1,721,108 research outputs found

    On coupled systems of PDEs with unbounded coefficients

    Full text link
    We study the Cauchy problem associated with parabolic systems of the form Dtu = A(t)u in Cb (Rd; Rm), the space of continuous and bounded functions f: Rd → Rm. Here A(t) is a coupled nonautonomous elliptic operator acting on vector-valued functions, having diffusion and drift coefficients which change from equation to equation. We prove existence and uniqueness of the evolution operator G(t, s) which governs the problem in Cb (Rd; Rm) and its positivity. The compactness of G(t, s) inCb (Rd; Rm) and some of its consequences are also studied. Finally, we extend the evolution operator G(t, s) to the Lp-spaces related to the so called “evolution system of measures” and we provide conditions for the compactness of G(t, s) in this setting

    Instability of free interfaces in premixed flame propagation

    Full text link
    In this survey, we are interested in the instability of flame fronts regarded as free interfaces. We successively consider a classical Arrhenius kinetics (thin flame) and a stepwise ignition-tempera ture kinetics (thick flame) with two free interfaces. A general method initially developed for thin flame problems subject to interface jump conditions is proving to be an effective strategy for smoother thick flame systems. It relies on the elimination of the free interface(s) and reduction to a fully nonlinear parabolic problem. The theory of analytic semigroups is a key tool to study the linearized operators

    Generation of semigroups associated to strongly coupled elliptic operators in Lp(Rd;Rm)

    Full text link
    A class of vector-valued elliptic operators with unbounded coefficients, coupled up to the second-order is investigated in the Lebesgue space Lp (Rd ; Rm ) with p ∈ (1, ∞), providing sufficient conditions for the generation of an analytic C0-semigroup T (t). Under further assumptions, a characterization of the domain of the infinitesimal generator is given

    Follicular dendritic cell sarcoma

    No full text
    Follicular dendritic cells (FDC) are mesenchymal-derived dendritic cells located in B-follicles where they play a pivotal role in triggering and maintaining B-cell adaptive immune response. In 1986 Dr. Juan Rosai first reported a series of neoplasms showing features of FDC and defined it as Follicular Dendritic Cell Tumor, subsequently renamed as “sarcoma” (FDCS). In its seminal and subsequent articles Rosai and colleagues highlighted the heterogeneous microscopic appearance of FDCS and its immunohistochemical and ultrastructural features. FDCS mostly occurs in extranodal sites (79.4% of cases) and lymph nodes (15.1%); in about 7%-10% of cases it is associated with hyaline-vascular Castleman disease. Given its significant growth pattern and cytological variability, FDCS can be confused with various neoplasms and even inflammatory processes. The diagnosis requires the use of a broad spectrum of FDC markers (e.g. CD21, CD23, CD35, clusterin, CXCL13, podoplanin), particularly considering that tumor antigen-loss is frequent. The inflammatory-pseudotumor-like (IPT-like) variant of FDCS, in addition to its peculiar histopathological and clinical features, is characterized by positivity of tumor cells for Epstein-Barr virus, representing a diagnostic requisite. No distinctive genetic and molecular anomalies have been identified in FDCS. It often carries an aberrant clonal karyotype and chromosomal structural alterations, frequently involving onco-suppressor genes. Direct or next generation sequencing showed alterations on genes belonging to the NF-κB regulatory pathway and cell-cycle regulators. In contrast to hematopoietic-derived histiocytic and dendritic cells tumors, FDCS typically lacks mutations in genes related to the MAPK pathway. FDCS recurs locally in 28% and metastasizes in 27% of cases. Extent of the disease, surgical resectability and histopathological features are significantly associated with the outcome. IPT-like FDCS behaves as an indolent tumor, even if it often recurs locally over years. Complete surgical excision is the gold standard of treatment. Data on targeted therapies (e.g.: tyrosine kinase inhibitors) or immune checkpoint inhibitors are very limited and responses are variable. A better understanding of the molecular drivers of this tumor may lead to potential new therapeutic strategies

    Histopathological Aspects of Coeliac Disease

    No full text
    Currently, the diagnosis of coeliac disease (CD) is based on the combination of raised serum anti-tissue transglutaminase or antiendomysial antibodies and the presence of histological alterations of variable degree in the duodenal mucosa. Interpretation of duodenal biopsies depends on a number of variables - biopsy number, size, orientation, handling and staining - and the lack of standardisation may cause diagnostic controversy or even misdiagnosis. Biopsy handling and orientation are of utmost importance in order to avoid artifacts that may impair the pathologist's ability to detect pathology. Immunostaining with anti-CD3 monoclonal antibody should be carried out and a simplified histological classification may help to distinguish atrophic from non-atrophic stages of CD enteropathy, to differentiate it from other entities and from some complications as refractory CD and lymphoma. © 2011 Touch Briefings
    corecore