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.

A Literary Turn : Rethinking the Roles of Generalization and Theory in Anglo-American Moral Philosophy

This work investigates the role of narrative literature in late-20th century and contemporary Anglo-American moral philosophy. It aims to show the trend of reading narrative literature for purposes of moral philosophy from the 1970 s and early 80 s to the present day as a part of a larger movement in Anglo-American moral philosophy, and to present a view of its significance for moral philosophy overall. Chapter 1 provides some preliminaries concerning the view of narrative literature which my discussion builds on. In chapter 2 I give an outline of how narrative literature is considered in contemporary Anglo-American moral philosophy, and connect this use to the broad trend of neo-Aristotelian ethics in this context. In chapter 3 I connect the use of literature to the idea of the non-generalizability of moral perception and judgment, which is central to the neo-Aristotelian trend, as well as to a range of moral particularisms and anti-theoretical positions of late 20th century and contemporary ethics. The joint task of chapters 2 and 3 is to situate the trend of reading narrative literature for the purposes of moral philosophy in the present context of moral philosophy. In the following two chapters, 4 and 5, I move on from the particularizing power of narrative literature, which is emphasized by neo-Aristotelians and particularists alike, to a broader under-standing of the intellectual potential of narrative literature. In chapter 4 I argue that narrative literature has its own forms of generalization which are enriching for our understanding of the workings of ethical generalizations in philosophy. In chapter 5 I discuss Iris Murdoch s and Martha Nussbaum s respective ways of combining ethical generality and particularity in a philosophical framework where both systematic moral theory and narrative literature are taken seriously. In chapter 6 I analyse the controversy between contemporary anti-theoretical conceptions of ethics and Nussbaum s refutation of these. I present my suggestion for how the significance of the ethics/literature discussion for moral philosophy can be understood if one wants to overcome the limitations of both Nussbaum s theory-centred, equilibrium-seeking perspective, and the anti-theorists repudiation of theory. I call my position the inclusive approach .

Gustaf III inför sina undersåtar : Konsten att härska och politikens kulturhistoria

The dissertation analyses the political culture of Sweden during the reign of King Gustav III (1771-1792). This period commonly referred to as the Gustavian era followed the so-called Age of Liberty ending half a century of strong parliamentary rule in Sweden. The question at the heart of this study engages with the practice of monarchical rule under Gustav III, its ideological origins and power-political objectives as well as its symbolic expression. The study thereby addresses the very nature of kingship. In concrete terms, why did Gustav III, his court, and his civil service vigorously pursue projects that contemporaneous political opponents and, in particular, subsequent historiography have variously pictured as irrelevant, superficial, or as products of pure vanity? The answer, the study argues, is to be found in patterns of political practice as developed and exercised by Gustav III and his administration, which formed a significant part of the political culture of Gustavian Sweden. The dissertation is divided into three parts. The first traces the use and development of royal graces chivalric orders, medals, titles, privileges, and other gifts issued by the king. The practice of royal reward is illustrated through two case studies: the 1772 coup d état that established Gustav III s rule, and the birth and baptism of the crown prince, Gustav Adolf, in 1778. The second part deals with the establishment of the Court of Appeal in Vasa in 1776. The formation of the Appeals Court was accompanied by a host of ceremonial, rhetorical, emblematic, and architectural features solidifying its importance as one of Gustav III s most symbolic administrative reform projects and hence portraying the king as an enlightened monarch par excellence. The third and final part of the thesis engages with war as a cultural phenomenon and focuses on the Russo-Swedish War of 1788-1790. In this study, the war against Russia is primarily seen as an arena for the king and other players to stage, create and re-create as well as articulate themselves through scenes and roles adhering to a particular cultural idiom. Its codes and symbolic forms, then, were communicated by means of theatre, literature, art, history, and classical mythology. The dissertation makes use of a host of sources: protocols, speeches, letters, diaries, newspapers, poetry, art, medals, architecture, inscriptions and registers. Traditional political source material and literary and art sources are studied as totalities, not as separate entities. Also it is argued that political and non-fictional sources cannot be understood properly without acknowledging the context of genre, literary conventions, and artistic modes. The study critically views the futile, but nonetheless almost habitual juxtaposition of the reality of images, ideas, and metaphors, and the reality of supposedly factual historical events. Significantly, the thesis presumes the symbolic dimension to be a constitutive element of reality, not its cooked up misrepresentation. This presumption is reflected in a discussion of the concept of role , which should not be anachronistically understood as roles in which the king cast himself at different times and in different situations. Neither Gustav III nor other European sovereigns of this period played the roles as rulers or majesties. Rather, they were monarchs both in their own eyes and in the eyes of their contemporaries as well as in all relations and contexts. Key words: Eighteenth-Century, Gustav III, Cultural History, Monarchs, Royal Graces, the Vasa Court of Appeal, the Russo-Swedish War 1788–1790.

J. L. Runebergs samlade skrifter i textkritisk belysning

The Collected Works of J. L. Runeberg from the Viewpoint of Textual Scholarship The theoretical framework of this dissertation builds on textual scholarship. The dissertation explores the history of Runeberg’s publications and his relations with his publishers, from his debut and the first editions, through the editions of collected works published during the course of his life, to the later commercial editions, including the critical edition, published in 1933–2005 by the Svenska Vitterhetssamfundet (The Swedish Society for Belles Lettres) and The Svenska litteratursällskapet i Finland (The Society of Swedish Literature in Finland). The various editions of Runeberg’s collected works are situated in their respective critical traditions, from the 19th century German Ausgabe letzter Hand, to the influence of Anglo-American bibliography on Swedish textual criticism in the late 20th century. By making use of primary material previously not used for research purposes, the author is able to present a new view on Runebergian publishing history, including Runeberg’s fees and his relations with the censor authorities. There are indications that his Finnish publishers could not bear the cost of his sizable fees, that were in proportion neither with the book market in Finland nor with the numbers of copies sold. Apart from a certain body of editions the primary material is comprised of correspondences, publishing contracts, printing house invoices, as well as censor authority records. One of the conclusions drawn is that the early and detailed biography, Biografiska anteckningar om Johan Ludvig Runeberg (Biographical Notes on …) by J. E. Strömborg is not reliable in matters concerning publishing history, and that this work has been used far too uncritically. The history of the critical edition gets a chapter of its own, based on primary material in Swedish and Finnish archives. Finally, the author analyses the critical choices, made primarily in the critical edition, and uses examples from the commercial editions to study the editors’ interventions over time, from the 1850s to the 1920s. The changes to the text are usually small and subtle, but cumulative – and in some cases, crucial for the interpretation of the work. One objective of textual scholarship should be to examine the publishing history of a single work or of an author’s œuvre, and another to pay attention both to changes in a work as such and to the shifts of meaning they might entail.

Kaunhiista kauhniiseen, satheesta satteeseen : Jälkitavuissa säilyneen h:n variaatiosta Pellossa vuoden 1995 aineiston valossa

Tutkielmassa tarkastellaan jälkitavuissa säilyneen, alun perin vokaalienvälisen h:n nykyedustusta Tornionlaakson Pellossa sosiolingvistisen teorian valossa. Keskeisenä tutkimusongelmana on variaation jasen muuttumisen suunnan selvittäminen, mitä tutkitaan sekä näennäis- että reaaliajallisen metodin turvin. Lisäksi pohditaan, millaiset kielensisäiset tekijät muutoksia ohjaavat. Reaaliaikaisen vertailun mahdollistavat Kirsi Kunnarin vuonna 1983 valmistuneen pro gradu -työn jälkitavujen h:ta koskevat tulokset Pellosta (informantit syntyneet vuosina 1898-1967). Pääpaino on kuitenkin näennäisajallisessa vertailussa; variaatiota tarkastellaan yksityiskohtaisesti erityisesti kielelliseltä kannalta, mikä on vaatinut perusteellista aineiston käsittelyä. Näennäisajallisessa tarkastelussa verrataankahden haastatellun ikäryhmän kieltä: nuorten (syntyneet vuosina 1986-1977) ja keski-ikäisten (syntyneet vuosina 1964-1945). Nuoria informantteja, joita on 14, on haastateltu pääosin pareittan. Vertailuryhmä, keski-ikäiset, koostuu heidän vanhem mistaan (7 informanttia). Nauhatunteja on yhteensä n. 13. Tulokset osoittavat, että toisin kuin muualla Peräpohjolassa, yleiskielen mukainen katovariantti (kou-luun) ei ole merkittävästi yleistynyt pellolaisten puhekielessä viimeisten neljän sukupolven aikana. Vokaalienvälisessä asemassa (koulu-h-un) h:ta ei nykypellolaisilla enää tapaa, ja ns. sisäheittoinenvariantti (koul-huun) on nuorten ryhmässä selvästi vähemmän suosiossa kuin keski-ikäisillä. Tornionjoki­laaksolainen, metateettinen h-variantti (kouh-luun) on yhä elinvoimainen: sen käyttö on nuorillakin lisääntynyt. Metateesi ei ole kuitenkaan kvantitatiivisesti juurikaan yleistynyt niissä fonotaktisissa ympäristöissä, joissa se aiheesta tehdyn väitöskirjan (1992) mukaan on ollut aiemmilla sukupolvilla harvinainen. Tätä saattaa osittain selittää tiettyjen puhekielisyyksien yleistyvä käyttö, mikä vaikuttaa eniten juuri näissä fonotaktisissa ympäristöissä siten, ettei metateesin toteutumiselle ole edellytyksiä. Pellon nykyisessä jälkitavujen h:n variaatiossa on osallisena vielä yksi variantti: assimiloitunut h (talhoon > talloon; toisheen > toisseen; kauphaan > kauppaan). Aiemmin tutkituilla sukupolvilla assimilaatiomuutos on ollut harvinainen, mutta nyt se on yleistynyt erityisesti nuorilla tytöillä. h:n assimilaatiossa syntyvät muodot lankeavat usein yhteen alueella jokseenkin fonemaattisena esiintyvän yleisgeminaation kanssa, osa muodoista muistuttaa erikoisgeminaatiota ja pieni osa yleiskielisiä muotoja. Tutkielmassa kyseenalaistetaan kielellisten seikkojen nojalla kyseisten muotojen tulkitseminen h:n assimilaatiosta johtuvaksi: assimiloituneiksi tulkituissa h-tapauksissa sekä konsonantin että sitä seuraavan vokaalin pituusdistribuutiot tukevat ajatusta, että ainakin yleisgeminaatiokonteksteissa assimilaatiomuodot ovat puhujan kannalta "mentaalista geminaatiota". Assimilaatiomuodot rinnastetaan tutkielmassa katomuotoihin sikäli, että niissäkin h on tasoittunut. Merkittävä ero on tavujen kvantiteettisuhteissa: assimilaatiomuodoissa ne säilyvät ennallaan (tal-hoon > tal-loon), katomuodoissa muuttuvat (ta-loon). h:n assimilaatiolla ja metateesilla epäillään aineistonperusteella olevan yhteisen tehtävän: sisäheittoisten talhoon, satheen -muotojen karttaminen tavujen kavantiteettisuhteita rikkomatta. Esitetyn hypoteesin mukaan syynä ovat suomen fonotaksille vieraat konsonantin + h:n yhtymät, jotka aikoinaan syntyivät murteeseen vokaalin heityttyä h:n edeltä.

Surveillance in hereditary nonpolyposis colorectal cancer syndrome

Hereditary nonpolyposis colorectal cancer (HNPCC) is an inherited cancer predisposition syn-drome characterized by early onset colorectal cancer (CRC) and several other extra-colonic cancers, most commonly endometrial cancer (EC) and gastric cancer. Our aim was to evaluate the efficiency and results of the ongoing CRC and EC surveillance programs and to investigate the grounds for future gastric cancer screening by comparing the gastric biopsies of mutation positive and negative siblings in search for premalignant lesions. We also compared a new surveillance method, computerized tomographic colonoscopy (CTC) with optic colonoscopy. The patient material consisted of 579 family members from 111 Finnish HNPCC families al-most all harboring a known mismatch repair gene mutation. The efficacy of CRC and EC surveillance programs on HNPCC patients was evaluated by comparing the stage and survival of cancer cases detected with surveillance versus without. The performance of a new technique, CTC, was explored using a same-day colonoscopy as a reference standard. The use of intrauterine aspiration biopsies for EC surveillance was intro-duced for the first time in a HNPCC setting. Upper GI endoscopies were performed and biop-sies taken from mutation carriers and their mutation-negative siblings. The present surveillance program for CRC proved to be efficient. The CRC cases detected by surveillance were at a significantly more favorable stage than those in the non-surveilled group. This advantage was reflected in a significantly higher CRC-specific survival in the sur-veilled group. The performance of a new technique, CTC was found insufficient for polyp detection in this population in which every polyp, no matter the size, should be detected and removed. Colono-scopy was confirmed as a better surveillance modality than CTC. We could not observe any of the assumed differences in the gastric mucosa from mutation carriers and their mutation-negative siblings and no cases of gastric cancer were detected. The results gave no support for gastric surveillance. The EC surveillance program (transvaginal ultrasound and intra-uterine biopsy every 2-3 years) seemed to be efficient. It yielded several asymptomatic cancer cases and premalignant lesions. The stage distribution of the endometrial cancers in the group under surveillance tended to be more favorable than that of the mutation-positive, symptomatic EC patients who had no surveillance. None of the surveilled EC patients died of EC compared to six in the non-surveilled patients during the follow up. The improvement was, however, not statistically sig-nificant, thus far. Another observation was the good performance of endometrial aspiration biopsies used in this setting for the first time.