Gauge Field Theories, Quantum Space-Time and Some Applications

In this thesis, the possibility of extending the Quantization Condition of Dirac for Magnetic Monopoles to noncommutative space-time is investigated. The three publications that this thesis is based on are all in direct link to this investigation. Noncommutative solitons have been found within certain noncommutative field theories, but it is not known whether they possesses only topological charge or also magnetic charge. This is a consequence of that the noncommutative topological charge need not coincide with the noncommutative magnetic charge, although they are equivalent in the commutative context. The aim of this work is to begin to fill this gap of knowledge. The method of investigation is perturbative and leaves open the question of whether a nonperturbative source for the magnetic monopole can be constructed, although some aspects of such a generalization are indicated. The main result is that while the noncommutative Aharonov-Bohm effect can be formulated in a gauge invariant way, the quantization condition of Dirac is not satisfied in the case of a perturbative source for the point-like magnetic monopole.

Effect of soil preparation of boreal spruce forest on air and soil temperature conditions in forest regeneration areas.

The effect of scarification, ploughing and cross-directional plouhing on temperature conditions in the soil and adjacent air layer have been studied during 11 consecutive growth periods by using an unprepared clear-cut area as a control site. The maximum and minimum temperatures were measured daily in the summer months, and other temperature observations were made at four-hour intervals by means of a Grant measuring instrument. The development of the seedling stand was also followed in order to determine its shading effect on the soil surface. Soil preparation decreased the daily temperature amplitude of the air at the height of 10 cm. The maximum temperatures on sunny days were lower in the tilts of the ploughed and in the humps of the cross-directional ploughed sites compared with the unprepared area. Correspondingly, the night temperatures were higher and so the soil preparation considerably reduced the risk of night frost. In the soil at the depth of 5 cm, soil preparation increased daytime temperatures and reduced night temperatures compared with unprepared area. The maximum increase in monthly mean temperatures was almost 5 °C, and the daily variation in the surface parts of the tilts and humps increased so that excessively high temperatures for the optimal growth of the root system were measured from time to time. The temperature also rose at the depths of 50 and 100 cm. Soil preparation also increased the cumulative temperature sum. The highest sums accumulated during the summer months were recorded at the depth of 5 cm in the humps of cross-directional ploughed area (1127 dd.) and in the tilts of the ploughed area (1106 dd.), while the corresponding figure in the unprepared soil was 718 dd. At the height of 10 cm the highest temperature sum was 1020 dd. in the hump, the corresponding figure in the unprepared area being 925 dd. The incidence of high temperature amplitudes and percentage of high temperatures at the depth of 5 cm decreased most rapidly in the humps of cross-directional ploughed area and in the ploughing tilts towards the end of the measurement period. The decrease was attributed principally to the compressing of tilts, the ground vegetation succession and the growth of seedlings. The mean summer temperature in the unprepared area was lower than in the prepared area and the difference did not diminish during the period studied. The increase in temperature brought about by soil preparation thus lasts at least more than 10 years.

Decomposition of Scots pine fine woody debris in boreal conditions

"Litter quality and environmental effects on Scots pine (Pinus sylvestris L.) fine woody debris (FWD) decomposition were examined in three forestry-drained peatlands representing different site types along a climatic gradient from the north boreal (Northern Finland) to south (Southern Finland) and hemiboreal (Central Estonia) conditions. Decomposition (percent mass loss) of FWD with diameter <= 10 mm (twigs) and FWD with diameter > 10 mm (branches) was measured using the litter bag method over 1-4-year periods. Overall, decomposition rates increased from north to south, the rate constants (k values) varying from 0.128 to 0.188 year(-1) and from 0.066 to 0.127 year(-1) for twigs and branches, respectively. On average, twigs had lost 34%, 19% and 19%, and branches 25%, 17% and 11% of their initial mass after 2 years of decomposition at the hemiboreal, south boreal and north boreal sites, respectively. After 4 years at the south boreal site the values were 48% for twigs and 42% for branches. Based on earlier studies, we suggest that the decomposition rates that we determined may be used for estimating Scots pine FWD decomposition in the boreal zone, also in upland forests. Explanatory models accounted for 50.4% and 71.2% of the total variation in FWD decomposition rates when the first two and all years were considered, respectively. The variables most related to FWD decomposition included the initial ash, water extractives and Klason lignin content of litter, and cumulative site precipitation minus potential evapotranspiration. Simulations of inputs and decomposition of Scots pine FWD and needle litter in south boreal conditions over a 60-year period showed that 72 g m(-2) of organic matter from FWD vs. 365 g m(-2) from needles accumulated in the forest floor. The annual inputs varied from 5.7 to 15.6 g m(-2) and from 92 to 152 g m(-2) for FWD and needles, respectively. Each thinning caused an increase in FWD inputs, Up to 510 g m(-2), while the needle inputs did not change dramatically. Because the annual FWD inputs were lowered following the thinnings, the overall effect of thinnings on C accumulation from FWD was slightly negative. The contribution of FWD to soil C accumulation, relative to needle litter, seems to be rather minor in boreal Scots pine forests. (C) 2008 Elsevier B.V. All rights reserved."

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.

Identification of collagenolytic MMP networks as potential biomarkers in progressive chronic periodontitis subjects and MMP-8 null allele model

Chronic periodontitis results from a complex aetiology, including the formation of a subgingival biofilm and the elicitation of the host s immune and inflammatory response. The hallmark of chronic periodontitis is alveolar bone loss and soft periodontal tissue destruction. Evidence supports that periodontitis progresses in dynamic states of exacerbation and remission or quiescence. The major clinical approach to identify disease progression is the tolerance method, based on sequential probing. Collagen degradation is one of the key events in periodontal destructive lesions. Matrix metalloproteinase (MMP)-8 and MMP-13 are the primary collagenolytic MMPs that are associated with the severity of periodontal inflammation and disease, either by a direct breakdown of the collagenised matrix or by the processing of non-matrix bioactive substrates. Despite the numerous host mediators that have been proposed as potential biomarkers for chronic periodontitis, they reflect inflammation rather than the loss of periodontal attachment. The aim of the present study was to determine the key molecular MMP-8 and -13 interactions in gingival crevicular fluid (GCF) and gingival tissue from progressive periodontitis lesions and MMP-8 null allele mouse model. In study (I), GCF and gingival biopsies from active and inactive sites of chronic periodontitis patients, which were determined clinically by the tolerance method, and healthy GCF were analysed for MMP-13 and tissue inhibitor of matrix metalloproteinases (TIMP)-1. Chronic periodontitis was characterised by increased MMP-13 levels and the active sites showed a tendency of decreased TIMP-1 levels associated with increments of MMP-13 and total protein concentration compared to inactive sites. In study (II), we investigated whether MMP-13 activity was associated with TIMP-1, bone collagen breakdown through ICTP levels, as well as the activation rate of MMP-9 in destructive lesions. The active sites demonstrated increased GCF ICTP levels as well as lowered TIMP-1 detection along with elevated MMP-13 activity. MMP-9 activation rate was enhanced by MMP-13 in diseased gingival tissue. In study (III), we analysed the potential association between the levels, molecular forms, isoenzyme distribution and degree of activation of MMP-8, MMP-14, MPO and the inhibitor TIMP-1 in GCF from periodontitis progressive patients at baseline and after periodontal therapy. A positive correlation was found for MPO/MMP-8 and their levels associated with progression episodes and treatment response. Because MMP-8 is activated by hypochlorous acid in vitro, our results suggested an interaction between the MPO oxidative pathway and MMP-8 activation in GCF. Finally, in study (IV), on the basis of the previous finding that MMP-8-deficient mice showed impaired neutrophil responses and severe alveolar bone loss, we aimed to characterise the detection patterns of LIX/CXCL5, SDF-1/CXCL12 and RANKL in P. gingivalis-induced experimental periodontitis and in the MMP-8-/- murine model. The detection of neutrophil-chemoattractant LIX/CXCL5 was restricted to the oral-periodontal interface and its levels were reduced in infected MMP-8 null mice vs. wild type mice, whereas the detection of SDF-1/CXCL12 and RANKL in periodontal tissues increased in experimentally-induced periodontitis, irrespectively from the genotype. Accordingly, MMP-8 might regulate LIX/CXCL5 levels by undetermined mechanisms, and SDF-1/CXCL12 and RANKL might promote the development and/or progression of periodontitis.