level corrections of soft gluons. When the magnitude of the loop-momentum corresponds to the hard scale, the correction that contains the loop becomes proportional to a tree-level amplitude and breaks the perturbative expansion. The effective theory answers this problem by resumming the propagators and vertex functions and using the new quantities in place of the ordinary ones. With perturbation theory and the effective descriptions, the equation of state of cold quark matter and the pressure extracted from it, have been solved partially up to and including order g6ln2g2 in coupling. The meaning of this thesis is to present the methods of finite-temperature field theory and the supporting effective theories and their implementation to study the equation of state of cold quark matter. The results for QCD pressure will be presented to the last known order in coupling. Also, the effect of a massive strange quark and the role of cold quark matter in solving the neutron star equation of state will be discussed briefly.

Tavoitteet. Suomalaisten peruskoulua päättävien oppilaiden matematiikan osaamistaso on kääntynyt kansainvälisten vertailututkimusten mukaan laskuun 2000-luvulla. Matematiikan taitotaso on 9.- luokkalaisten keskuudessa laskenut vuodesta 2006 vuoteen 2015 yhden vuoden kouluopetuksen tuoman taitotasomuutoksen verran. Matematiikan oppijoiden osaamisessa on ollut havaittavissa polarisoitumista, ja heikkojen osaajien määrä on kasvanut. Heikko osaaminen näyttää kasaantuvan usein joillekin yksilöille läpi eri kouluaineiden. Tutkielmassa pyritään selvittämään syitä tai selittäviä tekijöitä matematiikan heikon osaamisen yleistymiselle. Menetelmät. Tutkielmassa esitellään erilaisten kansainvälisten ja kansallisten osaamistutkimusten aineistoa ja tuloksia. Tutkielman tutkimuksellinen, empiirinen aineisto kerättiin kesällä 2018 järjestetyn tiedeleirin yhteydessä kyselyllä, johon vastasi 12 leirille osallistunutta 4.–6.-luokkalaista nuorta. Vastaajat osallistuivat leirille vapaaehtoisesti. Aineistoa kerättiin monivalintalomakkeilla ja avoimilla kysymyksillä. Aineistoa analysoitiin tilastollisin menetelmin ja kvalitatiivisesti. Tulokset ja johtopäätökset. Tutkielman perusteella näyttäisi siltä, että alakoulun oppilaiden mukaan luokan työrauhalla on huomattava merkitys oppimisessa suoriutumiseen, keskittymiseen ja siihen, kuinka positiivisena luokkatyöskentely koetaan. Tulokset saavat vahvistusta kirjallisuudessa aiemmin esitetyistä tulkinnoista. Työrauha-asiaan vahvasti liittyy 2010 toteutettu uudistus, jossa pysyvät erityisopetusryhmät lakkautettiin. Resurssipula on vaivannut kouluja, eikä oppilaille ole pystytty tarjoamaan riittävää tukea henkilökohtaisen oppimisen edistämiseksi. Tutkielman sivutuotteena luotiin yläkoulun opettajille tarkoitettu kysely, jolla voitaisiin selvittää opettajien näkökulmasta nykykoulun ongelmakohtia ja edelleen syitä heikolle oppimenestykselle.

The mafic-ultramafic Kevitsa intrusion, located within the Central Lapland Greenstone Belt in Northern Finland, hosts a disseminated Ni-Cu-PGE deposit. Drillhole KVX018 penetrates through the intrusion, intersecting its bottom contact at 1772 meters and is associated with relatively low resistivity at the bottom of the intrusion. The KVX018 drillhole is the deepest drilled into the intrusion so far and the observed low resistivity zone is unique for the study area. Previous studies have shown the bottom contact of the Kevitsa intrusion to be associated with seismic reflections and possible mineralization. This paper studies the characteristics of the bottom contact of the Kevitsa intrusion from the drill core KVX018 and interprets the origin of the low resistivity and its relationship with mineralogy. From geochemical and petrophysical characteristics, four layers with different characteristics were observed within the studied section: footwall, contact zone, lower cumulates and upper cumulates. The lower cumulates were found to be strongly contaminated by elements associated to hydrothermal fluids from country rocks. The contamination was observed for 125 meters upwards from the basal contact as elevated concentrations of e.g. lithium, lanthanum, rubidium and potassium, and footwall rocks close to the contact were found to be depleted in these elements. The contact zone was found to be strongly altered by silicification and albitization. Hydrothermal fluid activity at the bottom contact was also observed by epidote alteration of plagioclase feldspar. Contact zone mineralization was observed and it was found to be false ore type with Ni tenor of 2.28 %. Upwards from contact mineralization, the mineralization was found first to change into local low-grade Ni-PGE ore and then into normal ore on top part of the studied drill core section. Ultramafic intrusive rocks were observed to be pervasively altered by amphibole alteration locally into a degree where in many rocks, alteration had overprinted the primary mineralogy and textures to be undistinguishable. Alteration intensity was found to increase downwards within the lowermost part of the intrusion. Salt minerals were observed by eye on the surface of some samples and by X-Ray Diffraction in one sample. XRD studies indicated nitratine and sylvite minerals present in the studied sample. These salt minerals are presented commonly in evaporites and their presence indicates an evaporitic source. Resistivity of rocks is generally affected by e.g. sulfide content, salinity, porosity and alteration. Resistivity and chargeability were found to be correlative, indicating resistivity to correlate also with presence of sulfide minerals. However, after depth of 680 meters, resistivity decreases without a correlating trend in other petrophysical properties. This paper concludes that the observed low resistivity is resulted from a presence of salt and sulfide minerals as well as alteration intensity.

The Bjurböle meteorite, which fell near Porvoo in 1899, is categorised as a fall. The Bjurböle meteorite is classified as an L/LL4 ordinary chondrite. Chondrites are undifferentiated meteorites that contain notable amounts of non-volatile elements of the early solar system. Chondrites usually contain small spherical igneous chondrules and they are classified into three groups: carbonaceous (C), enstatite (E) and ordinary chondrites (O). Ordinary chondrites are further classified into groups H, L and LL according to their metallic iron content. Chondrites are classified into petrologic types 1 – 6 based on their metamorphic grade so that Type 3 is the least metamorphosed and Type 6 is the most strongly metamorphosed, whereas Type 1 and Type 2, on the other hand correspond to meteorites that are, respectively, strongly and mildly affected by low-temperature aqueous alteration processes. The chemical equilibration of chondrites is controlled by the degree of metamorphism they go through. The more equilibrated a chondrite is, the more simplified its mineral assemble is and the more homogenised compositions the minerals have. Chondrules contain mostly olivine, pyroxene and interchondrule matrix. They are classified into Type I and Type II by the compositions of their olivine and pyroxene. Chondrule types can be further divided into A, B and AB by their olivine content. In addition, chondrules can be classified according to their texture into porphyritic, barred, radial, granular, cryptocrystalline, and metallic chondrules. The aim of this thesis is to inspect the variation in olivine composition in Bjurböle meteorite chondrules, to document the petrography of the Bjurböle meteorite and to find connections between petrographic discoveries and olivine composition. Furthermore, in this study I will discuss about the classification of the Bjurböle meteorite and the formation of chondrules in the Bjurböle meteorite. For this study, I examined 11 thin sections and three epoxy buttons that have 34 chondrules in total. Thin sections were inspected by microscope and six of the uncoated thin sections were also inspected under cold-cathode luminescence. The epoxy buttons were inspected with a scanning electron microscope, scanning electron microscope cathodoluminescence and scanning electron microscope energy-dispersive X-ray spectroscopy. Most of the inspected chondrules in the Bjurböle meteorite samples have very uniform olivine composition, as reported in earlier studies. Most of the olivines are Fo75–78, but there is also a bimodal peak at Fo89–92. The E1 chondrules (small) have very uniform olivine compositions of approximately Fo76–77. The E2 chondrules (medium) have also olivines of approximately Fo76–77, but some of the olivines reach Fo80–83. The E3 chondrules (large) have the broadest olivine composition variation at Fo74–93. However, most of the E3 olivines are Fo76–79. The E3-2 chondrule, in particular, has a broad olivine composition variation and its Fo-value increases up to 93 in the core of the chondrule. All chondrules with broader olivine variation have barred texture and are relatively large. Cathodoluminescence did not provide substantial data for the study. Other links between olivine compositions and petrography were not observed and, for example, proximity to metallic phases did not seem to have any effect on the olivine composition, and the exceptionally Mg-rich (Fo90) olivines may represent primary compositions. E3-6 and E3-7 chondrules are abundant in sulphide and metallic phases. The E3-7 chondrule resembles something that might be called micropallasite. Based on porosity, magnetic susceptibility, metamorphic signs, and the Fe variation in olivine and mineral assemblages, the Bjurböle meteorite fits the classification of an L/LL4 ordinary chondrite. Chondrules of the Bjurböle meteorite also have diverse forming histories.

Geological Survey of Finland conducted bedrock mapping in the eastern parts of Central Finland Granitoid Complex (CFGC) and the area next to the Archean craton in the 1990s. The area consists mainly of Paleo-proterozoic paragneisses, with minor volcanic rocks present. The granitoids belonging to the Central Finland Granitoid Complex make up part of the bedrock in the area. The granitoids of CFGC are divided into a 1.89-1.88 Ga syn-kinematic group, and a crosscutting, 1.88-1.87 Ga post-kinematic group. In this Master’s thesis, three post-kinematic granitoid intrusions of Löytölamminvuori, Sorsakoski and Karvalevä are studied, covering their lithological, petrographical and geochemical features. The intrusions are non-foliated, porphyritic granites and quartz-monzonites, with a minor mafic phase of mostly dioritic composition in the Karvalevä intrusion. The main mafic silicates in the granite phase are biotite and hornblende, in the quartz-monzonite and mafic phases also clino- and orthopyroxene are present. Resembling the other post-kinematic plutons of the CFGC, the studied intrusions are geochemically high in Al2O3, FeO and K2O, and low in MgO, CaO and Sr. One U-Pb age of 1876+6 Ma has been measured for the Löytölamminvuori intrusion, which places the intrusion at the same time frame as the other post-kinematic plutons. Geochemically the intrusions show A-type affinity and close similarities to the post-kinematic pluton Types 2 and 3, fitting best with the Type 3a, which is transitional between the two. The magmas forming Löytölamminvuori, Sorsakoski and Karvalevä were derived from partial melting of mantle derived basalts, which underwent crustal contamination by partial melts from the lower crust. Slight deviation in composition from the strictly A-type magma and the volcanic arc affinity can be explained by the crustal component. The mafic phases show more primitive geochemistry, and thus present the mantle-derived source component with less crustal assimilation in the source. The intrusions show signs of bimodal mafic-felsic magmatism, the dioritic phases in Karvalevä intrusion and one syn-plutonic dyke in Sorsakoski intrusion representing the mafic component. The mafic magmatism was cogenetic with the felsic phases, but not comagmatic, the diorites intruding simultaneously but slightly after the felsic phases. The mafic phases show a continuum in chemical composition to the granites and quartz-monzonites, but with a slight compositional gap.

The orbicular quartz monzonite from Kuohenmaa, Southwest Finland, is one of the most beautiful and well-known orbicular rocks in the world. The cores of the orbicules are peraluminous in composition, most likely of xenolithic metasedimentary origin. The cores are surrounded by orbicule mantles, which consist of several alternating biotite- and plagioclase-rich shells. There are three types of orbicules in Kuohenmaa orbicular rock: proto-, small-, and large-orbicular types. Proto-orbicules have only a few shells, small orbicules ~ 50 shells in average, and large orbicules over 250 distinct shells. In addition to shells, one sample was observed to be associated with comb layering in the contact of proto-orbicular and large orbicular types. Structures and textures of the comb layer resembles those of the outer shells of large orbicules. The orbicules are embedded in interstitial coarse-grained groundmass that forms locally almost pegmatitic patches. The petrographic observations were acquired from eight samples or sample photographs gathered from different collections. A mineral chemistry dataset was measured from a single large orbicule from the University of Helsinki collections. The main minerals of the Kuohenmaa orbicular rock are plagioclase, biotite, microcline, muscovite, and chlorite. The shell textures vary from branching plagioclase-rich shells to fine-grained plagioclase- or biotite-rich shells. Branching shells are mainly oligoclase, but a few granular andesine crystals were detected in the core. Peculiar interstitial fibrous allanite masses were found in the inner branching plagioclase-rich shells. The plagioclase compositions generally follow a regular fractional crystallization trend from core to groundmass, but some changes towards more primary compositions are observed in the orbicule mantle. Plagioclase crystals display only minor compositional zoning, suggesting rather quick crystallization. Biotite is very aluminous (Al2O3 17.63–18.53) in composition, and the compositional changes seem to have somewhat positive correlation with plagioclase compositions, suggesting changes in their crystallization conditions. Injections of primary melt from a deeper source most likely caused the observed changes to more primitive composition in plagioclase and biotite composition. Through the detailed petrographic and geochemical studies, a model of undercooling caused by decompression driven fluid saturation is proposed as a mechanism for orbicule formation in the Kuohenmaa orbicular rock. Branching plagioclase with interstitial fibrous allanite masses and several fluid inclusions in plagioclase indicates separate aqueous REE-enriched melt and rapid crystallization. Further studies of fluid inclusions and REE-enriched phases could provide information of the fluid origin and crystallization conditions.

Komatiites are extrusive rocks crystallized from mantle derived high-MgO magmas. They formed mainly during the Archean as the required high degree partial melting of the mantle peridotite (>20%) was facilitated by the geotherm of that time. Komatiites are classified as volcanic rocks with >18 wt.% MgO and <1 wt. % TiO2. By their physical features komatiite melts are of high-temperature and low-viscosity. Komatiitic rock suites are abundant in the Archean bedrock of the eastern Finnish Lapland. They are mainly found as cumulate bodies with also their related komatiitic basalts and mafic volcanic rocks being abundant in the Tulppio Metavolcanic belt. Typical of Archean terrains in Fennoscandia, all komatiitic rocks in the eastern Lapland are extensively deformed and primary mineral assemblages and textures are rare. Mapping and sampling was performed in the municipalities of Savukoski and Salla, NE Finland, in order to clarify the geochemical characteristics and petrogenesis of the komatiitic suites of the Eastern Lapland Archean Domain (ELAD). On the basis of their lithology and previous studies, three komatiitic cumulate complexes were selected for detailed geochemical and petrographical comparison. These are the Jänesselkä mafic-ultramafic complex, the Tulppio ultramafic complex, also referred to as the Tulppio dunite, and the Värriöjoki ultramafic complex. The first two are situated in the Tulppio metavolcanic belt whereas the Tuntsa metasedimentary belt hosts the Värriöjoki ultramafic complex. The lithology and geochemical characteristics of the Jänesselkä mafic-ultramafic complex suggest it having a different origin than the komatiitic rocks forming the Tulppio metavolcanic belt. Based on parental magma calculation and near continuum of rock types observed the Jänesselkä mafic-ultramafic complex represents a fractionated magma chamber with a basaltic composition (~6 wt. % MgO). The dunitic Värriöjoki ultramafic-complex is a feeder cumulate formed from a magma with a composition of high-MgO basalt (~12 wt. % MgO). Due to the similarities in their major- and trace element contents and suggested ages (2.45 Ga), the possibility of Värriöjoki and Jänesselkä being Paleoproterozoic suites with a similar primary magma is notable. Therefore, a petrogenetic link to the widespread 2.4–2.5 Ga mafic-ultramafic magmatism in the NE parts of the Fennoscandian shield, is proposed. The Tulppio ultramafic complex shows geochemical features suggesting a different origin in comparison to the two other complexes studies. Estimates on the parental magma composition (~17 wt. % MgO) and near chondritic REE contents suggest Tulppio being a feeder cumulate of earlier, possibly Archean magmatism in the area. Owing mainly to the poor level of exposure and heavy post magmatic modification, any detailed interpretations on the origin of the target complexes are rather difficult to. Therefore, isotope studies are seen as a necessity to clarify these topics.

In the thesis ”P-Fredholmness of Band-dominated Operators, and its Equivalence to Invertibility of Limit Operators and the Uniform Boundedness of Their Inverses”, we present the generalization of the classical Fredholm-Riesz theory with respect to a sequence of approximating projections on direct sums of spaces. The thesis is a progessive introduction to understanding and proving the core result in the generalized Fredholm-Riesz theory, which is stated in the title. The stated equivalence has been further improved and it can be generalized further by omitting either the initial condition of richness of the operator or the uniform boundedness criterion. Our focal point is on the elementary form of this result. We lay the groundwork for the classical Fredholm-Riesz theory by introducing compact operators and defining Fredholmness as invertibility on modulo compact operators. Thereafter we introduce the concept of approximating projections in infinite direct sums of Banach spaces, that is we operate continuous operators with a sequence of projections which approach the identity operator in the limit and examine whether we have convergence in the norm sense. This method yields us a way to define P-compactness, P-strong converngence and finally PFredholmness. We introduce the notion of limit operators operators by first shifting, then operating and then shifting back an operator with respect to an element in a sequence and afterwards investigating what happens in the P-strong limit of this sequence. Furthermore we define band-dominated operators as uniform limits of linear combinations of simple multiplication and shift operators. In this subspace of operators we prove that indeed for rich operators the core result holds true.