3,460 research outputs found
Heat Trace Asymptotics on Noncommutative Spaces
This is a mini-review of the heat kernel expansion for generalized Laplacians
on various noncommutative spaces. Applications to the spectral action
principle, renormalization of noncommutative theories and anomalies are also
considered.Comment: This is a contribution to the Proceedings of the 2007 Midwest
Geometry Conference in honor of Thomas P. Branson, published in SIGMA
(Symmetry, Integrability and Geometry: Methods and Applications) at
http://www.emis.de/journals/SIGMA
Continuous and Random Vapnik-Chervonenkis Classes
We show that if is a dependent theory then so is its Keisler
randomisation . In order to do this we generalise the notion of a
Vapnik-Chervonenkis class to families of -valued functions (a
\emph{continuous} Vapnik-Chervonenkis class), and we characterise families of
functions having this property via the growth rate of the mean width of an
associated family of convex compacts
String Theory and the Fuzzy Torus
We outline a brief description of non commutative geometry and present some
applications in string theory. We use the fuzzy torus as our guiding example.Comment: Invited review for IJMPA rev1: an imprecision corrected and a
reference adde
Weakly fuzzy topological entropy
summary:In 2005, İ. Tok fuzzified the notion of the topological entropy R. A. Adler et al. (1965) using the notion of fuzzy compactness of C. L. Chang (1968). In the present paper, we have proposed a new definition of the fuzzy topological entropy of fuzzy continuous mapping, namely weakly fuzzy topological entropy based on the notion of weak fuzzy compactness due to R. Lowen (1976) along with its several properties. We have shown that the topological entropy R. A. Adler et al. (1965) of continuous mapping , where is compact, is equal to the weakly fuzzy topological entropy of . We have also established an example that shows that the fuzzy topological entropy of İ. Tok (2005) cannot give such a bridge result to the topological entropy of Adler et al. (1965). Moreover, our definition of the weakly fuzzy topological entropy can be applied to find the topological entropy (namely weakly fuzzy topological entropy ) of the mapping (where is either compact or weakly fuzzy compact), whereas the topological entropy of Adler does not exist for the mapping (where is non-compact weakly fuzzy compact). Finally, a product theorem for the weakly fuzzy topological entropy has been established
Characterizations of minimal T3 1/2 L-topological spaces
AbstractFor L a closed sets lattice, we prove the existence and a characterization theorem of the minimal elements of T3 1/2 LX, where T3 1/2 LX is the set of all closed sets L-topologies on X ordered by inclusion
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