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.

The Phraseology and Structure of Latin Building Inscriptions in Roman North Africa

This study analyses the diction of Latin building inscriptions. Despite its importance, this topic has rarely been discussed before: the most substantial contribution on the subject is a short dissertation by Klaus Gast (1965) that focuses on 100 inscriptions dating mostly from the Republican period. Marietta Horster (2001) also touched upon this theme in her thesis on imperial building inscriptions. I have collected my source material in North Africa because more Latin building inscriptions dating from the Imperial period have survived there than in any other area of the Roman Empire. By means of a thorough and independent survey, I have assembled all relevant African Latin building inscriptions datable to the Roman period (between 146 BC and AD 425), 1002 texts, into a corpus. These inscriptions are all fully edited in Appendix 1; Appendix 2 contains references to earlier editions. To facilitate search operations, both are also available in electronic form. They are downloadable from the address http://www.helsinki.fi/hum/kla/htm/jatkoopinnot.htm. Chapter one is an introduction dealing with the nature of building inscriptions as source material. Chapter two offers a statistical overview of the material. The following main section of the work falls into five chapters, each of which analyses one main part of a building inscription. An average building inscription can be divided into five parts: the starting phrase opens the inscription (a dedication to gods, for example), the subject part identifies the builder, the object part describes the constructed or repaired building, the predicate part records the building activity and the supplement part offers additional information on the project (it can specify the funding, for instance). These chapters are systematic and chronological and their purpose is to register and interpret the phrases used, to analyse reasons for their use and for their popularity among the different groups of builders. Chapter eight, which follows the main section of the work, creates a typology of building inscriptions based on their structure. It also presents the most frequently attested types of building inscriptions. The conclusion describes, on a general level, how the diction of building inscriptions developed during the period of study and how this striking development resulted from socio-economic changes that took place in Romano-African society during Antiquity. This study shows that the phraseology of building inscriptions had a clear correlation both with the type of builder and with the date of carving. Private builders tended to accentuate their participation (especially its financial side) in the project; honouring the emperor received more emphasis in the building inscriptions set up by communities; the texts produced by the army were concise. The chronological development is so clear that it enables stylistic dating. At the beginning of the imperial period the phrases were clear, concrete, formal and stereotyped but by Late Antiquity they have become vague, subjective, flexible, varied and even rhetorically or poetically coloured.

Structure informationnelle et constructions du kabyle : Etude de trois types de phrase dans le cadre de la grammaire constructionnelle

Information structure and Kabyle constructions Three sentence types in the Construction Grammar framework The study examines three Kabyle sentence types and their variants. These sentence types have been chosen because they code the same state of affairs but have different syntactic structures. The sentence types are Dislocated sentence, Cleft sentence, and Canonical sentence. I argue first that a proper description of these sentence types should include information structure and, second, that a description which takes into account information structure is possible in the Construction Grammar framework. The study thus constitutes a testing ground for Construction Grammar for its applicability to a less known language. It constitutes a testing ground notably because the differentiation between the three types of sentences cannot be done without information structure categories and, consequently, these categories must be integrated also in the grammatical description. The information structure analysis is based on the model outlined by Knud Lambrecht. In that model, information structure is considered as a component of sentence grammar that assures the pragmatically correct sentence forms. The work starts by an examination of the three sentence types and the analyses that have been done in André Martinet s functional grammar framework. This introduces the sentence types chosen as the object of study and discusses the difficulties related to their analysis. After a presentation of the state of the art, including earlier and more recent models, the principles and notions of Construction Grammar and of Lambrecht s model are introduced and explicated. The information structure analysis is presented in three chapters, each treating one of the three sentence types. The analyses are based on spoken language data and elicitation. Prosody is included in the study when a syntactic structure seems to code two different focus structures. In such cases, it is pertinent to investigate whether these are coded by prosody. The final chapter presents the constructions that have been established and the problems encountered in analysing them. It also discusses the impact of the study on the theories used and on the theory of syntax in general.

Biophysical Characterization of Oxidized Phospholipids : Implications for Altered Membrane Structure and Function

The present study aims to elucidate the modifications in the structure and functionality of the phospholipid matrix of biological membranes brought about by free radical-mediated oxidative damage of its molecular constituents. To this end, the surface properties of two oxidatively modified phospholipids bearing an aldehyde or carboxyl function at the end of truncated sn-2 acyl chain were studied using a Langmuir balance. The results obtained reveal both oxidized species to have a significant impact on the structural dynamics of phospholipid monolayers, as illustrated by the progressive changes in force-area isotherms with increasing mole fraction of the oxidized lipid component. Moreover, surface potential measurements revealed considerable modifications in the electric properties of oxidized phospholipid containing monolayers during film compression, suggesting a packing state-controlled reorientation of the intramolecular electric dipoles of the lipid headgroups and acyl chains. Based on the above findings, a model describing the conformational state of oxidized phospholipid molecules in biological membranes is proposed, involving the protrusion of the acyl chains bearing the polar functional groups out from the hydrocarbon phase to the surrounding aqueous medium. Oxidative modifications alter profoundly the physicochemical properties of unsaturated phospholipids and are therefore readily anticipated to have important implications for their interactions with membrane-associating molecules. Along these lines, the carboxyl group bearing lipid was observed to bind avidly the peripheral membrane protein cytochrome c. The binding was reversed following increase in ionic strength or addition of polyanionic ATP, thus suggesting it to be driven by electrostatic interactions between cationic residues of the protein and the deprotonated lipid carboxyl exposed to the aqueous phase. The presence of aldehyde function bearing oxidized phospholipid was observed to enhance the intercalation of four antimicrobial peptides into phospholipid monolayers and liposomal bilayers. Partitioning of the peptides to monolayers was markedly attenuated by the aldehyde scavenger methoxyamine, revealing it to be mediated by the carbonyl moiety possibly through efficient hydrogen bonding or, alternatively, formation of covalent adduct in form of a Schiff base between the lipid aldehydes and primary amine groups of the peptide molecules. Lastly, both oxidized phospholipid species were observed to bind with high affinity three small membrane-partitioning therapeutic agents, viz. chlorpromazine, haloperidol, and doxorubicin. In conclusion, the results of studies conducted using biomimetic model systems support the notion that oxidative damage influences the molecular architecture as well as the bulk physicochemical properties of phospholipid membranes. Further, common polar functional groups carried by phospholipids subjected to oxidation were observed to act as molecular binding sites at the lipid-water interface. It is thus plausible that oxidized phospholipid species may elicit cellular level effects by modulating integration of various membrane-embedded and surface-associated proteins and peptides, whose conformational state, oligomerization, and functionality is known to be controlled by highly specific lipid-protein interactions and proper physical state of the membrane environment.

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.

Population structure of Pyrenophora teres, the causal agent of net blotch of barley

Spring barley is the most important crop in Finland based on cultivated land area. Net blotch, a disease caused by Pyrenophora teres Drech., is the most damaging disease of barley in Finland. The pressure to improve the economics and efficiency of agriculture has increased the need for more efficient plant protection methods. Development of durable host-plant resistance to net blotch is a promising possibility. However, deployment of disease resistant crops could initiate selection pressure on the pathogen (P. teres) population. The aim of this study was to understand the population biology of P. teres and to estimate the evolutionary potential of P. teres under selective pressure following deployment of resistance genes and application of fungicides. The study included mainly Finnish P. teres isolates. Population samples from Russia and Australia were also included. Using AFLP markers substantial genotypic variation in P. teres populations was identified. Differences among isolates were least within Finnish fields and significantly higher in Krasnodar, Russia. Genetic differentiation was identified among populations from northern Europe and from Australia, and between the two forms P. teres f. teres (PTT, net form of net blotch) and P. teres f. maculata (PTM, spot form of net blotch) in Australia. Differentiation among populations was also identified based on virulence between Finnish and Russian populations, and based on prochloraz (fungicide) tolerance in the Häme region in Finland. Surprisingly only PTT was recovered from Finland and Russia although both forms were earlier equally common in Finland. The reason for the shift in occurrence of forms in Finland remained uncertain. Both forms were found within several fields in Australia. Sexual reproduction of P. teres was supported by recover of both mating types in equal ratio in those areas although the prevalence of sexual mating seems to be less in Finland than in Australia. Population from Krasnodar was an exception since only one mating type was found in there. Based on the substantial high genotypic variation in Krasnodar it was suggested go represent an old P. teres population, whereas the Australian samples were suggested to represent newer populations. In conclusion, P. teres populations are differentiated at several levels. Human assistance in dispersal of P. teres on infected barley seed is obvious and decreases the differentiation among populations. This can increase the plant protection problems caused by this pathogen. P. teres is capable of sexual reproduction in several areas but the prevalence varies. Based on these findings it is apparent that P. teres has the potential to pose more serious problems in barley cultivation if plant protection is neglected. Therefore, good agricultural practices, including crop rotation and the use of healthy seed, are recommended.

Properties of intramuscular connective tissue in pork and poultry with reference to weakening of structure

The most common connective tissue research in meat science has been conducted on the properties of intramuscular connective tissue (IMCT) in connection with eating quality of meat. From the chemical and physical properties of meat, researchers have concluded that meat from animals younger than physiological maturity is the most tender. In pork and poultry, different challenges have been raised: the structure of cooked meat has weakened. In extreme cases raw porcine M. semimembranosus (SM) and in most turkey M. pectoralis superficialis (PS) can be peeled off in strips along the perimysium which surrounds the muscle fibre bundles (destructured meat), and when cooked, the slices disintegrate. Raw chicken meat is generally very soft and when cooked, it can even be mushy. The overall aim of this thesis was to study the thermal properties of IMCT in porcine SM in order to see if these properties were in association with destructured meat in pork and to characterise IMCT in poultry PS. First a 'baseline' study to characterise the thermal stability of IMCT in light coloured (SM and M. longissimus dorsi in pigs and PS in poultry) and dark coloured (M. infraspinatus in pigs and a combination of M. quadriceps femoris and M. iliotibialis lateralis in poultry) muscles was necessary. Thereafter, it was investigated whether the properties of muscle fibres differed in destructured and normal porcine muscles. Collagen content and also solubility of dark coloured muscles were higher than in light coloured muscles in pork and poultry. Collagen solubility was especially high in chicken muscles, approx. 30 %, in comparison to porcine and turkey muscles. However, collagen content and solubility were similar in destructured and normal porcine SM muscles. Thermal shrinkage of IMCT occurred at approximately 65 °C in pork and poultry. It occurred at lower temperature in light coloured muscles than in dark coloured muscles, although the difference was not always significant. The onset and peak temperatures of thermal shrinkage of IMCT were lower in destructured than in normal SM muscles, when the IMCT from SM muscles exhibiting ten lowest and ten highest ultimate pH values were investigated (onset: 59.4 °C vs. 60.7 °C, peak: 64.9 °C vs. 65.7 °C). As the destructured meat was paler than normal meat, the PSE (pale, soft, exudative) phenomenon could not be ruled out. The muscle fibre cross sectional area (CSA), the number of capillaries per muscle fibre CSA and per fibre and sarcomere length were similar in destructured and normal SM muscles. Drip loss was clearly higher in destructured than in normal SM muscles. In conclusion, collagen content and solubility and thermal shrinkage temperature vary between porcine and poultry muscles. One feature in the IMCT could not be directly associated with weakening of the meat structure. Poultry breast meat is very homogenous within the species.

Glycoalkaloid Content and Starch Structure in Solanum Species and Interspecific Somatic Potato Hybrids

When genome sections of wild Solanum species are bred into the cultivated potato (S. tuberosum L.) to obtain improved potato cultivars, the new cultivars must be evaluated for their beneficial and undesirable traits. Glycoalkaloids present in Solanum species are known for their toxic as well as for beneficial effects on mammals. On the other hand, glycoalkaloids in potato leaves provide natural protection against pests. Due to breeding, glycoalkaloid profile of the plant is affected. In addition, the starch properties in potato tubers can be affected as a result of breeding, because the crystalline properties are determined by the botanical source of the starch. Starch content and composition affect the texture of cooked and processed potatoes. In order to determine glycoalkaloid contents in Solanum species, simultaneous separation of glycoalkaloids and aglycones using reversed-phase high-performance liquid chromatography (HPLC) was developed. Clean-up of foliage samples was improved using a silica-based strong cation exchanger instead of octadecyl phases in solid-phase extraction. Glycoalkaloids alpha-solanine and alpha-chaconine were detected in potato tubers of cvs. Satu and Sini. The total glycoalkaloid concentration of non-peeled and immature tubers was at an acceptable level (under 20 mg/100 g of FW) in the cv. Satu, whereas concentration in cv. Sini was 23 mg/100 g FW. Solanum species (S. tuberosum, S. brevidens, S. acaule, and S. commersonii) and interspecific somatic hybrids (brd + tbr, acl + tbr, cmm + tbr) were analyzed for their glycoalkaloid contents using liquid chromatography-electrospray ionization-mass spectrometry (LC-ESI-MS). The concentrations in the tubers of the brd + tbr and acl + tbr hybrids remained under 20 mg/100 g FW. Glycoalkaloid concentration in the foliage of the Solanum species was between 110 mg and 890 mg/100 g FW. However, the concentration in the foliage of S. acaule was as low as 26 mg/100 g FW. The total concentrations of brd + tbr, acl + tbr, and cmm + tbr hybrid foliages were 88 mg, 180 mg, and 685 mg/100 g FW, respectively. Glycoalkaloids of both parental plants as well as new combinations of aglycones and saccharides were detected in somatic hybrids. The hybrids contained mainly spirosolanes, and glycoalkaloid structures having no 5,6-double bond in the aglycone. Based on these results, the glycoalkaloid profiles of the hybrids may represent a safer and more beneficial spectrum of glycoalkaloids than that found in currently cultivated varieties. Starch nanostructure of three different cultivars (Satu, Saturna, and Lady Rosetta), a wild species S. acaule, and interspecific somatic hybrids were examined by wide-angle and small-angle X-ray scattering (WAXS, SAXS). For the first time, the measurements were conducted on fresh potato tuber samples. Crystallinity of starch, average crystallite size, and lamellar distance were determined from the X-ray patterns. No differences in the starch nanostructure between the three different cultivars were detected. However, tuber immaturity was detected by X-ray scattering methods when large numbers of immature and mature samples were measured and the results were compared. The present study shows that no significant changes occurred in the nanostructures of starches resulting from hybridizations of potato cultivars.

Autoxidation of conjugated linoleic acid methyl ester in the presence of α-tocopherol: the hydroperoxide pathway

The autoxidation of conjugated linoleic acid (CLA) is poorly understood in spite of increasing interest in the beneficial biological properties of CLA and growing consumption of CLA-rich foods. In this thesis, the autoxidation reactions of the two major CLA isomers, 9-cis,11-trans-octadecadienoic acid and 10-trans,12-cis-octadecadienoic acid, are investigated. The results contribute to an understanding of the early stages of the autoxidation of CLA methyl ester, and provide for the first time a means of producing and separating intact CLA methyl ester hydroperoxides as well as basic knowledge on lipid hydroperoxides and their hydroxy derivatives. Conjugated diene allylic monohydroperoxides were discovered as primary autoxidation products formed during autoxidation of CLA methyl esters in the presence and absence of α-tocopherol. This established that one of the autoxidation pathways of CLA methyl ester is the hydroperoxide pathway. Hydroperoxides were produced from the two major CLA methyl esters by taking advantage of the effect of α-tocopherol to promote hydroperoxide formation. The hydroperoxides were analysed and separated first as methyl hydroxyoctadecadienoates and then as intact hydroperoxides by HPLC. The isolated products were characterized by UV, GC-MS, and NMR techniques. In the presence of a high amount of α-tocopherol, the autoxidation of CLA methyl ester yields six kinetically-controlled conjugated diene monohydroperoxides and is diastereoselective in favour of one particular geometric isomer as a pair of enantiomers. The primary autoxidation products produced from the two major CLA isomers include new positional isomers of conjugated diene monohydroperoxides, the 8-, 10-, 12-, and 14-hydroperoxyoctadecadienoates. Furthermore, two of these new positional isomers have an unusual structure for a cis,trans lipid hydroperoxide where the allylic methine carbon is adjacent to the cis instead of the usual trans double bond. The 1H and 13C NMR spectra of nine isomeric methyl hydroxyoctadecadienoates and of ten isomeric methyl hydroperoxyoctadecadienoates including the unusual cis,trans hydroperoxides, i.e. Me 8-OOH-9c,11t and Me 14-OOH-10t,12c, were fully assigned with the aid of 2D NMR spectroscopy. The assigned NMR data enabled determination of the effects of the hydroxyl and hydroperoxyl groups on the carbon chemical shifts of CLA isomers, identification of diagnostic signals, and determination of chemical shift differences of the olefinic resonances that may help with the assignment of structure to as yet unknown lipid hydroperoxides either as hydroxy derivatives or as intact hydroperoxides. A mechanism for the hydroperoxide pathway of CLA autoxidation in the presence of a high amount of α-tocopherol was proposed based on the characterized primary products, their relative distribution, and theoretical calculations. This is an important step forward in CLA research, where exact mechanisms for the autoxidation of CLA have not been presented before. Knowledge of these hydroperoxide formation steps is of crucial importance for understanding the subsequent steps and the different pathways of the autoxidation of CLA. Moreover, a deeper understanding of the autoxidation mechanisms is required for ensuring the safety of CLA-rich foods. Knowledge of CLA oxidation and how it differs from the oxidation of nonconjugated polyunsaturated fatty acids may also be the key to understanding the biological mechanisms of CLA activity.

Cavity-enhanced laser spectroscopic studies of vibrational overtones of acetylene

This thesis contains five experimental spectroscopic studies that probe the vibration-rotation energy level structure of acetylene and some of its isotopologues. The emphasis is on the development of laser spectroscopic methods for high-resolution molecular spectroscopy. Three of the experiments use cavity ringdown spectroscopy. One is a standard setup that employs a non-frequency stabilised continuous wave laser as a source. In the other two experiments, the same laser is actively frequency stabilised to the ringdown cavity. This development allows for increased repetition rate of the experimental signal and thus the spectroscopic sensitivity of the method is improved. These setups are applied to the recording of several vibration-rotation overtone bands of both H(12)C(12)CH and H(13)C(13)CH. An intra-cavity laser absorption spectroscopy setup that uses a commercial continuous wave ring laser and a Fourier transform interferometer is presented. The configuration of the laser is found to be sub-optimal for high-sensitivity work but the spectroscopic results are good and show the viability of this type of approach. Several ro-vibrational bands of carbon-13 substituted acetylenes are recorded and analysed. Compared with earlier work, the signal-to-noise ratio of a laser-induced dispersed infrared fluorescence experiment is enhanced by more than one order of magnitude by exploiting the geometric characteristics of the setup. The higher sensitivity of the spectrometer leads to the observation of two new symmetric vibrational states of H(12)C(12)CH. The precision of the spectroscopic parameters of some previously published symmetric states is also improved. An interesting collisional energy transfer process is observed for the excited vibrational states and this phenomenon is explained by a simple step-down model.