Partial Order Structure Based Image Retrieval

2019 ◽  
pp. 122-134
Author(s):  
Zhuoyi Li ◽  
Guanghua Gu ◽  
Jiangtao Liu
Keyword(s):  
Image Retrieval ◽  
Partial Order ◽  
Order Structure

scholarly journals Infinite decreasing chains in the Mitchell order

2021 ◽  
Author(s):  
Omer Ben-Neria ◽  
Sandra Müller
Keyword(s):  
Partial Order ◽  
Order Structure

AbstractIt is known that the behavior of the Mitchell order substantially changes at the level of rank-to-rank extenders, as it ceases to be well-founded. While the possible partial order structure of the Mitchell order below rank-to-rank extenders is considered to be well understood, little is known about the structure in the ill-founded case. The purpose of the paper is to make a first step in understanding this case, by studying the extent to which the Mitchell order can be ill-founded. Our main results are (i) in the presence of a rank-to-rank extender there is a transitive Mitchell order decreasing sequence of extenders of any countable length, and (ii) there is no such sequence of length $$\omega _1$$ ω 1 .

Order in open intervals of computable reals

1999 ◽  
Vol 9 (1) ◽  
pp. 103-108 ◽  
Author(s):  
JAN VON PLATO
Keyword(s):  
Partial Order ◽  
Order Structure ◽  
Order Relations ◽  
Suitable Definition ◽  
Definition Of

In constructive theories, an apartness relation is often taken as basic and its negation used as equality. An apartness relation should be continuous in its arguments, as in the case of computable reals. A similar approach can be taken to order relations. We shall here study the partial order on open intervals of computable reals. Since order on reals is undecidable, there is no simple uniformly applicable lattice meet operation that would always produce non-negative intervals as values. We show how to solve this problem by a suitable definition of apartness for intervals. We also prove the strong extensionality of the lattice operations, where by strong extensionality of an operation f on elements a, b we mean that apartness of values implies apartness in some of the arguments: f(a, b)≠f(c, d) ⊃a≠c∨b≠d.Most approaches to computable reals start from a concrete definition. We shall instead represent them by an abstract axiomatically introduced order structure.

CANTOR-TYPE SETS IN HYPERBOLIC NUMBERS

Fractals ◽  
2016 ◽  
Vol 24 (04) ◽  
pp. 1650051 ◽  
Author(s):  
A. S. BALANKIN ◽  
J. BORY-REYES ◽  
M. E. LUNA-ELIZARRARÁS ◽  
M. SHAPIRO
Keyword(s):  
Partial Order ◽  
Fractal Geometry ◽  
Hyperbolic Plane ◽  
General Framework ◽  
Cantor Set ◽  
Order Structure ◽  
Hyperbolic Numbers ◽  
The Real ◽  
Modern Physics ◽  
Complementary Nature

The construction of the ternary Cantor set is generalized into the context of hyperbolic numbers. The partial order structure of hyperbolic numbers is revealed and the notion of hyperbolic interval is defined. This allows us to define a general framework of the fractal geometry on the hyperbolic plane. Three types of the hyperbolic analogues of the real Cantor set are identified. The complementary nature of the real Cantor dust and the real Sierpinski carpet on the hyperbolic plane are outlined. The relevance of these findings in the context of modern physics are briefly discussed.

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