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Spectral Analysis on Graph-like Spaces
Small-radius tubular structures have attracted considerable attention in the last few years, and are frequently used in different areas such as Mathematical Physics, Spectral Geometry and Global Analysis. In this monograph, we analyse Laplace-like operators on thin tubular structures ("graph-like spaces''), and their natural limits on metric graphs. In particular, we explore norm resolvent convergence, convergence of the spectra and resonances. Since the underlying spaces in the thin radius limit change, and become singular in the limit, we develop new tools such as norm convergence of operators acting in different Hilbert spaces, an extension of the concept of boundary triples to partial differential operators, and an abstract definition of resonances via boundary triples. These tools are formulated in an abstract framework, independent of the original problem of graph-like spaces, so that they can be applied in many other situations where the spaces are perturbed.
The Bookseller
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Olaf Stapledon
William Olaf Stapledon is best remembered for the extraordinary works of speculative fiction he published between 1930 and 1950. As a novelist, he was known as the spokesman for the Age of Einstein and has influenced writers as diverse as Virginia Woolf, Arthur C. Clarke, and Doris Lessing. This biography is the first to draw on a vast body of unpublished and private documents—interviews, correspondence, archival material, and papers in private hands—to reveal fully the internal struggles that shaped Stapledon's life and reclaim for public attention a distinctive voice of the modern era. Late in his life in an unpublished "letter to the future" Stapledon unwittingly provided the rational...
The Postal Record
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Symmetries of Nonlinear PDEs on Metric Graphs and Branched Networks
This Special Issue focuses on recent progress in a new area of mathematical physics and applied analysis, namely, on nonlinear partial differential equations on metric graphs and branched networks. Graphs represent a system of edges connected at one or more branching points (vertices). The connection rule determines the graph topology. When the edges can be assigned a length and the wave functions on the edges are defined in metric spaces, the graph is called a metric graph. Evolution equations on metric graphs have attracted much attention as effective tools for the modeling of particle and wave dynamics in branched structures and networks. Since branched structures and networks appear in d...
