By Armen H. Zemanian
This self-contained ebook examines effects on transfinite graphs and networks completed via a continual learn attempt up to now numerous years. those new effects, protecting the mathematical concept of electric circuits, are various from these provided in formerly released books through the writer, Transfiniteness for Graphs, electric Networks, and Random Walks and Pristine Transfinite Graphs and Permissive electric Networks.
Two preliminary chapters current the initial conception summarizing all crucial principles wanted for the ebook and should relieve the reader from any have to seek advice these previous books. next chapters are committed totally to novel effects and canopy:
* Connectedness ideas---considerably extra advanced for transfinite graphs in comparison to these of finite or conventionally countless graphs----and their dating to hypergraphs
* Distance ideas---which play an immense function within the thought of finite graphs---and their extension to transfinite graphs with extra problems, corresponding to the alternative of natural-number distances by means of ordinal-number distances
* Nontransitivity of path-based connectedness alleviated by way of exchanging paths with walks, resulting in a extra strong conception for transfinite graphs and networks
Additional positive aspects include:
* using nonstandard research in novel ways in which ends up in a number of completely new effects relating hyperreal working issues for transfinite networks and hyperreal transients on transfinite transmission traces; this use of hyperreals encompasses for the 1st time transfinite networks and transmission traces containing inductances and capacitances, as well as resistances
* an invaluable appendix with ideas from nonstandard research utilized in the book
* could function a reference textual content or as a graduate-level textbook in classes or seminars
Graphs and Networks: Transfinite and Nonstandard will entice a various readership, together with graduate scholars, electric engineers, mathematicians, and physicists engaged on endless electric networks. additionally, the growing to be and shortly giant variety of mathematicians operating in nonstandard research could be attracted through the unconventional program of the research hired within the paintings.