- In mathematics, an
ultrametric space is a
metric space in
which the
triangle inequality is
strengthened to d ( x , z ) ≤ max { d ( x , y ) , d ( y , z...
-
absolute value is
called an
ultrametric, non-Archimedean or p {\displaystyle p} -adic
place of K {\displaystyle K} . For any
ultrametric place v we have that...
-
example of an
additive distance matrix and its
corresponding tree: The
ultrametric distance matrix is
defined as an
additive matrix which models the constant...
- ways p-adic
analysis is less
subtle than
classical analysis,
since the
ultrametric inequality means, for example, that
convergence of
infinite series of...
-
statistical mechanics. An
ultrametric pseudo-differential
equation is an
equation which contains p-adic
numbers in an
ultrametric space.
Mathematical models...
- max ( | x | , | y | ) {\displaystyle |x+y|\leq \max(|x|,|y|)} is an
ultrametric absolute value. An
absolute value induces a
metric (and thus a topology)...
-
Archimedean or
satisfies the
stronger condition,
referred to as the
ultrametric triangle inequality, | x + y | ≤ max ( | x | , | y | ) , {\displaystyle...
-
equations and
quantum field theory, e.g. in
mathematical models that
include ultrametric pseudo-differential
equations in a non-Archimedean space. The
study of...
- make
sense and is
replaced with an
ultrametric inequality. This
leads to the
notion of a
generalized ultrametric.
These generalizations still induce...
- Theory,
International Journal of
Number Theory, and P-adic Numbers,
Ultrametric Analysis and Applications.
Thakur is a
founding member of-and for 15...
