scholarly journals Topological Complexity of Manifolds of Preferences

1986 ◽  
Author(s):  
Graciela Chichilnisky
Keyword(s):  
Topological Complexity ◽  
Complexity Of Manifolds

scholarly journals On the topological complexity of manifolds with abelian fundamental group

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Daniel C. Cohen ◽  
Lucile Vandembroucq
Keyword(s):  
Fundamental Group ◽  
Large Class ◽  
Closed Manifold ◽  
Topological Complexity ◽  
Nonorientable Surfaces ◽  
Lusternik Schnirelmann ◽  
Complexity Of Manifolds

Abstract We find conditions which ensure that the topological complexity of a closed manifold M with abelian fundamental group is nonmaximal, and see through examples that our conditions are sharp. This generalizes results of Costa and Farber on the topological complexity of spaces with small fundamental group. Relaxing the commutativity condition on the fundamental group, we also generalize results of Dranishnikov on the Lusternik–Schnirelmann category of the cofibre of the diagonal map Δ : M → M × M {\Delta:M\to M\times M} for nonorientable surfaces by establishing the nonmaximality of this invariant for a large class of manifolds.

Topological Complexity of Algorithms

1990 ◽  
Author(s):  
A. Libgober
Keyword(s):  
Topological Complexity ◽  
Complexity Of Algorithms

Dehydration-driven evolution of topological complexity in ethylamonium uranyl selenates

2017 ◽  
Vol 247 ◽  
pp. 105-112 ◽  
Author(s):  
Vladislav V. Gurzhiy ◽  
Sergey V. Krivovichev ◽  
Ivan G. Tananaev
Keyword(s):  
Topological Complexity

scholarly journals Topological complexity of frictional interfaces: friction networks

2012 ◽  
Vol 19 (2) ◽  
pp. 215-225 ◽  
Author(s):  
H. O. Ghaffari ◽  
R. P. Young
Keyword(s):  
Topological Complexity ◽  
Type Ii ◽  
Stored Energy ◽  
Fracture Permeability ◽  
Radiated Energy ◽  
Universal Power Law ◽  
Shear Rupture ◽  
Crack Type ◽  
Network Properties ◽  
Highly Correlated

Abstract. Through research conducted in this study, a network approach to the correlation patterns of void spaces in rough fractures (crack type II) was developed. We characterized friction networks with several networks characteristics. The correlation among network properties with the fracture permeability is the result of friction networks. The revealed hubs in the complex aperture networks confirmed the importance of highly correlated groups to conduct the highlighted features of the dynamical aperture field. We found that there is a universal power law between the nodes' degree and motifs frequency (for triangles it reads T(k) ∝ kβ (β ≈ 2 ± 0.3)). The investigation of localization effects on eigenvectors shows a remarkable difference in parallel and perpendicular aperture patches. Furthermore, we estimate the rate of stored energy in asperities so that we found that the rate of radiated energy is higher in parallel friction networks than it is in transverse directions. The final part of our research highlights 4 point sub-graph distribution and its correlation with fluid flow. For shear rupture, we observed a similar trend in sub-graph distribution, resulting from parallel and transversal aperture profiles (a superfamily phenomenon).

scholarly journals Erratum to “Topological complexity is a fibrewise L–S category” [Topology Appl. 157 (1) (2010) 10–21]

2012 ◽  
Vol 159 (10-11) ◽  
pp. 2810-2813 ◽  
Author(s):  
Norio Iwase ◽  
Michihiro Sakai
Keyword(s):  
Topological Complexity

scholarly journals Topological complexity of the telescope

2012 ◽  
Vol 159 (5) ◽  
pp. 1357-1360
Author(s):  
Aleksandra Franc
Keyword(s):  
Topological Complexity

Ladders of information: what contributes to the structural complexity of inorganic crystals

2018 ◽  
Vol 233 (3-4) ◽  
pp. 155-161 ◽  
Author(s):  
Sergey V. Krivovichev
Keyword(s):  
Crystal Structures ◽  
Inorganic Compounds ◽  
Structural Complexity ◽  
Unit Cell ◽  
Shannon Information ◽  
Topological Complexity ◽  
Crystal Chemical ◽  
Quantitative Estimates ◽  
Hydration State ◽  
Inorganic Crystals

AbstractComplexity is one of the important characteristics of crystal structures, which can be measured as the amount of Shannon information per atom or per unit cell. Since complexity may arise due to combination of different factors, herein we suggest a method of ladder diagrams for the analysis of contributions to structural complexity from different crystal-chemical phenomena (topological complexity, superstructures, modularity, hydration state, etc.). The group of minerals and inorganic compounds based upon the batagayite-type [M(TO4)ϕ] layers (M=Fe, Mg, Mn, Ni, Zn, Co; T=P, As; ϕ=OH, H2O) is used as an example. It is demonstrated that the method allows for the quantitative estimates of various contributions to the complexity of the whole structure.

Sign in / Sign up

Export Citation Format

Share Document