scholarly journals Derivations of a Sullivan Model and the Rationalized G -Sequence

2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
Oteng Maphane
Keyword(s):  
Grassmann Manifold ◽  
Dimensional Vector ◽  
Sullivan Model ◽  
Sullivan Models ◽  
Rational Evaluation ◽  
Vector Subspaces

Let G k , n ℂ for 2 ≤ k < n denote the Grassmann manifold of k -dimensional vector subspaces of ℂ n . In this paper, we compute, in terms of the Sullivan models, the rational evaluation subgroups and, more generally, the G -sequence of the inclusion G 2 , n ℂ ↣ G 2 , n + r ℂ for r ≥ 1 .

scholarly journals Rational homotopy of maps between certain complex Grassmann manifolds

2018 ◽  
Vol 68 (1) ◽  
pp. 181-196 ◽  
Author(s):  
Prateep Chakraborty ◽  
Shreedevi K. Masuti
Keyword(s):  
Grassmann Manifold ◽  
Dimensional Vector ◽  
Rational Homotopy ◽  
Grassmann Manifolds ◽  
Continuous Map ◽  
Complex Grassmann Manifold ◽  
Vector Subspaces

AbstractLetGn,kdenote the complex Grassmann manifold ofk-dimensional vector subspaces of ℂn. Assumel,k≤ ⌊n/2⌋. We show that, for sufficiently largen, any continuous maph:Gn,l→Gn,kis rationally null homotopic if (i) 1 ≤k<l, (ii) 2 < l <k< 2(l− 1), (iii) 1 < l <k,ldividesnbutldoes not dividek.

scholarly journals A measure of non-immersability of the Grassmann manifolds in some euclidean spaces

1998 ◽  
Vol 41 (1) ◽  
pp. 197-205
Author(s):  
Cornel Pintea
Keyword(s):  
Critical Points ◽  
Grassmann Manifold ◽  
Dimensional Vector ◽  
Differentiable Mapping ◽  
Euclidean Spaces ◽  
Grassmann Manifolds ◽  
Vector Subspaces

LetGk, n, be the Grassmann manifold consisting in all non-orientedk-dimensional vector subspaces of the spaceRk+n. In this paper we will show that any differentiable mappingf:Gk, n→Rm, has infinitely many critical points for suitable choices of the numbersm,n,k.

scholarly journals The expected dimension of a sum of vector subspaces

1992 ◽  
Vol 45 (3) ◽  
pp. 467-477 ◽  
Author(s):  
David E. Dobbs ◽  
Mark J. Lancaster
Keyword(s):  
Vector Space ◽  
Vector Subspace ◽  
Dimensional Vector ◽  
Dimensional Vector Space ◽  
Limiting Value ◽  
Vector Subspaces

Let W be an n−dimensional vector space over a field F. It is shown that the expected dimension of a vector subspace of W is n/2. If F is infinite, the expected dimension of a sum of a pair of subspaces of W is (n + 1)/2 if n > 1; and 3/4 if n = 1. If F is finite, with q elements, the expected dimension of a sum of subspaces of W depends on q and n. For fixed n, the limiting value of this expectation as q → ∞ is n if n is even; and n − 1/4 if n is odd. Moreover, if F is finite and n > 1, the expected dimension of a sum of three (not necessarily distinct) subspaces of W has limit n as q → ∞.

Model Based Defect Detection in Multi-Dimensional Vector Spaces

2011 ◽  
Vol 131 (9) ◽  
pp. 1633-1641
Author(s):  
Toshifumi Honda ◽  
Kenji Obara ◽  
Minoru Harada ◽  
Hajime Igarashi
Keyword(s):  
Defect Detection ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Model Based

A closer look at the stable completion

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Inverse Limit ◽  
Unit Vector ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Compact Sets ◽  
Linear Topology ◽  
Topological Embedding ◽  
Definable Set ◽  
Finite Dimensional ◽  
The One

This chapter introduces the concept of stable completion and provides a concrete representation of unit vector Mathematical Double-Struck Capital A superscript n in terms of spaces of semi-lattices, with particular emphasis on the frontier between the definable and the topological categories. It begins by constructing a topological embedding of unit vector Mathematical Double-Struck Capital A superscript n into the inverse limit of a system of spaces of semi-lattices L(Hsubscript d) endowed with the linear topology, where Hsubscript d are finite-dimensional vector spaces. The description is extended to the projective setting. The linear topology is then related to the one induced by the finite level morphism L(Hsubscript d). The chapter also considers the condition that if a definable set in L(Hsubscript d) is an intersection of relatively compact sets, then it is itself relatively compact.

Thermodynamics of the interaction between the spike protein of severe acute respiratory syndrome- coronavirus-2 and the receptor of human angiotensin converting enzyme 2. Effects of possible ligands

2020 ◽  
Author(s):  
Cristina Garcia-Iriepa ◽  
Cecilia Hognon ◽  
Antonio Francés-Monerris ◽  
Isabel Iriepa ◽  
Tom Miclot ◽  
...  
Keyword(s):  
Angiotensin Converting Enzyme ◽  
Molecular Mechanisms ◽  
Molecular Design ◽  
Binding Free Energy ◽  
Transmembrane Protein ◽  
Spike Protein ◽  
Converting Enzyme ◽  
Angiotensin Converting Enzyme 2 ◽  
Rational Molecular Design ◽  
Rational Evaluation

<div><p>Since the end of 2019, the coronavirus SARS-CoV-2 has caused more than 180,000 deaths all over the world, still lacking a medical treatment despite the concerns of the whole scientific community. Human Angiotensin-Converting Enzyme 2 (ACE2) was recently recognized as the transmembrane protein serving as SARS-CoV-2 entry point into cells, thus constituting the first biomolecular event leading to COVID-19 disease. Here, by means of a state-of-the-art computational approach, we propose a rational evaluation of the molecular mechanisms behind the formation of the complex and of the effects of possible ligands. Moreover, binding free energy between ACE2 and the active Receptor Binding Domain (RBD) of the SARS-CoV-2 spike protein is evaluated quantitatively, assessing the molecular mechanisms at the basis of the recognition and the ligand-induced decreased affinity. These results boost the knowledge on the molecular grounds of the SARS-CoV-2 infection and allow to suggest rationales useful for the subsequent rational molecular design to treat severe COVID-19 cases.</p></div>

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