23 research outputs found

    Geometry of jet spaces and integrable systems

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    An overview of some recent results on the geometry of partial differential equations in application to integrable systems is given. Lagrangian and Hamiltonian formalism both in the free case (on the space of infinite jets) and with constraints (on a PDE) are discussed. Analogs of tangent and cotangent bundles to a differential equation are introduced and the variational Schouten bracket is defined. General theoretical constructions are illustrated by a series of examples.Comment: 54 pages; v2-v6 : minor correction

    Global wealth disparities drive adherence to COVID-safe pathways in head and neck cancer surgery

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    Activity of the osteocalcin promoter in skeletal sites of transgenic mice and during osteoblast differentiation in bone marrow-derived stromal cell cultures: effects of age and sex

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    The bone-specific osteocalcin gene is a well established marker of osteoblast activity. We have studied osteocalcin transcription in transgenic mice carrying rat osteocalcin promoter-chloramphenicol acetyltransferase (CAT) reporter constructs. Transgenic lines carrying each of the 1.7-, 1.1-, 0.72-, or 0.35-kilobase promoter constructs expressed the reporter gene in a tissue-specific manner. However, each of these constructs was sensitive to site of integration effects, reflected by a high frequency of nonexpressing transgenic lines. High expression of the 1.7-kilobase promoter in osseous tissues was accompanied by low ectopic expression in the brain. Analysis of CAT expression in femurs, calvariae, and lumbar vertebrae of this line indicated considerable variability in promoter activity among individual transgenic animals. Analysis of the variance in CAT activity demonstrated a linkage between promoter activities in these distant skeletal sites. Promoter activity was inversely correlated with age, and females exhibited severalfold higher activity than age-matched males. Bone marrow stromal cells from these animals, cultured under conditions that support osteoblast differentiation, exhibited the expected postproliferative onset of osteocalcin promoter activity, as assessed by CAT assay. The ex vivo CAT activity was not dependent on the sex or the age of the donor transgenic mouse. Taken together, our results are consistent with the hypothesis that a common, probably humoral, factor(s) regulates osteocalcin transcription in distant skeletal sites. We suggest that the abundance of this factor(s) is different between males and females and among individual mice at a given time point, and that ex vivo culturing of osteoblasts reduces the variation in osteocalcin promoter activity by eliminating the physiological contribution of this factor
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