3,350 research outputs found
Projective Systems of Noncommutative Lattices as a Pregeometric Substratum
We present an approximation to topological spaces by {\it noncommutative}
lattices. This approximation has a deep physical flavour based on the
impossibility to fully localize particles in any position measurement. The
original space being approximated is recovered out of a projective limit.Comment: 30 pages, Latex. To appear in `Quantum Groups and Fundamental
Physical Applications', ISI Guccia, Palermo, December 1997, D. Kastler and M.
Rosso Eds., (Nova Science Publishers, USA
Knowledge reduction of dynamic covering decision information systems with varying attribute values
Knowledge reduction of dynamic covering information systems involves with the
time in practical situations. In this paper, we provide incremental approaches
to computing the type-1 and type-2 characteristic matrices of dynamic coverings
because of varying attribute values. Then we present incremental algorithms of
constructing the second and sixth approximations of sets by using
characteristic matrices. We employ experimental results to illustrate that the
incremental approaches are effective to calculate approximations of sets in
dynamic covering information systems. Finally, we perform knowledge reduction
of dynamic covering information systems with the incremental approaches
Covering compact metric spaces greedily
A general greedy approach to construct coverings of compact metric spaces by
metric balls is given and analyzed. The analysis is a continuous version of
Chvatal's analysis of the greedy algorithm for the weighted set cover problem.
The approach is demonstrated in an exemplary manner to construct efficient
coverings of the n-dimensional sphere and n-dimensional Euclidean space to give
short and transparent proofs of several best known bounds obtained from
deterministic constructions in the literature on sphere coverings.Comment: (v2) 10 pages, minor revision, accepted in Acta Math. Hunga
Combinatorial and topological phase structure of non-perturbative n-dimensional quantum gravity
We provide a non-perturbative geometrical characterization of the partition
function of -dimensional quantum gravity based on a coarse classification of
riemannian geometries. We show that, under natural geometrical constraints, the
theory admits a continuum limit with a non-trivial phase structure parametrized
by the homotopy types of the class of manifolds considered. The results
obtained qualitatively coincide, when specialized to dimension two, with those
of two-dimensional quantum gravity models based on random triangulations of
surfaces.Comment: 13 page
Characteristic of partition-circuit matroid through approximation number
Rough set theory is a useful tool to deal with uncertain, granular and
incomplete knowledge in information systems. And it is based on equivalence
relations or partitions. Matroid theory is a structure that generalizes linear
independence in vector spaces, and has a variety of applications in many
fields. In this paper, we propose a new type of matroids, namely,
partition-circuit matroids, which are induced by partitions. Firstly, a
partition satisfies circuit axioms in matroid theory, then it can induce a
matroid which is called a partition-circuit matroid. A partition and an
equivalence relation on the same universe are one-to-one corresponding, then
some characteristics of partition-circuit matroids are studied through rough
sets. Secondly, similar to the upper approximation number which is proposed by
Wang and Zhu, we define the lower approximation number. Some characteristics of
partition-circuit matroids and the dual matroids of them are investigated
through the lower approximation number and the upper approximation number.Comment: 12 page
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