By Peter Kuchment

This booklet addresses a brand new interdisciplinary quarter rising at the border among quite a few components of arithmetic, physics, chemistry, nanotechnology, and computing device technological know-how. the focal point this is on difficulties and strategies with regards to graphs, quantum graphs, and fractals that parallel these from differential equations, differential geometry, or geometric research. additionally incorporated are such diversified subject matters as quantity concept, geometric workforce thought, waveguide conception, quantum chaos, quantum twine structures, carbon nano-structures, metal-insulator transition, computing device imaginative and prescient, and conversation networks. This quantity incorporates a precise selection of professional experiences at the major instructions in research on graphs (e.g., on discrete geometric research, zeta-functions on graphs, lately rising connections among the geometric team conception and fractals, quantum graphs, quantum chaos on graphs, modeling waveguide platforms and modeling quantum graph structures with waveguides, regulate idea on graphs), in addition to learn articles.

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