Optimization in Finite Spaces

2020 ◽  
pp. 43-65
Author(s):  
Alan J. Lockett
Keyword(s):  
Finite Spaces

scholarly journals One-point reductions of finite spaces,h–regular CW–complexes and collapsibility

2008 ◽  
Vol 8 (3) ◽  
pp. 1763-1780 ◽  
Author(s):  
Jonathan Barmak ◽  
Elias Minian
Keyword(s):  
Cw Complexes ◽  
Finite Spaces

scholarly journals Orthogonal Arrays with Parameters $OA(s^3,s^2+s+1,s,2)$ and 3-Dimensional Projective Geometries

10.37236/556 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Kazuaki Ishii
Keyword(s):  
Orthogonal Array ◽  
Prime Power ◽  
Orthogonal Arrays ◽  
3 Dimensional ◽  
Projective Geometries ◽  
Finite Spaces ◽  
Alpha Type

There are many nonisomorphic orthogonal arrays with parameters $OA(s^3,s^2+s+1,s,2)$ although the existence of the arrays yields many restrictions. We denote this by $OA(3,s)$ for simplicity. V. D. Tonchev showed that for even the case of $s=3$, there are at least 68 nonisomorphic orthogonal arrays. The arrays that are constructed by the $n-$dimensional finite spaces have parameters $OA(s^n, (s^n-1)/(s-1),s,2)$. They are called Rao-Hamming type. In this paper we characterize the $OA(3,s)$ of 3-dimensional Rao-Hamming type. We prove several results for a special type of $OA(3,s)$ that satisfies the following condition: For any three rows in the orthogonal array, there exists at least one column, in which the entries of the three rows equal to each other. We call this property $\alpha$-type. We prove the following. (1) An $OA(3,s)$ of $\alpha$-type exists if and only if $s$ is a prime power. (2) $OA(3,s)$s of $\alpha$-type are isomorphic to each other as orthogonal arrays. (3) An $OA(3,s)$ of $\alpha$-type yields $PG(3,s)$. (4) The 3-dimensional Rao-Hamming is an $OA(3,s)$ of $\alpha$-type. (5) A linear $OA(3,s)$ is of $\alpha $-type.

scholarly journals Direct limits of finite spaces of orderings

1984 ◽  
Vol 112 (2) ◽  
pp. 391-406 ◽  
Author(s):  
Mieczysław Kula ◽  
Murray Marshall ◽  
Andrzej Sładek
Keyword(s):  
Spaces Of Orderings ◽  
Direct Limits ◽  
Finite Spaces

scholarly journals Finite spaces of signatures: research anouncement

1989 ◽  
Vol 19 (3) ◽  
pp. 893-896
Author(s):  
V. Powers
Keyword(s):  
Finite Spaces

Information Measures

2015 ◽  
pp. 129-142
Keyword(s):  
Information Theory ◽  
Mutual Information ◽  
Order Logic ◽  
Unified Framework ◽  
Higher Order Logic ◽  
Absolutely Continuous ◽  
Information Measures ◽  
Finite Spaces ◽  
Nikodym Derivative ◽  
Lebesgue Integration

This chapter presents a higher-order-logic formalization of the main concepts of information theory (Cover & Thomas, 1991), such as the Shannon entropy and mutual information, using the formalization of the foundational theories of measure, Lebesgue integration, and probability. The main results of the chapter include the formalizations of the Radon-Nikodym derivative and the Kullback-Leibler (KL) divergence (Coble, 2010). The latter provides a unified framework based on which most of the commonly used measures of information can be defined. The chapter then provides the general definitions that are valid for both discrete and continuous cases and then proves the corresponding reduced expressions where the measures considered are absolutely continuous over finite spaces.

ANNOUNCEMENT — "Geometry of Locally Finite Spaces"

2008 ◽  
Vol 14 (02) ◽  
pp. 231-232 ◽  
Author(s):  
VLADIMIR A. KOVALEVSKY
Keyword(s):  
Locally Finite ◽  
Finite Spaces

scholarly journals C*-Algebras over Topological Spaces: Filtrated K-Theory

2012 ◽  
Vol 64 (2) ◽  
pp. 368-408 ◽  
Author(s):  
Ralf Meyer ◽  
Ryszard Nest
Keyword(s):  
Exact Sequence ◽  
Topological Space ◽  
Spectral Sequence ◽  
Topological Spaces ◽  
C Algebra ◽  
C Algebras ◽  
Finite Spaces ◽  
K Theory ◽  
Universal Coefficient Theorem ◽  
Kasparov Theory

AbstractWe define the filtrated K-theory of a C*-algebra over a finite topological spaceXand explain how to construct a spectral sequence that computes the bivariant Kasparov theory overXin terms of filtrated K-theory.For finite spaces with a totally ordered lattice of open subsets, this spectral sequence becomes an exact sequence as in the Universal Coefficient Theorem, with the same consequences for classification. We also exhibit an example where filtrated K-theory is not yet a complete invariant. We describe two C*-algebras over a spaceXwith four points that have isomorphic filtrated K-theory without being KK(X)-equivalent. For this spaceX, we enrich filtrated K-theory by another K-theory functor to a complete invariant up to KK(X)-equivalence that satisfies a Universal Coefficient Theorem.

scholarly journals Relationship between the concave integrals and the pan-integrals on finite spaces

2015 ◽  
Vol 424 (2) ◽  
pp. 975-987 ◽  
Author(s):  
Yao Ouyang ◽  
Jun Li ◽  
Radko Mesiar
Keyword(s):  
Finite Spaces
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