Abstract A Lagrangian coherent structure (LCS) in a nonautonomous flow can be viewed as an open dynamical system, Cheap Nike Air Max Nz from which there is time-dependent escape or entry. A difficulty with this viewpoint is formulating a definition for the time-dependent boundary of the LCS, since it does not correspond to an entity across which there is zero transport. Complementary to this is the question of how to determine the escape rate—the time-dependent fluid flux—across this purported boundary. http://www.nikeairprestonz.nu These questions are addressed within the context of nonautonomously perturbed two-dimensional compressible flow. The LCS boundaries are thought of in terms of time-varying stable and unstable manifolds, whose primary locations are quantified. A definition for the time-varying flux across these is offered, and… computationally tractable formulæ with a strong relation to Melnikov functions are provided. Nike Air Max Nz Mens Simplifications of these formulæ for frequently considered situations (incompressibility, time-periodic perturbations) are demonstrated to be easily computable using Fourier transforms. Explicit connections to lobe areas and the average flux are also provided.
We report a unique case of adenoid cystic carcinoma (ACC) of the maxillary sinus, with gradual histologic transformation from lower-grade ACC (cribriform and tubular types) to high-grade adenocarcinoma (HGA) showing a sequential histologic spectrum via solid-type ACC. A 74-year-old man presented with swelling and mild pain of the right cheek. Nike Air Presto Nz CT scan showed a mass measuring approximately 4 cm, with marked bone destruction in the right maxillary sinus. A surgically resected specimen revealed that the tumor was comprised of three different components: HGA and solid-type ACC in the central portion and lower-grade ACC in the periphery. http://www.nikeairprestonz.nu The tumor was discriminated from a dedifferentiated carcinoma or hybrid tumor. Autopsy specimens also demonstrated both solid-type ACC and HGA components in… the lung and spleen. Immunohistochemically, positive staining of p53 protein was detected on both solid-type ACC and HGA cells, but cyclin D1 and HER2/neu was only seen in HGA cells. Solid-type ACC cells were immunoreactive for CD117 (c-kit), but lower-grade ACC and HGA cells were negative. Cheap Nike Air Max This case suggests that the overexpression of CD117, p53 protein, cyclin D1, and HER2/neu might be involved in the progression from lower-grade ACC to solid-type ACC and HGA.
We consider the class of quadratically-constrained quadratic-programming methods in the framework extended from optimization to more general variational problems. Previously, in the optimization case, Anitescu (SIAM J. Nike Air Max Nz Wholesale Optim. 12, 949–978, 2002 ) showed superlinear convergence of the primal sequence under the Mangasarian-Fromovitz constraint qualification and the quadratic growth condition. Quadratic convergence of the primal-dual sequence was established by Fukushima, http://www.nikeairprestonz.nu Luo and Tseng (SIAM J. Optim. 13, 1098–1119, 2003 ) under the assumption of convexity, the Slater constraint qualification, and a strong second-order sufficient condition. We obtain a new local convergence result, which complements the above (it is neither stronger nor weaker): we prove primal-dual quadratic convergence… under the linear independence constraint qualification, strict complementarity, and a second-order sufficiency condition. Nike Air Max Tavas White Additionally, our results apply to variational problems beyond the optimization case. Finally, we provide a necessary and sufficient condition for superlinear convergence of the primal sequence under a Dennis-Moré type condition.