The Dirichlet-to-Neumann operator for divergence form problems

We present a way of defining the Dirichlet-to-Neumann operator on general Hilbert spaces using a pair of operators for which each one's adjoint is formally the negative of the other. In particular, we define an abstract analogue of trace spaces and are able to give meaning to the Dirichlet-to-Neumann operator of divergence form operators perturbed by a bounded potential in cases where the boundary of the underlying domain does not allow for a well-defined trace. Moreover, a representation of the Dirichlet-to-Neumann operator as a first-order system of partial differential operators is provided. Using this representation, we address convergence of the Dirichlet-to-Neumann operators in the case that the appropriate reciprocals of the leading coefficients converge in the weak operator topology. We also provide some extensions to the case where the bounded potential is not coercive and consider resolvent convergence

The Dirichlet-to-Neumann operator for divergence form problems

We present a way of defining the Dirichlet-to-Neumann operator on general Hilbert spaces using a pair of operators for which each one’s adjoint is formally the negative of the other. In particular, we define an abstract analogue of trace spaces and are able to give meaning to the Dirichlet-to-Neumann operator of divergence form operators perturbed by a bounded potential in cases where the boundary of the underlying domain does not allow for a well-defined trace. Moreover, a representation of the Dirichlet-to-Neumann operator as a first-order system of partial differential operators is provided. Using this representation, we address convergence of the Dirichlet-to-Neumann operators in the case that the appropriate reciprocals of the leading coefficients converge in the weak operator topology. We also provide some extensions to the case where the bounded potential is not coercive and consider resolvent convergence

Transcriptome profiling of ontogeny in the acridid grasshopper Chorthippus biguttulus

Acridid grasshoppers (Orthoptera:Acrididae) are widely used model organisms for developmental, evolutionary, and neurobiological research. Although there has been recent influx of orthopteran transcriptomic resources, many use pooled ontogenetic stages obscuring information about changes in gene expression during development. Here we developed a de novo transcriptome spanning 7 stages in the life cycle of the acridid grasshopper Chorthippus biguttulus. Samples from different stages encompassing embryonic development through adults were used for transcriptomic profiling, revealing patterns of differential gene expression that highlight processes in the different life stages. These patterns were validated with semi-quantitative RT-PCR. Embryonic development showed a strongly differentiated expression pattern compared to all of the other stages and genes upregulated in this stage were involved in signaling, cellular differentiation, and organ development. Our study is one of the first to examine gene expression during post-embryonic development in a hemimetabolous insect and we found that only the fourth and fifth instars had clusters of genes upregulated during these stages. These genes are involved in various processes ranging from synthesis of biogenic amines to chitin binding. These observations indicate that post-embryonic ontogeny is not a continuous process and that some instars are differentiated. Finally, genes upregulated in the imago were generally involved in aging and immunity. Our study highlights the importance of looking at ontogeny as a whole and indicates promising directions for future research in orthopteran development

CMS physics technical design report : Addendum on high density QCD with heavy ions

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