Boundary controllability problems for the wave equation in a parallelepiped

AbstractThe wave equation in an N-dimensional parallelepiped with boundary control equal zero everywhere except of an edge of dimension N − 2 is considered. The other case which is investigated is the boundary control acting on a face of dimension N − 1 and depending on N − 1 independent variables (including t). It is proved that, in both cases, the system is not approximately controllable for any T > 0

Divided Differences & Restriction Operator on Paley-Wiener Spaces PWtaupPW_{tau}^{p} for N−N-Carleson Sequences

For a sequence of complex numbers $\Lambda$ we consider the restriction operator $R_{\Lambda}$ defined on Paley-Wiener spaces $PW_{\tau}^{p}$ ($1<p<\infty$). Lyubarskii and Seip gave necessary and sufficient conditions on $\Lambda$ for $R_{\Lambda}$ to be an isomorphism between $PW_{\tau}^{p}$ and a certain weighted $l^{p}$ space. The Carleson condition appears to be necessary. We extend their result to $N-$Carleson sequences (finite unions of $N$ disjoint Carleson sequences). More precisely, we give necessary and sufficient conditions for $R_{\Lambda}$ to be an isomorphism between $PW_{\tau}^{p}$ and an appropriate sequence space involving divided differences

Identification of a piecewise constant coefficient in the beam equation

AbstractIn this paper we recover an unknown piecewise constant coefficient in the beam equation by a given boundary input–output map. We extend the boundary control method in inverse problems to the case of the string and beam equations with nonsmooth coefficients and reduce the dynamical inverse problem to a spectral one

Cyclosporine A up-regulates angiotensin II receptors and calcium responses in human vascular smooth muscle cells.

Cyclosporine A up-regulates angiotensin II receptors and calcium responses in human vascular smooth muscle cells.BackgroundThe most widely used immunosuppressive drug for preventing graft rejection and treating autoimmune diseases is currently cyclosporine A (CsA). However, CsA also causes vasoconstriction, which is considered to be at the origin of CsA-induced nephrotoxicity and hypertension. To evaluate the cellular basis for these side effects, we studied the influence of CsA on the regulation of the free cytosolic Ca2+ concentration ([Ca2+]c) in cultured human vascular smooth muscle cells (SMCs).MethodsSMCs were isolated from the medial layer of human aorta. [Ca2+]c regulation was studied by fluorimetry with fura 2 and by measuring 45Ca2+ effluxes. Angiotensin II (Ang II) receptors were detected by [125I]Ang II binding.ResultsPretreatment of human SMCs for 24hours with CsA in its therapeutic concentration range (0.1 to 10.0 μm) had no effect on basal [Ca2+]c, but increased the [Ca2+]c elevation and 45Ca2+ efflux when cells were stimulated with Ang II. Half-maximal effects occurred at approximately 1 μm CsA. The CsA effects on [Ca2+]c were accompanied by a nearly twofold increase in Ang II receptor number, whereas no change in affinity to Ang II was observed. CsA did not alter endothelin-1- or thapsigargin-induced 45Ca2+ efflux. Increases in both Ca2+ responses and [125I]Ang II binding were attenuated by the transcriptional inhibitor actinomycin D. The effects of CsA did not appear to be mediated by calcineurin inhibition because cyclosporine H, which is not immunosuppressive, also increased the Ang II-induced 45Ca2+ efflux.ConclusionThese data suggest that CsA preferentially up-regulates the transcription of Ang II receptors, which very likely leads to vasoconstriction in vivo and could be at the origin of CsA-induced hypertension and nephrotoxicity in humans

Optimal boundary control of the wave equation with pointwise control constraints

Optimal control, Boundary control, Dirichlet control, Wave equation, Control constraints, Discretization, Finite differences, Discretization error,