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Books > Reference & Interdisciplinary > Communication studies > Information theory > Cybernetics & systems theory
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Pristine Transfinite Graphs and Permissive Electrical Networks (Hardcover, 2001 ed.)
Loot Price: R1,712
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Pristine Transfinite Graphs and Permissive Electrical Networks (Hardcover, 2001 ed.)
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A transfinite graph or electrical network of the first rank is
obtained conceptually by connecting conventionally infinite graphs
and networks together at their infinite extremities. This process
can be repeated to obtain a hierarchy of transfiniteness whose
ranks increase through the countable ordinals. This idea, which is
of recent origin, has enriched the theories of graphs and networks
with radically new constructs and research problems. The book
provides a more accessible introduction to the subject that, though
sacrificing some generality, captures the essential ideas of
transfiniteness for graphs and networks. Thus, for example, some
results concerning discrete potentials and random walks on
transfinite networks can now be presented more concisely.
Conversely, the simplifications enable the development of many new
results that were previously unavailable. Topics and features: *A
simplified exposition provides an introduction to transfiniteness
for graphs and networks.*Various results for conventional graphs
are extended transfinitely. *Minty's powerful analysis of monotone
electrical networks is also extended transfinitely.*Maximum
principles for node voltages in linear transfinite networks are
established. *A concise treatment of random walks on transfinite
networks is developed. *Conventional theory is expanded with
radically new constructs. Mathematicians, operations researchers
and electrical engineers, in particular, graph theorists,
electrical circuit theorists, and probabalists will find an
accessible exposition of an advanced subject.
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