Composition operators on vector-valued BMOA and related function spaces

A composition operator is a linear operator between spaces of analytic or harmonic functions on the unit disk, which precomposes a function with a fixed self-map of the disk. A fundamental problem is to relate properties of a composition operator to the function-theoretic properties of the self-map. During the recent decades these operators have been very actively studied in connection with various function spaces. The study of composition operators lies in the intersection of two central fields of mathematical analysis; function theory and operator theory. This thesis consists of four research articles and an overview. In the first three articles the weak compactness of composition operators is studied on certain vector-valued function spaces. A vector-valued function takes its values in some complex Banach space. In the first and third article sufficient conditions are given for a composition operator to be weakly compact on different versions of vector-valued BMOA spaces. In the second article characterizations are given for the weak compactness of a composition operator on harmonic Hardy spaces and spaces of Cauchy transforms, provided the functions take values in a reflexive Banach space. Composition operators are also considered on certain weak versions of the above function spaces. In addition, the relationship of different vector-valued function spaces is analyzed. In the fourth article weighted composition operators are studied on the scalar-valued BMOA space and its subspace VMOA. A weighted composition operator is obtained by first applying a composition operator and then a pointwise multiplier. A complete characterization is given for the boundedness and compactness of a weighted composition operator on BMOA and VMOA. Moreover, the essential norm of a weighted composition operator on VMOA is estimated. These results generalize many previously known results about composition operators and pointwise multipliers on these spaces.

On Orlicz-Sobolev capacities

This thesis consists of three articles on Orlicz-Sobolev capacities. Capacity is a set function which gives information of the size of sets. Capacity is useful concept in the study of partial differential equations, and generalizations of exponential-type inequalities and Lebesgue point theory, and other topics related to weakly differentiable functions such as functions belonging to some Sobolev space or Orlicz-Sobolev space. In this thesis it is assumed that the defining function of the Orlicz-Sobolev space, the Young function, satisfies certain growth conditions. In the first article, the null sets of two different versions of Orlicz-Sobolev capacity are studied. Sufficient conditions are given so that these two versions of capacity have the same null sets. The importance of having information about null sets lies in the fact that the sets of capacity zero play similar role in the Orlicz-Sobolev space setting as the sets of measure zero do in the Lebesgue space and Orlicz space setting. The second article continues the work of the first article. In this article, it is shown that if a Young function satisfies certain conditions, then two versions of Orlicz-Sobolev capacity have the same null sets for its complementary Young function. In the third article the metric properties of Orlicz-Sobolev capacities are studied. It is usually difficult or impossible to calculate a capacity of a set. In applications it is often useful to have estimates for the Orlicz-Sobolev capacities of balls. Such estimates are obtained in this paper, when the Young function satisfies some growth conditions.

Properties of Toeplitz operators on analytic function spaces : from function symbols to distributions

Toeplitz operators are among the most important classes of concrete operators with applications to several branches of pure and applied mathematics. This doctoral thesis deals with Toeplitz operators on analytic Bergman, Bloch and Fock spaces. Usually, a Toeplitz operator is a composition of multiplication by a function and a suitable projection. The present work deals with generalizing the notion to the case where the function is replaced by a distributional symbol. Fredholm theory for Toeplitz operators with matrix-valued symbols is also considered. The subject of this thesis belongs to the areas of complex analysis, functional analysis and operator theory. This work contains five research articles. The articles one, three and four deal with finding suitable distributional classes in Bergman, Fock and Bloch spaces, respectively. In each case the symbol class to be considered turns out to be a certain weighted Sobolev-type space of distributions. The Bergman space setting is the most straightforward. When dealing with Fock spaces, some difficulties arise due to unboundedness of the complex plane and the properties of the Gaussian measure in the definition. In the Bloch-type spaces an additional logarithmic weight must be introduced. Sufficient conditions for boundedness and compactness are derived. The article two contains a portion showing that under additional assumptions, the condition for Bergman spaces is also necessary. The fifth article deals with Fredholm theory for Toeplitz operators having matrix-valued symbols. The essential spectra and index theorems are obtained with the help of Hardy space factorization and the Berezin transform, for instance. The article two also has a part dealing with matrix-valued symbols in a non-reflexive Bergman space, in which case a condition on the oscillation of the symbol (a logarithmic VMO-condition) must be added.

Is a Majority Enough? Psychological Well-being and Its Relation to Academic and Prosocial Motivation, Self-regulation and Achievement at school

This cross-sectional study analyzed psychological well-being at school using the Self-Determination theory as a theoretical frame-work. The study explored basic psychological needs fulfillment (BPNS), academic (SRQ-A), prosocial self-regulation (SRQ-P) and motivation, and their relationship with achievement in general, special and selective education (N=786, 444 boys, 345 girls, mean age 12 yrs 8 mths). Motivation starts behavior which becomes guided by self-regulation. The perceived locus of control (PLOC) affects how self-determined this behavior will be; in other words, to what extent it is autonomously regulated. In order learn and thus to be able to accept external goals, a student has to feel emotionally safe and have sufficient ego-flexibility—all of which builds on satisfied psychological needs. In this study those conditions were explored. In addition to traditional methods Self-organizing maps (SOM), was used in order to cluster the students according to their well-being, self-regulation, motivation and achievement scores. The main impacts of this research were: a presentation of the theory based alternative of studying psychological well-being at school and usage of both the variable and person-oriented approach. In this Finnish sample the results showed that the majority of students felt well, but the well-being varied by group. Overall about for 11–15% the basic needs were deprived depending on the educational group. Age and educational group were the most effective factors; gender was important in relation to prosocial identified behavior. Although the person-oriented SOM-approach, was in a large extent confirming what was no-ticed by using comparison of the variables: the SEN groups had lower levels of basic needs fulfillment and less autonomous self-regulation, interesting deviations of that rule appeared. Some of the SEL- and GEN-group members ended up in the more unfavorable SOM-clusters, and not all SEN-group members belonged to the poorest clusters (although not to the best either). This evidence refines the well-being and self-regulation picture, and may re-direct intervention plans, and turn our focus also on students who might otherwise remain unnoticed. On the other hand, these results imply simultaneously that in special education groups the average is not the whole truth. On the basis of theoretical and empirical considerations an intervention model was sug-gested. The aim of the model was to shift amotivation or external motivation in a more intrinsic direction. According to the theoretical and empirical evidence this can be achieved first by studying the self-concept a student has, and then trying to affect both inner and environmental factors—including a consideration of the basic psychological needs. Keywords: academic self-regulation, prosocial self-regulation, basic psychological needs, moti-vation, achievement

Oral health behaviour, conditions and care among dentate elderly patients in Lithuania: preventive aspects

The present cross-sectional study aimed to assess oral health behaviour, dental and periodontal conditions, dental care, and their relationships among elderly dentate patients in Lithuania. The target population in the study were dentate patients aged 60 and older attending public dental services in Kedainiai, Lithuania. The data collection took place between the autumn of 1999 and the winter of 2001. Data were collected by means of a self-administered questionnaire for all (n=174) and a clinical examination targeting about half of the subjects (n=100). The questionnaire inquired about oral health behaviour, the life-first and also the most recent dental treatments, sources on and self-assessed knowledge of oral self-care, a self-reported number of teeth, and socio-demographic information. The clinical examination included basic dental and periodontal conditions. A total of 82 women and 92 men completed the questionnaire; their mean age was 69.2 and their average number of teeth was 16.2 (CI 95% 15.4-17.1). In all, 25% had 21 or more teeth and 32% indicated wearing removable dentures. The oral health behaviour, the participants reported, was poor: 30% reported twice daily toothbrushing, 57% responded that they always use fluoride toothpaste, 19% indicated daily interdental cleaning, nearly all said they take sugar in their coffee and tea, and 30% indicated going for check-ups. As the main source of information on oral self-care, the subjects indicated health professionals (82%), followed by social contacts (72%), broadcasted media (58%), and printed media (42%). A total of 34% assessed their knowledge of oral self-care as good, and their self-assessed knowledge correlated (r=0.52) with professional guidance they had received about oral self-care. In their most recent treatment, conservative (39%) and non-conservative (34%) treatments dominated, and preventive ones were the least reported (7%). Regarding guidance in oral self-care, 54% reported having received such about toothbrushing, 32% about interdental cleaning, and 33% had been given visual information. Clinical examinations revealed the presence of plaque, calculus, bleeding on probing and deepened pockets in all of the subjects; 70% of the subjects were diagnosed with pockets of 6mm and deeper, 94% with caries, and 73% with overhangs of restorations. Those subjects assessing their knowledge of oral self-care as good and reporting a higher intensity of guidance in oral self-care as received, indicated practicing the recommended oral self-care more frequently. Twice daily toothbrushing was associated with good self-assessed knowledge of oral self-care (OR 4.1, p<0.001) and a university education (OR 5.6, p<0.001). Those subjects with better oral health behaviour had a greater number of teeth. Having 21 or more teeth was associated with good self-assessed knowledge of oral self-care (OR 4.1, p=0.03). Better periodontal conditions were associated with a higher frequency of toothbrushing. The presence of periodontal pockets of 6mm and deeper was associated with the level of self-assessed knowledge of oral self-care being below good (OR=3.0, p=0.04) and the level of dental cleanliness being poor (OR=2.7, p=0.02). To conclude, oral health behaviour and conditions call for improvement in elderly subjects in Lithuania. To improve the oral health of their elderly dentate patients, dentists should apply all the available tools of chair-side prevention and active guidance. The latter would be an effective means of updating the knowledge of oral self-care and supporting recommended oral health behaviour. A preventive approach should be strongly emphasized in countries with limited resources for oral health care, such as Lithuania. Author’s address: Sonata Vyšniauskaite, Department of Oral Public Health, Institute of Dentistry, University of Helsinki, P.O.Box 41, FI-00014 Helsinki, Finland. E-mail: sonata.vysniauskaite@helsinki.fi

Associations among working conditions and behavioral risk factors : The Helsinki Health Study with International Comparisons

Adverse health behaviors as well as obesity are key risk factors for chronic diseases. Working conditions also contribute to health outcomes. It is possible that the effects of psychosocially strenuous working conditions and other work-related factors on health are, to some extent, explained by adverse behaviors. Previous studies about the associations between several working conditions and behavioral outcomes are, however, inconclusive. Moreover, the results are derived mostly from male populations, one national setting only, and with limited information about working conditions and behavioral risk factors. Thus, with an interest in employee health, this study was set to focus on behavioral risk factors among middle-aged employees. More specifically, the main aim was to shed light on the associations of various working conditions with health behaviors, weight gain, obesity, and symptoms of angina pectoris. In addition to national focus, international comparisons were included to test the associations across countries thereby aiming to produce a more comprehensive picture. Furthermore, a special emphasis was on gaining new evidence in these areas among women. The data derived from the Helsinki Health Study, and from collaborative partners at the Whitehall II Study, University College London, UK, and the Toyama University, Japan. In Helsinki, the postal questionnaires were mailed in 2000-2002 to employees of the City of Helsinki, aged 40 60 years (n=8960). The questionnaire data covered e.g., socio-economic indicators and working conditions such as Karasek s job demands and job control, work fatigue, working overtime, work-home interface, and social support. The outcome measures consisted of smoking, drinking, physical activity, food habits, weight gain, obesity, and symptoms of angina pectoris. The international cohorts included comparable data. Logistic regression analysis was used. The models were adjusted for potential confounders such as age, education, occupational class, and marital status subject to specific aims. The results showed that working conditions were mostly unassociated with health behaviors, albeit some associations were found. Low job strain was associated with healthy food habits and non-smoking among women in Helsinki. Work fatigue, in turn, was related to drinking among men and physical inactivity among women. Work fatigue and working overtime were associated with weight gain in Helsinki among both women and men. Finally, work fatigue, low job control, working overtime, and physically strenuous work were associated with symptoms of angina pectoris among women in Helsinki. Cross-country comparisons confirmed mostly non-existent associations. High job strain was associated with physical inactivity and smoking, and passive work with physical inactivity and less drinking. Working overtime, in turn, related to non-smoking and obesity. All these associations were, however, inconsistent between cohorts and genders. In conclusion, the associations of the studied working conditions with the behavioral risk factors lacked general patters, and were, overall, weak considering the prevalence of psychosocially strenuous work and overtime hours. Thus, based on this study, the health effects of working conditions are likely to be mediated by adverse behaviors only to a minor extent. The associations of work fatigue and working overtime with weight gain and symptoms of angina pectoris are, however, of potential importance to the subsequent health and work ability of employees.

Fuel conditions and fire behavior characteristics of managed Picea abies and Pinus sylvestris forests in Finland

The objectives of this study were to analyze the impact of structural stand characteristics on ignition potential, surface fuel moisture, and fire behavior in Pinus sylvestris L. and Picea abies (L.) Karst stands in Finland and to explain stand-specific fire danger using the Canadian Fire Weather Index System and the Finnish Fire Risk Index. Additionally, the study analyzes the relationship between observed fire activity and fire weather indices at different stages of growing season. Field experiments were carried out in Pinus sylvestris or Picea abies dominated stands during fire seasons 2001 and 2002. Observations on ignition potential, fuel moisture, and fire behavior were analyzed in relation to stand structure and the outputs of the Finnish and Canadian fire weather indices. Seasonal patterns of fire activity were examined based on national fire statistics 1996 2003, effective temperature sum, and the fire weather indices. Point fire ignition potential was highest in Pinus clear-cuts and lowest in closed Picea stands. Moss-dominated surface fuels were driest in clear-cut and sapling stage stands and presented the highest moisture content under closed Picea canopy. Pinus sylvestris stands carried fire under a wide range of fire weather conditions under which Picea abies stands failed to sustain fire. In the national fire records, the daily number of reported ignitions presented its highest value during late fire season whereas the daily area burned peaked most substantially during early season. The fire weather indices correlated significantly with ignition potential and fuel moisture but were unable to explain fire behavior in the experimental fires. During the initial and final stages of the growing season, fire activity was disconnected from weather-based fire danger ratings. Information on stand structure and season stage would benefit the assessment of fire danger in Finnish forest landscape for fire suppression and controlled burning purposes.

Fen ecosystem carbon gas dynamics in changing hydrological conditions

Northern peatlands are thought to store one third of all soil carbon (C). Besides the C sink function, peatlands are one of the largest natural sources of methane (CH4) to the atmosphere. Climate change may affect the C gas dynamics as well as the labile C pool. Because the peatland C sequestration and CH4 emissions are governed by high water levels, changes in hydrology are seen as the driving factor in peatland ecosystem change. This study aimed to quantify the carbon dioxide (CO2) and CH4 dynamics of a fen ecosystem at different spatial scales: plant community components scale, plant community scale and ecosystem scale, under hydrologically normal and water level drawdown conditions. C gas exchange was measured in two fens in southern Finland applying static chamber and eddy covariance techniques. During hydrologically normal conditions, the ecosystem was a CO2 sink and CH4 source to the atmosphere. Sphagnum mosses and sedges were the most important contributors to the community photosynthesis. The presence of sedges had a major positive impact on CH4 emissions while dwarf shrubs had a slightly attenuating impact. C fluxes varied considerably between the plant communities. Therefore, their proportions determined the ecosystem scale fluxes. An experimental water level drawdown markedly reduced the photosynthesis and respiration of sedges and Sphagnum mosses and benefited shrubs. Consequently, changes were smaller at the ecosystem scale than at the plant group scale. The decrease in photosynthesis and the increase in respiration, mostly peat respiration, made the fen a smaller CO2 sink. CH4 fluxes were significantly lowered, close to zero. The impact of natural droughts was similar to, although more modest than, the impact of the experimental water level drawdown. The results are applicable to the short term impacts of the water level drawdown and to climatic conditions in which droughts become more frequent.

The role of pollen in the changing environmental conditions of Scots pine

Rapid change in climate is challenge for the adaptation of forest trees in the future. In wind pollinated tree species pollen mediated long distance gene flow may provide alleles that are (pre)adapted to a future climate. In order to examine the long distance pollen flow in Scots pine (Pinus sylvestris L.), we measured the amount and viability of airborne pollen and flowering phenology in central, northern, and northernmost Finland during four years. Viable airborne pollen grains were detected during female flowering and before local pollen shedding in all study sites. The situation when there was nonlocal pollen in the air lasted from one to four days depending on the year and study site. The amount of nonlocal airborne pollen varied also between years and study sites, the total amount of nonlocal viable pollen in the air was 2.3% from all detected viable pollen grains. The effect of pollen origin on seeds siring ability was studied with artificial pollination experiments. Pollen genotypes originating from southern Finland sired 76% and 48 % of the analysed seeds in competition studies where both pollen origin were introduced simultaneously into the female strobili. We examined the importance of arrival order of pollen grains in to the strobili in a study where pollen genotypes of different origin were introduced in two hours interval. Northern genotypes sired 76% of the analysed seeds when it was injected first, but in the "southern first" experiment both pollen types sired equal amount of seeds. The first pollen grain in the pollen chamber do not always fertilizes the ovum, instead there likely is more complex way of competition between pollen grains. To examine chemically mediated pollen-pollen interactions we conducted in vitro germination experiment where different pollen genotypes had chemical but not physical contact. Both positive and negative effects of interactions were found. We found highly negative effects in germinability of northern pollen grains when they were germinating with southern pollen, and increase in the germinability of southern pollen. There were no variation in the size of the dry pollen grains between pollen origins, and minor variation between different genotypes. After hydration and germination northern pollen grains were larger than southern pollen. Pollen genotypes having high hydration rates had low germinability and tube growth rate, however, germinated pollen grains were larger in size than nongerminated. This supports the suggestion that the early germination and growth of pollen tube is dependent on pollen storage materialsand less dependent on water intake and hydration. Long distance pollen movements and good competition ability of southern pollen makes gene flow possible, although rising temperature and timing of pollen movements may affect pollen competition and the amount of gene flow.

Soil hydrological properties and conditions, site preparation, and the long-term performance of planted Scots pine (Pinus sylvestris L.) on upland forest sites in Finnish Lapland

Scots pine (Pinus sylvestris L.) and Norway spruce (Picea abies (L.) Karst.) forests dominate in Finnish Lapland. The need to study the effect of both soil factors and site preparation on the performance of planted Scots pine has increased due to the problems encountered in reforestation, especially on mesic and moist, formerly spruce-dominated sites. The present thesis examines soil hydrological properties and conditions, and effect of site preparation on them on 10 pine- and 10 spruce-dominated upland forest sites. Finally, the effects of both the site preparation and reforestation methods, and soil hydrology on the long-term performance of planted Scots pine are summarized. The results showed that pine and spruce sites differ significantly in their soil physical properties. Under field capacity or wetter soil moisture conditions, planted pines presumably suffer from excessive soil water and poor soil aeration on most of the originally spruce sites, but not on the pine sites. The results also suggested that site preparation affects the soil-water regime and thus prerequisites for forest growth over two decades after site preparation. High variation in the survival and mean height of planted pine was found. The study suggested that on spruce sites, pine survival is the lowest on sites that dry out slowly after rainfall events, and that height growth is the fastest on soils that reach favourable aeration conditions for root growth soon after saturation, and/or where the average air-filled porosity near field capacity is large enough for good root growth. Survival, but not mean height can be enhanced by employing intensive site preparation methods on spruce sites. On coarser-textured pine sites, site preparation methods don t affect survival, but methods affecting soil fertility, such as prescribed burning and ploughing, seem to enhance the height growth of planted Scots pines over several decades. The use of soil water content in situ as the sole criterion for sites suitable for pine reforestation was tested and found to be a relatively uncertain parameter. The thesis identified new potential soil variables, which should be tested using other data in the future.

Regulation of strawberry growth and development

Strawberries (Fragaria sp.) are adapted to diverse environmental conditions from the tropics to about 70ºN, so different responses to environmental conditions can be found. Most genotypes of garden strawberry (F. x ananassa Duch.) and woodland strawberry (F. vesca L.) are short-day (SD) plants that are induced to flowering by photoperiods under a critical limit, but also various photoperiod x temperature interactions can be found. In addition, continuously flowering everbearing (EB) genotypes are found. In addition to flowering, axillary bud differentiation in strawberry is regulated by photoperiod. In SD conditions, axillary buds differentiate to rosette-like structures called "branch crowns", whereas in long-day conditions (LD) they form runners, branches with 2 long internodes followed by a daughter plant (leaf rosette). The number of crown branches determines the yield of the plant, since inflorescences are formed from the apical meristems of the crown. Although axillary bud differentiation is an important developmental process in strawberries, its environmental and hormonal regulation has not been characterized in detail. Moreover, the genetic mechanisms underlying axillary bud differentiation and regulation of flowering time in these species are almost completely unresolved. These topics have been studied in this thesis in order to enhance strawberry research, cultivation and breeding. The results showed that 8-12 SD cycles suppressed runner initiation from the axillary buds of the garden strawberry cv. Korona with the concomitant induction of crown branching, and 3 weeks of SD was sufficient for the induction of flowering in the main crown. Furthermore, a second SD treatment given a few weeks after the first SD period can be used to induce flowering in the primary branch crowns and to induce the formation of secondary branches. Thus, artificial SD treatments effectively stimulate crown branching, providing one means for the increase of cropping (yield) potential in strawberry. It was also shown by growth regulation applications, quantitave hormone analysis and gene expression analysis that gibberellin (GA) is one of the key signals involved in the photoperiod control of shoot differentiation. The results indicate that photoperiod controls GA activity specifically in axillary buds, thereby determining bud fate. It was further shown that chemical control of GA biosynthesis by prohexadione-calcium can be utilized to prevent excessive runner formation and induce crown branching in strawberry fields. Moreover, ProCa increased berry yield up to 50%, showing that it is an easier and more applicable alternative to artificial SD treatments for controlling strawberry crown development and yield. Finally, flowering gene pathways in Fragaria were explored by searching for homologs of 118 Arabidopsis thaliana flowering-time genes. In total, 66 gene homologs were identified, and they distributed to all known flowering pathways, suggesting the presence of these pathways also in strawberry. Expression analysis of selected genes revealed that the mRNA of putative floral identity gene APETALA1 accumulated in the shoot apex of the EB genotype after the induction of flowering, whereas it was absent in vegetative SD genotype, indicating the usefulness of this gene product as the marker of floral initiation. The present data enables the further exploration of strawberry flowering pathways with genetic transformation, gene mapping and transcriptomics methods.

Nitrogen dynamics and nitrogen use efficiency of spring cereals under Finnish growing conditions

Nitrogen (N) is one of the main inputs in cereal cultivation and as more than half of the arable land in Finland is used for cereal production, N has contributed substantially to agricultural pollution through fertilizer leaching and runoff. Based on this global phenomenon, the European Community has launched several directives to reduce agricultural emissions to the environment. Trough such measures, and by using economic incentives, it is expected that northern European agricultural practices will, in the future, include reduced N fertilizer application rates. Reduced use of N fertilizer is likely to decrease both production costs and pollution, but could also result in reduced yields and quality if crops experience temporary N deficiency. Therefore, more efficient N use in cereal production, to minimize pollution risks and maximize farmer income, represents a current challenge for agronomic research in the northern growing areas. The main objective of this study was to determine the differences in nitrogen use efficiency (NUE) among spring cereals grown in Finland. Additional aims were to characterize the multiple roles of NUE by analysing the extent of variation in NUE and its component traits among different cultivars, and to understand how other physiological traits, especially radiation use efficiency (RUE) and light interception, affect and interact with the main components of NUE and contribute to differences among cultivars. This study included cultivars of barley (Hordeum vulgare L.), oat (Avena sativa L.) and wheat (Triticum aestivum L.). Field experiments were conducted between 2001 and 2004 at Jokioinen, in Finland. To determine differences in NUE among cultivars and gauge the achievements of plant breeding in NUE, 17-18 cultivars of each of the three cereal species released between 1909 and 2002 were studied. Responses to nitrogen of landraces, old cultivars and modern cultivars of each cereal species were evaluated under two N regimes (0 and 90 kg N ha-1). Results of the study revealed that modern wheat, oat and barley cultivars had similar NUE values under Finnish growing conditions and only results from a wider range of cultivars indicated that wheat cultivars could have lower NUE than the other species. There was a clear relationship between nitrogen uptake efficiency (UPE) and NUE in all species whereas nitrogen utilization efficiency (UTE) had a strong positive relationship with NUE only for oat. UTE was clearly lower in wheat than in other species. Other traits related to N translocation indicated that wheat also had a lower harvest index, nitrogen harvest index and nitrogen remobilisation efficiency and therefore its N translocation efficiency was confirmed to be very low. On the basis of these results there appears to be potential and also a need for improvement in NUE. These results may help understand the underlying physiological differences in NUE and could help to identify alternative production options, such as the different roles that species can play in crop rotations designed to meet the demands of modern agricultural practices.