Extending the Support Theorem to Infinite Dimensions

The Radon transform is one of the most useful and applicable tools in functional analysis. First constructed by John Radon in 1917 it has now been adapted to several settings. One of the principle theorems involving the Radon transform is the Support Theorem. In this paper, we discuss how the Radon transform can be constructed in the white noise setting. We also develop a Support Theorem in this setting.Comment: 22 page

A Limiting Process to Invert the Gauss-Radon Transform

In this work we extend the finite dimensional Radon transform [23] to the Gaussian measure. We develop an inversion formula for this GaussRadon transform by way of Fourier inversion formula. We then proceed to extend these results to the infinite dimensional setting

Phylogenetic analysis identifies the invertebrate pathogen Helicosporidium sp. as a green alga (Chlorophyta)

Historically, the invertebrate pathogens of the genus Helicosporidium were considered to be either protozoa or fungi, but the taxonomic position of this group has not been considered since 1931. Recently, a Helicosporidium sp., isolated from the blackfly Simulium jonesi Stone & Snoddy (Diptera: Simuliidae), has been amplified in the heterologous host Helicoverpa zea. Genomic DNA has been extracted from gradient-purified cysts. The 185, 28S and 5.8S regions of the Helicosporidium rDNA, as well as partial sequences of the actin and beta-tubulin genes, were amplified by PCR and sequenced. Comparative analysis of these nucleotide sequences was performed using neighbour-joining and maximum-parsimony methods. All inferred phylogenetic trees placed Helicosporidium sp. among the green algae (Chlorophyta), and this association was supported by bootstrap and parsimony jackknife values. Phylogenetic analysis focused on the green algae depicted Helicosporidium sp. as a close relative of Prototheca wickerhamii and Prototheca zopfii (Chlorophyta, Trebouxiophyceae), two achlorophylous, pathogenic green algae. On the basis of this phylogenetic analysis, Helicosporidium sp. is clearly neither a protist nor a fungus, but appears to be the first described algal invertebrate pathogen. These conclusions lead us to propose the transfer of the genus Helicosporidium to Chlorophyta, Trebouxiophyceae

Life cycle and epizootiology of Amblyospora ferocis (Microspora: Amblyosporidae) in the mosquito Psorophora ferox (Diptera: Culicidae)

A natural population of Psorophora ferox (Humbold, 1820) infected with the microsporidium Amblyospora ferocis García et Becnel, 1994 was sampled weekly during a seven-month survey in Punta Lara, Buenos Aires Province, Argentina. The sequence of development of A. ferocis in larvae of P. ferox leading to the formation of meiospores followed the developmental pathway previously reported for various species of Amblyospora. The natural prevalence of A. ferocis in the larval population of P. ferox ranged from 0.4% to 13.8%. Spores were detected in the ovaries of field-collected females of P. ferox and were shown to be responsible for transovarial transmission of A. ferocis to the next generation of mosquito larvae in laboratory tests. These spores were binucleate and slightly pyriform in shape. The prevalence of A. ferocis in the adult population ranged from 2.7% to 13.9%. Data on effects of the infection on female fecundity showed that infected field-collected adults of P. ferox laid an average of 47.6 ± 6.5 eggs of which 35.8% ± 4.1% hatched. Uninfected field-collected adults of P. ferox laid 82.8 ± 6.8 eggs of which 64.1% ± 5.5% hatched. Six species of copepods living together with P. ferox were fed meiospores from field-infected larvae but none became infected. Horizontal transmission of A. ferocis to P. ferox larvae remains unknown.Centro de Estudios Parasitológicos y de Vectore

Life cycle and epizootiology of Amblyospora ferocis (Microspora: Amblyosporidae) in the mosquito Psorophora ferox (Diptera: Culicidae)

A natural population of Psorophora ferox (Humbold, 1820) infected with the microsporidium Amblyospora ferocis García et Becnel, 1994 was sampled weekly during a seven-month survey in Punta Lara, Buenos Aires Province, Argentina. The sequence of development of A. ferocis in larvae of P. ferox leading to the formation of meiospores followed the developmental pathway previously reported for various species of Amblyospora. The natural prevalence of A. ferocis in the larval population of P. ferox ranged from 0.4% to 13.8%. Spores were detected in the ovaries of field-collected females of P. ferox and were shown to be responsible for transovarial transmission of A. ferocis to the next generation of mosquito larvae in laboratory tests. These spores were binucleate and slightly pyriform in shape. The prevalence of A. ferocis in the adult population ranged from 2.7% to 13.9%. Data on effects of the infection on female fecundity showed that infected field-collected adults of P. ferox laid an average of 47.6 ± 6.5 eggs of which 35.8% ± 4.1% hatched. Uninfected field-collected adults of P. ferox laid 82.8 ± 6.8 eggs of which 64.1% ± 5.5% hatched. Six species of copepods living together with P. ferox were fed meiospores from field-infected larvae but none became infected. Horizontal transmission of A. ferocis to P. ferox larvae remains unknown.Centro de Estudios Parasitológicos y de Vectore

Comparison of plastid 16S rDNA (rrn16) genes from Helicosporidium spp.: evidence supporting the reclassification of Helicosporidia as green algae (Chlorophyta)

The Helicosporidia are invertebrate pathogens that have recently been identified as non-photosynthetic green algae (Chlorophyta). In order to confirm the algal nature of the genus Helicosporidium, the presence of a retained chloroplast genome in Helicosporidia cells was investigated. Fragments homologous to plastid 16S rRNA (rrn16) genes were amplified successfully from cellular DNA extracted from two different Helicosporidium isolates. The fragment sequences are 1269 and 1266 bp long, are very AT-rich (60.7 %) and are similar to homologous genes sequenced from non-photosynthetic green algae. Maximum-parsimony, maximum-likelihood and neighbour-joining methods were used to infer phylogenetic trees from an rrn16 sequence alignment. All trees depicted the Helicosporidia as sister taxa to the non-photosynthetic, pathogenic alga Prototheca zopfii. Moreover, the trees identified Helicosporidium spp. as members of a clade that included the heterotrophic species Prototheca spp. and the mesotrophic species Chlorella protothecoides. The clade is always strongly supported by bootstrap values, suggesting that all these organisms share a most recent common ancestor. Phylogenetic analyses inferred from plastid 16S rRNA genes confirmed that the Helicosporidia are non-photosynthetic green algae, close relatives of the genus Prototheca (Chlorophyta, Trebouxiophyceae). Such phylogenetic affinities suggest that Helicosporidium spp. are likely to possess Prototheca-like organelles and organelle genomes

TRIMOLECULAR REACTIONS OF URANIUM HEXAFLUORIDE WITH WATER

The hydrolysis reaction of uranium hexafluoride (UF{sub 6}) is a key step in the synthesis of uranium dioxide (UO{sub 2}) powder for nuclear fuels. Mechanisms for the hydrolysis reactions are studied here with density functional theory and the Stuttgart small-core scalar relativistic pseudopotential and associated basis set for uranium. The reaction of a single UF{sub 6} molecule with a water molecule in the gas phase has been previously predicted to proceed over a relatively sizeable barrier of 78.2 kJ {center_dot} mol{sup -1}, indicating this reaction is only feasible at elevated temperatures. Given the observed formation of a second morphology for the UO{sub 2} product coupled with the observations of rapid, spontaneous hydrolysis at ambient conditions, an alternate reaction pathway must exist. In the present work, two trimolecular hydrolysis mechanisms are studied with density functional theory: (1) the reaction between two UF{sub 6} molecules and one water molecule, and (2) the reaction of two water molecules with a single UF{sub 6} molecule. The predicted reaction of two UF{sub 6} molecules with one water molecule displays an interesting 'fluorine-shuttle' mechanism, a significant energy barrier of 69.0 kJ {center_dot} mol{sup -1} to the formation of UF{sub 5}OH, and an enthalpy of reaction ({Delta}H{sub 298}) of +17.9 kJ {center_dot} mol{sup -1}. The reaction of a single UF{sub 6} molecule with two water molecules displays a 'proton-shuttle' mechanism, and is more favorable, having a slightly lower computed energy barrier of 58.9 kJ {center_dot} mol{sup -1} and an exothermic enthalpy of reaction ({Delta}H{sub 298}) of -13.9 kJ {center_dot} mol{sup -1}. The exothermic nature of the overall UF{sub 6} + 2 {center_dot} H{sub 2}O trimolecular reaction and the lowering of the barrier height with respect to the bimolecular reaction are encouraging; however, the sizable energy barrier indicates further study of the UF{sub 6} hydrolysis reaction mechanism is warranted to resolve the remaining discrepancies between the predicted mechanisms and experimental observations

TRANSITION STATE FOR THE GAS-PHASE REACTION OF URANIUM HEXAFLUORIDE WITH WATER

Density Functional Theory and small-core, relativistic pseudopotentials were used to look for symmetric and asymmetric transitions states of the gas-phase hydrolysis reaction of uranium hexafluoride, UF{sub 6}, with water. At the B3LYP/6-31G(d,p)/SDD level, an asymmetric transition state leading to the formation of a uranium hydroxyl fluoride, U(OH)F{sub 5}, and hydrogen fluoride was found with an energy barrier of +77.3 kJ/mol and an enthalpy of reaction of +63.0 kJ/mol (both including zero-point energy corrections). Addition of diffuse functions to all atoms except uranium led to only minor changes in the structure and relative energies of the reacting complex and transition state. However, a significant change in the product complex structure was found, significantly reducing the enthalpy of reaction to +31.9 kJ/mol. Similar structures and values were found for PBE0 and MP2 calculations with this larger basis set, supporting the B3LYP results. No symmetric transition state leading to the direct formation of uranium oxide tetrafluoride, UOF{sub 4}, was found, indicating that the reaction under ambient conditions likely includes several more steps than the mechanisms commonly mentioned. The transition state presented here appears to be the first published transition state for the important gas-phase reaction of UF{sub 6} with water