Maximal equivariant compactification of the Urysohn spaces and other metric structures

Methods and algorithms for the complete processing of a post-detector low-contrast optical image (OI) of an unknown remote object obtained by ground-based optical means of observation under conditions of a complex background situation are considered. The purpose of processing is to separate and interpret at least with the help of the analyst, of the main constructive elements using the integrated indicators introduced in [6] and the characteristics of the analyzed OI, which are connected by the information, topological and metric structures of the OI. The stages of processing the OI include extracting the image-containing information object of the image portion (detection) and filtration of the OI, using recursive rank filtering. The final stages of processing include the segmentation of the OI and the allocation on it constructive elements using the apparatus of graph theory. An example of image processing of a Spot-5 spacecraft obtained in real conditions is given. It is shown that in this case at the detection stage it is possible to reduce the volume of information processed at subsequent stages by 8 times, in the filtration process to increase the compactness of the OI and to increase its connectivity in comparison with the post-detection OI. As a result of segmentation and allocation of constructive elements, three structural elements that can be interpreted as a spacecraft case and two remote panels can be identified with the analyst’s participation.

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Proof-theoretic uniform boundedness and bounded collection principles and countable Heine–Borel compactness

Archive for Mathematical Logic ◽

10.1007/s00153-021-00771-w ◽

2021 ◽

Author(s):

Ulrich Kohlenbach

Keyword(s):

Uniform Boundedness ◽

Metric Structures

AbstractIn this note we show that proof-theoretic uniform boundedness or bounded collection principles which allow one to formalize certain instances of countable Heine–Borel compactness in proofs using abstract metric structures must be carefully distinguished from an unrestricted use of countable Heine–Borel compactness.

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A new solution to the problem of finding all numerical solutions to ordered metric structures

Psychometrika ◽

10.1007/bf02293603 ◽

1980 ◽

Vol 45 (1) ◽

pp. 135-137 ◽

Cited By ~ 8

Author(s):

Paul E. Lehner ◽

Elliot Noma

Keyword(s):

Numerical Solutions ◽

Metric Structures

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Omitting types in logic of metric structures

Journal of Mathematical Logic ◽

10.1142/s021906131850006x ◽

2018 ◽

Vol 18 (02) ◽

pp. 1850006 ◽

Cited By ~ 3

Author(s):

Ilijas Farah ◽

Menachem Magidor

Keyword(s):

Complete Theory ◽

Simple Test ◽

Finite Sets ◽

Complete Type ◽

Metric Structures ◽

Omitting Types ◽

Theory Formula

This paper is about omitting types in logic of metric structures introduced by Ben Yaacov, Berenstein, Henson and Usvyatsov. While a complete type is omissible in some model of a countable complete theory if and only if it is not principal, this is not true for the incomplete types by a result of Ben Yaacov. We prove that there is no simple test for determining whether a type is omissible in a model of a theory [Formula: see text] in a countable language. More precisely, we find a theory in a countable language such that the set of types omissible in some of its models is a complete [Formula: see text] set and a complete theory in a countable language such that the set of types omissible in some of its models is a complete [Formula: see text] set. Two more unexpected examples are given: (i) a complete theory [Formula: see text] and a countable set of types such that each of its finite sets is jointly omissible in a model of [Formula: see text], but the whole set is not and (ii) a complete theory and two types that are separately omissible, but not jointly omissible, in its models.

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Classification of 3-dimensional left-invariant almost paracontact metric structures

Advances in Geometry ◽

10.1515/advgeom-2017-0025 ◽

2017 ◽

Vol 17 (3) ◽

Author(s):

Giovanni Calvaruso ◽

Antonella Perrone

Keyword(s):

Lie Groups ◽

Three Dimensional ◽

Complete Classification ◽

Natural Assumption ◽

Geometric Properties ◽

3 Dimensional ◽

Metric Structures

AbstractWe study left-invariant almost paracontact metric structures on arbitrary three-dimensional Lorentzian Lie groups. We obtain a complete classification and description under a natural assumption, which includes relevant classes as normal and almost para-cosymplectic structures, and we investigate geometric properties of these structures.

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Natural Paracontact Magnetic Trajectories on Unit Tangent Bundles

Axioms ◽

10.3390/axioms9030072 ◽

2020 ◽

Vol 9 (3) ◽

pp. 72

Author(s):

Mohamed Tahar Kadaoui Abbassi ◽

Noura Amri

Keyword(s):

Gaussian Curvature ◽

Tangent Bundle ◽

Two Dimensional ◽

Constant Gaussian Curvature ◽

Metric Structures ◽

Unit Tangent Bundle ◽

Tangent Bundles ◽

Full Classification ◽

Kaluza Klein

In this paper, we study natural paracontact magnetic trajectories in the unit tangent bundle, i.e., those that are associated to g-natural paracontact metric structures. We characterize slant natural paracontact magnetic trajectories as those satisfying a certain conservation law. Restricting to two-dimensional base manifolds of constant Gaussian curvature and to Kaluza–Klein type metrics on their unit tangent bundles, we give a full classification of natural paracontact slant magnetic trajectories (and geodesics).

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