483 research outputs found

    Boundedness of Pseudodifferential Operators on Banach Function Spaces

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    We show that if the Hardy-Littlewood maximal operator is bounded on a separable Banach function space X(Rn)X(\mathbb{R}^n) and on its associate space X(Rn)X'(\mathbb{R}^n), then a pseudodifferential operator Op(a)\operatorname{Op}(a) is bounded on X(Rn)X(\mathbb{R}^n) whenever the symbol aa belongs to the H\"ormander class Sρ,δn(ρ1)S_{\rho,\delta}^{n(\rho-1)} with 0<ρ10<\rho\le 1, 0δ<10\le\delta<1 or to the the Miyachi class Sρ,δn(ρ1)(ϰ,n)S_{\rho,\delta}^{n(\rho-1)}(\varkappa,n) with 0δρ10\le\delta\le\rho\le 1, 0δ00\le\delta0. This result is applied to the case of variable Lebesgue spaces Lp()(Rn)L^{p(\cdot)}(\mathbb{R}^n).Comment: To appear in a special volume of Operator Theory: Advances and Applications dedicated to Ant\'onio Ferreira dos Santo

    The Insoluble Carbonaceous Material of CM Chondrites as Possible Source of Discrete Organics During the Asteroidal Aqueous Phase

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    The larger portion of the organic carbon in carbonaceous chondrites (CC) is present as a complex and heterogeneous macromolecular material that is insoluble in acids and most solvents (IOM). So far, it has been analyzed only as a whole by microscopy (TEM) and spectroscopy (IR, NMR, EPR), which have offered and overview of its chemical nature, bonding, and functional group composition. Chemical or pyrolytic decomposition has also been used in combination with GC-MS to identify individual compounds released by these processes. Their value in the recognition of the original IOM structure resides in the ability to properly interpret the decomposition pathways for any given process. We report here a preliminary study of IOM from the Murray meteorite that combines both the analytical approaches described above, under conditions that would realistically model the IOM hydrothermal exposure in the meteorite parent body. The aim is to document the possible release of water and solvent soluble organics, determine possible changes in NMR spectral features, and ascertain, by extension, the effect of this loss on the frame of the IOM residue. Additional information is included in the original extended abstract

    Life-Detection Technologies for the Next Two Decades

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    Since its inception six decades ago, astrobiology has diversified immensely to encompass several scientific questions including the origin and evolution of Terran life, the organic chemical composition of extraterrestrial objects, and the concept of habitability, among others. The detection of life beyond Earth forms the main goal of astrobiology, and a significant one for space exploration in general. This goal has galvanized and connected with other critical areas of investigation such as the analysis of meteorites and early Earth geological and biological systems, materials gathered by sample-return space missions, laboratory and computer simulations of extraterrestrial and early Earth environmental chemistry, astronomical remote sensing, and in-situ space exploration missions. Lately, scattered efforts are being undertaken towards the R&D of the novel and as-yet-space-unproven life-detection technologies capable of obtaining unambiguous evidence of extraterrestrial life, even if it is significantly different from Terran life. As the suite of space-proven payloads improves in breadth and sensitivity, this is an apt time to examine the progress and future of life-detection technologies.Comment: 6 pages, the white paper was submitted to and cited by the National Academy of Sciences in support of the Astrobiology Science Strategy for the Search for Life in the Univers

    Expression Profiling of PBMC-based Diagnostic Gene Markers Isolated from Vasculitis Patients

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    Vasculitis (angiitis) is a systemic autoimmune disease that often causes fatal symptoms. We aimed to isolate cDNA markers that would be useful for diagnosing not only vasculitis but also other autoimmune diseases. For this purpose, we used stepwise subtractive hybridization and cDNA microarray analyses to comprehensively isolate the genes whose expressions are augmented in peripheral blood mononuclear cells (PBMCs) pooled from vasculitis patients. Subsequently, we used quantitative real-time polymerase chain reaction (qRT–PCR) to examine the mRNA levels of each candidate gene in individual patients. These analyses indicated that seven genes exhibit remarkably augmented expression in many vasculitis patients. Of these genes, we analyzed G0/G1 switch gene 2 (G0S2) further because G0S2 expression is also enhanced in the PBMCs of patients with systemic lupus erythematodes (SLE). We generated G0S2 transgenic mice that ubiquitously overexpress human G0S2. Although we did not observe any obvious vasculitis-related histopathologic findings in these mice, these mice are unhealthy as they produce only few offspring and showed elevated serum levels of two autoimmunity-related antibodies, anti-nuclear antibody, and anti-double strand DNA antibody. Thus, our large-scale gene profiling study may help finding sensitive and specific DNA markers for diagnosing autoimmune diseases including vasculitis and SLE

    RASSF1A–LATS1 signalling stabilizes replication forks by restricting CDK2-mediated phosphorylation of BRCA2

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    Genomic instability is a key hallmark of cancer leading to tumour heterogeneity and therapeutic resistance. ​BRCA2 has a fundamental role in error-free DNA repair but also sustains genome integrity by promoting ​RAD51 nucleofilament formation at stalled replication forks. ​CDK2 phosphorylates ​BRCA2 (pS3291-​BRCA2) to limit stabilizing contacts with polymerized ​RAD51; however, how replication stress modulates ​CDK2 activity and whether loss of pS3291-​BRCA2 regulation results in genomic instability of tumours are not known. Here we demonstrate that the Hippo pathway kinase ​LATS1 interacts with ​CDK2 in response to genotoxic stress to constrain pS3291-​BRCA2 and support ​RAD51 nucleofilaments, thereby maintaining genomic fidelity during replication stalling. We also show that ​LATS1 forms part of an ​ATR-mediated response to replication stress that requires the tumour suppressor ​RASSF1A. Importantly, perturbation of the ​ATR–​RASSF1A–​LATS1 signalling axis leads to genomic defects associated with loss of ​BRCA2 function and contributes to genomic instability and ‘BRCA-ness’ in lung cancers
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