26 research outputs found

    Thermoacoustic tomography with an arbitrary elliptic operator

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    Thermoacoustic tomography is a term for the inverse problem of determining of one of initial conditions of a hyperbolic equation from boundary measurements. In the past publications both stability estimates and convergent numerical methods for this problem were obtained only under some restrictive conditions imposed on the principal part of the elliptic operator. In this paper logarithmic stability estimates are obatined for an arbitrary variable principal part of that operator. Convergence of the Quasi-Reversibility Method to the exact solution is also established for this case. Both complete and incomplete data collection cases are considered.Comment: 16 page

    Topics in Mathematical Analysis

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    This volume contains most of the lectures of the "Minicorsi of Mathematical Analysis" held at the University of Padova in the years 2000-2003

    Widespread Endogenization of Genome Sequences of Non-Retroviral RNA Viruses into Plant Genomes

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    Non-retroviral RNA virus sequences (NRVSs) have been found in the chromosomes of vertebrates and fungi, but not plants. Here we report similarly endogenized NRVSs derived from plus-, negative-, and double-stranded RNA viruses in plant chromosomes. These sequences were found by searching public genomic sequence databases, and, importantly, most NRVSs were subsequently detected by direct molecular analyses of plant DNAs. The most widespread NRVSs were related to the coat protein (CP) genes of the family Partitiviridae which have bisegmented dsRNA genomes, and included plant- and fungus-infecting members. The CP of a novel fungal virus (Rosellinia necatrix partitivirus 2, RnPV2) had the greatest sequence similarity to Arabidopsis thaliana ILR2, which is thought to regulate the activities of the phytohormone auxin, indole-3-acetic acid (IAA). Furthermore, partitivirus CP-like sequences much more closely related to plant partitiviruses than to RnPV2 were identified in a wide range of plant species. In addition, the nucleocapsid protein genes of cytorhabdoviruses and varicosaviruses were found in species of over 9 plant families, including Brassicaceae and Solanaceae. A replicase-like sequence of a betaflexivirus was identified in the cucumber genome. The pattern of occurrence of NRVSs and the phylogenetic analyses of NRVSs and related viruses indicate that multiple independent integrations into many plant lineages may have occurred. For example, one of the NRVSs was retained in Ar. thaliana but not in Ar. lyrata or other related Camelina species, whereas another NRVS displayed the reverse pattern. Our study has shown that single- and double-stranded RNA viral sequences are widespread in plant genomes, and shows the potential of genome integrated NRVSs to contribute to resolve unclear phylogenetic relationships of plant species

    Closterovirus bipolar virion: Evidence for initiation of assembly by minor coat protein and its restriction to the genomic RNA 5′ region

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    The long flexuous virions of the Closteroviridae have a unique bipolar architecture incorporating two coat proteins, with most of the helical nucleocapsid encapsidated by the major coat protein (CP) and a small portion of one end encapsidated by the minor coat protein (CPm). It is not known whether CPm encapsidates the genomic RNA and, if so, which end and what effects transition between the two coat proteins. Two other virus-encoded proteins, an HSP70 homolog (HSP70h) and an ≈61-kDa protein, are required to augment virion assembly. In this work, we examine the in vivo encapsidation of Citrus tristeza virus by its CPm in the absence of CP. In the absence of other assembly-related proteins, CPm protected a family of 5′ coterminal RNAs, apparently because of pausing at different locations along the genomic RNA. Most of the nucleocapsids formed by CPm were short, but a few were full-length and infectious. Mutations within the 5′ nontranslated region demonstrated that the CPm origin of assembly overlaps the previously described conserved stem-and-loop structures that function as a cis-acting element required for RNA synthesis. Thus, in the absence of CP, the CPm encapsidation is initiated from the 5′ end of the genomic RNA. Coexpression of HSP70h and the p61 protein with CPm in protoplasts restricted encapsidation to the 5′ ≈630 nucleotides, which is close to the normal boundary of the bipolar virion, whereas the presence of either HSP70h or the p61 protein alone did not limit encapsidation by CPm
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