37 resultados para Numbers, Complex.


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Fuzzy subsets and fuzzy subgroups are basic concepts in fuzzy mathematics. We shall concentrate on fuzzy subgroups dealing with some of their algebraic, topological and complex analytical properties. Explorations are theoretical belonging to pure mathematics. One of our ideas is to show how widely fuzzy subgroups can be used in mathematics, which brings out the wealth of this concept. In complex analysis we focus on Möbius transformations, combining them with fuzzy subgroups in the algebraic and topological sense. We also survey MV spaces with or without a link to fuzzy subgroups. Spectral space is known in MV algebra. We are interested in its topological properties in MV-semilinear space. Later on, we shall study MV algebras in connection with Riemann surfaces. In fact, the Riemann surface as a concept belongs to complex analysis. On the other hand, Möbius transformations form a part of the theory of Riemann surfaces. In general, this work gives a good understanding how it is possible to fit together different fields of mathematics.

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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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HTSC materials are relevant in modern microelectronics, because of their transformation from the normal state to the superconducting. That is why the idea of producing HTSC in industrial amounts is actual nowadays. To decrease cost of their production it is important to use magnetron sputtering systems which give the best results for essential parameters. Modeling is the simplest and the fastest way to determine optimum sputtering condition. This thesis concentrates on determination the phases of the whole sputtering process and to find out basic factors of each phase using the modeling. It was find out, that the main factors which influence on the mode of occurrence of the initial stages are the current density of the magnetron discharge and the pressure of sputtering gas. With the modeling also velocity dependences were obtained for YBCO and SmFeAsO. These were compared and difference between them was examined. To support represented model comparison was made with experimental results. This showed that the model gives good results, very similar to the experimental ones. The results of this work were published in annual conference of the finnish physical society.

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In this work a fuzzy linear system is used to solve Leontief input-output model with fuzzy entries. For solving this model, we assume that the consumption matrix from di erent sectors of the economy and demand are known. These assumptions heavily depend on the information obtained from the industries. Hence uncertainties are involved in this information. The aim of this work is to model these uncertainties and to address them by fuzzy entries such as fuzzy numbers and LR-type fuzzy numbers (triangular and trapezoidal). Fuzzy linear system has been developed using fuzzy data and it is solved using Gauss-Seidel algorithm. Numerical examples show the e ciency of this algorithm. The famous example from Prof. Leontief, where he solved the production levels for U.S. economy in 1958, is also further analyzed.

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Since its introduction, fuzzy set theory has become a useful tool in the mathematical modelling of problems in Operations Research and many other fields. The number of applications is growing continuously. In this thesis we investigate a special type of fuzzy set, namely fuzzy numbers. Fuzzy numbers (which will be considered in the thesis as possibility distributions) have been widely used in quantitative analysis in recent decades. In this work two measures of interactivity are defined for fuzzy numbers, the possibilistic correlation and correlation ratio. We focus on both the theoretical and practical applications of these new indices. The approach is based on the level-sets of the fuzzy numbers and on the concept of the joint distribution of marginal possibility distributions. The measures possess similar properties to the corresponding probabilistic correlation and correlation ratio. The connections to real life decision making problems are emphasized focusing on the financial applications. We extend the definitions of possibilistic mean value, variance, covariance and correlation to quasi fuzzy numbers and prove necessary and sufficient conditions for the finiteness of possibilistic mean value and variance. The connection between the concepts of probabilistic and possibilistic correlation is investigated using an exponential distribution. The use of fuzzy numbers in practical applications is demonstrated by the Fuzzy Pay-Off method. This model for real option valuation is based on findings from earlier real option valuation models. We illustrate the use of number of different types of fuzzy numbers and mean value concepts with the method and provide a real life application.

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According to several surveys and observations, the percentage of successfully conducted IT projects without over-budgeting and delays in time schedule are extremely low. Many projects also are evaluated as failures in terms of delivered functionality. Nuldén (1996) compares IT projects with bad movies; after watching for 2 hours, one still tries to finish it even though one understands that it is a complete waste of time. The argument for that is 'I've already invested too much time to terminate it now'. The same happens with IT projects: sometimes the company continues wasting money on these projects for a long time, even though there are no expected benefits from these projects. Eventually these projects are terminated anyway, but until this moment, the company spends a lot. The situation described above is a consequence of “escalation of commitment” - project continuation even after a manager receives negative feedback of the project’s success probability. According to Keil and Mähring (2010), even though escalation can occur in any type of project, it is more common among complex technological projects, such as IT projects. Escalation of commitment very often results in runaway projects. In order to avoid it, managers use de-escalation strategies, which allow the resources to be used in more effective. These strategies lead to project termination or turning around, which stops the flow of wasted investments. Numbers of researches explore escalation of commitment phenomena based on experiments and business cases. Moreover, during the last decade several frameworks were proposed for de-escalation strategy. However, there is no evidence of successful implementation of the de-escalation of commitment strategy in the literature. In addition, despite that fact that IT project management methodologies are widely used in the companies, none of them cover the topic of escalation of commitment risks. At the same time, there are no researches proposing the way to implement de-escalation of commitment strategy into the existing project management methodology The research is focused on a single case of large ERP implementation project by the consulting company. Hence, the main deliverables of the study include suggestions of improvement in de-escalation methods and techniques in the project and in the company. Moreover, the way to implement these methods into existing project management methodology and into the company general policies is found.

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Oxidized starch is a key component in the paper industry, where it is used as both surfacing sizer and filler. Large quantities are annually used for this purpose; however, the methods for the oxidation are not environmentally friendly. In our research, we have studied the possibility to replace the harmful oxidation agents, such as hypochlorite or iodates and transition metal catalysts, with a more environmentally friendly oxidant, hydrogen peroxide (H2O2), and a special metal complex catalyst (FePcS), of which only a small amount is needed. The work comprised batch and semi-batch studies by H2O2, ultrasound studies of starch particles, determination of low-molecular by-products and determination of the decomposition kinetics of H2O2 in the presence of starch and the catalyst. This resulted in a waste-free oxidation method, which only produces water and oxygen as side products. The starch oxidation was studied in both semi-batch and batch modes in respective to the oxidant (H2O2) addition. The semi-batch mode proved to yield a sufficient degree of substitution (COOH groups) for industrial purposes. Treatment of starch granules by ultrasound was found to improve the reactivity of starch. The kinetic results were found out to have a rather complex pattern – several oxidation phases were observed, apparently due to the fact that the oxidation reaction in the beginning only took place on the surface, whereas after a prolonged reaction time, partial degradation of the solid starch granules allowed further reaction in the interior parts. Batch-mode experiments enabled a more detailed study of the mechanisms of starch in the presence of H2O2 and the catalyst, but yielded less oxidized starch due to rapid decomposition of H2O2 due to its high concentrations. The effect of the solid-liquid (S/L) ratio in the reaction system was studied in batch experiments. These studies revealed that the presence of the catalyst and the starch enhance the H2O2 decomposition.

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The thesis presents results obtained during the authors PhD-studies. First systems of language equations of a simple form consisting of just two equations are proved to be computationally universal. These are systems over unary alphabet, that are seen as systems of equations over natural numbers. The systems contain only an equation X+A=B and an equation X+X+C=X+X+D, where A, B, C and D are eventually periodic constants. It is proved that for every recursive set S there exists natural numbers p and d, and eventually periodic sets A, B, C and D such that a number n is in S if and only if np+d is in the unique solution of the abovementioned system of two equations, so all recursive sets can be represented in an encoded form. It is also proved that all recursive sets cannot be represented as they are, so the encoding is really needed. Furthermore, it is proved that the family of languages generated by Boolean grammars is closed under injective gsm-mappings and inverse gsm-mappings. The arguments apply also for the families of unambiguous Boolean languages, conjunctive languages and unambiguous languages. Finally, characterizations for morphisims preserving subfamilies of context-free languages are presented. It is shown that the families of deterministic and LL context-free languages are closed under codes if and only if they are of bounded deciphering delay. These families are also closed under non-codes, if they map every letter into a submonoid generated by a single word. The family of unambiguous context-free languages is closed under all codes and under the same non-codes as the families of deterministic and LL context-free languages.

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The Travel and Tourism field is undergoing changes due to the rapid development of information technology and digital services. Online travel has profoundly changed the way travel and tourism organizations interact with their customers. Mobile technology such as mobile services for pocket devices (e.g. mobile phones) has the potential to take this development even further. Nevertheless, many issues have been highlighted since the early days of mobile services development (e.g. the lack of relevance, ease of use of many services). However, the wide adoption of smartphones and the mobile Internet in many countries as well as the formation of so-called ecosystems between vendors of mobile technology indicate that many of these issues have been overcome. Also when looking at the numbers of downloaded applications related to travel in application stores like Google Play, it seems obvious that mobile travel and tourism services are adopted and used by many individuals. However, as business is expected to start booming in the mobile era, many issues have a tendency to be overlooked. Travelers are generally on the go and thus services that work effectively in mobile settings (e.g. during a trip) are essential. Hence, the individuals’ perceived drivers and barriers to use mobile travel and tourism services in on-site or during trip settings seem particularly valuable to understand; thus this is one primary aim of the thesis. We are, however, also interested in understanding different types of mobile travel service users. Individuals may indeed be very different in their propensity to adopt and use technology based innovations (services). Research is also switching more from investigating issues of mobile service development to understanding individuals’ usage patterns of mobile services. But designing new mobile services may be a complex matter from a service provider perspective. Hence, our secondary aim is to provide insights into drivers and barriers of mobile travel and tourism service development from a holistic business model perspective. To accomplish the research objectives seven different studies have been conducted over a time period from 2002 – 2013. The studies are founded on and contribute to theories within diffusion of innovations, technology acceptance, value creation, user experience and business model development. Several different research methods are utilized: surveys, field and laboratory experiments and action research. The findings suggest that a successful mobile travel and tourism service is a service which supports one or several mobile motives (needs) of individuals such as spontaneous needs, time-critical arrangements, efficiency ambitions, mobility related needs (location features) and entertainment needs. The service could be customized to support travelers’ style of traveling (e.g. organized travel or independent travel) and should be easy to use, especially easy to take into use (access, install and learn) during a trip, without causing security concerns and/or financial risks for the user. In fact, the findings suggest that the most prominent barrier to the use of mobile travel and tourism services during a trip is an individual’s perceived financial cost (entry costs and usage costs). It should, however, be noted that regulations are put in place in the EU regarding data roaming prices between European countries and national telecom operators are starting to see ‘international data subscriptions’ as a sales advantage (e.g. Finnish Sonera provides a data subscription in the Baltic and Nordic region at the same price as in Finland), which will enhance the adoption of mobile travel and tourism services also in international contexts. In order to speed up the adoption rate travel service providers could consider e.g. more local initiatives of free Wi-Fi networks, development of services that can be used, at least to some extent, in an offline mode (do not require costly network access during a trip) and cooperation with telecom operators (e.g. lower usage costs for travelers who use specific mobile services or travel with specific vendors). Furthermore, based on a developed framework for user experience of mobile trip arrangements, the results show that a well-designed mobile site and/or native application, which preferably supports integration with other mobile services, is a must for true mobile presence. In fact, travel service providers who want to build a relationship with their customers need to consider a downloadable native application, but in order to be found through the mobile channel and make contact with potential new customers, a mobile website should be available. Moreover, we have made a first attempt with cluster analysis to identify user categories of mobile services in a travel and tourism context. The following four categories were identified: info-seekers, checkers, bookers and all-rounders. For example “all-rounders”, represented primarily by individuals who use their pocket device for almost any of the investigated mobile travel services, constituted primarily of 23 to 50 year old males with high travel frequency and great online experience. The results also indicate that travel service providers will increasingly become multi-channel providers. To manage multiple online channels, closely integrated and hybrid online platforms for different devices, supporting all steps in a traveler process should be considered. It could be useful for travel service providers to focus more on developing browser-based mobile services (HTML5-solutions) than native applications that work only with specific operating systems and for specific devices. Based on an action research study and utilizing a holistic business model framework called STOF we found that HTML5 as an emerging platform, at least for now, has some limitations regarding the development of the user experience and monetizing the application. In fact, a native application store (e.g. Google Play) may be a key mediator in the adoption of mobile travel and tourism services both from a traveler and a service provider perspective. Moreover, it must be remembered that many device and mobile operating system developers want service providers to specifically create services for their platforms and see native applications as a strategic advantage to sell more devices of a certain kind. The mobile telecom industry has moved into a battle of ecosystems where device makers, developers of operating systems and service developers are to some extent forced to choose their development platforms.

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The necessity of EC (Electronic Commerce) and enterprise systems integration is perceived from the integrated nature of enterprise systems. The proven benefits of EC to provide competitive advantages to the organizations force enterprises to adopt and integrate EC with their enterprise systems. Integration is a complex task to facilitate seamless flow of information and data between different systems within and across enterprises. Different systems have different platforms, thus to integrate systems with different platforms and infrastructures, integration technologies, such as middleware, SOA (Service-Oriented Architecture), ESB (Enterprise Service Bus), JCA (J2EE Connector Architecture), and B2B (Business-to-Business) integration standards are required. Huge software vendors, such as Oracle, IBM, Microsoft, and SAP suggest various solutions to address EC and enterprise systems integration problems. There are limited numbers of literature about the integration of EC and enterprise systems in detail. Most of the studies in this area have focused on the factors which influence the adoption of EC by enterprise or other studies provide limited information about a specific platform or integration methodology in general. Therefore, this thesis is conducted to cover the technical details of EC and enterprise systems integration and covers both the adoption factors and integration solutions. In this study, many literature was reviewed and different solutions were investigated. Different enterprise integration approaches as well as most popular integration technologies were investigated. Moreover, various methodologies of integrating EC and enterprise systems were studied in detail and different solutions were examined. In this study, the influential factors to adopt EC in enterprises were studied based on previous literature and categorized to technical, social, managerial, financial, and human resource factors. Moreover, integration technologies were categorized based on three levels of integration, which are data, application, and process. In addition, different integration approaches were identified and categorized based on their communication and platform. Also, different EC integration solutions were investigated and categorized based on the identified integration approaches. By considering different aspects of integration, this study is a great asset to the architectures, developers, and system integrators in order to integrate and adopt EC with enterprise systems.

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The present thesis discusses the coherence or lack of coherence in the book of Numbers, with special regard to its narrative features. The fragmented nature of Numbers is a well-known problem in research on the book, affecting how we approach and interpret it, but to date there has not been any thorough investigation of the narrative features of the work and how they might contribute to the coherence or the lack of coherence in the book. The discussion is pursued in light of narrative theory, and especially in connection to three parameters that are typically understood to be invoked in the interpretation of narratives: 1) a narrative paradigm, or ‘story,’ meaning events related to each other temporally, causally, and thematically, in a plot with a beginning, middle, and end; 2) discourse, being the expression plane of a narrative, or the devices that an author has at hand in constructing a narrative; 3) the situation or languagegame of the narrative, prototypical examples being factual reports, which seeks to depict a state of affairs, and storytelling narratives, driven by a demand for tellability. In view of these parameters the present thesis argues that it is reasonable to form four groups to describe the narrative material of Numbers: genuine narratives (e.g. Num 12), independent narrative sequences (e.g. Num 5:1-4), instrumental scenes and situations (e.g. Num 27:1-5), and narrative fragments (e.g. Num 18:1). These groups are mixed throughout with non-narrative materials. Seen together, however, the narrative features of these groups can be understood to create an attenuated narrative sequence from beginning to end in Numbers, where one thing happens after another. This sequence, termed the ‘larger story’ of Numbers, concerns the wandering of Israel from Sinai to Moab. Furthermore, the larger story has a fragmented plot. The end-point is fixed on the promised land, Israel prepares for the wandering towards it (Num 1-10), rebels against wandering and the promise and is sent back into the wilderness (Num 13-14), returns again after forty years (Num 21ff.), and prepares for conquering the land (Num 22-36). Finally, themes of the promised land, generational succession, and obedience-disobedience, operate in this larger story. Purity is also a significant theme in the book, albeit not connected to plot in the larger story. All in all, sequence, plot, and theme in the larger story of Numbers can be understood to bring some coherence to the book. However, neither aspect entirely subsumes the whole book, and the four groups of narrative materials can also be understood to underscore the incoherence of the work in differentiating its variegated narrative contents. Numbers should therefore be described as an anthology of different materials that are loosely connected through its narrative features in the larger story, with the aim of informing Israelite identity by depicting a certain period in the early history of the people.

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Plant-virus interactions are very complex in nature and lead to disease and symptom formation by causing various physiological, metabolic and developmental changes in the host plants. These interactions are mainly the outcomes of viral hijacking of host components to complete their infection cycles and of host defensive responses to restrict the viral infections. Viral genomes contain only a small number of genes often encoding for multifunctional proteins, and all are essential in establishing a viral infection. Thus, it is important to understand the specific roles of individual viral genes and their contribution to the viral life cycles. Among the most important viral proteins are the suppressors of RNA silencing (VSRs). These proteins function to suppress host defenses mediated by RNA silencing and can also serve in other functions, e.g. in viral movement, transactivation of host genes, virus replication and protein processing. Thus these proteins are likely to have a significant impact on host physiology and metabolism. In the present study, I have examined the plant-virus interactions and the effects of three different VSRs on host physiology and gene expression levels by microarray analysis of transgenic plants that express these VSR genes. I also studied the gene expression changes related to the expression of the whole genome of Tobacco mosaic virus (TMV) in transgenic tobacco plants. Expression of the VSR genes in the transgenic tobacco plants causes significant changes in the gene expression profiles. HC-Pro gene derived from the Potyvirus Y (PVY) causes alteration of 748 and 332 transcripts, AC2 gene derived from the African cassava mosaic virus (ACMV) causes alteration of 1118 and 251transcripts, and P25 gene derived from the Potyvirus X (PVX) causes alterations of 1355 and 64 transcripts in leaves and flowers, respectively. All three VSRs cause similar up-regulation in defense, hormonally regulated and different stress-related genes and down-regulation in the photosynthesis and starch metabolism related genes. They also induce alterations that are specific to each viral VSR. The phenotype and transcriptome alterations of the HC-Pro expressing transgenic plants are similar to those observed in some Potyvirus-infected plants. The plants show increased protein degradation, which may be due to the HC-Pro cysteine endopeptidase and thioredoxin activities. The AC2-expressing transgenic plants show a similar phenotype and gene expression pattern as HC-Pro-expressing plants, but also alter pathways related to jasmonic acid, ethylene and retrograde signaling. In the P25 expressing transgenic plants, high numbers of genes (total of 1355) were up-regulated in the leaves, compared to a very low number of down-regulated genes (total of 5). Despite of strong induction of the transcripts, only mild growth reduction and no other distinct phenotype was observed in these plants. As an example of whole virus interactions with its host, I also studied gene expression changes caused by Tobacco mosaic virus (TMV) in tobacco host in three different conditions, i.e. in transgenic plants that are first resistant to the virus, and then become susceptible to it and in wild type plants naturally infected with this virus. The microarray analysis revealed up and down-regulation of 1362 and 1422 transcripts in the TMV resistant young transgenic plants, and up and down-regulation of a total of 1150 and 1200 transcripts, respectively, in the older plants, after the resistance break. Natural TMV infections in wild type plants caused up-regulation of 550 transcripts and down-regulation of 480 transcripts. 124 up-regulated and 29 down-regulated transcripts were commonly altered between young and old TMV transgenic plants, and only 6 up-regulated and none of the down-regulated transcripts were commonly altered in all three plants. During the resistant stage, the strong down-regulation in translation-related transcripts (total of 750 genes) was observed. Additionally, transcripts related to the hormones, protein degradation and defense pathways, cell division and stress were distinctly altered. All these alterations may contribute to the TMV resistance in the young transgenic plants, and the resistance may also be related to RNA silencing, despite of the low viral abundance and lack of viral siRNAs or TMV methylation activity in the plants.

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Global challenges, complexity and continuous uncertainty demand development of leadership approaches, employees and multi-organisation constellations. Current leadership theories do not sufficiently address the needs of complex business environments. First of all, before successful leadership models can be applied in practice, leadership needs to shift from the industrial age to the knowledge era. Many leadership models still view leadership solely through the perspective of linear process thinking. In addition, there is not enough knowledge or experience in applying these newer models in practice. Leadership theories continue to be based on the assumption that leaders possess or have access to all the relevant knowledge and capabilities to decide future directions without external advice. In many companies, however, the workforce consists of skilled professionals whose work and related interfaces are so challenging that the leaders cannot grasp all the linked viewpoints and cross-impacts alone. One of the main objectives of this study is to understand how to support participants in organisations and their stakeholders to, through practice-based innovation processes, confront various environments. Another aim is to find effective ways of recognising and reacting to diverse contexts, so companies and other stakeholders are better able to link to knowledge flows and shared value creation processes in advancing joint value to their customers. The main research question of this dissertation is, then, to seek understanding of how to enhance leadership in complex environments. The dissertation can, on the whole, be characterised as a qualitative multiple-case study. The research questions and objectives were investigated through six studies published in international scientific journals. The main methods applied were interviews, action research and a survey. The empirical focus was on Finnish companies, and the research questions were examined in various organisations at the top levels (leaders and managers) and bottom levels (employees) in the context of collaboration between organisations and cooperation between case companies and their client organisations. However, the emphasis of the analysis is the internal and external aspects of organisations, which are conducted in practice-based innovation processes. The results of this study suggest that the Cynefin framework, complexity leadership theory and transformational leadership represent theoretical models applicable to developing leadership through practice-based innovation. In and of themselves, they all support confronting contemporary challenges, but an implementable method for organisations may be constructed by assimilating them into practice-based innovation processes. Recognition of diverse environments, their various contexts and roles in the activities and collaboration of organisations and their interest groups is ever-more important to achieving better interaction in which a strategic or formal status may be bypassed. In innovation processes, it is not necessarily the leader who is in possession of the essential knowledge; thus, it is the role of leadership to offer methods and arenas where different actors may generate advances. Enabling and supporting continuous interaction and integrated knowledge flows is of crucial importance, to achieve emergence of innovations in the activities of organisations and various forms of collaboration. The main contribution of this dissertation relates to applying these new conceptual models in practice. Empirical evidence on the relevance of different leadership roles in practice-based innovation processes in Finnish companies is another valuable contribution. Finally, the dissertation sheds light on the significance of combining complexity science with leadership and innovation theories in research.