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We study mixed boundary value problems for an elliptic operator A on a manifold X with boundary Y, i.e., Au = f in int X, T (+/-) u = g(+/-) on int Y+/-, where Y is subdivided into subsets Y+/- with an interface Z and boundary conditions T+/- on Y+/- that are Shapiro-Lopatinskij elliptic up to Z from the respective sides. We assume that Z subset of Y is a manifold with conical singularity v. As an example we consider the Zaremba problem, where A is the Laplacian and T- Dirichlet, T+ Neumann conditions. The problem is treated as a corner boundary value problem near v which is the new point and the main difficulty in this paper. Outside v the problem belongs to the edge calculus as is shown in Bull. Sci. Math. ( to appear). With a mixed problem we associate Fredholm operators in weighted corner Sobolev spaces with double weights, under suitable edge conditions along Z {v} of trace and potential type. We construct parametrices within the calculus and establish the regularity of solutions.
Rezensiertes Werk:
Frank, Robert: Phrase Structure Composition and Syntactic Dependencies. - Cambridge, MA : MIT Press, 2002. - xiv + 326 S.
A novel quantum method to deal with typical system-bath dynamical problems is introduced. Subsystem discrete variable representation and bath coherent-state sets are used to write down a multiconfigurational expansion of the wave function of the whole system. With the help of the Dirac-Frenkel variational principle, simple equations of motion-a kind of Schrodinger-Langevin equation for the subsystem coupled to (pseudo) classical equations for the bath-are derived. True dissipative dynamics at all times is obtained by coupling the bath to a secondary, classical Ohmic bath, which is modeled by adding a friction coefficient in the derived pseudoclassical bath equations. The resulting equations are then solved for a number of model problems, ranging from tunneling to vibrational relaxation dynamics. Comparison of the results with those of exact, multiconfiguration time-dependent Hartree calculations in systems with up to 80 bath oscillators shows that the proposed method can be very accurate and might be of help in studying realistic problems with very large baths. To this end, its linear scaling behavior with respect to the number of bath degrees of freedom is shown in practice with model calculations using tens of thousands of bath oscillators.
A fluidic chip system was developed, which combines a stable generation of superoxide radicals and hydrogen peroxide with their sensorial detection. The generation of both reactive oxygen species was achieved by immobilization of xanthine oxidase on controlled pore glass in a reaction chamber. Antioxidants can be introduced into the fluidic chip system by means of mixing chamber. The detection of both species is based on the amperometric principle using a biosensor chip with two working electrodes. As sensing protein for both electrodes cytochrome c was used. The novel system was designed for the quantification of the antioxidant efficiency of different potential scavengers of the respective reactive species in an aqueous medium. Several model antioxidants such as ascorbic acid or catalase have been tested under flow conditions.
We present experimental results showing the diffuse reflection of a Bose Einstein condensate from a rough mirror, consisting of a dielectric substrate supporting a blue-detuned evanescent wave. The scattering is anisotropic, more pronounced in the direction of the surface propagation of the evanescent wave. These results agree very well with theoretical predictions.
Teleseismic tomography reveals no signature of the Dead Sea Transform in the upper mantle structure
(2006)
We present results of a tomographic inversion of teleseismic data recorded at 48 stations of a temporary network which was installed in the area of the Dead Sea Transform (DST) and operated for 1 yr in the framework of the multidisciplinary DESERT Project. The 3366 teleseismic P and PKP phases from 135 events were hand picked and corrected for surface topography and crustal thickness. The inversion shows pronounced low-velocity anomalies in the crust, beneath the DST, which are consistent with recent results from local-source tomography. These anomalies are likely related to the young sediments and fractured rocks in the fault zone. The deeper the retrieved anomalies are quite weak. Most prominent is the high-velocity strip-like anomaly striking SE-NW. We attribute this anomaly to the inherited heterogeneity of lithospheric structure, with a possible contribution by the shallow Precambrian basement east of the DST and to lower crustal heterogeneity reported in this region by other seismic studies. We do not observe reliable signature of the DST in the upper mantle structure. Some weak indications of low-velocity anomalies in the upper mantle beneath the DST may well result from the down-smearing of the strong upper crustal anomalies. We also see very little topography of the lithosphere-asthenosphere boundary beneath the DST, which would generate significant horizontal velocity variations. These results are consistent with predictions from a recent thereto-mechanical model of the DST. Our tomographic model provides some indication of hot mantle flow from the deeper upper mantle rooted in the region of the Red Sea. However, resolution tests show that this anomaly may well be beyond resolution of the model. (c) 2006 Elsevier B.V. All rights reserved.
Maldanids are usually divided into several subfamilies: Euclymeninae, Lumbriclymeninae, Maldaninae, Nicomachinae, Rhodininae, Clymenurinae, Notoproctinae, and Boguinae. The taxonomy of maldanids and the delimination of these taxa are mainly based on head morphology, total number of segments, chaetal structure, shape of the pygidium, and position of the anus. The maldanid ingroup relationships, as well as the monophyly of the proposed subfamilies, have so far not been investigated. Pilgrim (1977) described a shift of the notopodial chaetal rows from a transverse direction in anterior chaetigers to a more longitudinal one in posterior chaetigers in Clymene torquata (Leidy, 1855) and Euclymene oerstedii (Claparede, 1863), both belonging to the Euclymeninae. We investigated several maldanid species to assess the usefulness of this character for maldanid systematics and used 3D-reconstruction techniques to reveal the complete geometry of the chaetal sacs. Our investigation shows that a shift is apparent in Euclymene, Axiothella, Johnstonia (all Euclymeninae) and Clymenura (Clymenurinae), but absent in species like Maldane sarsi (Malmgren, 1865), Metasychis disparidentata (Moore, 1904) (both Maldaninae) and Petaloproctus borealis Ardwisson, 1906 (Nicomachinae). The shift is not typical for sedentary polychaetes and is apomorphic within maldanid polychaetes. It thus argues for a close relationship between Euclymeninae and Clymenurinae. The investigation of further maldanid species of different subfamilies may shed additional light on maldanid systematics.
We present experimental and numerical evidence of synchronization of burst events in two different modulated CO2 lasers. Bursts appear randomly in each laser as trains of large amplitude spikes intercalated by a small amplitude chaotic regime. Experimental data and model show the frequency locking of bursts in a suitable interval of coupling strength. We explain the mechanism of this phenomenon and demonstrate the inhibitory properties of the implemented coupling.
Recent research using the complex network approach has revealed a rich and complicated network topology in the cortical connectivity of mammalian brains. It is of importance to understand the implications of such complex network structures in the functional organization of the brain activities. Here we study this problem from the viewpoint of dynamical complex networks. We investigate synchronization dynamics on the corticocortical network of the cat by modeling each node (cortical area) of the network with a sub-network of interacting excitable neurons. We find that the network displays clustered synchronization behavior, and the dynamical clusters coincide with the topological community structures observed in the anatomical network. Our results provide insights into the relationship between the global organization and the functional specialization of the brain cortex.