By Armen H. Zemanian
This self-contained e-book examines effects on transfinite graphs and networks accomplished via a continuous study attempt in past times a number of years. those new effects, overlaying the mathematical thought 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 concept summarizing all crucial principles wanted for the booklet and may 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 complex for transfinite graphs compared to these of finite or conventionally endless graphs----and their dating to hypergraphs
* Distance ideas---which play a tremendous position within the idea of finite graphs---and their extension to transfinite graphs with extra problems, equivalent to the substitute of natural-number distances through ordinal-number distances
* Nontransitivity of path-based connectedness alleviated by means of changing paths with walks, resulting in a extra strong idea for transfinite graphs and networks
Additional good points include:
* using nonstandard research in novel ways in which results in numerous solely new effects pertaining to 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. in addition, the becoming and shortly great variety of mathematicians operating in nonstandard research might be attracted by means of the unconventional software of the research hired within the paintings.