On the Rademacher maximal function

Tools known as maximal functions are frequently used in harmonic analysis when studying local behaviour of functions. Typically they measure the suprema of local averages of non-negative functions. It is essential that the size (more precisely, the L^p-norm) of the maximal function is comparable to the size of the original function. When dealing with families of operators between Banach spaces we are often forced to replace the uniform bound with the larger R-bound. Hence such a replacement is also needed in the maximal function for functions taking values in spaces of operators. More specifically, the suprema of norms of local averages (i.e. their uniform bound in the operator norm) has to be replaced by their R-bound. This procedure gives us the Rademacher maximal function, which was introduced by Hytönen, McIntosh and Portal in order to prove a certain vector-valued Carleson's embedding theorem. They noticed that the sizes of an operator-valued function and its Rademacher maximal function are comparable for many common range spaces, but not for all. Certain requirements on the type and cotype of the spaces involved are necessary for this comparability, henceforth referred to as the “RMF-property”. It was shown, that other objects and parameters appearing in the definition, such as the domain of functions and the exponent p of the norm, make no difference to this. After a short introduction to randomized norms and geometry in Banach spaces we study the Rademacher maximal function on Euclidean spaces. The requirements on the type and cotype are considered, providing examples of spaces without RMF. L^p-spaces are shown to have RMF not only for p greater or equal to 2 (when it is trivial) but also for 1 < p < 2. A dyadic version of Carleson's embedding theorem is proven for scalar- and operator-valued functions. As the analysis with dyadic cubes can be generalized to filtrations on sigma-finite measure spaces, we consider the Rademacher maximal function in this case as well. It turns out that the RMF-property is independent of the filtration and the underlying measure space and that it is enough to consider very simple ones known as Haar filtrations. Scalar- and operator-valued analogues of Carleson's embedding theorem are also provided. With the RMF-property proven independent of the underlying measure space, we can use probabilistic notions and formulate it for martingales. Following a similar result for UMD-spaces, a weak type inequality is shown to be (necessary and) sufficient for the RMF-property. The RMF-property is also studied using concave functions giving yet another proof of its independence from various parameters.

High-quality polar UV measurements : scientific analyses and transfer of the irradiance scale

The Earth's ecosystems are protected from the dangerous part of the solar ultraviolet (UV) radiation by stratospheric ozone, which absorbs most of the harmful UV wavelengths. Severe depletion of stratospheric ozone has been observed in the Antarctic region, and to a lesser extent in the Arctic and midlatitudes. Concern about the effects of increasing UV radiation on human beings and the natural environment has led to ground based monitoring of UV radiation. In order to achieve high-quality UV time series for scientific analyses, proper quality control (QC) and quality assurance (QA) procedures have to be followed. In this work, practices of QC and QA are developed for Brewer spectroradiometers and NILU-UV multifilter radiometers, which measure in the Arctic and Antarctic regions, respectively. These practices are applicable to other UV instruments as well. The spectral features and the effect of different factors affecting UV radiation were studied for the spectral UV time series at Sodankylä. The QA of the Finnish Meteorological Institute's (FMI) two Brewer spectroradiometers included daily maintenance, laboratory characterizations, the calculation of long-term spectral responsivity, data processing and quality assessment. New methods for the cosine correction, the temperature correction and the calculation of long-term changes of spectral responsivity were developed. Reconstructed UV irradiances were used as a QA tool for spectroradiometer data. The actual cosine correction factor was found to vary between 1.08-1.12 and 1.08-1.13. The temperature characterization showed a linear temperature dependence between the instrument's internal temperature and the photon counts per cycle. Both Brewers have participated in international spectroradiometer comparisons and have shown good stability. The differences between the Brewers and the portable reference spectroradiometer QASUME have been within 5% during 2002-2010. The features of the spectral UV radiation time series at Sodankylä were analysed for the time period 1990-2001. No statistically significant long-term changes in UV irradiances were found, and the results were strongly dependent on the time period studied. Ozone was the dominant factor affecting UV radiation during the springtime, whereas clouds played a more important role during the summertime. During this work, the Antarctic NILU-UV multifilter radiometer network was established by the Instituto Nacional de Meteorogía (INM) as a joint Spanish-Argentinian-Finnish cooperation project. As part of this work, the QC/QA practices of the network were developed. They included training of the operators, daily maintenance, regular lamp tests and solar comparisons with the travelling reference instrument. Drifts of up to 35% in the sensitivity of the channels of the NILU-UV multifilter radiometers were found during the first four years of operation. This work emphasized the importance of proper QC/QA, including regular lamp tests, for the multifilter radiometers also. The effect of the drifts were corrected by a method scaling the site NILU-UV channels to those of the travelling reference NILU-UV. After correction, the mean ratios of erythemally-weighted UV dose rates measured during solar comparisons between the reference NILU-UV and the site NILU-UVs were 1.007±0.011 and 1.012±0.012 for Ushuaia and Marambio, respectively, when the solar zenith angle varied up to 80°. Solar comparisons between the NILU-UVs and spectroradiometers showed a ±5% difference near local noon time, which can be seen as proof of successful QC/QA procedures and transfer of irradiance scales. This work also showed that UV measurements made in the Arctic and Antarctic can be comparable with each other.

Quantum Space-Time and Noncommutative Gauge Field Theories

Arguments arising from quantum mechanics and gravitation theory as well as from string theory, indicate that the description of space-time as a continuous manifold is not adequate at very short distances. An important candidate for the description of space-time at such scales is provided by noncommutative space-time where the coordinates are promoted to noncommuting operators. Thus, the study of quantum field theory in noncommutative space-time provides an interesting interface where ordinary field theoretic tools can be used to study the properties of quantum spacetime. The three original publications in this thesis encompass various aspects in the still developing area of noncommutative quantum field theory, ranging from fundamental concepts to model building. One of the key features of noncommutative space-time is the apparent loss of Lorentz invariance that has been addressed in different ways in the literature. One recently developed approach is to eliminate the Lorentz violating effects by integrating over the parameter of noncommutativity. Fundamental properties of such theories are investigated in this thesis. Another issue addressed is model building, which is difficult in the noncommutative setting due to severe restrictions on the possible gauge symmetries imposed by the noncommutativity of the space-time. Possible ways to relieve these restrictions are investigated and applied and a noncommutative version of the Minimal Supersymmetric Standard Model is presented. While putting the results obtained in the three original publications into their proper context, the introductory part of this thesis aims to provide an overview of the present situation in the field.

Applications of dimensional reduction to electroweak and QCD matter

When heated to high temperatures, the behavior of matter changes dramatically. The standard model fields go through phase transitions, where the strongly interacting quarks and gluons are liberated from their confinement to hadrons, and the Higgs field condensate melts, restoring the electroweak symmetry. The theoretical framework for describing matter at these extreme conditions is thermal field theory, combining relativistic field theory and quantum statistical mechanics. For static observables the physics is simplified at very high temperatures, and an effective three-dimensional theory can be used instead of the full four-dimensional one via a method called dimensional reduction. In this thesis dimensional reduction is applied to two distinct problems, the pressure of electroweak theory and the screening masses of mesonic operators in quantum chromodynamics (QCD). The introductory part contains a brief review of finite-temperature field theory, dimensional reduction and the central results, while the details of the computations are contained in the original research papers. The electroweak pressure is shown to converge well to a value slightly below the ideal gas result, whereas the pressure of the full standard model is dominated by the QCD pressure with worse convergence properties. For the mesonic screening masses a small positive perturbative correction is found, and the interpretation of dimensional reduction on the fermionic sector is discussed.

HALLINNONTASOJEN VÄLINEN DIALOGI JA ERITYISOPETUKSEN MUUTOS BYROKRAATTISENA INSTITUUTIONA : - Kymppikuntien loppuraportin ja Erityisopetuksen strategian sisällönanalyyttinen vertailu

The rise of Special education numbers in Finland has caused a situation where Finland s ten largest LEA s so called kymppikunnat (ten communes) have expressed their growing concern of organizing the special education in the current institutional settings. The LEA s started the conversation of redefining special education system in 2004. Their aim was to target the governments attention to the problematics of special education. By the request of the Ministry of Education the LEA s prepared a final report concerning the central questions in the Finnish special education system. On the basis of the LEA s survey it became even clearer that the legislation, funding system and curriculum are tightly linked together. The following LEA s took part into the writing process Espoo, Helsinki, Jyväskylä, Kuopio, Lahti, Lappeenranta, Tampere, Turku and Vantaa. The report was hand over to the Ministry of Education at 18.8.2006. After the delivery the Ministry organized special education development group meetings 17 times in the year 2007. The result of the LEA s report and the development meetings was a new Special Education Strategy 2007. I am observing the dialogue between administrational levels in governmental institutions change process. The research is a content analysis where I compare the Erityistä tukea tarvitsevan oppilaan opetuksen järjestämisen uudistaminen osana yhtenäistä perusopetusta- kohti laatua ja joustavuutta (The renewal of the organization of teaching for student with special educational needs as part of unified education for all - towards quality and flexibility) document to Erityisopetuksen strategia (Special education strategy) document. My aim was to find out how much of their own interests have the LEA s been able to integrate into the official governmental documentation. The data has been organized and analyzed quantitatively with Macros created as additional parts in Microsoft Excel software. The document material has also been arranged manually on sentence based categorization into an Excel matrix. The results have been theoretically viewed from the special education reform dialogue perspective, and from the angle of the change process of a bureaucratic institution. My target has been to provide a new viewpoint to the change of special education system as a bureaucratic institution. The education system has traditionally been understood as a machine bureaucracy. By the review provided in my pro gradu analysis it seems however that the administrational system in special education is more of a postmodern network bureaucracy than machine bureaucracy. The system appears to be constructed by overlapping, crossing and complex networks where things are been decided. These kinds of networks are called "governance networks . It seems that the governmental administrational - and politic levels, the third sector actors and other society s operators are mixed in decision making.

Inhomogeneous Structures in Holographic Superfluids I

We begin an investigation of inhomogeneous structures in holographic superfluids. As a first example, we study domain wall like defects in the 3+1 dimensional Einstein-Maxwell-Higgs theory, which was developed as a dual model for a holographic superconductor. In [1], we reported on such "dark solitons" in holographic superfluids. In this work, we present an extensive numerical study of their properties, working in the probe limit. We construct dark solitons for two possible condensing operators, and find that both of them share common features with their standard superfluid counterparts. However, both are characterized by two distinct coherence length scales (one for order parameter, one for charge condensate). We study the relative charge depletion factor and find that solitons in the two different condensates have very distinct depletion characteristics. We also study quasiparticle excitations above the holographic superfluid, and find that the scale of the excitations is comparable to the soliton coherence length scales.

Elämänmuutoksen, jännityksen ja asiantuntijuuden representointi Veikkaus Oy:n mainonnassa vuosina 1970— 2006

Aim of this master's thesis paper for consumer economics, is to research gambling advertisements in Finland over a period of 35 years, from 1970 to 2006. Veikkaus Oy (later Veikkaus), was founded in 1940, as one of the three licensed gambling organizations in Finland. Material for the current research comprised 1494 advertisements published by Veikkaus in newspapers and magazines at that time. Veikkaus has the exclusive licence to organize lotto games, sport games, instant games and other draw games in Finland. The other two operators, The Finnish Slot Machine Association RAY and Fintoto (on-track horse betting), were not included in the current analysis. This study has been completed according to research contract and grand by the Finnish Foundation for Gaming Research (Pelitoiminnan tutkimussäätiö). In general, advertisements reflect surrounding culture and time, and their message is built on stratified meanings, symbols and codes. Advertising draws the viewer's attention, introduces the advertised subject, and finally, affects the individual's consumption habits. However, advertisements not only work on individual level, but also influence public perception of the advertised product. Firstly, in order to assess gambling as a phenomenon, this paper discusses gambling as consumer behaviour, and also reviews history of gambling in Finland. Winning is a major feature of gambling, and dreaming about positive change of life is a centre of most gambling ads. However, perceived excitement through risk of losing can also be featured in gambling ads. Secondly, this study utilizes Veikkaus’ large advertising archives, were advertising data is analyzed by content analysis and the semiotic analysis. Two methods have been employed to support analyzing outcome in a synergistic way. Content analysis helps to achieve accuracy and comprehensiveness. Semiotic analysis allows deeper and more sensitive analysis to emerged findings and occurrences. It is important to understand the advertised product, as advertising is bound to the culture and time. Hence, to analyze advertising, it is important to understand the environment where the ads appear. Content analysis of Veikkaus data discovered the main gambling and principal advertisement style for each.period. Interestingly, nearly half of Veikkaus’ advertisements promoted topic other than “just winning the bet”. Games of change, like Lotto, typically advertised indirectly represented dreams about winning. In the category of skill gambling, features were represented as investment, and the excitement of sporting expertise was emphasized. In addition, there were a number of gambling ads that emphasize social responsibility of Veikkaus as a government guided organization. Semiotic methods were employed to further elaborate on findings of content analysis. Dreaming in the advertisements was represented by the product of symbols, (e.g. cars and homes) that were found to have significance connection with each other. Thus, advertising represents change of life obtained by the winning. Interestingly, gambling ads promoting jackpots were often representing religious symbolisms. Ads promoting social responsibility were found to be the most common during economical depression of the 90’s. Deeper analysis showed that at that time, advertisements frequently represented depression-related meanings, such as unemployment and bank loans. Skill gaming ads were often represented by sports expertise – late 90’s, their number started sky rocketing, and continued increasing until 2006 (when this study ended). One may conclude that sport betting draws its meanings from the relevant consumer culture, and from the rules and features of the betted sport.

Noncommutative Quantum Field Theory : Problem of Time and Some Applications

In this thesis the current status and some open problems of noncommutative quantum field theory are reviewed. The introduction aims to put these theories in their proper context as a part of the larger program to model the properties of quantized space-time. Throughout the thesis, special focus is put on the role of noncommutative time and how its nonlocal nature presents us with problems. Applications in scalar field theories as well as in gauge field theories are presented. The infinite nonlocality of space-time introduced by the noncommutative coordinate operators leads to interesting structure and new physics. High energy and low energy scales are mixed, causality and unitarity are threatened and in gauge theory the tools for model building are drastically reduced. As a case study in noncommutative gauge theory, the Dirac quantization condition of magnetic monopoles is examined with the conclusion that, at least in perturbation theory, it cannot be fulfilled in noncommutative space.

The Tourism-Development Nexus in Namibia : A Study on National Tourism Policy and Local Tourism Enterprises' Policy Knowledge

The tourism development nexus in southern Africa involves highly topical issues related to tourism planning, power relations, community participation, and natural resources. Namibia offers a particularly interesting context for the study of these issues due to its colonial legacy, vast tourism potential, recently adopted tourism policy and community-based approaches to tourism and natural resource management. This study is an interdisciplinary endeavour to analyse the role of tourism in Namibia s post-apartheid transformation process by focusing on Namibian tourism policy and local tourism enterprises' policy knowledge. Major attention is paid to how the tourism policy's national development objectives are understood and conceptualised by the representatives of different tourism enterprises and the ways in which they relate to the practical needs of the enterprises. Through such local policy knowledge the study explores various opportunities, challenges and constraints related to the promotion of tourism as a development strategy. The study utilises a political economy approach to tourism and development through three current and interrelated discourses which are relevant in the Namibian context. These are tourism, power and inequality, tourism and sustainable development, and tourism and poverty reduction. The qualitative research material was gathered in Namibia in 2006-2007 and 2008. This material consists of 34 semi-structured interviews in 16 tourism enterprises, including private trophy hunting farms and private lodges, small tour operators and community-based tourism enterprises. In addition, the research material consists of observations in the enterprises, and 37 informal and 23 expert interviews. The findings indicate that in the light of local tourism enterprises the tourism policy objectives appear more complex and ambiguous. Furthermore, they involve multiple meanings and interpretations which reflect the socio-economic stratification of the informants and Namibian society, together with the professional stratification of the tourism enterprises and restrictions on the capacity of tourism to address the development objectives. In the light of such findings it is obvious that aspects of power and inequality affect the tourism development nexus in Namibia. The study concludes that, as in the case of other southern African countries, in order to promote sustainable development and reduce poverty, Namibia should not only target tourism growth but pay attention to who benefits from that growth and how. From a political economy point of view, it is important that prevailing structural challenges are addressed equally in the planning of tourism, development and natural resource management. Such approach would help the Namibian majority to enjoy the benefits of increasing tourism in the country.

Diakoniatyön paikka ihmisten arjessa

This study examines the diaconia work of the Finnish Evangelical Lutheran Church from the standpoint of clients. The role of diaconia work has grown since the early 1990s recession, and since it established itself as one of the actors along with other social organizations. Previous studies have described the changing role of diaconal work, especially from the standpoint of diaconia workers and co-operators. This research goes back to examine, beyond the activities of the diaconia work of everyday practices, its relations of ruling which are determining practices. The theoretical and methodological framework rises from the thinking of Dorothy E. Smith, the creator of institutional ethnography. Its origins are in feminism, Marxism, phenomenology, etnomethodology, and symbolic interactionism. However, it does not represent any school. Unlike the objectivity-based traditional sociology, institutional ethnography has its starting point in everyday life, and people s subjective experience of it. Everyday life is just a starting point, and is used to examine everyday life s experiences of hidden relations of ruling, linking people and organizations. The level of generalization is just on the relations of ruling. The research task is to examine those meanings of diaconia work which are embedded in its clients experiences. The research task is investigated with two questions: how diaconia work among its clients takes shape and what kinds of relations of ruling exist in diaconia work. The meanings of diaconia work come through an examination of the relations of ruling, which create new forms of diaconal work compared with previous studies. For the study, two kinds of data were collected: a questionnaire and ethnographic fieldwork. The first data set was collected from diaconal workers using the questionnaire. It gives background information of the diaconia work process from the standpoint of the clients. In the ethnographic study there were two phases. The first ethnographic material was collected from one local parish by observing, interviewing clients and diaconal workers and gathering documents. The number of observations was 36 customer appointments, and 29 interviews. The second ethnographic material was included as a part of the analysis, in which ruling relations in people s experiences were collected from the transcribed data. Close reading and narrative analysis are used as analysing methods. The analysis has three phases. First, the experiences are identified with close reading; the following step is to select some of the institutional processes that are shaping those experiences and are relevant for the research. At the third stage, those processes are investigated in order to describe analytically how they determine people s experience. The analysis produces another narrative about diaconia work, which provides tools for examining the diaconal work from a new perspective. Through the analysis it is possible to see diaconia as an exchange ratio, in which the exchange takes place between a client and a diaconia worker, but also more broadly with other actors, such as social workers, shop clerks, or with other parishioners. The exchange ratio is examined from the perspective of power which is embedded in the client s experiences. The analysis reveals that the most important relations of ruling are humiliation and randomness in the exchange ratio of diaconia work; valuating spirituality above the bodily being; and replacing official social work. The results give a map about the relations of ruling of diaconia work which gives tools to look at diaconia work s meanings to the clients. The hidden element of humiliation in the exchange ratio breaks the current picture of diaconia work. The ethos of the holistic encounters and empathic practices are shown to be of another kind when spirituality is preferred to the bodily being. Nevertheless, diaconia appears to be a place for a respectful encounter, especially in situations where the public sector s actors are retreating on liability or clients are in a life crisis. The collapse of the welfare state structures imposes on diaconia work tasks that have not previously belonged to it. At the local level, clients receive partners from diaconia workers in order to advocate them in the welfare system. Actions to influence the wider societal structures are not reached because of lacking resources. An awareness of the oppressive practices of diaconia work and their critical reviewing are the keys to the development of diaconia work, since there are such practices even in holistic and respectful diaconia work. While the research raises new information for the development of diaconia work, it also opens up new aspects for developing other kinds of social work by emphasizing the importance of taking people s experiences seriously. Keywords: diaconia work, institutional ethnography, Dorothy E. Smith, experience, customer, relations of ruling.

Global, Local and Vector-Valued Tb Theorems on Non-Homogeneous Metric Spaces

Various Tb theorems play a key role in the modern harmonic analysis. They provide characterizations for the boundedness of Calderón-Zygmund type singular integral operators. The general philosophy is that to conclude the boundedness of an operator T on some function space, one needs only to test it on some suitable function b. The main object of this dissertation is to prove very general Tb theorems. The dissertation consists of four research articles and an introductory part. The framework is general with respect to the domain (a metric space), the measure (an upper doubling measure) and the range (a UMD Banach space). Moreover, the used testing conditions are weak. In the first article a (global) Tb theorem on non-homogeneous metric spaces is proved. One of the main technical components is the construction of a randomization procedure for the metric dyadic cubes. The difficulty lies in the fact that metric spaces do not, in general, have a translation group. Also, the measures considered are more general than in the existing literature. This generality is genuinely important for some applications, including the result of Volberg and Wick concerning the characterization of measures for which the analytic Besov-Sobolev space embeds continuously into the space of square integrable functions. In the second article a vector-valued extension of the main result of the first article is considered. This theorem is a new contribution to the vector-valued literature, since previously such general domains and measures were not allowed. The third article deals with local Tb theorems both in the homogeneous and non-homogeneous situations. A modified version of the general non-homogeneous proof technique of Nazarov, Treil and Volberg is extended to cover the case of upper doubling measures. This technique is also used in the homogeneous setting to prove local Tb theorems with weak testing conditions introduced by Auscher, Hofmann, Muscalu, Tao and Thiele. This gives a completely new and direct proof of such results utilizing the full force of non-homogeneous analysis. The final article has to do with sharp weighted theory for maximal truncations of Calderón-Zygmund operators. This includes a reduction to certain Sawyer-type testing conditions, which are in the spirit of Tb theorems and thus of the dissertation. The article extends the sharp bounds previously known only for untruncated operators, and also proves sharp weak type results, which are new even for untruncated operators. New techniques are introduced to overcome the difficulties introduced by the non-linearity of maximal truncations.

A maximal operator, Carleson's embedding, and tent spaces for vector-valued functions

This thesis is concerned with the area of vector-valued Harmonic Analysis, where the central theme is to determine how results from classical Harmonic Analysis generalize to functions with values in an infinite dimensional Banach space. The work consists of three articles and an introduction. The first article studies the Rademacher maximal function that was originally defined by T. Hytönen, A. McIntosh and P. Portal in 2008 in order to prove a vector-valued version of Carleson's embedding theorem. The boundedness of the corresponding maximal operator on Lebesgue-(Bochner) -spaces defines the RMF-property of the range space. It is shown that the RMF-property is equivalent to a weak type inequality, which does not depend for instance on the integrability exponent, hence providing more flexibility for the RMF-property. The second article, which is written in collaboration with T. Hytönen, studies a vector-valued Carleson's embedding theorem with respect to filtrations. An earlier proof of the dyadic version assumed that the range space satisfies a certain geometric type condition, which this article shows to be also necessary. The third article deals with a vector-valued generalizations of tent spaces, originally defined by R. R. Coifman, Y. Meyer and E. M. Stein in the 80's, and concerns especially the ones related to square functions. A natural assumption on the range space is then the UMD-property. The main result is an atomic decomposition for tent spaces with integrability exponent one. In order to suit the stochastic integrals appearing in the vector-valued formulation, the proof is based on a geometric lemma for cones and differs essentially from the classical proof. Vector-valued tent spaces have also found applications in functional calculi for bisectorial operators. In the introduction these three themes come together when studying paraproduct operators for vector-valued functions. The Rademacher maximal function and Carleson's embedding theorem were applied already by Hytönen, McIntosh and Portal in order to prove boundedness for the dyadic paraproduct operator on Lebesgue-Bochner -spaces assuming that the range space satisfies both UMD- and RMF-properties. Whether UMD implies RMF is thus an interesting question. Tent spaces, on the other hand, provide a method to study continuous time paraproduct operators, although the RMF-property is not yet understood in the framework of tent spaces.