Suomen rautakautiset kulkuset, kellot ja kelloriipukset : äänimaiseman arkeologiaa

The thesis addresses the problem of Finnish Iron Age bells, pellet bells and bell pendants, previously unexplored musical artefacts from 400–1300 AD. The study, which contributes to the field of music archaeology, aims to provide a gateway to ancient soundworlds and ideas of music making. The research questions include: Where did these metal artefacts come from? How did they sound? How were they used? What did their sound mean to the people of the Iron Age? The data collected at the National Museum of Finland and at several provincial museums covers a total of 486 bells, pellet bells and bell pendants. By means of a cluster analysis, each category was divided into several subgroups. The subgroups, which all seem to have a different dating and geographical distribution, represent a spread of both local and international manufacturing traditions. According to an elemental analysis, the material varies from iron to copper-tin, copper-lead and copper-tin-lead alloys. Clappers, pellets and pebbles prove that the bells and pellet bells were indisputably instruments intended for sound production. Clusters of small bell pendants, however, probably produced sound by jingling against each other. Spectrogram plots reveal that the partials of the still audible sounds range from 1 000 to 19 850 Hz. On the basis of 129 inhumation graves, hoards, barrows and stray finds, it seems evident that the bells, pellet bells and bell pendants were fastened to dresses and horse harnesses or carried in pouches and boxes. The resulting acoustic spaces could have been employed in constructing social hierarchies, since the instruments usually appear in richly furnished graves. Furthermore, the instruments repeatedly occur with crosses, edge tools and zoomorphic pendants that in the later Finnish-Karelian culture were regarded as prophylactic amulets. In the Iron Age as well as in later folk culture, the bell sounds seem to have expressed territorial, social and cosmological boundaries.

Signifying Angels : Analyses and Interpretations of Rautavaara s Instrumental Compositions

The subject of doctoral thesis is the analysis and interpretation of instrumental pieces composed by Einojuhani Rautavaara (b. 1928) that have been given angelic titles: Archangel Michael Fighting the Antichrist from the suite Icons (1955)/Before the Icons (2006), Angels and Visitations (1978), the Double Bass Concerto Angel of Dusk (1980), Playgrounds for Angels (1981)and the Seventh Symphony Angel of Light (1994). The aim of the work is to find those musical elements common to these pieces that distinguish them from Rautavaara s other works and to determine if they could be thought of as a series. I prove that behind the common elements and titles stands the same extramusical idea the figure of an angel that the composer has described in his commentaries. The thesis is divided into three parts. Since all of the compositions possess titles that refer to the spiritual symbol of an angel, the first part offers a theoretical background to demonstrate the significant role played by angels in various religions and beliefs, and the means by which music has attempted to represent this symbol throughout history. This background traces also Rautavaara s aesthetic attitude as a spiritual composer whose output can be studied with reference to his extramusical interests including literature, psychology, painting, philosophy and myths. The second part focuses on the analysis of the instrumental compositions with angelic titles, without giving consideration to their commentaries and titles. The analyses concentrate in particular on those musical features that distinguish these pieces from Rautavaara s other compositions. In the third part these musical features are interpreted as symbols of the angel through comparison with vocal and instrumental pieces which contain references to the character of an angel, structures of mythical narration, special musical expressions, use of instruments and aspects of brightness. Finally I explore the composer s interpretative codes, drawing on Rilke s cycle of poems Ten Duino Elegies and Jung s theory of archetypes, and analyze the instrumental pieces with angelic titles in the light of the theory of musical ekphrasis.

Writing Otherwise than Seeing : Writing and Exteriority in Maurice Blanchot

Maurice Blanchot (1907-2003), the French writer and novelist, is one of the most important figures in post-war French literature and philosophy. The main intention of this study is to figure out his position and originality in the field of phenomenology. Since this thesis concentrates on the notion of vision in Blanchot s work, its primary context is the post-war discussion of the relation between seeing and thinking in France, and particularly the discussion of the conditions of non-violent vision and language. The focus will be on the philosophical conversation between Blanchot and his contemporary philosophers. The central premise is the following: Blanchot relates the criticism of vision to the criticism of the representative model of language. In this thesis, Blanchot s definition of literary language as the refusal to reveal anything is read as a reference pointing in two directions. First, to Hegel s idea of naming as negativity which reveals Being incrementally to man, and second, to Heidegger s idea of poetry as the simultaneity of revealing and withdrawal; the aim is to prove that eventually Blanchot opposes both Hegel s idea of naming as a gradual revelation of the totality of being and Heidegger s conception of poetry as a way of revealing the truth of Being. My other central hypothesis is that for Blanchot, the criticism of the privilege of vision is always related to the problematic of the exteriority. The principal intention is to trace how Blanchot s idea of language as infinity and exteriority challenges both the Hegelian idea of naming as conceptualizing things and Heidegger s concept of language as a way to truth (as aletheia). The intention is to show how Blanchot, with his concepts of fascination, resemblance and image, both affirms and challenges the central points of Heidegger s thinking on language. Blanchot s originality in, and contribution to, the discussion about the violence of vision and language is found in his answer to the question of how to approach the other by avoiding the worst violence . I claim that by criticizing the idea of language as naming both in Hegel and Heidegger, Blanchot generates an account of language which, since it neither negates nor creates Being, is beyond the metaphysical opposition between Being and non-Being.

Kilpailukykyvaltion koululainsäädännön rakentuminen : Suomen eduskunta ja 1990-luvun koulutuspoliittinen käänne

Finnish education policy, educational legislation and the entire education system changed significantly during the 1990s as part of a general restructuring of public administration. There has been a clear divergence from the former tradition of a system of regulation, founded on detailed legislation and the principle of equality. The new governance, which is based more on individual choice, efficiency and evaluation, emphasizes that the development of a high standard of education is a necessity in the light of global competition. This study explores the legislative process regarding education policy in the Finnish Parliament during the 1990s, and highlights in particular how the international discourse on education policies was restructured in the context of Finnish legislation. The research material consists of all the public parliamentary documents relating to education, including government proposals, minutes from the discussions in the chamber and archive material (final protocols, reports and statements) for the Committee for Education and Culture. The discourse on the process of drafting and passing education legislation is modelled on three interrelated policy technologies (market, management and performance), which are understood here as mechanisms connecting general political ideas to normative legislation. The changes in the regulation of education were part of a general public administration reform instigated during the mid 1980s. The research results will prove that during the left-right coalition cabinet of PM Harri Holkeri, new policy technologies affected the parliamentary discourse on education policy. This was particularly influenced by a change in the preconditions for the management of education that was created as a result of the numerous demands to deregulate and delegate decision-making authority to the local and school levels while rendering the whole education system more effective. At the turn of the decade, market-type mechanisms were more indirectly manifested in the forms of individuality and freedom of choice, which were reflected, for example, in proposals to “lower the hurdles” by separating general from vocational secondary education with a view to encouraging students to select courses from other educational establishments, in addition to relaxing the requirements for establishing private schools and abolishing a hundred-year-old strict national catchment-area system. Later, in the course of the 1990s, after the subjects, players, and methods of evaluation had been more precisely defined, evaluation based on performance would result in the active measurement of the attainment of set objectives. In the spring of 1991, from the outset of PM Esko Aho's right-centre coalition cabinet, the education budget suffered cutbacks as a result of a global recession and this influenced the legislative work of, and discourses in, parliament. Representatives of the parties in power regarded the recession solely as an external factor that was remote from the political arena. In their view, the education system should rise to the challenge by ensuring the efficient and innovative use of the resources available and by developing new forms of indicators for evaluating results. Representatives of the opposition opposed the cabinet’s standpoint as a result of the recession, criticized the measures taken by pointing out the harmful effect of constantly cutting the budget and argued that the government had made political capital out of the recession by using it as an opportunity to give more room to market, management and performance technologies within the Finnish education system. Criticism of the new education policy became even stronger during PM Paavo Lipponen's first “rainbow” coalition cabinet with critical views being expressed not only from the opposition but also from representatives within the government. Representatives from the left demanded legislative restrictions and the instigation of measures to relieve the presumed negative effects of market, management and performance in the name of educational equality. The new management by results steering method within the university sector and the introduction of commercial education services in compulsory education were fiercely criticized. The argument over “setting outer limits” including, for example, the demands for more detailed legislation and earmarked state subsidies was characteristic of Parliament’s legislative discourse in the latter part of the 1990s. Keywords: education policy, education legislation, Parliament of Finland

Sweet potato chlorotic stunt virus: Studies on viral synergism and suppression of RNA silencing

The studies presented in this thesis aimed to a better understanding of the molecular biology of Sweet potato chlorotic stunt virus (SPCSV, Crinivirus, Closteroviridae) and its role in the development of synergistic viral diseases. The emphasis was on the severe sweet potato virus disease (SPVD) that results from a synergistic interaction of SPCSV and Sweet potato feathery mottle virus (SPFMV, Potyvirus, Potyviridae). SPVD is the most important disease affecting sweetpotato. It is manifested as a significant increase in symptom severity and SPFMV titres. This is accompanied by a dramatic sweetpotato yield reduction. SPCSV titres remain little affected in the diseased plants. Viral synergistic interactions have been associated with the suppression of an adaptive general defence mechanism discovered in plants and known as RNA silencing. In the studies of this thesis two novel proteins (RNase3 and p22) identified in the genome of a Ugandan SPCSV isolate were shown to be involved in suppression of RNA silencing. RNase3 displayed a dsRNA-specific endonuclease activity that enhanced the RNA-silencing suppression activity of p22. Comparative analyses of criniviral genomes revealed variability in the gene content at the 3´end of the genomic RNA1. Molecular analyses of different isolates of SPCSV indicated a marked intraspecific heterogeneity in this region where the p22 and RNase3 genes are located. Isolates of the East African strain of SPCSV from Tanzania and Peru and an isolate from Israel were missing a 767-nt fragment that included the p22 gene. However, regardless of the absence of p22, all SPCSV isolates acted synergistically with SPFMV in co-infected sweetpotato, enhanced SPFMV titres and caused SPVD. These results showed that p22 is dispensable for development of SPVD. The role of RNase3 in SPVD was then studied by generating transgenic plants expressing the RNase3 protein. These plants had increased titres of SPFMV (ca. 600-fold higher in comparison with nontransgenic plants) 2-3 weeks after graft inoculation and displayed the characteristic SPVD symptoms. RNA silencing suppression (RSS) activity of RNase3 was detected in agroinfiltrated leaves of Nicotiana bethamiana. In vitro studies showed that RNase3 was able to cleave small interferring RNAs (siRNA) to products of ~14-nt. The data thus identified RNase3 as a suppressor of RNA silencing able to cleave siRNAs. RNase3 expression alone was sufficient for breaking down resistance to SPFMV in sweetpotato and for the development of SPVD. Similar RNase III-like genes exist in animal viruses which points out a novel and possibly more general mechanism of RSS by viruses. A reproducible method of sweetpotato transformation was used to target RNA silencing against the SPCSV polymerase region (RdRp) with an intron-spliced hairpin construct. Hence, engineered resistance to SPCSV was obtained. Ten out of 20 transgenic events challenged with SPCSV alone showed significantly reduced virus titres. This was however not sufficient to prevent SPVD upon coinfection with SPFMV. Immunity to SPCSV seems to be required to control SPVD and targeting of different SPCSV regions need to be assessed in further studies. Based on the identified key role of RNase3 in SPVD the possibility to design constructs that target this gene might prove more efficient in future studies.

Cereulide producing B. cereus and amylosin producing B. subtilis and B. mojavensis : characterization of strains and toxigenicities

B. cereus is one of the most frequent occurring bacteria in foods . It produces several heat-labile enterotoxins and one stable non-protein toxin, cereulide (emetic), which may be pre-formed in food. Cereulide is a heat stable peptide whose structure and mechanism of action were in the past decade elucidated. Until this work, the detection of cereulide was done by biological assays. With my mentors, I developed the first quantitative chemical assay for cereulide. The assay is based on liquid chromatography (HPLC) combined with ion trap mass spectrometry and the calibration is done with valinomycin and purified cereulide. To detect and quantitate valinomycin and cereulide, their [NH4+] adducts, m/z 1128.9 and m/z 1171 respectively, were used. This was a breakthrough in the cereulide research and became a very powerful tool of investigation. This tool made it possible to prove for the first time that the toxin produced by B. cereus in heat-treated food caused human illness. Until this thesis work (Paper II), cereulide producing B. cereus strains were believed to represent a homogenous group of clonal strains. The cereulide producing strains investigated in those studies originated mostly from food poisoning incidents. We used strains of many origins and analyzed them using a polyphasic approach. We found that the cereulide producing B. cereus strains are genetically and biologically more diverse than assumed in earlier studies. The strains diverge in the adenylate kinase (adk) gene (two sequence types), in ribopatterns obtained with EcoRI and PvuII (three patterns), tyrosin decomposition, haemolysis and lecithine hydrolysis (two phenotypes). Our study was the first demonstration of diversity within the cereulide producing strains of B. cereus. To manage the risk for cereulide production in food, understanding is needed on factors that may upregulate cereulide production in a given food matrix and the environmental factors affecting it. As a contribution towards this direction, we adjusted the growth environment and measured the cereulide production by strains selected for diversity. The temperature range where cereulide is produced was narrower than that for growth for most of the producer strains. Most cereulide was by most strains produced at room temperature (20 - 23ºC). Exceptions to this were two faecal isolates which produced the same amount of cereulide from 23 ºC up until 39ºC. We also found that at 37º C the choice of growth media for cereulide production differed from that at the room temperature. The food composition and temperature may thus be a key for understanding cereulide production in foods as well as in the gut. We investigated the contents of [K+], [Na+] and amino acids of six growth media. Statistical evaluation indicated a significant positive correlation between the ratio [K+]:[Na+] and the production of cereulide, but only when the concentrations of glycine and [Na+] were constant. Of the amino acids only glycine correlated positively with high cereulide production. Glycine is used worldwide as food additive (E 640), flavor modifier, humectant, acidity regulator, and is permitted in the European Union countries, with no regulatory quantitative limitation, in most types of foods. B. subtilis group members are endospore-forming bacteria ubiquitous in the environment, similar to B. cereus in this respect. Bacillus species other than B. cereus have only sporadically been identified as causative agents of food-borne illnesses. We found (Paper IV) that food-borne isolates of B. subtilis and B. mojavensis produced amylosin. It is possible that amylosin was the agent responsible for the food-borne illness, since no other toxic substance was found in the strains. This is the first report on amylosin production by strains isolated from food. We found that the temperature requirement for amylosin production was higher for the B. subtilis strain F 2564/96, a mesophilic producer, than for B. mojavensis strains eela 2293 and B 31, psychrotolerant producers. We also found that an atmosphere with low oxygen did not prevent the production of amylosin. Ready-to-eat foods packaged in micro-aerophilic atmosphere and/or stored at temperatures above 10 °C, may thus pose a risk when toxigenic strains of B. subtilis or B. mojavensis are present.

Lake sediment research as a part of lake management - case studies and implications from southern Finland

In Finland one of the most important current issues in the environmental management is the quality of surface waters. The increasing social importance of lakes and water systems has generated wide-ranging interest in lake restoration and management, concerning especially lakes suffering from eutrophication, but also from other environmental impacts. Most of the factors deteriorating the water quality in Finnish lakes are connected to human activities. Especially since the 1940's, the intensified farming practices and conduction of sewage waters from scattered settlements, cottages and industry have affected the lakes, which simultaneously have developed in to recreational areas for a growing number of people. Therefore, this study was focused on small lakes, which are human impacted, located close to settlement areas and have a significant value for local population. The aim of this thesis was to obtain information from lake sediment records for on-going lake restoration activities and to prove that a well planned, properly focused lake sediment study is an essential part of the work related to evaluation, target consideration and restoration of Finnish lakes. Altogether 11 lakes were studied. The study of Lake Kaljasjärvi was related to the gradual eutrophication of the lake. In lakes Ormajärvi, Suolijärvi, Lehee, Pyhäjärvi and Iso-Roine the main focus was on sediment mapping, as well as on the long term changes of the sedimentation, which were compared to Lake Pääjärvi. In Lake Hormajärvi the role of different kind of sedimentation environments in the eutrophication development of the lake's two basins were compared. Lake Orijärvi has not been eutrophied, but the ore exploitation and related acid main drainage from the catchment area have influenced the lake drastically and the changes caused by metal load were investigated. The twin lakes Etujärvi and Takajärvi are slightly eutrophied, but also suffer problems associated with the erosion of the substantial peat accumulations covering the fringe areas of the lakes. These peat accumulations are related to Holocene water level changes, which were investigated. The methods used were chosen case-specifically for each lake. In general, acoustic soundings of the lakes, detailed description of the nature of the sediment and determinations of the physical properties of the sediment, such as water content, loss on ignition and magnetic susceptibility were used, as was grain size analysis. A wide set of chemical analyses was also used. Diatom and chrysophycean cyst analyses were applied, and the diatom inferred total phosphorus content was reconstructed. The results of these studies prove, that the ideal lake sediment study, as a part of a lake management project, should be two-phased. In the first phase, thoroughgoing mapping of sedimentation patterns should be carried out by soundings and adequate corings. The actual sampling, based on the preliminary results, must include at least one long core from the main sedimentation basin for the determining the natural background state of the lake. The recent, artificially impacted development of the lake can then be determined by short-core and surface sediment studies. The sampling must be focused on the basis of the sediment mapping again, and it should represent all different sedimentation environments and bottom dynamic zones, considering the inlets and outlets, as well as the effects of possible point loaders of the lake. In practice, the budget of the lake management projects of is usually limited and only the most essential work and analyses can be carried out. The set of chemical and biological analyses and dating methods must therefore been thoroughly considered and adapted to the specific management problem. The results show also, that information obtained from a properly performed sediment study enhances the planning of the restoration, makes possible to define the target of the remediation activities and improves the cost-efficiency of the project.

Boundedness and convergence of singular integrals on fractal type sets

The topic of this dissertation lies in the intersection of harmonic analysis and fractal geometry. We particulary consider singular integrals in Euclidean spaces with respect to general measures, and we study how the geometric structure of the measures affects certain analytic properties of the operators. The thesis consists of three research articles and an overview. In the first article we construct singular integral operators on lower dimensional Sierpinski gaskets associated with homogeneous Calderón-Zygmund kernels. While these operators are bounded their principal values fail to exist almost everywhere. Conformal iterated function systems generate a broad range of fractal sets. In the second article we prove that many of these limit sets are porous in a very strong sense, by showing that they contain holes spread in every direction. In the following we connect these results with singular integrals. We exploit the fractal structure of these limit sets, in order to establish that singular integrals associated with very general kernels converge weakly. Boundedness questions consist a central topic of investigation in the theory of singular integrals. In the third article we study singular integrals of different measures. We prove a very general boundedness result in the case where the two underlying measures are separated by a Lipshitz graph. As a consequence we show that a certain weak convergence holds for a large class of singular integrals.

Inverse Problem for Fractional Brownian Motion with Discrete Data

The problem of recovering information from measurement data has already been studied for a long time. In the beginning, the methods were mostly empirical, but already towards the end of the sixties Backus and Gilbert started the development of mathematical methods for the interpretation of geophysical data. The problem of recovering information about a physical phenomenon from measurement data is an inverse problem. Throughout this work, the statistical inversion method is used to obtain a solution. Assuming that the measurement vector is a realization of fractional Brownian motion, the goal is to retrieve the amplitude and the Hurst parameter. We prove that under some conditions, the solution of the discretized problem coincides with the solution of the corresponding continuous problem as the number of observations tends to infinity. The measurement data is usually noisy, and we assume the data to be the sum of two vectors: the trend and the noise. Both vectors are supposed to be realizations of fractional Brownian motions, and the goal is to retrieve their parameters using the statistical inversion method. We prove a partial uniqueness of the solution. Moreover, with the support of numerical simulations, we show that in certain cases the solution is reliable and the reconstruction of the trend vector is quite accurate.

Renormalization methods in KAM theory

It is well known that an integrable (in the sense of Arnold-Jost) Hamiltonian system gives rise to quasi-periodic motion with trajectories running on invariant tori. These tori foliate the whole phase space. If we perturb an integrable system, the Kolmogorow-Arnold-Moser (KAM) theorem states that, provided some non-degeneracy condition and that the perturbation is sufficiently small, most of the invariant tori carrying quasi-periodic motion persist, getting only slightly deformed. The measure of the persisting invariant tori is large together with the inverse of the size of the perturbation. In the first part of the thesis we shall use a Renormalization Group (RG) scheme in order to prove the classical KAM result in the case of a non analytic perturbation (the latter will only be assumed to have continuous derivatives up to a sufficiently large order). We shall proceed by solving a sequence of problems in which theperturbations are analytic approximations of the original one. We will finally show that the approximate solutions will converge to a differentiable solution of our original problem. In the second part we will use an RG scheme using continuous scales, so that instead of solving an iterative equation as in the classical RG KAM, we will end up solving a partial differential equation. This will allow us to reduce the complications of treating a sequence of iterative equations to the use of the Banach fixed point theorem in a suitable Banach space.

Homogeneous model theory of metric structures

This thesis studies homogeneous classes of complete metric spaces. Over the past few decades model theory has been extended to cover a variety of nonelementary frameworks. Shelah introduced the abstact elementary classes (AEC) in the 1980s as a common framework for the study of nonelementary classes. Another direction of extension has been the development of model theory for metric structures. This thesis takes a step in the direction of combining these two by introducing an AEC-like setting for studying metric structures. To find balance between generality and the possibility to develop stability theoretic tools, we work in a homogeneous context, thus extending the usual compact approach. The homogeneous context enables the application of stability theoretic tools developed in discrete homogeneous model theory. Using these we prove categoricity transfer theorems for homogeneous metric structures with respect to isometric isomorphisms. We also show how generalized isomorphisms can be added to the class, giving a model theoretic approach to, e.g., Banach space isomorphisms or operator approximations. The novelty is the built-in treatment of these generalized isomorphisms making, e.g., stability up to perturbation the natural stability notion. With respect to these generalized isomorphisms we develop a notion of independence. It behaves well already for structures which are omega-stable up to perturbation and coincides with the one from classical homogeneous model theory over saturated enough models. We also introduce a notion of isolation and prove dominance for it.

Integral Transformations of Volterra Gaussian Processes

We study integral representations of Gaussian processes with a pre-specified law in terms of other Gaussian processes. The dissertation consists of an introduction and of four research articles. In the introduction, we provide an overview about Volterra Gaussian processes in general, and fractional Brownian motion in particular. In the first article, we derive a finite interval integral transformation, which changes fractional Brownian motion with a given Hurst index into fractional Brownian motion with an other Hurst index. Based on this transformation, we construct a prelimit which formally converges to an analogous, infinite interval integral transformation. In the second article, we prove this convergence rigorously and show that the infinite interval transformation is a direct consequence of the finite interval transformation. In the third article, we consider general Volterra Gaussian processes. We derive measure-preserving transformations of these processes and their inherently related bridges. Also, as a related result, we obtain a Fourier-Laguerre series expansion for the first Wiener chaos of a Gaussian martingale. In the fourth article, we derive a class of ergodic transformations of self-similar Volterra Gaussian processes.

Direct and Inverse Scattering for Beltrami Fields

We consider an obstacle scattering problem for linear Beltrami fields. A vector field is a linear Beltrami field if the curl of the field is a constant times itself. We study the obstacles that are of Neumann type, that is, the normal component of the total field vanishes on the boundary of the obstacle. We prove the unique solvability for the corresponding exterior boundary value problem, in other words, the direct obstacle scattering model. For the inverse obstacle scattering problem, we deduce the formulas that are needed to apply the singular sources method. The numerical examples are computed for the direct scattering problem and for the inverse scattering problem.

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.

Mikä on ihme ja mitä ihmeistä voidaan tietää? : Keskustelu ihmeistä uusimmassa englanninkielisessä uskonnonfilosofiassa

What is a miracle and what can we know about miracles? A discussion of miracles in anglophone philosophy of religion literature since the late 1960s. The aim of this study is to systematically describe and philosophically examine the anglophone discussion on the subject of miracles since the latter half of the 1960s. The study focuses on two salient questions: firstly, what I will term the conceptual-ontological question of the extent to which we can understand miracles and, secondly, the epistemological question of what we can know about miracles. My main purpose in this study is to examine the various viewpoints that have been submitted in relation to these questions, how they have been argued and on what presuppositions these arguments have been based. In conducting the study, the most salient dimension of the various discussions was found to relate to epistemological questions. In this regard, there was a notable confrontation between those scholars who accept miracles and those who are sceptical of them. On the conceptual-ontological side I recognised several different ways of expressing the concept of miracle . I systematised the discussion by demonstrating the philosophical boundaries between these various opinions. The first and main boundary was related to ontological knowledge. On one side of this boundary I placed the views which were based on realism and objectivism. The proponents of this view assumed that miraculousness is a real property of a miraculous event regardless of how we can perceive it. On the other side I put the views which tried to define miraculousness in terms of subjectivity, contextuality and epistemicity. Another essential boundary which shed light on the conceptual-ontological discussion was drawn in relation to two main views of nature. The realistic-particularistic view regards nature as a certain part of reality. The adherents of this presupposition postulate a supernatural sphere alongside nature. Alternatively, the nominalist-universalist view understands nature without this kind of division. Nature is understood as the entire and infinite universe; the whole of reality. Other, less important boundaries which shed light on the conceptual-ontological discussion were noted in relation to views regarding the laws of nature, for example. I recognised that the most important differences between the epistemological approaches were in the different views of justification, rationality, truth and science. The epistemological discussion was divided into two sides, distinguished by their differing assumptions in relation to the need for evidence. Adherents of the first (and noticeably smaller) group did not see any epistemological need to reach a universal and common opinion about miracles. I discovered that these kinds of views, which I called non-objectivist, had subjectivist and so-called collectivist views of justification and a contextualist view of rationality. The second (and larger) group was mainly interested in discerning the grounds upon which to establish an objective and conclusive common view in relation to the epistemology of miracles. I called this kind of discussion an objectivist discussion and this kind of approach an evidentialist approach. Most of the evidentialists tried to defend miracles and the others attempted to offer evidence against miracles. Amongst both sides, there were many different variations according to emphasis and assumption over how they saw the possibilities to prove their own view. The common characteristic in all forms of evidentialism was a commitment to an objectivist notion of rationality and a universalistic notion of justification. Most evidentialists put their confidence in science in one way or another. Only a couple of philosophers represented the most moderate version of evidentialism; they tried to remove themselves from the apparent controversy and contextualised the different opinions in order to make some critical comments on them. I called this kind of approach a contextualising form of evidentialism. In the final part of the epistemological chapter, I examined the discussion about the evidential value of miracles, but nothing substantially new was discovered concerning the epistemological views of the authors.