scholarly journals The size of some vanishing and critical sets

2020 ◽  
Vol 65 (4) ◽  
pp. 651-659
Author(s):  
Cornel Pintea
Keyword(s):  
Orientable Manifold ◽  
Compact Case ◽  
Critical Sets

We prove that the vanishing sets of all top forms on a non-orientable manifold are at least 1-dimensional in the general case and at most $1$-codimen\-sional in the compact case. We apply these facts to show that the critical sets of some differentiable maps are at least 1-dimensional in the general case and at most 1-codimensional when the source manifold is compact.

Finding Critical Sets.

1985 ◽  
Author(s):  
Donald W. Loveland
Keyword(s):  
Critical Sets

scholarly journals A Discussion of a Cryptographical Scheme Based in F-Critical Sets of a Latin Square

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 285
Author(s):  
Laura M. Johnson ◽  
Stephanie Perkins
Keyword(s):  
Necessary Conditions ◽  
Latin Square ◽  
Latin Squares ◽  
Critical Sets ◽  
Long Cycles ◽  
The Given

This communication provides a discussion of a scheme originally proposed by Falcón in a paper entitled “Latin squares associated to principal autotopisms of long cycles. Applications in cryptography”. Falcón outlines the protocol for a cryptographical scheme that uses the F-critical sets associated with a particular Latin square to generate access levels for participants of the scheme. Accompanying the scheme is an example, which applies the protocol to a particular Latin square of order six. Exploration of the example itself, revealed some interesting observations about both the structure of the Latin square itself and the autotopisms associated with the Latin square. These observations give rise to necessary conditions for the generation of the F-critical sets associated with certain autotopisms of the given Latin square. The communication culminates with a table which outlines the various access levels for the given Latin square in accordance with the scheme detailed by Falcón.

Critical Sets of Full n-Latin Squares

2015 ◽  
Vol 32 (2) ◽  
pp. 543-552 ◽  
Author(s):  
Nicholas J. Cavenagh ◽  
Vaipuna Raass
Keyword(s):  
Latin Squares ◽  
Critical Sets

scholarly journals 1-Saturating Sets, Caps, and Doubling-Critical Sets in Binary Spaces

2010 ◽  
Vol 24 (1) ◽  
pp. 169-190 ◽  
Author(s):  
David J. Grynkiewicz ◽  
Vsevolod F. Lev
Keyword(s):  
Critical Sets

Topology of ambient manifolds of non-singular Morse – Smale flows with three periodic orbits

2021 ◽  
Vol 29 (6) ◽  
pp. 863-868
Author(s):  
Danila Shubin ◽  
◽  
Keyword(s):  
Periodic Orbits ◽  
Three Dimensional ◽  
Solid Torus ◽  
Lens Space ◽  
Tubular Neighborhood ◽  
Lens Spaces ◽  
Ambient Manifold ◽  
Orientable Manifold ◽  
Smale Flows ◽  
Published Result

The purpose of this study is to establish the topological properties of three-dimensional manifolds which admit Morse – Smale flows without fixed points (non-singular or NMS-flows) and give examples of such manifolds that are not lens spaces. Despite the fact that it is known that any such manifold is a union of circular handles, their topology can be investigated additionally and refined in the case of a small number of orbits. For example, in the case of a flow with two non-twisted (having a tubular neighborhood homeomorphic to a solid torus) orbits, the topology of such manifolds is established exactly: any ambient manifold of an NMS-flow with two orbits is a lens space. Previously, it was believed that all prime manifolds admitting NMS-flows with at most three non-twisted orbits have the same topology. Methods. In this paper, we consider suspensions over Morse – Smale diffeomorphisms with three periodic orbits. These suspensions, in turn, are NMS-flows with three periodic trajectories. Universal coverings of the ambient manifolds of these flows and lens spaces are considered. Results. In this paper, we present a countable set of pairwise distinct simple 3-manifolds admitting NMS-flows with exactly three non-twisted orbits. Conclusion. From the results of this paper it follows that there is a countable set of pairwise distinct three-dimensional manifolds other than lens spaces, which refutes the previously published result that any simple orientable manifold admitting an NMS-flow with at most three orbits is lens space.

scholarly journals On essential components and critical sets of a graph

1998 ◽  
Vol 178 (1-3) ◽  
pp. 137-153
Author(s):  
S. Markossian ◽  
G. Gasparian ◽  
I. Karapetian ◽  
A. Markosian
Keyword(s):  
Essential Components ◽  
Critical Sets

scholarly journals On the functional Hodrick–Prescott filter with non-compact operators

2016 ◽  
Vol 24 (1) ◽  
Author(s):  
Boualem Djehiche ◽  
Astrid Hilbert ◽  
Hiba Nassar
Keyword(s):  
Compact Operators ◽  
Closed Range ◽  
Underlying Distribution ◽  
Smoothing Operator ◽  
Optimal Smoothing ◽  
Compact Case ◽  
Densely Defined

AbstractWe study a version of the functional Hodrick–Prescott filter in the case when the associated operator is not necessarily compact but merely closed and densely defined with closed range. We show that the associated optimal smoothing operator preserves the structure obtained in the compact case when the underlying distribution of the data is Gaussian.

scholarly journals A Spectral Sequence for the Hochschild Cohomology of a Coconnective DGA

2013 ◽  
Vol 112 (2) ◽  
pp. 182 ◽  
Author(s):  
Shoham Shamir
Keyword(s):  
Spectral Sequence ◽  
Loop Space ◽  
Hochschild Cohomology ◽  
Derived Category ◽  
Orientable Manifold ◽  
Support Varieties ◽  
Mod P

A spectral sequence for the computation of the Hochschild cohomology of a coconnective dga over a field is presented. This spectral sequence has a similar flavour to the spectral sequence presented in [7] for the computation of the loop homology of a closed orientable manifold. Using this spectral sequence we identify a class of spaces for which the Hochschild cohomology of their mod-$p$ cochain algebra is Noetherian. This implies, among other things, that for such a space the derived category of mod-$p$ chains on its loop-space carries a theory of support varieties.

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