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.

Variation in the Understanding of Lutheranism and Its Implications for Religious Education : Meaning Discernment of Students and Teachers in Finnish Upper Secondary Schools

The study investigated variation in the ways in which a group of students and teachers of Evangelical Lutheran religious education in Finnish upper secondary schools understand Lutheranism and searched for educational implications for learning in religious education. The aim of understanding the qualitative variation in understanding Lutheranism was explored through the relationship between the following questions, which correspond to the results reported in the following original refereed publications: 1) How do Finnish students understand Lutheranism? 2) How do Finnish teachers of religious education constitute the meaning of Lutheranism? 3) How could phenomenography and the Variation Theory of Learning contribute to learning about and from religion in the context of Finnish Lutheran Religious Education as compared to religious education in the UK? Two empirical studies (Hella, 2007; Hella, 2008) were undertaken from a phenomenographic research perspective (e.g., Marton, 1981) and the Variation Theory of Learning (e.g., Marton & Tsui et al. 2004) that developed from it. Data was collected from 63 upper secondary students and 40 teachers of religious education through written tasks with open questions and complementary interviews with 11 students and 20 teachers for clarification of meanings. The two studies focused on the content and structure of meaning discernment in students and teachers expressed understandings of Lutheranism. Differences in understandings are due to differences in the meanings that are discerned and focused on. The key differences between the ways students understand varied from understanding Lutheranism as a religion to personal faith with its core in mercy. The logical relationships between the categories that describe variation in understanding express a hierarchy of ascending complexity, according to which more developed understandings are inclusive of less developed ones. The ways the teachers understand relate to student s understandings in a sequential manner. Phenomenography and Variation Theory were discussed in the context of religious education in Finland and the UK in relation to the theoretical notion of learning about and from religion (Hella & Wright, 2008). The thesis suggests that variation theory enables religious educators to recognise the unity of learning about and from religion, as learning is always learning about something and involves simultaneous engagement with the object of learning and development as a person. The study also suggests that phenomenography and variation theory offer a means by which it is possible for academics, policy makers, curriculum designers, teachers and students to learn to discern different ways of understanding the contested nature of religions. Keywords: Lutheranism, understanding, variation, teaching, learning, phenomenography, religious education

Eru Ilúvatar : Jumala J.R.R. Tolkienin legendariumissa

The purpose of my research is to inquire into the essence and activity of God in the legendarium of the English philologist and writer J.R.R. Tolkien (1892-1973). The legendarium, composed of Tolkien’s writings related to Middle-earth, was begun when he created two Elvish languages, Quenya based on Finnish, Sindarin based on Welsh. Tolkien developed his mythology inspired by Germanic myths and The Kalevala. It is a fictional ancient history set in our world. The legendarium is monotheistic: God is called Eru ‘The One’ and Ilúvatar ‘Father of All’. Eru is the same as the Christian God, for Tolkien wanted to keep his tales consistent with his faith. He said his works were Christian by nature, with the religious element absorbed into the story and the symbolism. In The Silmarillion, set in the primeval ages of Middle-earth, the theological aspects are more conspicuous, while in The Lord of the Rings, which brings the stories to an end, they are mostly limited to symbolic references. The legendarium is unified by its realistic outlook on creaturely abilities and hope expressing itself as humbly defiant resistance. ”The possibility of complexity or of distinctions in the nature of Eru” is a part of the legendarium. Eru Ilúvatar is Trinitarian, as per Tolkien’s faith. Without contextual qualifiers, Eru seems to refer to God the Father, like God in the Bible. Being the creator who dwells outside the world is attributed to Him. The Holy Spirit is the only Person of the Trinity bestown with names: the Flame Imperishable and the Secret Fire. When Eru creates the material world with His word, He sends the Flame Imperishable to burn at the heart of the world. The Secret Fire signifies the Creative Power that belongs to God alone, and is a part of Him. The Son, the Word, is not directly mentioned, but according to one writing Eru must step inside the world in order to save it from corruption, yet remain outside it at the same time. The inner structure of the legendarium refers to the need for a future salvation. The creative word of Eru, “Eä! Let these things Be!”, probably has a connection with the Logos in Christianity. Thus we can find three “distinctions” in Eru: a Creator who dwells outside the world, a Sustainer who dwells inside it and a Redeemer who shall step inside it. Some studies of Tolkien have claimed that Eru is distant and remote. This seems to hold water only partially. Ilúvatar, the Father of All, has a special relation with the Eruhíni, His Children, the immortal Elves and the mortal Men. He communicates with them directly only through the Valar, who resemble archangels. Nevertheless, only the Children of Eru can fight against evil, because their tragic fortunes turn evil into good. Even though religious activities are scarce among them, the fundamental faith and ultimate hope of the “Free Peoples” is directed towards Eru. He is present in the drama of history as the “Author of the Story”, who at times also interferes with its course through catastrophes and eucatastrophes, ‘good catastrophes’. Eru brings about a catastrophe when evil would otherwise bring good to an end, and He brings about a eucatasrophe when creaturely strength is not sufficent for victory. Victory over corruption is especially connected with mortal Men, of whom the most (or least) insignificant people are the Hobbits. However, because of the “primeval disaster” (that is, fall) of Mankind, ultimate salvation can only remain open, a hope for the far future.

Puukaupan säännöt : Yksityismetsänomistajien ja metsäteollisuuden puukauppa Itä-Suomessa 1919 - 1939

The Finnish forest industry bought more than half of the timber used in factories and sawmills in the 1930s from non-industrial private forests (NIPF). This research investigates the rules conformed to this timber trade. The main research questions are: what were the rules that influenced the timber trade; and by whom they were set up? Attention is also paid to the factors which advanced the forest owners’ negotiation possibilities. A variety of sources were used: legal and company statutes, timber trade contracts, archives of the forest companies and organisations. Moreover, the written reminiscences collected by the Finnish Literature Society in the early 1970s were used to analyse the views of individual sellers and buyers. An institutional economics approach was applied as the theoretical framework of this study. In the timber trade the seller (forest owner) and the buyer (the employee of the forest company) agreed to the rules of the timber trade. They agreed about the amount and the price of the timber on sale, but also rules concerning, e.g., timber marking and harvesting. The forest companies had a strong control over the written contracts. Neither the private forest owners nor the forest organisations had much influence over these contracts. However, they managed to influence the rules which could not be found in the contracts. These written and unwritten rules regulated, for instance, the timber marking and measurement. The forest organisations such as Central Forestry Board Tapio (Keskusmetsäseura Tapio) and associations of forest owners (metsänhoitoyhdistykset) helped private forest owners in gaining more control over the timber marking. In timber marking, the forest owner selected trees to be included in the timber trade and gained more information, which he could use in the negotiations. The other rule, which was changed despite forest companies’ resistance, was the timber measurement. The Central Union of Agricultural Producers (MTK) negotiated with the Central Association of Finnish Woodworking Industries (SPKL) about changing the rules of the measurement practices. Even though SPKL did not support any changes, the new timber measurement law was accepted in the year 1938. The new law also created a supervisory authority to solve possible disagreements. Despite this the forest companies were still in charge of the measurement process in most cases. The private forest owners attained changes in the rules of the timber trade mainly during the 1930s. Earlier the relative weakness of the private forest organisations had diminished their negotiation positions. This changed in the 1930s as the private forest owners and their organisations became more active. At the same time the forest industry experienced a shortage of timber, especially pulp wood, and this provided the private forest owners with more leverage. Full-text (in Finnish) available at http://helda.helsinki.fi/handle/10224/4081

Revision of the family Alycidae (Acariformes, Acari), with special reference to European species

The thesis provides a proposal to divide Alycidae G. Canestrini & Fanzago into two subfamilies and four tribes. This new hierarchy is based on a reassessment and reranking of new and previously known synapomorphies of the clusters concerned by cladistic analysis, using 60 morphological characters for 48 ingroup species. The basic characters of the taxa are illustrated either by SEM micrographs (Scanning Electron Microscopy) or by outline drawings. The presented classification includes the definitions of Alycini G. Canestrini & Fanzago new rank; Bimichaeliini Womersley new rank; Petralycini new rank; and the (re)descriptions of Alycus C.L. Koch, Pachygnathus Dugès, Amphialycus Zachvatkin, Bimichaelia Thor and Laminamichaelia gen. nov. The species described or redescribed are: Pachygnathus wasastjernae sp. nov. from Kvarken (Merenkurkku), Finland; Pachygnathus villosus Dugès (in Oken); Alycus roseus C.L. Koch; Alycus denasutus (Grandjean) comb. and stat. nov.; Alycus trichotus (Grandjean) comb. nov.; Alycus marinus (Schuster) comb. nov.; Amphialycus (Amphialycus) pentophthalmus Zachvatkin; Amphialycus (Amphialycus) leucogaster (Grandjean); and Amphialycus (Orthacarus) oblongus (Halbert) comb. nov.; Bimichaelia augustana (Berlese); Bimichaelia sarekensis Trägårdh; Laminamichaelia setigera (Berlese) comb. nov.; Laminamichelia arbusculosa (Grandjean) comb. nov.; Laminamichelia subnuda (Berlese) comb. nov. and Petralycus unicornis Grandjean. Fourteen nominal species were found to be junior synonymies. The importance of sensory organs in taxonomy is well recognized, but inclusion of the elaborate skin pattern seemed to improve essentially the usefulness of the prodorsal sensory area. The detailed pictures of the prodorsa of the European alycids could be used like passport photographs for the species. A database like this of prodorsa of other mite taxa as well might be an answer to future needs of species identification in soil zoology, ecology and conservation.

The influence of school smoking policy and school prevention programs on the smoking behaviour of high school students in Prince Edward Island, Canada

The aim of the study was to examine the influence of school smoking policy and school smoking prevention programs on the smoking behaviour of students in high schools in Prince Edward Island using the School Health Action Planning Evaluation System (SHAPES). A total sample included 13,131 observations of students in grades 10-12 in ten high schools in Prince Edward Island over three waves of data collection (1999, 2000, and 2001). Changes in prevalence of smoking and factors influencing smoking behaviour were analyzed using descriptive statistics and Chi-Square tests. Multi-level logistic regression analyses were used to examine how both school and student characteristics were associated with smoking behaviour (I, II, III, IV). Since students were located within schools, a basic 2-level nested structure was used in which individual students (level 1) were nested within schools (level 2). For grade 12 students, the combination of both school policies and programs was not associated with the risk of smoking and the presence of the new policy was not associated with decreased risk of smoking, unless there were clear rules in place (I). For the grade 10 study, (II) schools with both policies and programs were not associated with decreased risk of smoking. However, the smoking behaviour of older students (grade 12) at a school was associated with younger students’ (grade 10) smoking behaviour. Students first enrolled in a high school in grade 9, rather than grade 10, were at increased risk of occasional smoking. For students who transitioned from grade 10 to 12 (III), close friends smoking had a substantial influence on smoking behaviour for both males and females (III). Having one or more close friends who smoke (Odds Ratio (OR) = 37.46; 95% CI = 19.39 to 72.36), one or more smokers in the home (OR = 2.35; 95% CI = 1.67 to 3.30) and seeing teachers and staff smoking on or near school property (OR=1.78; 95% CI = 1.13 to 2.80), were strongly associated with increased risk of smoking for grade 12 students. Smoking behaviour increased for both junior (Group 1) and senior (Group 2) students (IV). Group 1 students indicated a greater decrease in smoking behaviour and factors influencing smoking behaviour compared to those of Group 2. Students overestimating the percentage of youth their age who smoke was strongly associated with increased likelihood of smoking. Smoking rates showed a decreasing trend (1999, 2000, and 2001). However, policies and programs alone were not successful in influencing smoking behaviour of youth. Rather, factors within the students and schools contextual environment influenced smoking behaviour. Comprehensive approaches are required for school-based tobacco prevention interventions. Keywords: schools, policy, programs, smoking prevention, adolescents Subject Terms: school-based programming, public health, health promotion

On gravitational fields of stars in f(R) gravity theories

Einstein's general relativity is a classical theory of gravitation: it is a postulate on the coupling between the four-dimensional, continuos spacetime and the matter fields in the universe, and it yields their dynamical evolution. It is believed that general relativity must be replaced by a quantum theory of gravity at least at extremely high energies of the early universe and at regions of strong curvature of spacetime, cf. black holes. Various attempts to quantize gravity, including conceptually new models such as string theory, have suggested that modification to general relativity might show up even at lower energy scales. On the other hand, also the late time acceleration of the expansion of the universe, known as the dark energy problem, might originate from new gravitational physics. Thus, although there has been no direct experimental evidence contradicting general relativity so far - on the contrary, it has passed a variety of observational tests - it is a question worth asking, why should the effective theory of gravity be of the exact form of general relativity? If general relativity is modified, how do the predictions of the theory change? Furthermore, how far can we go with the changes before we are face with contradictions with the experiments? Along with the changes, could there be new phenomena, which we could measure to find hints of the form of the quantum theory of gravity? This thesis is on a class of modified gravity theories called f(R) models, and in particular on the effects of changing the theory of gravity on stellar solutions. It is discussed how experimental constraints from the measurements in the Solar System restrict the form of f(R) theories. Moreover, it is shown that models, which do not differ from general relativity at the weak field scale of the Solar System, can produce very different predictions for dense stars like neutron stars. Due to the nature of f(R) models, the role of independent connection of the spacetime is emphasized throughout the thesis.

Stadilaispojat, rikokset ja lastensuojelu : Viisi tapaustutkimusta kuudelta vuosikymmeneltä

Societal reactions to norm breaking behavior of children reveal, how we understand childhood, the relations between generations and communitie's ratio of tolerance. In Finland the children that repeatedly commit crimes receive social service measures that are based on Child Welfare Act. In the city of Helsinki (Stadi in the slang of Helsinki) existed an agency specifically established for ill-behaving children until the 1980's, agter which an unified agency for the maltreated and maladjusted children was founded. Through five boys' welfare cases, this research aims at defining what kind of positions, social relations and structures are constructed in the social dynamics of these children's everyday lives. The cases cover different decades from the 1940s to the present. At the same time the cases reflect the child welfare and societal practices, and reveal how the communities have participated in constructing deviance in different eras. The research is meta-theoretically based on critical realism and specifically on Roy Bhaskar's transformative model of social activity. The cases are analyzed in the framework of Edwin M. Lemert's societal reaction theory. Thus the focus of the study is on the wide structural context of the institutional and societal definitions of deviance. The research is methodologically based on a qualitative multiple case study research. The primary data consist of classified child welfare case files collected from the archives of the city of Helsinki. The data of the institutional level consist of the annual reports from 1943 to 2004 and the ordinances from 1907 onwards, and of various committee documents produced in the law-making process of child welfare, youth and criminal legislation of the 20th century. Empirical finding are interpreted in a dialogue with previous historical and child welfare research, contemporary literature and studies on the urban development. The analysis is based on Derek Layder's model of adaptive theory. The research forms a viewpoint to the historical study of child welfare, in which the historical era, its agents and the dynamics of their mutual relations are studied through an individual level reconstruction based on the societal reaction theory. The case analyses reveal how the positions of the children form differently in the different eras of child welfare practices. In the 1940s the child is positioned as a psychopath and a criminal type. The measures are aimed at protecting the community from the disturbed child, and at adjusting the individual by isolation. From 1960s to 1980s the child is positioned as a child in need of help and support. The child becomes a victim, a subject that occupies rights, and a target of protection. In the turn of the millennium a norm breaking child is positioned as a dangerous individual that, in the name of the community safety, has to be confined. The case analyses also reveal the prevailing academic and practical paradigms of the time. Keywords: childhood, youth, child protection, child welfare, delinquency, crime, deviance, history, critical realism, case study research

Retirement Transition and Well-being : A 16-year Longitudinal Study

The ageing of the labour force and falling employment rates have forced policy makers in industrialized countries to find means of increasing the well-being of older workers and of lengthening their work careers. The main objective of this thesis was to study longitudinally how health, functional capacity, subjective well-being, and lifestyle change as people grow older, and what effect retirement has on these factors and on their relationships. The present study is a follow-up questionnaire study of Finnish municipal workers, conducted in 1981 to 1997 at the Finnish Institute of Occupational Health. In 1981, a postal questionnaire was sent to 7344 municipal workers in different parts of Finland. The respondents were born between 1923 and 1937. A total of 6257 persons responded to the first questionnaire. In the end, a total of 3817 persons had responded to all four (1981, 1985, 1992, 1997) questionnaires. (The response rate was 69% of the living participants). Cross-tabulations, comparison of means, logistic regression analyses and general linear models with repeated measures were used to derive the results. The transition from work life to retirement, and the following years as a pensioner were associated with many changes. Involvement in various activities increased during the transition stage but later decreased to the previous level. Physical exercise was an exception: it became increasingly popular over the years. Perceived health improved markedly from the working stage to the retirement transition stage, even though morbidity increased steadily during the follow-up. On the other hand, functional capacity decreased over the follow-up, especially among those who were occupationally active until the retirement stage. Subjective well-being remained stable during the follow-up period. There were, however, great differences based on the type of work, favouring those whose work had been mental in nature. The impact of activity level on maintaining well-being became greater during the follow-up, whereas the effect of physical functioning diminished. Good physical functioning and an active life-style contributed to staying on at work until normal retirement age. Also work-related factors, i.e. possibilities for development and influence at work, responsibility for others, meaningful work, and satisfaction with working time arrangements were positively related to continuing working. The transition from work to retirement had a positive impact on a person s health and functional capacity. The study results support the view that it should be possible to ease one s work pace during the last years of a work career. This might lower the threshold between work and retirement and convince people that there will still be time to enjoy retirement also a few years later.

Search for R-Parity Violating Decays of Sneutrinos to eμ, μτ, and eτ Pairs in pp̅ Collisions at √s=1.96 TeV

We present a search for tau sneutrino production using the Tevatron ppbar collision data collected with the CDF II detector and corresponding to an integrated luminosity of 1 fb^-1. We focus on the scenarios predicted by the R-parity violating (RPV) supersymmetric models in which tau sneutrinos decay to two charged leptons of different flavor. With the data consistent with the standard model expectations, we set the upper limits on sigma(ppbar -> tau sneutrino)*BR(tau sneutrino ->emu,mutau,etau) and use these results to constrain the RPV couplings as a function of tau sneutrino mass.

Ironi som forskningsobjekt. Är det möjligt att forska i det som finns mellan raderna?

Abstract (Irony as object of research: Is it possible to explore what is between the lines?): The main concern of this article is the interpretation of irony: how is it brought about and how can it be investigated? The method applied is based on authentic texts and their elicited interpretations − a method referred to in this article response analysis. Interpretation of irony in the approach taken is seen as being crucially dependent on the notion of coherence. A text is perceived as being coherent if it (a) makes sense and if it(b) hangs together. Incoherent texts can result in an ironic interpretation; however, the incoherence must also be perceived as being intentional, and intentionality in turn is a sign of the edge of the ironist. Ironic interpretation is defined as a combination of five factors: (1) an ironic edge that (2) reflects the intention of the ironist, and (3) has a target and (4) a victim too. Essential to irony is its fifth factor, the fact that one or more of these four factors must be inferred from co(n)text. This definition of irony is crucial in distinguishing irony from non-irony, and it also helps to discern the differences as well as the similarities between irony and related phenomena.

Growth and Convergence: The case of China

Growth and Convergence: The Case of China Since the initiation of economic reforms in 1978, China has become one of the world’s fast-growing economies. The rapid growth, however, has not been shared equally across the different regions in China. The prominent feature of substantial differences in incomes and growth rates across the different Chinese regions has attracted the attention of many researchers. This book focuses on issues related to economic growth and convergence across the Chinese regions over the past three decades. The book has eight chapters. Apart from an introduction chapter and a concluding chapter, all the other chapters each deal with some certain aspects of the central issue of regional growth and convergence across China over the past three decades. The whole book is organized as follows. Chapter 1 provides an introduction to the basic issues involved in this book. Chapter 2 tests economic growth and convergence across 31 Chinese provinces during 1981-2005, based on the theoretical framework of the Solow growth model. Chapter 3 investigates the relationship between openness to foreign economic activities, such as foreign trade and foreign direct investment, and the regional economic growth in the case of China during 1981-2005. Chapter 4, based on data of 31 Chinese provinces over the period 1980-2004, presents new evidence on the effects of structural shocks and structural transformation on growth and convergence among the Chinese regions. Chapter 5, by building up an empirical model that takes account of different potential effects of foreign direct investment, focuses on the impacts of foreign direct investment on China’s regional economic performance and growth. Chapter 6 reconsiders the growth and convergence problem of the Chinese regions in an alternative theoretical framework with endogenous saving behavior and capital mobility across regions. Chapter 7, by building up a theoretical model concerning comparative advantage and transaction efficiency, focuses on one of the potential mechanisms through which China achieves its fast economic growth over the past few decades. Chapter 8 concludes the book by summarizing the results from the previous chapters and suggesting directions for further studies.