67,232 research outputs found

    A refined invariant subspace method and applications to evolution equations

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    The invariant subspace method is refined to present more unity and more diversity of exact solutions to evolution equations. The key idea is to take subspaces of solutions to linear ordinary differential equations as invariant subspaces that evolution equations admit. A two-component nonlinear system of dissipative equations was analyzed to shed light on the resulting theory, and two concrete examples are given to find invariant subspaces associated with 2nd-order and 3rd-order linear ordinary differential equations and their corresponding exact solutions with generalized separated variables.Comment: 16 page

    Finite dimensional integrable Hamiltonian systems associated with DSI equation by Bargmann constraints

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    The Davey-Stewartson I equation is a typical integrable equation in 2+1 dimensions. Its Lax system being essentially in 1+1 dimensional form has been found through nonlinearization from 2+1 dimensions to 1+1 dimensions. In the present paper, this essentially 1+1 dimensional Lax system is further nonlinearized into 1+0 dimensional Hamiltonian systems by taking the Bargmann constraints. It is shown that the resulting 1+0 dimensional Hamiltonian systems are completely integrable in Liouville sense by finding a full set of integrals of motion and proving their functional independence.Comment: 10 pages, in LaTeX, to be published in J. Phys. Soc. Jpn. 70 (2001

    Tick-borne encephalitis virus induces chemokine RANTES expression via activation of IRF-3 pathway.

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    BACKGROUND: Tick-borne encephalitis virus (TBEV) is one of the most important flaviviruses that targets the central nervous system (CNS) and causes encephalitides in humans. Although neuroinflammatory mechanisms may contribute to brain tissue destruction, the induction pathways and potential roles of specific chemokines in TBEV-mediated neurological disease are poorly understood. METHODS: BALB/c mice were intracerebrally injected with TBEV, followed by evaluation of chemokine and cytokine profiles using protein array analysis. The virus-infected mice were treated with the CC chemokine antagonist Met-RANTES or anti-RANTES mAb to determine the role of RANTES in affecting TBEV-induced neurological disease. The underlying signaling mechanisms were delineated using RANTES promoter luciferase reporter assay, siRNA-mediated knockdown, and pharmacological inhibitors in human brain-derived cell culture models. RESULTS: In a mouse model, pathological features including marked inflammatory cell infiltrates were observed in brain sections, which correlated with a robust up-regulation of RANTES within the brain but not in peripheral tissues and sera. Antagonizing RANTES within CNS extended the survival of mice and reduced accumulation of infiltrating cells in the brain after TBEV infection. Through in vitro studies, we show that virus infection up-regulated RANTES production at both mRNA and protein levels in human brain-derived cell lines and primary progenitor-derived astrocytes. Furthermore, IRF-3 pathway appeared to be essential for TBEV-induced RANTES production. Site mutation of an IRF-3-binding motif abrogated the RANTES promoter activity in virus-infected brain cells. Moreover, IRF-3 was activated upon TBEV infection as evidenced by phosphorylation of TBK1 and IRF-3, while blockade of IRF-3 activation drastically reduced virus-induced RANTES expression. CONCLUSIONS: Our findings together provide insights into the molecular mechanism underlying RANTES production induced by TBEV, highlighting its potential importance in the process of neuroinflammatory responses to TBEV infection
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