scholarly journals Heuristic Classification of an Intransitively Ordered Set

1983 ◽  
Vol 19 (2) ◽  
pp. 144-150
Author(s):  
Yajiro MORITA ◽  
Yuzo OKA ◽  
Haruo NIWAYA
2019 ◽  
Vol 39 (5) ◽  
pp. 767-781 ◽  
Author(s):  
Liang Wei ◽  
Chonggang Xu ◽  
Steven Jansen ◽  
Hang Zhou ◽  
Bradley O Christoffersen ◽  
...  

1987 ◽  
Vol 39 (2) ◽  
pp. 257-296
Author(s):  
Horst Behncke ◽  
George A. Elliott

Besides the simple ones, there are several other kinds of C*-algebras which it has proved interesting to try to classify. For instance, a large body of results relates to the extensions of one given C*-algebra, possibly simple, by another. Extrapolating in this direction, we have considered the class of C*-algebras which can be decomposed in the strongest possible nontrivial sense in terms of their simple subquotients, and such that these simple subquotients in turn are as uncomplicated as possible.We have found that the classification of these C*-algebras, namely, the lexicographic direct sums of elementary C*-algebras, is to a large degree tractable, and yet involves an interesting new invariant in the antiliminary case, which is the case of no minimal ideals. Even the postliminary case, which is the case that the ordered set of simple subquotients satisfies the decreasing chain condition, is not without interest as an extension of the case of finitely many simple subquotients, analysed in the earlier papers [1] and [2].


1994 ◽  
Vol 03 (02) ◽  
pp. 233-265 ◽  
Author(s):  
XIAOLONG HAO ◽  
JASON T.L. WANG ◽  
MICHAEL P. BIEBER ◽  
PETER A. NG

Document Processing Systems (DPSs) support office workers to manage information. Document classification is a major function of DPSs. By analyzing a document’s layout and conceptual structures, we present in this paper a sample-based approach to document classification. We represent a document’s layout structure by an ordered labeled tree through a procedure known as nested segmentation and represent the document’s conceptual structure by a set of attribute type pairs. The layout similarities between the document to be classified and sample documents are determined by a previously developed approximate tree matching toolkit. The conceptual similarities between the documents are determined by analyzing their contents and by calculating the degree of conceptual closeness. The document type is identified by computing both the layout and conceptual similarities between the document to be classified and the samples in the document sample base. Some experimental results are presented, which demonstrate the effectiveness of the proposed techniques.


2014 ◽  
Vol 24 (08) ◽  
pp. 1085-1098 ◽  
Author(s):  
Rosali Brusamarello ◽  
Érica Zancanella Fornaroli ◽  
Ednei Aparecido Santulo

Let X be a connected partially ordered set and let K be a field of characteristic different from 2. We present necessary and sufficient conditions for two involutions on the finitary incidence algebra of X over K, FI (X), to be equivalent in the case when every multiplicative automorphism of FI (X) is inner. To get the classification of involutions we extend the concept of multiplicative automorphism to finitary incidence algebras and prove the Decomposition Theorem of involutions of [Anti-automorphisms and involutions on (finitary) incidence algebras, Linear Multilinear Algebra 60 (2012) 181–188] for finitary incidence algebras.


1956 ◽  
Vol 6 (1) ◽  
pp. 21-24
Author(s):  
Leroi Madison

2018 ◽  
Vol 26 (6) ◽  
pp. 2901-2915 ◽  
Author(s):  
Josef KROCIL ◽  
Zdenek MACHACEK ◽  
Jiri KOZIOREK ◽  
Radek MARTINEK ◽  
Jan NEDOMA ◽  
...  

1975 ◽  
Vol 12 (1) ◽  
pp. 101-109
Author(s):  
Gary Davis

When a totally-ordered set Ω has no points fixed by all automorphisms ve equip Ω with the support topology which has fixed-sets of automorphisms as basic closed sets. There is a mapping from Ω into the set of prime dual ideals of the lattice Φ(Ω) of basic closed sets and this allows us to classify the points of Ω as excellent, isolated, static, or extraordinary. There is an action of the group of automorphisms of Ω on the lattice Φ(Ω) and this allows us to see that automorphisms of Ω preserve the prime dual ideal classification of points of Ω. When the empty set is a basic closed subset of Ω the dual spectrum of Φ(Ω) is a compact T0 space (Hausdorff when all points of Ω are excellent) containing Ω as a dense subspace and allowing an extension of each automorphism of Ω ťo a homeomorphism of the dual spectrum.


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