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In this thesis we cover some fundamental topics in mathematical finance and construct market models for the option pricing. An option on an asset is a contract giving the owner the right, but not the obligation, to trade the underlying asset for a fixed price at a future date. Our main goal is to find a price for an option that will not allow the existence of an arbitrage, that is, a way to make a riskless profit. We will see that the hedging has an essential role in this pricing. Both the hedging and the pricing are very import tasks for an investor trading at constantly growing derivative markets. We begin our mission by assuming that the time parameter is a discrete variable. The advantage of this approach is that we are able to jump into financial concepts with just a small quantity of prerequisites. The proper understanding of these concepts in discrete time is crucial before moving to continuous-time market models, that is, models in which the time parameter is a continuous variable. This may seem like a minor transition, but it has a significant impact on the complexity of the mathematical theory. In discrete time, we review how the existence of an equivalent martingale measure characterizes market models. If such measure exists, then market model does not contain arbitrages and the price of an option is determined by this measure via the conditional expectation. Furthermore, if the measure also unique, then all the European options (ones that can be exercised only at a predetermined time) are hedgeable in the model, that is, we can replicate the payoffs of those options with strategies constructed from other assets without adding or withdrawing capital after initial investments. In this case the market model is called complete. We also study how the hedging can be done in incomplete market models, particularly how to build risk-minimizing strategies. After that, we derive some useful tools to the problems of finding optimal exercise and hedging strategies for American options (ones that can be exercised at any moment before a fixed time) and introduce the Cox-Ross-Rubinstein binomial model to use it as a testbed for the methods we have developed so far. In continuous time, we begin by constructing stochastic integrals with respect to the Brownian motion, which is a stochastic component in our models. We then study important properties of stochastic integrals extensively. These help us comprehend dynamics of asset prices and portfolio values. In the end, we apply the tools we have developed to deal with the Black-Scholes model. Particularly, we use the Itô’s lemma and the Girsanov’s theorem to derive the Black-Scholes partial differential equation and further we exploit the Feynman-Kac formula to get the celebrated Black-Scholes formula.

Tutkimuksen tarkoituksena oli tutkia, miksi matematiikkaa pidetään poikien aineena sekä pohtia keinoja, joiden avulla tyttöjä voisi rohkaista luottamaan omaan osaamiseensa. Tyttöjen ja poikien matematiikan osaamisessa ei peruskoulussa ole juurikaan eroa, mutta poikien asenteet matematiikkaa kohtaan ovat myönteisemmät kuin tyttöjen. Pojat luottavat enemmän omaan osaamiseensa ja ovat rohkeampia soveltamaan tietojaan. Tutkimuksessa kartoitetaan yhdeksäsluokkalaisten matematiikan opiskeluun liittyviä käsityksiä ja etsitään poikien ja tyttöjen välisiä eroja. Tutkimukseen osallistui 32 hämeenlinnalaisen yläkoulun oppilasta, joista 19 oli poikia ja 13 tyttöjä. Tutkimus toteutettiin matematiikan tunnin aikana toukokuussa 2013. Tutkimusaineisto kerättiin kyselylomakkeella, joka sisälsi avoimia kysymyksiä. Kysymyksenasettelulla pyrittiin siihen, että vastaukset olisivat yksiselitteisiä ja että niihin olisi helppo vastata kirjallisesti. Tutkimusaineisto analysoitiin sekä määrällisin että laadullisin menetelmin. Tutkimuksessa suurin osa oppilaista arvioi, että tytöt ja pojat osaavat matematiikkaa yhtä hyvin. Pojat vastasivat pitävänsä matematiikasta huomattavasti useammin kuin tytöt ja tyttöjen oman matematiikan osaamisen vähättely ja vähäisempi luottamus omiin matemaattisiin taitoihin tuli esille useissa vastauksissa. Onnistumisen kokemukset ovat merkityksellisiä matematiikan opiskelussa ja niiden avulla voidaan parantaa motivaatiota sekä saada parempia tuloksia. Onnistumista koetaan esimerkiksi hyvän koenumeron myötä ja silloin, kun osataan neuvoa kaveria jonkin tehtävän ratkaisemisessa tai kaveri auttaa vaikean tehtävän kanssa.

Partially ordered sets (posets) have various applications in computer science ranging from database systems to distributed computing. Content-based routing in publish/subscribe systems is a major poset use case. Content-based routing requires efficient poset online algorithms, including efficient insertion and deletion algorithms. We study the query and total complexities of online operations on posets and poset-like data structures. The main data structures considered are the incidence matrix, Siena poset, ChainMerge, and poset-derived forest. The contributions of this thesis are twofold: First, we present an online adaptation of the ChainMerge data structure as well as several novel poset-derived forest variants. We study the effectiveness of a first-fit-equivalent ChainMerge online insertion algorithm and show that it performs close to optimal query-wise while requiring less CPU processing in a benchmark setting. Second, we present the results of an empirical performance evaluation. In the evaluation we compare the data structures in terms of query complexity and total complexity. The results indicate ChainMerge as the best structure overall. The incidence matrix, although simple, excels in some benchmarks. Poset-derived forest is very fast overall if a 'true' poset data structure is not a requirement. Placing elements in smaller poset-derived forests and then merging them is an efficient way to construct poset-derived forests. Lazy evaluation for poset-derived forests shows some promise as well.

Capillary electrophoresis is a great option for analyzing metabolomics compounds since the analytes are often charged. The technique is simple and cost-efficient but it is not the most popular equipment because it lacks high concentration sensitivity. Therefore, on-line concentration techniques have been developed for capillary electrophoresis. The aim of this thesis is to give an introduction to the most common on-line concentration methods in capillary electrophoresis, and to demonstrate a novel on-line concentration technique termed electroextraction. Until now, the research of on-line concentration techniques in capillary electrophoresis is mainly focused on methods based on field amplification, transient isotachophoresis, titration incorporated methods or sweeping, which are presented in the literature section. In a two-phase electroextraction, the electrodes are placed in an aqueous acceptor phase and in an organic donor phase, in which the analytes are dissolved. When the voltage is applied, the conductivity difference in the two phases cause high local field strength on organic phase leading to fast migration of the cationic analytes towards the cathode. As soon as the analytes cross the solvent interface, their migration speed decrease and they are concentrated at the phase boundary. In these experiments, a normal capillary electrophoresis analyzer was used with a hanging aqueous phase droplet at the tip of the capillary inlet. The experimental part was carried out at Leiden University, Division of Analytical BioSciences in the Netherlands. An electroextraction-capillary electrophoresis system was built for the analysis of biological acylcarnitine compounds. After the method parameters were assessed with ultraviolet detection, the method was coupled with mass spectrometric detection, and the selectivity and repeatability were briefly tested. Sensitivity was enhanced with the electroextraction procedure but the extraction factors were not satisfactory yet. Selectivity of electroextraction was discovered when the extraction of acylcarnitines was performed using different solvents. All parameters affecting the electroextraction procedure were not tested, and therefore the instability of the method was not completely understood. Thus, the method should be further investigated and optimized. In fact, all on-line concentration methods ought to be optimized for the target analytes in their existing matrix.

Monolithic architecture has been the standard way to architect applications for years. Monolithic applications use a single codebase which makes the deploying and development easier without adding any additional complexity as long as the size of the application stays relatively small. When the size of the codebase grows the architecture might deteriorate. This slows down the development and making it harder to on-board new developers. Microservice architecture is a novel architec- ture style that tries to solve these issues in larger codebases. Microservice architecture consists of multiple small autonomous services that are deployed and developed separately. Microservice architecture enables more fine-grained scaling and makes it possible to have faster development cycles by decreasing the amount of regression testing that is needed, because each of the services can be deployed and updated separately from each other. Microservice architecture provides also multiple new challenges that have to be solved in order to get the benefit from them. These challenges are such as the handling of distributed transactions, communication between microservices, separation of concerns in microservices and so on. On top of the technical challenges there are also organizational and operational challenges. The operational challenges are such as monitoring, logging and automated deployment of microservices. This thesis studies the differences between monolithic and microservice architecture and pinpoints the main challenges on the transition from monolithic architecture to microservice architecture. A proof of concept on how to transform a single bounded context from monolith to microservices will be made to get a better understanding of the challenges. Also a plan how to migrate tangled bounded contexts from monolith to microservices will be made in order to fully support the transition process in the future. The results from the proof of concept and the plan that was made show that the cohesion and loose coupling is more likely to stay when the bounded context is transformed to microservice.

Abelian categories provide an abstract generalization of the category of modules over a unitary ring. An embedding theorem by Mitchell shows that one can, whenever an abelian category is sufficiently small, find a unitary ring such that the given category may be embedded in the category of left modules over this ring. An interesting consequence of this theorem is that one can use it to generalize all diagrammatic lemmas (where the conditions and claims can be formulated by exactness and commutativity) true for all module categories to all abelian categories.\\ The goal of this paper is to prove the embedding theorem, and then derive some of its corollaries. We start from the very basics by defining categories and their properties, and then we start constructing the theory of abelian categories. After that, we prove several results concerning functors, "homomorphisms" of categories, such as the Yoneda lemma. Finally, we introduce the concept of a Grothendieck category, the properties of which will be used to prove the main theorem. The final chapter contains the tools in generalizing diagrammatic results, a weaker but more general version of the embedding theorem, and a way to assign topological spaces to abelian categories. The reader is assumed to know nothing more than what abelian groups and unitary rings are, except for the final theorem in the proof of which basic homotopy theory is applied.

The aim of this masters thesis was to examine subjective wellbeing and personal happiness. Empirical study of happiness is part of broader wellbeing research and is based on an idea that the best experts of personal wellbeing are the individuals themselves. In addition to perceptions of personal happiness, the aim was also to acquire knowledge about personal values and components personal happiness is based on. In this study, moving into certain community and the characteristics of neigbourhood contributing happiness, were defined to represent these values. The object was, through comparative case-study, to obtain knowledge about subjective wellbeing of the individuals in two different residential areas inside metropolitan area of Helsinki. In comparative case study the intention usually is that the examined units represent spesific 'cases' from something broader and therefore the results can be somehow generalized. Consequently the chosen cases in this study were selected due to their image of 'urban village' and thus the juxtapositioning was constructed between secluded post-suburban village and more heterogeneous urban village better attached to existing urban structure. The research questions were formed as follows: Are there any differences between the areas regarding the components personal happiness is based on? Are there any differences between the areas regarding the level of residents subjective wellbeing? Based on the residents assessments, what are the most important characteristics of neighbourhood contributing personal happiness? The data used in order to gain answers to these questions was obtained from internet-based survey questionnaire. Based on the data residents of post-suburban village Sundsberg seem to share highly family oriented set of values and actualizing these values is ensured with high income, wealth and secure work situation. Instead in Kumpula the components of happiness seem place more towards learning and personal development, interesting leisure and hobbies and specially having an influence regarding communal decisions. Concerning subjective wellbeing of residents there can be seen some differences as well. Personal life is experienced a bit more happier in Sundsberg than in Kumpula. People are more satisfied with their personal health and job satisfaction in Sundsberg and additionally feelings of loneliness, inadequancy and frustration are bit more common in Kumpula. Regarding the characteristics of neighbourhood contributing happiness data suggests that key characteristics of area are peacefulness and safely, good location and connections and proximity of parks and recreational areas. These characteristics were considered highly significant in both areas but they were experienced to actualize better in Kumpula. In addition to these components the residents in Kumpula were overall more satisfied with various characteristics contributing happiness in their residential area. Besides these attributes mentioned above residents in Kumpula emphasize also some 'softer' elements connecting into social, functional and communal side of area. From Sundsberg point of view residential area best contributing happiness is child friendly and safe community based on likeminded people who share the same socio-economical situation. The results of this study can be linked back into the society and metropolitan area, which they were chosen from as a cases to be studied. The results can thereby be seen as an example of differentation of conditions of personal happiness between certain population segments. It is possible to detect an spatial dimension to this process as well and thereby the results suggests that regional segmentation affects between high-ranking residential areas as well. Thereby the results of this research contributes to the debate on innovative, diverse and dynamic urban area and as well cohesion of metropolitan area and the society in whole.

In this Thesis I present the general theory of semigroups of linear operators. From the philosophical point of view I begin by connecting deterministic evolution in time to dynamic laws that are stated in terms of a differential equation. This leads us to associate semigroups with the models for autonomic deterministic motion. From the historical point of view I reflect upon the history of the exponential function and its generalizations. I emphasize their role as solutions to certain linear differential equations that characterize both exponential functions and semigroups. This connection then invites us to consider semigroups as generalizations of the exponential function. I believe this angle of approach provides us with motivation as well as useful ideas. From the mathematical point of view I construct the basic elements of the theory. First I consider briefly uniformly and strongly continuous semigroups. After that I move on to the more general σ(X, F)-continuous case. Here F is a so called norming subspace of the dual X^*. I prove the existence of both the infinitesimal generator S of the semigroup and the resolvent (λ - S)^(-1) as well as some of their basic properties. Then I turn to the other direction and show how to create a semigroup starting from its generator. That is the content of the famous Hille—Yosida Theorem. From the practical point of view I give some useful characterizations of the generator in terms of dissipativity and accretivity. These techniques also lead us to an effortless proof of Stone's Theorem on unitary groups. Finally, from an illustrational point of view I give two applications. The first is about multiplicative semigroups on L^p spaces, where the setting is simple enough to allow intuition to accompany us. The second takes on a problem of generating a particular stochastic weak*-continuous semigroup. It serves to illustrate some of our results.

A model in mathematic logic is called pseudo-finite, in case it satisfies only such sentences of first-order predicate logic that have a finite model. Its main part modelled based on Jouko Väänänen's article 'Pseudo- finite model theory', this text studies classic model theory restricted to pseudo-finite models. We provide a range of classic results expressed in pseudo-finite terms, while showing that a set of other well-known theorems fail when restricted to the pseudo-finite, unless modified substantially. The main finding remains that a major portion of the classic theory, including Compactness Theorem, Craig Interpolation Theorem and Lidström Theorem, holds in an analogical form in the pseudo-finite theory. The thesis begins by introducing the basic first-order model theory with the restriction to relational formulas. This purely technically motivated limitation doesn't exclude any substantial results or methods of the first-order theory, but it simplifies many of the proofs. The introduction behind, the text moves on to present all the classic results that will later on be studied in terms of the pseudo-finite. To enable and ease this, we also provide some powerful tools, such as Ehrenfeucht-Fraïssé games. In the main part of the thesis we define pseudo-finiteness accurately and build a pseudo-finite model theory. We begin from easily adaptable results such as Compactness and Löwenheim-Skolem Theorems and move on to trickier ones, examplified by Craig Interpolation and Beth Definability. The section culminates to a Lidström Theorem, which is easy to formulate but hard to prove in pseudo-finite terms. The final chapter has two independent sections. The first one studies the requirements of a sentence for having a finite model, illustrates a construction of a finite model for a sentence that has one, and culminates into an exact finite model existence theorem. In the second one we define a class of models with a certain, island-like structure. We prove that the elements of this class are always pseudo-finite, and at the very end the text, we present a few examples of this class.

After 2013, the environmental protection department in China has significantly reduced on-road emission through the upgrade of emission standards, the improvement of fuel quality and economic tools. However, the specific effect of the control policies on emission and air quality is still difficult to quantify. This is mainly due to the data shortage on vehicle emission factors and vehicle activities. In this research, we developed the 2008-2018 on-road emissions inventory based on Emission Inventory Preparation Guide (GEI) and existing vehicle activity database. Our estimates suggest that CO and PM2.5 showed a relatively significant decrease, by 66.2% and 58.8%. However, the trend of NOx (5.8%) and NMVOC (-4.8%) was relatively stable. The Beijing-Tianjin-Hebei (BTH), Yangtze River Delta (YRD), Pearl River Delta (PRD) and Sichuan Basin (SCB) regions all showed a uniform trend especially in NOx. For Beijing-Tianjin-Hebei, the significant decline in NOx might be caused by earlier implementations in emission standard and fuel quality. In addition to this, we designed additional evaporation emission scenarios to verify the application of GEI in quantify emission impact on secondary pollutant (PM2.5 and O3). The results indicate that evaporation emission contributed to Maximum Daily Average 8-hour (MDA8) O3 concentration by about 3.5%, for Beijing, Shanghai and Nanjing. This value can reach up to 5.9%, 5.3% and 7.3%, but the impact on PM2.5is extremely limited. Our results indicate the feasibility of GEI in improving and lowering the technical barrier of on-road emission inventory establishment at the same time and its further application in quantifying on-road emission contribution to air quality. Besides that, it shows a strong potential in on-road policy environmental assessment and short-term air quality assessment.