Jumping numbers of a simple complete ideal in a two-dimensional regular local ring

The multiplier ideals of an ideal in a regular local ring form a family of ideals parametrized by non-negative rational numbers. As the rational number increases the corresponding multiplier ideal remains unchanged until at some point it gets strictly smaller. A rational number where this kind of diminishing occurs is called a jumping number of the ideal. In this manuscript we shall give an explicit formula for the jumping numbers of a simple complete ideal in a two dimensional regular local ring. In particular, we obtain a formula for the jumping numbers of an analytically irreducible plane curve. We then show that the jumping numbers determine the equisingularity class of the curve.

Plasmids and aromatic degradation in Sphingomonas for bioremediation : Aromatic ring cleavage genes in soil and rhizosphere

Microbial degradation pathways play a key role in the detoxification and the mineralization of polyaromatic hydrocarbons (PAHs), which are widespread pollutants in soil and constituents of petroleum hydrocarbons. In microbiology the aromatic degradation pathways are traditionally studied from single bacterial strains with capacity to degrade certain pollutant. In soil the degradation of aromatics is performed by a diverse community of micro-organisms. The aim of this thesis was to study biodegradation on different levels starting from a versatile aromatic degrader Sphingobium sp. HV3 and its megaplasmid, extending to revelation of diversity of key catabolic enzymes in the environment and finally studying birch rhizoremediation in PAH-polluted soil. To understand biodegradation of aromatics on bacterial species level, the aromatic degradation capacity of Sphingobium sp. HV3 and the role of the plasmid pSKY4, was studied. Toluene, m-xylene, biphenyl, fluorene, phenanthrene were detected as carbon and energy sources of the HV3 strain. Tn5 transposon mutagenesis linked the degradation capacity of toluene, m-xylene, biphenyl and naphthalene to the pSKY4 plasmid and qPCR expression analysis showed that plasmid extradiol dioxygenases genes (bphC and xylE) are inducted by phenanthrene, m-xylene and biphenyl whereas the 2,4-dichlorophenoxyacetic acid herbicide induced the chlorocatechol 1,2-dioxygenase gene (tfdC) from the ortho-pathway. A method to study upper meta-pathway extradiol dioxygenase gene diversity in soil was developed. The extradiol dioxygenases catalyse cleavage of the aromatic ring between a hydroxylated carbon and an adjacent non-hydroxylated carbon (meta-cleavage). A high diversity of extradiol dioxygenases were detected from polluted soils. The detected extradiol dioxygenases showed sequence similarity to known catabolic genes of Alpha-, Beta-, and Gammaproteobacteria. Five groups of extradiol dioxygenases contained sequences with no close homologues in the database, representing novel genes. In rhizoremediation experiment with birch (Betula pendula) treatment specific changes of extradiol dioxygenase communities were shown. PAH pollution changed the bulk soil extradiol dioxygenase community structure and birch rhizosphere contained a more diverse extradiol dioxygenase community than the bulk soil showing a rhizosphere effect. The degradation of pyrene in soil was enhanced with birch seedlings compared to soil without birch. The complete 280,923 kb nucleotide sequence of pSKY4 plasmid was determined. The open reading frames of pSKY4 were divided into putative conjugative transfer, aromatic degradation, replication/maintaining and transposition/integration function-encoding proteins. Aromatic degradation orfs shared high similarity to corresponding genes in pNL1, a plasmid from the deep subsurface strain Novosphingobium aromaticivorans F199. The plasmid backbones were considerably more divergent with lower similarity, which suggests that the aromatic pathway has functioned as a plasmid independent mobile genetic element. The functional diversity of microbial communities in soil is still largely unknown. Several novel clusters of extradiol dioxygenases representing catabolic bacteria, whose function, biodegradation pathways and phylogenetic position is not known were amplified with single primer pair from polluted soils. These extradiol dioxygenase communities were shown to change upon PAH pollution, which indicates that their hosts function in PAH biodegradation in soil. Although the degradation pathways of specific bacterial species are substantially better depicted than pathways in situ, the evolution of degradation pathways for the xenobiotic compounds is largely unknown. The pSKY4 plasmid contains aromatic degradation genes in putative mobile genetic element causing flexibility/instability to the pathway. The localisation of the aromatic biodegradation pathway in mobile genetic elements suggests that gene transfer and rearrangements are a competetive advantage for Sphingomonas bacteria in the environment.

Electromagnetic signatures of lightning near the HF frequency band

The dissertation deals with remote narrowband measurements of the electromagnetic radiation emitted by lightning flashes. A lightning flash consists of a number of sub-processes. The return stroke, which transfers electrical charge from the thundercloud to to the ground, is electromagnetically an impulsive wideband process; that is, it emits radiation at most frequencies in the electromagnetic spectrum, but its duration is only some tens of microseconds. Before and after the return stroke, multiple sub-processes redistribute electrical charges within the thundercloud. These sub-processes can last for tens to hundreds of milliseconds, many orders of magnitude longer than the return stroke. Each sub-process causes radiation with specific time-domain characteristics, having maxima at different frequencies. Thus, if the radiation is measured at a single narrow frequency band, it is difficult to identify the sub-processes, and some sub-processes can be missed altogether. However, narrowband detectors are simple to design and miniaturize. In particular, near the High Frequency band (High Frequency, 3 MHz to 30 MHz), ordinary shortwave radios can, in principle, be used as detectors. This dissertation utilizes a prototype detector which is essentially a handheld AM radio receiver. Measurements were made in Scandinavia, and several independent data sources were used to identify lightning sub-processes, as well as the distance to each individual flash. It is shown that multiple sub-processes radiate strongly near the HF band. The return stroke usually radiates intensely, but it cannot be reliably identified from the time-domain signal alone. This means that a narrowband measurement is best used to characterize the energy of the radiation integrated over the whole flash, without attempting to identify individual processes. The dissertation analyzes the conditions under which this integrated energy can be used to estimate the distance to the flash. It is shown that flash-by-flash variations are large, but the integrated energy is very sensitive to changes in the distance, dropping as approximately the inverse cube root of the distance. Flashes can, in principle, be detected at distances of more than 100 km, but since the ground conductivity can vary, ranging accuracy drops dramatically at distances larger than 20 km. These limitations mean that individual flashes cannot be ranged accurately using a single narrowband detector, and the useful range is limited to 30 kilometers at the most. Nevertheless, simple statistical corrections are developed, which enable an accurate estimate of the distance to the closest edge of an active storm cell, as well as the approach speed. The results of the dissertation could therefore have practical applications in real-time short-range lightning detection and warning systems.