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.

Crystallization as a Tool for Controlling and Designing Properties of Pharmaceutical Solids

The ability to deliver the drug to the patient in a safe, efficacious and cost-effective manner depends largely on the physicochemical properties of the active pharmaceutical ingredient (API) in the solid state. In this context, crystallization is of critical importance in pharmaceutical industry, as it defines physical and powder properties of crystalline APIs. An improved knowledge of the various aspects of crystallization process is therefore needed. The overall goal of this thesis was to gain better understanding of the relationships between crystallization, solid-state form and properties of pharmaceutical solids with a focus on a crystal engineering approach to design technological properties of APIs. Specifically, solid-state properties of the crystalline forms of the model APIs, erythromycin A and baclofen, and the influence of solvent on their crystallization behavior were investigated. In addition, the physical phenomena associated with wet granulation and hot-melting processing of the model APIs were examined at the molecular level. Finally, the effect of crystal habit modification of a model API on its tabletting properties was evaluated. The thesis enabled the understanding of the relationship between the crystalline forms of the model APIs, which is of practical importance for solid-state control during processing and storage. Moreover, a new crystalline form, baclofen monohydrate, was discovered and characterized. Upon polymorph screening, erythromycin A demonstrated high solvate-forming propensity thus emphasizing the need for careful control of the solvent effects during formulation. The solvent compositions that yield the desirable crystalline form of erythromycin A were defined. Furthermore, new examples on solvent-mediated phase transformations taking place during wet granulation of baclofen and hot-melt processing of erythromycin A dihydrate with PEG 6000 are reported. Since solvent-mediated phase transformations involve the crystallization of a stable phase and hence affect the dissolution kinetics and possibly absorption of the API these transformations must be well documented. Finally, a controlled-crystallization method utilizing HPMC as a crystal habit modifier was developed for erythromycin A dihydrate. The crystals with modified habit were shown to posses improved compaction properties as compared with those of unmodified crystals. This result supports the idea of morphological crystal engineering as a tool for designing technological properties of APIs and is of utmost practical interest.

Investigating physical properties of solid dosage forms during pharmaceutical processing : Process analytical applications of vibrational spectroscopy

In order to improve and continuously develop the quality of pharmaceutical products, the process analytical technology (PAT) framework has been adopted by the US Food and Drug Administration. One of the aims of PAT is to identify critical process parameters and their effect on the quality of the final product. Real time analysis of the process data enables better control of the processes to obtain a high quality product. The main purpose of this work was to monitor crucial pharmaceutical unit operations (from blending to coating) and to examine the effect of processing on solid-state transformations and physical properties. The tools used were near-infrared (NIR) and Raman spectroscopy combined with multivariate data analysis, as well as X-ray powder diffraction (XRPD) and terahertz pulsed imaging (TPI). To detect process-induced transformations in active pharmaceutical ingredients (APIs), samples were taken after blending, granulation, extrusion, spheronisation, and drying. These samples were monitored by XRPD, Raman, and NIR spectroscopy showing hydrate formation in the case of theophylline and nitrofurantoin. For erythromycin dihydrate formation of the isomorphic dehydrate was critical. Thus, the main focus was on the drying process. NIR spectroscopy was applied in-line during a fluid-bed drying process. Multivariate data analysis (principal component analysis) enabled detection of the dehydrate formation at temperatures above 45°C. Furthermore, a small-scale rotating plate device was tested to provide an insight into film coating. The process was monitored using NIR spectroscopy. A calibration model, using partial least squares regression, was set up and applied to data obtained by in-line NIR measurements of a coating drum process. The predicted coating thickness agreed with the measured coating thickness. For investigating the quality of film coatings TPI was used to create a 3-D image of a coated tablet. With this technique it was possible to determine coating layer thickness, distribution, reproducibility, and uniformity. In addition, it was possible to localise defects of either the coating or the tablet. It can be concluded from this work that the applied techniques increased the understanding of physico-chemical properties of drugs and drug products during and after processing. They additionally provided useful information to improve and verify the quality of pharmaceutical dosage forms

Studies on the pro-oxidative properties and neurotoxic potential of Angeli's salt-derived nitroxyl (HNO/NO-)

The biological function of nitric oxide and its oxidized forms has received a great deal of attention over the past two decades. However much less attention has been focused on the reduced nitric oxide, nitroxyl (HNO). Unlike NO, HNO is highly reactive species and thus it needs to be generated by using donor compounds under experimental conditions. Currently there is only one donor available, Angeli s salt, which releases HNO in a controlled fashion under pysiological conditions. Prior studies have shown the pro-oxidative and cytotoxic potential of Angeli s salt compared to NO donors. The high reactivity of HNO with cysteine thiols is considered to form the biochemical basis for its unique properties compared to other nitrogen oxides. Such thiol modification cold result in disturbances of vital cellular functions and subsequently to death of disturbance sensitive cells, such as neurons. Therefore modification of proteins and lipids was studied in vitro and the potential neurotoxicity was studied in vivo by local infusion of Angeli s salt into the rat central nervous system. The results show that under aerobic in vitro conditions, HNO can, subsequent to autoxidation, cause irreversible oxidative modification of proteins and lipids. These effects are not however seen in cell culture or following infusion of Angeli s salt directly into the rat central nervous tissue likely due to presence of lower oxygen and higher thiol concentration. However, due to high reactivity with thiols, HNO can cause irreversible inactivation of cysteine modification sensitive enzymes such as cysteine proteases papain in vitro and cathepsin B in cell culture. Furthermore it was shown that infusion of HNO releasing Angeli s salt into the rat central nervous system causes necrotic cell death and motor dysfunction following infusion into the lumbal intrathecal space. In conclusion, the acute neurotoxic potential of Angeli s salt was shown to be relatively low, but still higher compared to NO donors. HNO was shown to affect numerous cellular processes which could result in neurotoxicity if HNO was produced in vivo.

The structure of Norway spruce (Picea abies [L.] Karst.) stems in relation to wood properties of sawn timber

An important challenge in forest industry is to get the appropriate raw material out from the forests to the wood processing industry. Growth and stem reconstruction simulators are therefore increasingly integrated in industrial conversion simulators, for linking the properties of wooden products to the three-dimensional structure of stems and their growing conditions. Static simulators predict the wood properties from stem dimensions at the end of a growth simulation period, whereas in dynamic approaches, the structural components, e.g. branches, are incremented along with the growth processes. The dynamic approach can be applied to stem reconstruction by predicting the three-dimensional stem structure from external tree variables (i.e. age, height) as a result of growth to the current state. In this study, a dynamic growth simulator, PipeQual, and a stem reconstruction simulator, RetroSTEM, are adapted to Norway spruce (Picea abies [L.] Karst.) to predict the three-dimensional structure of stems (tapers, branchiness, wood basic density) over time such that both simulators can be integrated in a sawing simulator. The parameterisation of the PipeQual and RetroSTEM simulators for Norway spruce relied on the theoretically based description of tree structure developing in the growth process and following certain conservative structural regularities while allowing for plasticity in the crown development. The crown expressed both regularity and plasticity in its development, as the vertical foliage density peaked regularly at about 5 m from the stem apex, varying below that with tree age and dominance position (Study I). Conservative stem structure was characterized in terms of (1) the pipe ratios between foliage mass and branch and stem cross-sectional areas at crown base, (2) the allometric relationship between foliage mass and crown length, (3) mean branch length relative to crown length and (4) form coefficients in branches and stem (Study II). The pipe ratio between branch and stem cross-sectional area at crown base, and mean branch length relative to the crown length may differ in trees before and after canopy closure, but the variation should be further analysed in stands of different ages and densities with varying site fertilities and climates. The predictions of the PipeQual and RetroSTEM simulators were evaluated by comparing the simulated values to measured ones (Study III, IV). Both simulators predicted stem taper and branch diameter at the individual tree level with a small bias. RetroSTEM predictions of wood density were accurate. For focusing on even more accurate predictions of stem diameters and branchiness along the stem, both simulators should be further improved by revising the following aspects in the simulators: the relationship between foliage and stem sapwood area in the upper stem, the error source in branch sizes, the crown base development and the height growth models in RetroSTEM. In Study V, the RetroSTEM simulator was integrated in the InnoSIM sawing simulator, and according to the pilot simulations, this turned out to be an efficient tool for readily producing stand scale information about stem sizes and structure when approximating the available assortments of wood products.

The effects of thinning and fertilisation on wood and tracheid properties of Norway spruce (Picea abies) the results of long-term experiments

The aim of this thesis was to study the basic relationships between thinning and fertilisation, tree growth rate and wood properties of Norway spruce (Picea abies (L.) Karst.) throughout a stand rotation. The material consisted of a total of 109 trees from both long-term thinning (Heinola, 61°10'N, 26°01'E; Punkaharju, 61°49'N, 29°19'E) and fertilisation-thinning experiments (Parikkala, 61°36'N, 29°22'E; Suonenjoki, 62°45'N, 27°00'E) in Finland. Wood properties, i.e., radial increment, wood density, latewood proportion, tracheid length, cell wall thickness and lumen diameter, as well as relative lignin content, were measured in detail from the pith to the bark, as well as from the stem base towards the stem apex. Intensive thinning and fertilisation treatments of Norway spruce stands increased (8% 64%) the radial increment of studied trees at breast height (1.3 m). At the same time, a faster growth rate slightly decreased average wood density (2% 7%), tracheid length (0% 9%) and cell wall thickness (1% 17%). The faster growth resulted in only small changes (0% 9%) in lumen diameter and relative lignin content (1% 2%; lignin content was 25.4% 26%). However, the random variation in wood properties was large both between and within trees and annual rings. The results of this thesis indicate that the prevailing thinning and fertilisation treatments of Norway spruce stands in Fennoscandia may significantly enhance the radial increment of individual trees, and cause only small or no detrimental changes in wood and tracheid properties.

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.

Modifications of surface materials and their effects on cleanability as studied by radiochemical methods

Modifications of surface materials and their effects on cleanability have important impacts in many fields of activity. In this study the primary aim was to develop radiochemical methods suitable for evaluating cleanability in material research for different environments. Another aim was to investigate the effects of surface modifications on cleanabilitity and surface properties of plastics, ceramics, concrete materials and also their coatings in conditions simulating their typical environments. Several new 51Cr and 14C labelled soils were developed for testing situations. The new radiochemical methods developed were suitable for examining different surface materials and different soil types, providing quantitative information about the amount of soil on surfaces. They also take into account soil soaked into surfaces. The supporting methods colorimetric determination and ATP bioluminescence provided semi-quantitative results. The results from the radiochemical and supporting methods partly correlated with each other. From a material research point of view numerous new materials were evaluated. These included both laboratory-made model materials and commercial products. Increasing the amount of plasticizer decreased the cleanability of poly(vinyl chloride) (PVC) materials. Microstructured surfaces of plastics improved the cleanability of PVC from particle soils, whereas for oil soil microstructuring reduced the cleanability. In the case of glazed ceramic materials, coatings affected the cleanability. The roughness of surfaces correlated with cleanability from particle soils and the cleanability from oil soil correlated with the contact angles. Organic particle soil was removed more efficiently from TiO2-coated ceramic surfaces after UV-radiation than without UV treatment, whereas no effect was observed on the cleanability of oil soil. Coatings improved the cleanability of concrete flooring materials intended for use in animal houses.

Biochemical and structural properties of Potato virus A VPg

The potato virus A (PVA) genome linked protein (VPg) is a multifunctional protein that takes part in vital infection cycle events such as replication and movement of the virus from cell to cell. VPg is attached to the 5´ end of the genome and is carried in the tip structure of the filamentous virus particle. VPg is also the last protein to be cleaved from the polyprotein. VPg interacts with several viral and host proteins and is phosphorylated at several positions. These features indicate a central role in virus epidemiology and a requirement for an efficient but flexible mechanism for switching between different functions. -- This study examines some of the key VPg functions in more detail. Mutations in the positively charged region from Ala38 to Lys44 affected the NTP binding, uridylylation, and in vitro translation inhibition activities of VPg, whereas in vivo translation inhibition was not affected. Some of the data generated in this study implicated the structural flexibility of the protein in functional activities. VPg lacks a rigid structure, which could allow it to adapt conformationally to different functions as needed. A major finding of this study is that PVA VPg belongs to the class of ´intrinsically disordered proteins´ (IDPs). IDPs are a novel protein class that has helped to explain the observed lack of structure. The existence of IDPs clearly shows that proteins can be functional and adapt a native fold without a rigid structure. Evidence for the intrinsic disorder of VPg was provided by CD spectroscopy, NMR, fluorescence spectroscopy, bioinformatic analysis, and limited proteolytic digestion. The structure of VPg resembles that of a molten globule-type protein and has a hydrophobic core domain. Approximately 50% of the protein is disordered and an α-helical stabilization of these regions has been hypothesized. Surprisingly, VPg structure was stabilized in the presence of anionic lipid vesicles. The stabilization was accompanied by a change in VPg structure and major morphological modifications of the vesicles, including a pronounced increase in the size and appearance of pore or plaque like formations on the vesicle surface. The most likely scenario seems to be an α-helical stabilization of VPg which induces formation of a pore or channel-like structure on the vesicle surface. The size increase is probably due to fusion or swelling of the vesicles. The latter hypothesis is supported by the evident disruption of the vesicles after prolonged incubation with VPg. A model describing the results is presented and discussed in relation to other known properties of the protein.