36 resultados para Shifted Legendre polynomials

em Doria (National Library of Finland DSpace Services) - National Library of Finland, Finland


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The main topic of the thesis is optimal stopping. This is treated in two research articles. In the first article we introduce a new approach to optimal stopping of general strong Markov processes. The approach is based on the representation of excessive functions as expected suprema. We present a variety of examples, in particular, the Novikov-Shiryaev problem for Lévy processes. In the second article on optimal stopping we focus on differentiability of excessive functions of diffusions and apply these results to study the validity of the principle of smooth fit. As an example we discuss optimal stopping of sticky Brownian motion. The third research article offers a survey like discussion on Appell polynomials. The crucial role of Appell polynomials in optimal stopping of Lévy processes was noticed by Novikov and Shiryaev. They described the optimal rule in a large class of problems via these polynomials. We exploit the probabilistic approach to Appell polynomials and show that many classical results are obtained with ease in this framework. In the fourth article we derive a new relationship between the generalized Bernoulli polynomials and the generalized Euler polynomials.

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In this thesis, the main point of interest is the robust control of a DC/DC converter. The use of reactive components in the power conversion gives rise to dynamical effects in DC/DC converters and the dynamical effects of the converter mandates the use of active control. Active control uses measurements from the converter to correct errors present in the converter’s output. The controller needs to be able to perform in the presence of varying component values and different kinds of disturbances in loading and noises in measurements. Such a feature in control design is referred as robustness. This thesis also contains survey of general properties of DC/DC converters and their effects on control design. In this thesis, a linear robust control design method is studied. A robust controller is then designed and applied to the current control of a phase shifted full bridge converter. The experimental results are shown to match simulations.

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In this paper, a new two-dimensional shear deformable beam element based on the absolute nodal coordinate formulation is proposed. The nonlinear elastic forces of the beam element are obtained using a continuum mechanics approach without employing a local element coordinate system. In this study, linear polynomials are used to interpolate both the transverse and longitudinal components of the displacement. This is different from other absolute nodal-coordinate-based beam elements where cubic polynomials are used in the longitudinal direction. The accompanying defects of the phenomenon known as shear locking are avoided through the adoption of selective integration within the numerical integration method. The proposed element is verified using several numerical examples, and the results are compared to analytical solutions and the results for an existing shear deformable beam element. It is shown that by using the proposed element, accurate linear and nonlinear static deformations, as well as realistic dynamic behavior, can be achieved with a smaller computational effort than by using existing shear deformable two-dimensional beam elements.

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Tutkimuksen tarkoituksena on luoda suomalaisen rahastosijoittajan profiili. Tutkimuskohteena ovat sijoittajien demografiset ominaisuudet, rahastosijoitukset sekä rahastotransaktiot. Aineistona on erään suomalaisen rahastoyhtiön henkilöasiakastietokanta vuosilta 1998 - 2003. Tutkimustulosten mukaan rahastosijoittaminen on yleistynyt Suomessa viime vuosien aikana. Erityisesti naisten määrä rahastosijoittajien joukossa on kasvussa. Rahastosijoitusten suuruus riippuu sijoittajan iästä sekä sukupuolesta. Mitä vanhempi sijoittaja on, sitä enemmän hän on sijoittanut rahastoihin. Lisäksi miehet sijoittavat suurempia summia kuin naiset. Viimeisten kolmen vuoden aikana suomalaisten rahastosijoittajien sijoituskohteiden painopiste on muuttunut riskillisemmistä rahastoista vähäriskisiin rahastoihin, erityisesti lyhyen koron rahastoihin. Osakemarkkinoiden mennyt kehitys vaikuttaa sijoituspäätöksiin. Rahastosijoittajien markkina-ajoituskyky on kuitenkin melko heikko. Miehet tekevät aktiivisemmin merkintöjä ja lunastuksia ja lisäksi reagoivat naisia nopeammin markkinoiden muutoksiin.

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The aim of this study is to describe the structure of the pharmacy industry in four post-Soviet states on the Baltic Sea: Russia, Estonia, Latvia, and Lithuania. In addition to this, the opportunities that these markets have to offer for international pharmaceutical companies are explored. After the Soviet Union collapsed at the beginning of 1990s, the pharmacy sector has gone through tremendous changes. The pharmacy market shifted from a centrally controlled, one supplier system to an industry in which multiple distributors are competing in importing, wholesaling, and retailing of medicinal products. In the Baltic States, the number of pharmacies has not increased during the last years and companies have been growing mainly by acquisitions. Especially in Estonia the market is saturated and price competition is fierce. Similarly, in Latvia and Lithuania, markets are consolidating and wholesalers are growingly taking part in retailing by acquiring smaller chains. In Russia, the market is still fragmented and only one national pharmacy chain can be named, pharmacy chain “36.6”. Pharmacy chains are growing mostly through organic growth and competition between the biggest players is relatively low. The Russian market clearly offers many opportunities for international pharmaceutical operators. The ageing population, growing level of income, and changing living habits are creating new and growing needs for modern healthcare services and products.

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In this book, I apply a philosophical approach to study the precautionary principle in environmental (and health) risk decision-making. The principle says that unacceptable environmental and health risks should be anticipated, and they ought to be forestalled before the damage comes to fruition even if scientific understanding of the risks is inadequate. The study consists of introductory chapters, summary and seven original publications which aim at explicating the principle, critically analysing the debate on the principle, and constructing a basis for the well-founded use of the principle. Papers I-V present the main thesis of this research. In the two last papers, the discussion is widened to new directions. The starting question is how well the currently embraced precautionary principle stands up to critical philosophical scrutiny. The approach employed is analytical: mainly conceptual, argumentative and ethical. The study draws upon Anglo-American style philosophy on the one hand, and upon sources of law as well as concrete cases and decision-making practices at the European Union level and in its member countries on the other. The framework is environmental (and health) risk governance, including the related law and policy. The main thesis of this study is that the debate on the precautionary principle needs to be shifted from the question of whether the principle (or its weak or strong interpretation) is well-grounded in general to questions about the theoretical plausibility and ethical and socio-political justifiability of specific understandings of the principle. The real picture of the precautionary principle is more complex than that found (i.e. presumed) in much of the current academic, political and public debate surrounding it. While certain presumptions and interpretations of the principle are found to be sound, others are theoretically flawed or include serious practical problems. The analysis discloses conceptual and ethical presumptions and elementary understandings of the precautionary principle, critically assesses current practices invoked in the name of the precautionary principle and public participation, and seeks to build bridges between precaution, engagement and philosophical ethics. Hence, it is intended to provide a sound basis upon which subsequent academic scrutiny can build.

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IFRS standardit pyrkivät yhdenmukaistamaan yritysten taloudellisen informaation esittämistapaa ja lisäämään tilinpäätöksen läpinäkyvyyttä sijoittajien näkökulmasta. Tässä tutkielmassa tarkastellaan pankkien rahoitusomaisuuserien läpinäkyvyysvaatimusten toteutumista tutkimalla, kuinka rahoitusinstrumenttien arvostusmenetelmät ovat muuttuneet IFRS:n käyttöönoton myötä. Tutkimusmenetelmäksi valittiin monitapaustutkimus, jossa selvitettiin kuinka aineistoon valitut neljä pohjoismaista pankkia oust menetelleet rahoitusinstrumenttien arvostamisessa IFRS standardien käyttöönoton siirtymävaiheessa vuosina 2003 2007. Aineistona käytettiin pankkien julkisia tilinpäätöstietoja ja vuosikertomuksia. Tulosten perusteella rahoitusinstrumenttien läpinäkyvyyden voidaan sanoa jonkin verran lisääntyneen, sillä pankit olivat yleisesti ottaen siirtyneet käyvän arvon käyttämiseen aikaisemmasta hankintamenopohjaisesta menetelmästä. Käyvän arvon kaikki pankit oust määrittäneet markkinahintanoteerausten perusteella tai niiden puuttuessa erilaistenarvostusmenetelmien avulla. Pankin koko näytti olevan sidoksissa käytettavien arvostusmenetelmien monimutkaisuuteen.

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In my PhD dissertation, I have examined a group of people of Scandinavian origin received by Ospizio dei Convertendi. This group has been hitherto largely unknown to historical research. The Ospizio was an institute founded by the Oratorian Congregation in Rome in 1673 to provide religious instruction and material aid to both recent and aspirant converts to Roman Catholicism. My research traces the profile of converts and a typology of motives, examining different factors which influenced the conversion process. I show that the key factors were often of a social rather than a religious nature. Moreover, I have analyzed the hospice in the context of Counter-Reformation charity as well. In terms of numbers, the Scandinavians formed a somewhat marginal yet not insignificant group within the Roman hospice. Out of a total of 2203 guests received between 1673 and 1706, 4.6 % were Scandinavians: 74 Swedes (including Finland and Livonia) and 27 Danes (including Norway). They came from a rigorously Protestant region which reacted to Catholicism with severe legislative measures. Converts to Catholicism risked confiscation of their goods, expulsion or even capital punishment. Since both Sweden and Denmark were practically impenetrable to Catholicism at the time and clandestine missionary attempts often failed before they had even properly started, the Roman Catholic Church shifted its interest towards Northerners arriving in Rome, a preferred destination for young noblemen, artists and migrant craftsmen. The material related to Ospizio dei Convertendi, conserved in the Vatican archives, is a scarcely known yet unusually rich source, not only for the religious history of our continent, but also for social history and the study of migration in early modern Europe. It contains a wealth of information about members of the subordinate classes, of their travels and lives in Europe. The profile delineated in these documents is of individuals who had a wide range of different professions and different aspirations. These documents encompass a vast social spectrum that was highly mobile on a continent which by that time had become pluriconfessional. Therefore, these migrants faced the complex religious reality in their everyday life. The principal corpus of my research consists of two types of manuscript sources created for administrative and in a way also for apologetic purposes of the Roman Catholic Church. My starting point is the Primo registro generale of Ospizio dei Convertendi. This is a volume in which the following information about each guest was registered: name, nationality, city of origin, age, sex, profession, confession professed before converting, date of arrival, departure, abjuration and baptism. Typically, the convert was male, originating from Stockholm or Copenhagen, from 21 to 30 years of age. The biggest occupational groups in descending order were soldiers, noblemen, craftsmen and sailors. Thus the data reflects a multiform reality of interurban and long distance migration, ideals regarding the education of young noblemen and gentry as well as the need of European armies to hire foreign mercenaries in their various campaigns. Against this background the almost total absence of women is hardly surprising: there is only one woman in the material I have studied. The second main source, Nota degl’ospiti ricevuti e spese fatte per essi, sheds more light on the choices of the converts, their motivations and their lives outside Scandinavia before reaching Rome. This narrative material permits an analysis which completes but also goes far beyond the columns of the Institute’s general register. This material consists of reports written by Catholic priests based on an interview conducted upon each guest’s arrival. The material frequently includes information on what the converts would do following their departure from the Institute as well. These sources have a specific narrative form and contain short biographies, list reasons for converting and information about the journey from the North to the Mediterranean - a journey which in many cases took several years. Moreover, they show that certain unorthodox practices such as calling on the saints and pleading for help from them were not uncommon in the Protestant popular religion. The recording of information on conversions from Protestantism to Catholicism reflects both religious and social interest on the part of the receiving institute. The information obtained was used for the purposes of religious teaching, for finding adequate ways of inserting the convert into Italian society so that he could earn a living, and to find effective methods to convert others with a similar cultural and geographical background. The stories recorded were based on interviews with the newly-arrived, information obtained from a travel companion or fellow countrymen, or from written documents the aspirant converts carried with them. These sources illustrate, although sometimes in rather simplified ways, the circumstances and motivations which were relevant to the choice of changing one’s confession. In addition, I have examined petitions addressed to the hospice and other Roman authorities in order to get financial aid. These petitions were written by Italian scrittori, and they contain certain conventions and topoi of presenting the conversion with the purpose of improving the chances of obtaining financial aid. It is through these filters, which may seem initially almost invisible, that the remote voice of the converts reaches us. The results of the analysis are particularly interesting because they disagree with some of the principal conclusions of previous work on the subject. First, earlier research has focused almost exclusively on the conversions of noblemen, and has argued, second, that the Queen Christina of Sweden was the driving force behind their change of confession. The sources examined for this dissertation present a profile of long-distance migrants, many of them members of the subordinate classes, who were looking for ways to make their living in Europe. These people had in many cases left their country of origin several years earlier and not for religious reasons, so, crucially, we are not dealing with confessional migration in these cases. Rather, conversion was a complex process, intricately tied up with strategies of survival, integration and upward social mobility. At the same time, while these components are significant on their own right, they do not necessarily point to the absence of motivations of a more clearly religious nature.

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This PhD thesis in Mathematics belongs to the field of Geometric Function Theory. The thesis consists of four original papers. The topic studied deals with quasiconformal mappings and their distortion theory in Euclidean n-dimensional spaces. This theory has its roots in the pioneering papers of F. W. Gehring and J. Väisälä published in the early 1960’s and it has been studied by many mathematicians thereafter. In the first paper we refine the known bounds for the so-called Mori constant and also estimate the distortion in the hyperbolic metric. The second paper deals with radial functions which are simple examples of quasiconformal mappings. These radial functions lead us to the study of the so-called p-angular distance which has been studied recently e.g. by L. Maligranda and S. Dragomir. In the third paper we study a class of functions of a real variable studied by P. Lindqvist in an influential paper. This leads one to study parametrized analogues of classical trigonometric and hyperbolic functions which for the parameter value p = 2 coincide with the classical functions. Gaussian hypergeometric functions have an important role in the study of these special functions. Several new inequalities and identities involving p-analogues of these functions are also given. In the fourth paper we study the generalized complete elliptic integrals, modular functions and some related functions. We find the upper and lower bounds of these functions, and those bounds are given in a simple form. This theory has a long history which goes back two centuries and includes names such as A. M. Legendre, C. Jacobi, C. F. Gauss. Modular functions also occur in the study of quasiconformal mappings. Conformal invariants, such as the modulus of a curve family, are often applied in quasiconformal mapping theory. The invariants can be sometimes expressed in terms of special conformal mappings. This fact explains why special functions often occur in this theory.

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Maritime transports are very essential for Finland as over 80% of the foreign trade in the country is seaborne and possibilities to carry out these transports by are limited. Any disruption in maritime transports has negative consequences to many sectors in the Finnish economy. Maritime transport thus represents critical infrastructure for Finland. This report focuses on the importance of maritime transports on security of supply in Finland and for the so called critical industries in particular. The report summarizes the results of the Work Package 2 of the research project STOCA – “Study of cargo flows in the Gulf of Finland in emergency situations”. The aim of the research was to analyze the cargo flows and infrastructure that are vital for maintaining security of supply in Finland, as well as the consequences of disruptions in the maritime traffic for the Finnish critical industries and for the Finnish society. In the report we give a presentation of the infrastructure and transport routes which are critical for maintaining security of supply in Finland. We discuss import dependency of the critical industries, and the importance of the Gulf of Finland ports for Finland. We assess vulnerabilities associated with the critical material flows of the critical industries, and possibilities for alternative routings in case either one or several of the ports in Finland would be closed. As a concrete example of a transport disruption we analyze the consequences of the Finnish stevedore strike at public ports (4.3.–19.3.2010). The strike stopped approximately 80% of the Finnish foreign trade. As a result of the strike Finnish companies could not export their products and/or import raw materials, components and spare parts, or other essential supplies. We carried out personal interviews with representatives of the companies in Finnish critical industries to find out about the problems caused by the strike, how companies carried out they transports and how they managed to continue their operations during the strike. Discussions with the representatives of the companies gave us very practical insights about companies’ preparedness towards transport disruptions in general. Companies in the modern world are very vulnerable to transport disruptions because companies regardless of industries have tried to improve their performance by optimizing their resources and e.g. by reducing their inventory levels. At the same time they have become more and more dependent on continuous transports. Most companies involved in foreign trade have global operations and global supply chains, so any disruption anywhere in the world can have an impact on the operations of the company causing considerable financial loss. The volcanic eruption in Iceland in April 2010 stopping air traffic in the whole Northern Europe and most recently the earth quake causing a tsunami in Japan in March 2011 are examples of severe disruptions causing considerable negative impacts to companies’ supply chains. Even though the Finnish stevedore strike was a minor disruption compared to the natural catastrophes mentioned above, it showed the companies’ vulnerability to transport disruptions very concretely. The Finnish stevedore strike gave a concrete learning experience of the importance of preventive planning for all Finnish companies: it made them re-think their practical preparedness towards transport risks and how they can continue with their daily operations despite the problems. Many companies realized they need to adapt their long-term countermeasures against transport disruptions. During the strike companies did various actions to secure their supply chains. The companies raised their inventory levels before the strike began, they re-scheduled or postponed their deliveries, shifted customer orders between production plants among their company’s production network or in the extreme case bought finished products from their competitor to fulfil their customers’ order. Our results also show that possibilities to prepare against transport disruptions differ between industries. The Finnish society as a whole is very dependent on imports of energy, various raw materials and other supplies needed by the different industries. For many of the Finnish companies in the export industries and e.g. in energy production maritime transport is the only transport mode the companies can use due to large volumes of materials transported or due to other characteristics of the goods. Therefore maritime transport cannot be replaced by any other transport mode. In addition, a significant amount of transports are concentrated in certain ports. From a security of supply perspective attention should be paid to finding ways to decrease import dependency and ensuring that companies in the critical industries can ensure the continuity of their operations.

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Hankintatoimen merkitys yritysten kannattavuudelle on huomioitu viime vuosina aiempaa enemmän. Hankintatoimen rooli on muuttunut strategi-sen toiminnon suuntaan. Myös hankintatoimen suorituskyvyn johtamiseen on alettu kiinnittää enemmän huomiota. Tutkimuksen tavoitteena on suunnitella ja valita sopivat mittarit hankintatoimen suorituskyvyn mittaamista varten. Tutkimuksen toisena tavoitteena on arvioida sitä, mitkä valituista mittareista mittaavat organisaation aineetonta pääomaa. Tutkimus toteutetaan case-tutkimuksena. Aineiston keräämiseen ja ratkaisun toteuttamiseen käytetään kvalitatiivista tutkimusmenetelmää ja konstruktiivista tutkimus-otetta. Tutkimuksessa sovellettiin Balanced Scorecard -mittariston toteutuspro-sessia. Valitut mittarit ryhmiteltiin neljän näkökulman mukaisesti. Mittaris-toa ja näkökulmien soveltuvuutta tulee arvioida säännöllisesti käyttöönoton jälkeen. Aineettoman pääoman merkityksestä hankintatoimessa tarvitaan edelleen lisätutkimusta.

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Diplomityön tavoitteena oli kehittää vuokamallisille kartonkipakkauksille laadunvarmistuslaitteisto. Kirjallisen osan alussa esiteltiin vuokamallisten kartonkipakkausten valmistusprosessia. Tästä siirryttiin laatuasioihin, jossa tärkeimmät asiat olivat kartonkivuokien valmistuksessa esiintyvät laatupoikkeamat ja konenäkö. Tutkimusosan alussa esitellään Lappeenrannan teknillisessä yliopistossa kehitetty kartonkivuokien valmistuslinjasto. Tämän jälkeen vaatimuslistan pohjalta suunnitellaan kyseiseen linjastoon sopiva automaattinen laadunvalvontalaite, johon sisältyy myös kartonkivuokien siirtolaite. Suunnitteluprosessi aloitettiin koekuvaamalla kartonkivuokia erilaisilla kameroilla ja valaistusmenetelmillä. Koekuvausten perusteella valittiin konenäkölaitteisto. Tämän jälkeen toiminnoista luotiin periaatepiirroksia, joista kehitettiin varsinainen suunnitelma. Työn tuloksena saatiin suunnitelma konenäköön perustuvan automaattisen laadunvalvontalaitteen rakentamiselle.

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Pray and work. The development of Onni Puhakka: from innovator to nonconformist This ethnological biographical study examines the modernization which began in the mid-1800s, continued into the mid-1900s, and has changed Finnish society in many ways. This era has been studied on a general level quite extensively, but this work explores the life and everyday experiences of Onni Puhakka (1870−1955), a farmer who spent most of his life in the town of Liperi. The goal is to find new perspectives on the development of the modernization process in society through the experiences of an individual. In this study, a central theme is the rural co-operative movement represented in Finland by Pellervo as well as its development in this country and as a significant undertaking in Onni Puhakka’s life. The co-operative movement was one of the most significant sectors affecting modernization in rural communities. The main character in the study is the grandfather of the present author, and thus this research belongs to the newly accepted ethnological research tradition of studying one’s own community. Written documents, mainly collected and preserved by Onni Puhakka himself during his lifetime, form the research material. The material consists mainly of Puhakka’s extensive correspondence, personal notes and diaries, documents related to his farm, and photographs taken by him. Earlier research and other written material examining the general development of the period were used to provide a background for the study. The co-operative movement formed a comprehensive ideology for Onni Puhakka, in which the possibilities for the development of both individuals and the community were combined. His life was based on a religious conviction, and he felt that the co-operative movement was the application of Christian love for one’s neighbour in practice. At the beginning of his active working career, Puhakka was an innovator, a reformer at the forefront of progress, but quite soon he became a sworn critic of the development of the co-operative movement in particular. One of Puhakka’s criticisms of the co-operative movement was the shifting of decision-making power to professional managers and central organizations, far from the reach of local actors. A fundamental reason for his dissatisfaction was the development within the co-operative movement in which the ideological background was forgotten, and economic goals and making a profit took an excessive significance. This assessment of the co-operative movement made by Onni Puhakka and his predictions about its development were not unfounded. This has been shown by several studies examining the development of both the Pellervo and working class cooperative movements. The professionalization of management, managerialism, as well as the direct links between professional managers of local co-operatives and central organizations have lead to the situation in which fewer and fewer people make the decisions, and management has as its goal economic success and growth. Co-operative enterprises that have grown in size have become estranged from the everyday life of their members. Instead of taking care of relations with the membership of the co-op, competitive ability and the market share have become the most important concerns of the management. As the membership has become alienated, their interest in large-scale co-ops has also become largely economic. A significant change among the membership of the Pellervo movement occurred at the stage when the co-operative movement shifted from rural areas to urban centres. This meant that the commitment of the membership became much looser than it had been in the farmers’ production and consumer co-ops. From the point of view of its members, the nature of the co-operative movement has become diametrically opposed to its point of departure: the active members who previously formed the subject of the co-operative movement have become the object of the economic activities of that same movement. The co-operative movement has been transformed from the progressive agent of change of its early years into a business activity which no longer has any significant task as a social reformer. This study confirms the observations of the latest research on modernization which states that modernization has not been a straightforward and inevitable development that has lead to the present situation. For example, the criticism directed by Puhakka toward the co-operative movement includes information that shows that a few others who were initially actively involved also criticized the development of the movement. Despite his occasional frustration, Onni Puhakka continued his criticism and attempts to get the co-operative movement to change its course and return to its ‘roots’. In the early years of the cooperative movement he probably did not differ much from the other pioneers in the sense that many of them had adopted and internalized the same values and motive for being involved that he had. However, Puhakka differed from his colleagues in the sense that he was able to believe in what he called the “fundamental values” of the co-operative movement longer than many of them.

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Carbohydrates are one of the most abundant classes of biomolecules on earth. In the initial stages of research on carbohydrates much effort was focused on investigation and determination of the structural aspects and complex nature of individual monosaccharides. Later on, development of protective group strategies and methods for oligosaccharide synthesis became the main topics of research. Today, the methodologies developed early on are being utilized in the production of carbohydrates for biological screening events. This multidisciplinary approach has generated the new discipline of glycobiology which focuses on research related to the appearance and biological significance of carbohydrates. In more detail, studies in glycobiology have revealed the essential roles of carbohydrates in cell-cell interactions, biological recognition events, protein folding, cell growth and tumor cell metastasis. As a result of these studies, carbohydrate derived diagnostic and therapeutic agents are likely to be of growing interest in the future. In this doctoral thesis, a journey through the fundamentals of carbohydrate synthesis is presented. The research conducted on this journey was neither limited to the study of any particular phenomena nor to the addressing of a single synthetic challenge. Instead, the focus was deliberately shifted from time to time in order to broaden the scope of the thesis, to continue the learning process and to explore new areas of carbohydrate research. Throughout the work, several previously reported synthetic protocols, especially procedures related to glycosylation reactions and protective group manipulations, were evaluated, modified and utilized or rejected. The synthetic molecules targeted within this thesis were either required for biological evaluations or utilized to study phenomena occuring in larger molecules. In addition, much effort was invested in the complete structural characterization of the synthesized compounds by a combination of NMR spectroscopic techniques and spectral simulations with the PERCH-software. This thesis provides the basics of working with carbohydrate chemistry. In more detail, synthetic strategies and experimental procedures for many different reactions and guidelines for the NMR-spectroscopic characterization of oligosaccharides and glycoconjugates are provided. Therefore, the thesis should prove valuable to researchers starting their own journeys in the ever expanding field of carbohydrate chemistry.