scholarly journals Rigorous Validation of Isolating Blocks for Flows and Their Conley Indices

2014 ◽  
Vol 13 (4) ◽  
pp. 1847-1878 ◽  
Author(s):  
Thomas Stephens ◽  
Thomas Wanner
Keyword(s):  
Isolating Blocks

Computing libration point isolated invariant sets using isolating blocks

2020 ◽  
Vol 405 ◽  
pp. 132361 ◽  
Author(s):  
Rodney L. Anderson ◽  
Robert W. Easton ◽  
Martin W. Lo
Keyword(s):  
Libration Point ◽  
Invariant Sets ◽  
Isolating Blocks

A Morse equation in Conley's index theory for semiflows on metric spaces

1985 ◽  
Vol 5 (1) ◽  
pp. 123-143 ◽  
Author(s):  
Krzysztof P. Rybakowski ◽  
Eduard Zehnder
Keyword(s):  
Parabolic Equations ◽  
Metric Spaces ◽  
Index Theory ◽  
Invariant Set ◽  
Morse Decomposition ◽  
Cohomology Groups ◽  
Compact Spaces ◽  
Isolating Blocks ◽  
Isolated Invariant Set ◽  
Morse Decompositions

AbstractGiven a compact (two-sided) flow, an isolated invariant set S and a Morse-decomposition (M1, …, Mn) of S, there is a generalized Morse equation, proved by Conley and Zehnder, which relates the Alexander-Spanier cohomology groups of the Conley indices of the sets Mi and S with each other. Recently, Rybakowski developed the technique of isolating blocks and extended Conley's index theory to a class of one-sided semiflows on non-necessarily compact spaces, including e.g. semiflows generated by parabolic equations. Using these results, we discuss in this paper Morse decompositions and prove the above-mentioned Morse equation not only for arbitrary homology and cohomology groups, but also in this more general semiflow setting.

BACKGROUND STRUCTURE IN DOCUMENT IMAGES

1994 ◽  
Vol 08 (05) ◽  
pp. 1013-1030 ◽  
Author(s):  
HENRY S. BAIRD
Keyword(s):  
English Language ◽  
White Background ◽  
Training Algorithm ◽  
Document Images ◽  
Background Structure ◽  
Isolating Blocks ◽  
On Line ◽  
Printed Text ◽  
Experimental Trials ◽  
Geometric Layout

A method for analyzing the structure of the white background in document images is described, along with applications to the problem of isolating blocks of machine-printed text. The approach is based on computational-geometry algorithms for off-line enumeration of maximal white rectangles and on-line rectangle unification. These support a fast, simple, and general heuristic for geometric layout segmentation, in which white space is covered greedily by rectangles until all text blocks are isolated. Design of the heuristic can be substantially automated by an analysis of the empirical statistical distribution of properties of covering rectangles: for example, the stopping rule can be chosen by Rosenblatt’s perceptron training algorithm. Experimental trials show good behavior on the large and useful class of textual Manhattan layouts. On complex layouts from English-language technical journals of many publishers, the method finds good segmentations in a uniform and nearly parameter-free manner. On a variety of non-Latin texts, some with vertical text lines, the method finds good segmentations without prior knowledge of page and text-line orientation.

Isolating blocks and epsilon chains for maps

1989 ◽  
Vol 39 (1) ◽  
pp. 95-110 ◽  
Author(s):  
Robert Easton
Keyword(s):  
Isolating Blocks

scholarly journals Some properties of isolating blocks for planar systems

1999 ◽  
Vol 154 ◽  
pp. 103-110
Author(s):  
Shu-Xiang Yu
Keyword(s):  
Differential Equations ◽  
Qualitative Properties ◽  
Isolating Block ◽  
Isolating Blocks ◽  
Planar Systems

AbstractIn this paper, some qualitative properties of trajectories inside an isolating block for planar differential equations are obtained.

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