Some Remarks on Topological Spaces with an Infinite Number of Components

1962 ◽  
Vol 69 (10) ◽  
pp. 998
Author(s):  
Norman Levine
Keyword(s):  
Infinite Number ◽  
Topological Spaces ◽  
Number Of Components

CLASSICAL LINK INVARIANTS AND THE HAWAIIAN EARRINGS SPACE

1992 ◽  
Vol 01 (04) ◽  
pp. 327-342
Author(s):  
TIM D. COCHRAN
Keyword(s):  
Infinite Number ◽  
Number Of Components ◽  
Link Invariants ◽  
Classical Link

We show that, in search of link invariants more discriminating than Milnor's [Formula: see text]-invariants, one is naturally led to consider seemingly pathological objects such as links with an infinite number of components and the join of an infinite number of circles (Hawaiian earrings space). We define an infinite homology boundary link, and show that any finite sublink of an infinite homology boundary link has vanishing Milnor's invariants. Moreover, all links known to have vanishing Milnor's invariants are finite sublinks of infinite homology boundary links. We show that the exterior of an infinite homology boundary link admits a map to the Hawaiian earrings space, and that this may be employed to get a factorization of K. E. Orr's omega-invariant through a rather simple space.

A Possible Infinite Number of Components in a Single Crystalline Phase: On the Isomorphism of Brivaracetam–Guest Molecules

2018 ◽  
Vol 18 (9) ◽  
pp. 4807-4810 ◽  
Author(s):  
Nicolas Couvrat ◽  
Morgane Sanselme ◽  
Yohann Cartigny ◽  
Frederic De Smet ◽  
Sandrine Rome ◽  
...  
Keyword(s):  
Infinite Number ◽  
Crystalline Phase ◽  
Guest Molecules ◽  
Single Crystalline ◽  
Number Of Components

scholarly journals Minimally Supported Frequency (MSF) d-Dilation Wavelets

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1284
Author(s):  
Aparna Vyas ◽  
Gibak Kim
Keyword(s):  
Infinite Number ◽  
Geometric Construction ◽  
The Other ◽  
Wavelet Sets ◽  
Number Of Components ◽  
Wavelet Set

In this paper, we provide a geometric construction of a symmetric 2n-interval minimally supported frequency (MSF) d-dilation wavelet set with d∈(1,∞) and characterize all symmetric d-dilation wavelet sets. We also provide two special kinds of symmetric d-dilation wavelet sets, one of which has 4m-intervals whereas the other has (4m+2)-intervals, for m∈N. In addition, we construct a family of d-dilation wavelet sets that has an infinite number of components.

scholarly journals Hawkes processes with variable length memory and an infinite number of components

2017 ◽  
Vol 49 (1) ◽  
pp. 84-107 ◽  
Author(s):  
Pierre Hodara ◽  
Eva Löcherbach
Keyword(s):  
Infinite Number ◽  
Variable Length ◽  
Neural Nets ◽  
Interaction Graph ◽  
Hawkes Processes ◽  
Number Of Components ◽  
Stationary Version ◽  
Biological Neural Nets ◽  
Saturation Threshold ◽  
Type Decomposition

Abstract In this paper we propose a model for biological neural nets where the activity of the network is described by Hawkes processes having a variable length memory. The particularity in this paper is that we deal with an infinite number of components. We propose a graphical construction of the process and build, by means of a perfect simulation algorithm, a stationary version of the process. To implement this algorithm, we make use of a Kalikow-type decomposition technique. Two models are described in this paper. In the first model, we associate to each edge of the interaction graph a saturation threshold that controls the influence of a neuron on another. In the second model, we impose a structure on the interaction graph leading to a cascade of spike trains. Such structures, where neurons are divided into layers, can be found in the retina.

On the theory of reactions in continuous mixtures

1966 ◽  
Vol 260 (1112) ◽  
pp. 351-393 ◽  
Keyword(s):  
Experimental Data ◽  
Differential Equations ◽  
Infinite Number ◽  
Continuous Variable ◽  
Number Of Components ◽  
Thermodynamics And Kinetics ◽  
Complex Processes ◽  
Continuous Mixture ◽  
Kinetics Of

A mixture with a very large number of components approaches the condition of a continuous mixture in which the components are not distinguished by a discrete index but by a continuous variable. Such a mixture can be described by distributions of concentration and is capable of sustaining an infinite number of reactions. Polymerization and cracking reactions can be treated in this way and there may be applications to the very complex processes of biology. The aim of this paper is to lay the foundations for the stoicheiometry, thermodynamics and kinetics of such reactions and to outline several techniques for solving the resulting integro-differential equations. Attention is also paid to the problem of fitting the parameters of such a model to experimental data.

On connexion, invariance and stability in certain flows

1964 ◽  
Vol 60 (1) ◽  
pp. 51-55 ◽  
Author(s):  
D. Desbrow
Keyword(s):  
Infinite Number ◽  
Euclidean Plane ◽  
Number Of Components ◽  
Minimal Sets

1. Suppose that f is a homeomorphism of the Euclidean plane E2 onto itself. The set M ⊂ E2 is said to be invariant if f(M) = M and minimal if it is non-void, closed, invariant and irreducible with respect to these properties. In general, invariant and minimal sets in E2 can have a finite or infinite number of components.

scholarly journals Connectedness and Local Connectedness on Infra Soft Topological Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1759
Author(s):  
Tareq M. Al-shami ◽  
El-Sayed A. Abo-Tabl
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Finite Product ◽  
Number Of Components ◽  
Local Connectedness ◽  
Soft Topology ◽  
Soft Point ◽  
Soft Topological Space ◽  
Connected Spaces

This year, we introduced the concept of infra soft topology as a new generalization of soft topology. To complete our analysis of this space, we devote this paper to presenting the concepts of infra soft connected and infra soft locally connected spaces. We provide some descriptions for infra soft connectedness and elucidate that there is no relationship between an infra soft topological space and its parametric infra topological spaces with respect to the property of infra soft connectedness. We discuss the behaviors of infra soft connected and infra soft locally connected spaces under infra soft homeomorphism maps and a finite product of soft spaces. We complete this manuscript by defining a component of a soft point and establishing its main properties. We determine the conditions under which the number of components is finite or countable, and we discuss under what conditions the infra soft connected subsets are components.

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