Quasiconformal mappings and inequalities involving special functions

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.

I volontari italiani nelle Waffen-SS. Il pensiero politico, la formazione culturale e le motivazioni al volontariato. Una storia orale

My doctoral dissertation examines the experiences of the Italian volunteers in the Waffen-SS troops using in-depth interviews with former volunteers as the main primary source. This phenomenon, even if significant in size (depending on the source, some 15 000-20 000 Italian men volunteered in the Waffen-SS), has been hitherto largely unknown to historical research. The available literature on the Italian volunteers, mainly written by military history enthusiast journalists and methodologically weak, concentrates mainly on the combat operations and military organization, and offers a rather stereotypical profile of the volunteers. My dissertation does not aim to reconstruct the military history of the different divisions of the Waffen-SS in which Italian volunteers operated but instead to examine the subjective, private and intimate experience of the volunteers in order to understand the motivations, attitudes, beliefs and cultural and family background, as well as their political ideas. The main objective of my doctoral dissertation is to discover the ideological precepts of the volunteers’ political credo. As the last phase of fascism and its ideology, often defined as the “Germanisation” or “Nazification” of fascism, is still the object of wide academic debate, a better understanding of the volunteers’ ideology also contributes to deepening overall knowledge of the nature of this last phase. The theoretical frame of my dissertation lies in oral history, in particular in the postmodernist approach to oral history, through which I reconstruct the volunteers’ ideology. In-depth interviews with former volunteers are the main primary source, but multiple data collection methods have been adopted. Phone interviews and correspondence with the volunteers have also been considered as primary sources. In addition to interviews and correspondence, family archives consisting of diaries, correspondence with the volunteers’ relatives and photographic material have also been collected and examined. An ethnographic observation of the volunteers’ domestic spaces has been conducted during the in-depth interviews, and photo self-elicitation techniques have been used in cases where the volunteers were willing to share their photographs. An exhaustive portrait of the ideological structure of the volunteers has been obtained, as well as of the cultural and social origins of the values that contributed to the rise and adoption of this ideology. Further, the volunteers’ motivations to enlist have been clearly reconstructed, together with their cultural, political, social and military backgrounds. The results of the research are particularly relevant both for comprehension of the Italian phenomenon of volunteering in the Waffen-SS and for the reconstruction of the ideological dynamics of the last phase of fascism. The volunteers’ political and ideological system, which can be defined as the Italian SS-fascist ideology, disagrees strongly with the vaguely described ideological profile offered by previous studies that describe volunteers as generically “super-fascist”. The research also offers the opportunity for a deeper understanding of the final fascist ideological trajectory, currently defined, not without a certain level of approximation, as the “Germanisation” or “Nazification” of fascist ideology.

Jeg strikker, derfor er jeg! : læring og identitet i uformelle læringsrum

The dissertation ´I knit, therefore I am!´ Learning and identity in informal space has two main purposes. The first purpose being an investigation of how new value attributions and thinking can generate novel and usable knowledge to the field of craftsmanship, and the second purpose being a display of a different and overlooked philosophical and cultural potential in a reflexive mode of expression, which is able to reflect the normative comprehension of craftsmanship. The dissertation focuses on learning and identity in informal spaces of learning and how it is possible to relate such a learning perspective to crafts training in educational establishments. The empirical foundation of this dissertation is ‘craftivism’. In the dissertation activists from the Nordic countries have been interviewed about what they do when they put up their textile graffiti on lamp posts and house walls. Three research problems are presented: 1) What stories do people who work as crafts activists, tell about ways of relating and methods of action when they make crafts? 2) What do these stories tell about learning and identity? 3) How may the research results influence training and education in craftsmanship? These questions are being asked in order to acquire new knowledge in two aspects; first aspect being knowledge about crafts in relation to techniques, tradition and the objects in crafts, and the second aspect being knowledge about learning and identity in informal spaces of learning. The dissertations theoretical foundation is post structural and sociocultural combined with hermeneutical-inspired qualitative interviews. The author’s position and pre-understanding is subject to discussion in relation to the informant; the performing activist, as the background for both of them is craftsmanship. Starting from cultural studies, it is possible to see the activist subject’s conditions of possibilities in the culture, as the activism of the sub-cultural phenomenon’s craft lights up through a performing approach to the individual’s actions. First the research material has been analysed for events of textile graffiti and possible themes in the events, after which the results have been summarised. Next the research material has been analysed for events about learning and identity due to the author’s wish of comprehending the background of and motivational force in activism. The analysis is divided in main perspectives with different dimensions. The results of the analysis show the activist subject’s construction of an individual who actively takes part in a community by e.g. creating joy, changing the world’s perception of sustainability or by feminizing the public space. By taking crafts over the borders (and away from the class room) crafts become contextualized in a novel fashion thus obtaining an independent status. In this fashion the dissertation writes itself into a new method of comprehending and performing traditional craftsmanship techniques.

Semantic and fuzzy modelling for human behaviour recognition in smart spaces : a case study on ambient assisted living.

Human activity recognition in everyday environments is a critical, but challenging task in Ambient Intelligence applications to achieve proper Ambient Assisted Living, and key challenges still remain to be dealt with to realize robust methods. One of the major limitations of the Ambient Intelligence systems today is the lack of semantic models of those activities on the environment, so that the system can recognize the speci c activity being performed by the user(s) and act accordingly. In this context, this thesis addresses the general problem of knowledge representation in Smart Spaces. The main objective is to develop knowledge-based models, equipped with semantics to learn, infer and monitor human behaviours in Smart Spaces. Moreover, it is easy to recognize that some aspects of this problem have a high degree of uncertainty, and therefore, the developed models must be equipped with mechanisms to manage this type of information. A fuzzy ontology and a semantic hybrid system are presented to allow modelling and recognition of a set of complex real-life scenarios where vagueness and uncertainty are inherent to the human nature of the users that perform it. The handling of uncertain, incomplete and vague data (i.e., missing sensor readings and activity execution variations, since human behaviour is non-deterministic) is approached for the rst time through a fuzzy ontology validated on real-time settings within a hybrid data-driven and knowledgebased architecture. The semantics of activities, sub-activities and real-time object interaction are taken into consideration. The proposed framework consists of two main modules: the low-level sub-activity recognizer and the high-level activity recognizer. The rst module detects sub-activities (i.e., actions or basic activities) that take input data directly from a depth sensor (Kinect). The main contribution of this thesis tackles the second component of the hybrid system, which lays on top of the previous one, in a superior level of abstraction, and acquires the input data from the rst module's output, and executes ontological inference to provide users, activities and their in uence in the environment, with semantics. This component is thus knowledge-based, and a fuzzy ontology was designed to model the high-level activities. Since activity recognition requires context-awareness and the ability to discriminate among activities in di erent environments, the semantic framework allows for modelling common-sense knowledge in the form of a rule-based system that supports expressions close to natural language in the form of fuzzy linguistic labels. The framework advantages have been evaluated with a challenging and new public dataset, CAD-120, achieving an accuracy of 90.1% and 91.1% respectively for low and high-level activities. This entails an improvement over both, entirely data-driven approaches, and merely ontology-based approaches. As an added value, for the system to be su ciently simple and exible to be managed by non-expert users, and thus, facilitate the transfer of research to industry, a development framework composed by a programming toolbox, a hybrid crisp and fuzzy architecture, and graphical models to represent and con gure human behaviour in Smart Spaces, were developed in order to provide the framework with more usability in the nal application. As a result, human behaviour recognition can help assisting people with special needs such as in healthcare, independent elderly living, in remote rehabilitation monitoring, industrial process guideline control, and many other cases. This thesis shows use cases in these areas.

Remote Observation of Radioactive Permit-Required Confined Spaces – Case: Posiva Oy’s Fuel Handling Cell

Posiva Oy’s final disposal facility’s encapsulation plant will start to operate in the 2020s. Once the operation starts, the facility is designed to run more than a hundred years. The encapsulation plant will be first of its kind in the world, being part of the solution to solve a global issue of final disposal of nuclear waste. In the encapsulation plant’s fuel handling cell the spent nuclear fuel will be processed to be deposited into the Finnish bedrock, into ONKALO. In the fuel handling cell, the environment is highly radioactive forming a permit-required enclosed space. Remote observation is needed in order to monitor the fuel handling process. The purpose of this thesis is to map (Part I) and compare (Part II) remote observation methods to observe Posiva Oy’s fuel handling cell’s process, and provide a possible theoretical solution for this case. Secondary purpose for this thesis is to provide resources for other remote observation cases, as well as to inform about possible future technology to enable readiness in the design of the encapsulation plant. The approach was to theoretically analyze the mapped remote observation methods. Firstly, the methods were filtered by three environmental challenges. These are the high levels of radiation, the permit-required confined space and the hundred year timespan. Secondly, the most promising methods were selected by the experts designing the facility. Thirdly, a customized feasibility analysis was created and performed on the selected methods to rank the methods with scores. The results are the mapped methods and the feasibility analysis scores. The three highest scoring methods were radiation tolerant camera, fiberscope and audio feed. A combination of these three methods was given as a possible theoretical solution for this case. As this case is first in the world, remote observation methods for it had not been thoroughly researched. The findings in this thesis will act as initial data for the design of the fuel handling cell’s remote observation systems and can potentially effect on the overall design of the facility by providing unique and case specific information. In addition, this thesis could provide resources for other remote observation cases.