3 citations · 3 across the 9 of their papers we have counts for
9 papers
A Circuit-Theoretic Anomaly Resolved by Nonstandard Analysis
A. H. Zemanian
An anomaly in electrical circuit theory is the disappearance of some of the energy when two capacitors, one charged and the other uncharged, are connected together through resistan…
The Galaxies of Nonstandard Enlargements of Infinite and Transfinite grpahs of Higher Ranks: II
A. H. Zemanian
This report is an improvement of a prior report (Report 814). It sharpens the principal theorem (Theorem 5.1 of Report 814) and also simplifies its proof. There are also several mi…
Bounds on the Nodal Statuses of Some Transfinite Graphs
A. H. Zemanian
The bounds on the statuses of the nodes in a finite graph established by Entringer, Jackson, and Snyder are extended herein so that they apply to the nodes in a transfinite graph o…
The Galaxies of Nonstandard Enlargements of Transfinite Graphs of Higher Rsnks
A. H. Zemanian
In a prior work, the galaxies of the nonstandard enlargements of conventionally infinite graphs and also of transfinite graphs of the first rank of transfiniteness were defined, ex…
The Galaxies of Nonstandard Enlargements of Infinite and Transfinite Graphs
A. H. Zemanian
The galaxies of nonstandard enlargements of conventionally infinite as well as of transfinite graphs are defined, analyzed, and illustrated by some examples. It is then shown that…
Nonstandard Transfinite Graphs and Networks of Higher Ranks
A. H. Zemanian
In Chapter 8 of the Book, ``Graphs and Networks: Transfinite and Nonstandard'' (published by Birkhauser-Boston in 2004), nonstandard versions of transfinite graphs and of electrica…