scholarly journals Structures, Operations and their Applications to Topology

2021 ◽  
Vol 12 (2) ◽  
Author(s):  
Geetha Jeyalakshmi R, Et. al.
Keyword(s):  
Topological Space ◽  
Special Structure ◽  
Binary Relations ◽  
Filter Base

A structure on a non empty set X is a collection of subsets of X. Any kind of topology on a non empty set X is a special structure on X. A filter and a filter base  on X  are examples of  structures. Also any ideal of subsets of X is a structure. In this paper several structures are classified and the binary relations  and operations on structures are discussed.  Furthermore structures on a topological space are also discussed.

Variable Neighborhood Model for Agent Control Introducing Accessibility Relations Between Agents with Linear Temporal Logic

2014 ◽  
Vol 18 (6) ◽  
pp. 937-945
Author(s):  
Seiki Ubukata ◽  
◽  
Tetsuya Murai ◽  
Yasuo Kudo ◽  
Seiki Akama ◽  
...  
Keyword(s):  
Topological Space ◽  
Temporal Logic ◽  
Binary Relation ◽  
Linear Temporal Logic ◽  
Binary Relations ◽  
Cellular Space ◽  
Current Time ◽  
Low Level ◽  
Local Properties ◽  
Agent Control

In general, there are two types of agents, reflex and deliberative. The former does not have the ability for deep planning that produces higher-level actions to attain goals cooperatively, which is the ability of the latter. Can we cause reflex agents to act as though they could plan their actions? In this paper, we propose a variable neighborhood model for reflex agent control, that allows such agents to create plans in order to attain their goals. The model consists of three layers: (1) topological space, (2) agent space, and (3) linear temporal logic. Agents with their neighborhoods move in a topological space, such as a plane, and in a cellular space. Then, a binary relation between agents is generated each time from the agents’ position and neighborhood. We call the pair composed of a set of agents and binary relations the agent space. In order to cause reflex agents to have the ability to attain goals superficially, we consider the local properties of the binary relation between agents. For example, if two agents have a symmetrical relation at the current time, they can struggle to maintain symmetry or they could abandon symmetry at the next time, depending on the context. Then, low-level behavior, that is, the maintenance or abandonment of the local properties of binary relations, grant reflex agents a method for selecting neighborhoods for the next time. As a result, such a sequence of low-level behavior generates seemingly higher-level actions, as though reflex agents could attain a goal with such actions. This low-level behavior is shown through simulation to generate the achievement of a given goal, such as cooperation and target pursuing.

scholarly journals Zero-free fortifying homomorphisms and semigroups of relations

1969 ◽  
Vol 1 (2) ◽  
pp. 213-230 ◽  
Author(s):  
Kenneth D. Magill
Keyword(s):  
Topological Space ◽  
Topological Property ◽  
Binary Operation ◽  
Nonzero Ideal ◽  
Binary Relations ◽  
Compact Binary ◽  
Composition Of Relations ◽  
Necessary And Sufficient

In this paper, the concept of a fitted semigroup of binary relations is introduced. The binary operation for these semigroups is ordinary composition of relations. A particular type of homomorphism is investigated which maps a certain kind of subsemigroup of one fitted semigroup into another. The main result states that these homomorphisms are injective and gives a representation for them. This and several related results are then applied to the semigroup of all binary relations on a topological space which have a certain prescribed type of topological property. Compactness is one of these properties and the semigroup SK[X] of all compact binary relations on a Hausdorff k–space X is given special attention. It is shown that X and Y are homeomorphic if and only if a number of statements are true which relate the semigroups SK[x] and SK[y].For example, in order that X and y be homeomorphic it is both necessary and sufficient that some nonzero ideal of SK[X] be isomorphic to some nonzero ideal of SK[y].

Monadic binary relations and the monad systems at near-standard points

1987 ◽  
Vol 52 (3) ◽  
pp. 689-697
Author(s):  
Nader Vakil
Keyword(s):  
Topological Space ◽  
Binary Relation ◽  
Hausdorff Space ◽  
Equivalence Relations ◽  
Binary Relations ◽  
Completely Regular ◽  
General Topological Space ◽  
Image Position

AbstractLet (*X, *T) be the nonstandard extension of a Hausdorff space (X, T). After Wattenberg [6], the monad m(x) of a near-standard point x in *X is defined as m{x) = μT(st(x)). Consider the relationFrank Wattenberg in [6] and [7] investigated the possibilities of extending the domain of Rns to the whole of *X. Wattenberg's extensions of Rns were required to be equivalence relations, among other things. Because the nontrivial ways of constructing such extensions usually produce monadic relations, the said condition practically limits (to completely regular spaces) the class of spaces for which such extensions are possible. Since symmetry and transitivity are not, after all, characteristics of the kind of nearness that is obtained in a general topological space, it may be expected that if these two requirements are relaxed, then a monadic extension of Rns to *X should be possible in any topological space. A study of such extensions of Rns is the purpose of the present paper. We call a binary relation W ⊆ *X × *X an infinitesimal on *X if it is monadic and reflexive on *X. We prove, among other things, that the existence of an infinitesimal on *X that extends Rns is equivalent to the condition that the space (X, T) be regular.

FACTOR ANALYSIS OF GEOGRAPHIC COORDINATES AT POINTS OF THE CHANNEL OF A SMALL RIVER ON SPACE IMAGES

2020 ◽  
Author(s):  
Peter Matveevich Mazurkin ◽  
Yana Oltgovna Georgieva
Keyword(s):  
Correlation Coefficient ◽  
Geographical Location ◽  
Small River ◽  
Binary Relations ◽  
Catchment Basin ◽  
Space Images ◽  
The North ◽  
Inverse Effect ◽  
Characteristic Points ◽  
Fractal Representation

The purpose of the article is the analysis of asymmetric wavelets in binary relations between three coordinates at 290 characteristic points from the source to the mouth of the small river Irovka. The hypsometric characteristic is the most important property of the relief. The Irovka River belongs to a low level, at the mouth it is 89 m high, and at the source it is 148 m above sea level. Modeling of binary relations with latitude, longitude, and height has shown that local latitude receives the greatest quantum certainty. In this case, all paired regularities received a correlation coefficient of more than 0.95. Such a high adequacy of wave patterns shows that geomorphology can go over to the wave multiple fractal representation of the relief. The Irovka River is characterized by a small anthropogenic impact, therefore, the relief over a length of 69 km has the natural character of the oscillatory adaptation of a small river to the surface of the Vyatka Uval from its eastern side. This allows us to proceed to the analysis of the four tributaries of the small river Irovka, as well as to model the relief of the entire catchment basin of 917 km2. The greatest adequacy with a correlation coefficient of 0.9976 was obtained by the influence of latitude on longitude, that is, the geographical location of the relief of the river channel with respect to the geomorphology of the Vyatka Uval. In second place with a correlation of 0.9967 was the influence of the height of the points of the channel of the small river on local longitude and it is also mainly determined by the relief of the Vyatka Uval. In third place was the effect of latitude on height with a correlation coefficient of 0.9859. And in last sixth place is the inverse effect of altitude on local latitude in the North-South direction.

The Spatial Dimensions of Social Networks

2020 ◽  
pp. 367-383
Author(s):  
Zachary P. Neal
Keyword(s):  
Social Networks ◽  
Topological Space ◽  
Network Science ◽  
Spatial Dimensions

The first law of geography holds that everything is related to everything else, but near things are more related than distant things, where distance refers to topographical space. If a first law of network science exists, it would similarly hold that everything is related to everything else, but near things are more related than distant things, but where distance refers to topological space. Frequently these two laws collide, together holding that everything is related to everything else, but topographically and topologically near things are more related than topographically and topologically distant things. The focus of the spatial study of social networks lies in exploring a series of questions embedded in this combined law of geography and networks. This chapter explores the questions that have been asked and the answers that have been offered at the intersection of geography and networks.

Red phosphorus embedded in TiO2/C nanofibers to enhance the potassium-ion storage performance

Nanoscale ◽  
2021 ◽  
Vol 13 (13) ◽  
pp. 6635-6643
Author(s):  
Die Su ◽  
Jing Dai ◽  
Min Yang ◽  
Jiaxing Wen ◽  
Jianping Yang ◽  
...  
Keyword(s):  
Energy Storage ◽  
Electronic Conductivity ◽  
Potassium Ion ◽  
Special Structure ◽  
Red Phosphorus ◽  
Storage Performance ◽  
Ion Storage

TiO2-RP/CN was fabricated and found to possess a special structure and an excellent electronic conductivity, and the electrodes show outstanding energy storage in K half/full cells.

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