A Topological Characterization of Conjugate Nets

1977 ◽  
Vol 29 (4) ◽  
pp. 707-721
Author(s):  
Paul A. Vincent
Keyword(s):  
Level Sets ◽  
Harmonic Functions ◽  
Function Theory ◽  
Topological Analysis ◽  
Topological Characterization ◽  
Families Of Curves ◽  
Open Maps

One aspect of topological analysis that authors, such as G. T. Whyburn and Marston Morse, have pointed to ([16; 6] for instance) as being fundamental in the development of function theory is the topological study of the level sets of analytic and harmonic functions or of their topological analogues, light open maps and pseudo-harmonic functions. The first step in this direction seems to have been made by H. Whitney [14] when he studied families of curves, given abstractly using a condition of regularity.

Topological characterization of deterministic chaos: enforcing orientation preservation

2007 ◽  
Vol 366 (1865) ◽  
pp. 559-567 ◽  
Author(s):  
Marc Lefranc ◽  
Pierre-Emmanuel Morant ◽  
Michel Nizette
Keyword(s):  
Periodic Orbits ◽  
Topological Analysis ◽  
Three Dimensional ◽  
Deterministic Chaos ◽  
Three Dimensions ◽  
Unstable Periodic Orbits ◽  
Topological Characterization ◽  
Triangulated Surfaces ◽  
Theoretic Characterization

The determinism principle, which states that dynamical state completely determines future time evolution, is a keystone of nonlinear dynamics and chaos theory. Since it precludes that two state space trajectories intersect, it is a core ingredient of a topological analysis of chaos based on a knot-theoretic characterization of unstable periodic orbits embedded in a strange attractor. However, knot theory can be applied only to three-dimensional systems. Still, determinism applies in any dimension. We propose an alternative framework in which this principle is enforced by constructing an orientation-preserving dynamics on triangulated surfaces and find that in three dimensions our approach numerically predicts the correct topological entropies for periodic orbits of the horseshoe map.

PyLink: a PyMOL plugin to identify links

2019 ◽  
Vol 35 (17) ◽  
pp. 3166-3168 ◽  
Author(s):  
Aleksandra M Gierut ◽  
Pawel Dabrowski-Tumanski ◽  
Wanda Niemyska ◽  
Kenneth C Millett ◽  
Joanna I Sulkowska
Keyword(s):  
Mechanical Properties ◽  
Disulfide Bonds ◽  
Topological Analysis ◽  
Topological Characterization ◽  
Closed Loops ◽  
Ion Interactions ◽  
Pharmaceutical Applications ◽  
Exceptional Stability ◽  
Pymol Plugin

Abstract Summary Links are generalization of knots, that consist of several components. They appear in proteins, peptides and other biopolymers with disulfide bonds or ions interactions giving rise to the exceptional stability. Moreover because of this stability such biopolymers are the target of commercial and medical use (including anti-bacterial and insecticidal activity). Therefore, topological characterization of such biopolymers, not only provides explanation of their thermodynamical or mechanical properties, but paves the way to design templates in pharmaceutical applications. However, distinction between links and trivial topology is not an easy task. Here, we present PyLink—a PyMOL plugin suited to identify three types of links and perform comprehensive topological analysis of proteins rich in disulfide or ion bonds. PyLink can scan for the links automatically, or the user may specify their own components, including closed loops with several bridges and ion interactions. This creates the possibility of designing new biopolymers with desired properties. Availability and implementation The PyLink plugin, manual and tutorial videos are available at http://pylink.cent.uw.edu.pl.

scholarly journals Level sets of harmonic functions on the Sierpiński gasket

2002 ◽  
Vol 40 (2) ◽  
pp. 335-362 ◽  
Author(s):  
Anders Öberg ◽  
Robert S. Strichartz ◽  
Andrew Q. Yingst
Keyword(s):  
Level Sets ◽  
Harmonic Functions ◽  
Sierpinski Gasket ◽  
Sierpiński Gasket

Intersections of quotient rings and Prüfer v-multiplication domains

2016 ◽  
Vol 15 (08) ◽  
pp. 1650149 ◽  
Author(s):  
Said El Baghdadi ◽  
Marco Fontana ◽  
Muhammad Zafrullah
Keyword(s):  
Integral Domain ◽  
Algebraic Approach ◽  
Quotient Field ◽  
Topological Characterization ◽  
Locally Finite ◽  
Star Operation ◽  
Star Operations ◽  
Quotient Rings ◽  
Special Case

Let [Formula: see text] be an integral domain with quotient field [Formula: see text]. Call an overring [Formula: see text] of [Formula: see text] a subring of [Formula: see text] containing [Formula: see text] as a subring. A family [Formula: see text] of overrings of [Formula: see text] is called a defining family of [Formula: see text], if [Formula: see text]. Call an overring [Formula: see text] a sublocalization of [Formula: see text], if [Formula: see text] has a defining family consisting of rings of fractions of [Formula: see text]. Sublocalizations and their intersections exhibit interesting examples of semistar or star operations [D. D. Anderson, Star operations induced by overrings, Comm. Algebra 16 (1988) 2535–2553]. We show as a consequence of our work that domains that are locally finite intersections of Prüfer [Formula: see text]-multiplication (respectively, Mori) sublocalizations turn out to be Prüfer [Formula: see text]-multiplication domains (PvMDs) (respectively, Mori); in particular, for the Mori domain case, we reobtain a special case of Théorème 1 of [J. Querré, Intersections d’anneaux intègers, J. Algebra 43 (1976) 55–60] and Proposition 3.2 of [N. Dessagnes, Intersections d’anneaux de Mori — exemples, Port. Math. 44 (1987) 379–392]. We also show that, more than the finite character of the defining family, it is the finite character of the star operation induced by the defining family that causes the interesting results. As a particular case of this theory, we provide a purely algebraic approach for characterizing P vMDs as a subclass of the class of essential domains (see also Theorem 2.4 of [C. A. Finocchiaro and F. Tartarone, On a topological characterization of Prüfer [Formula: see text]-multiplication domains among essential domains, preprint (2014), arXiv:1410.4037]).

Topological characterization of dendrimer, benzenoid, and nanocone

2018 ◽  
Vol 74 (1-2) ◽  
pp. 35-43
Author(s):  
Wei Gao ◽  
Muhammad Kamran Siddiqui ◽  
Najma Abdul Rehman ◽  
Mehwish Hussain Muhammad
Keyword(s):  
Chemical Properties ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Zagreb Index ◽  
Topological Characterization ◽  
Complex Molecules ◽  
Chemical Structures ◽  
Physico Chemical ◽  
Quantitative Structure Activity Relationships

Abstract Dendrimers are large and complex molecules with very well defined chemical structures. More importantly, dendrimers are highly branched organic macromolecules with successive layers or generations of branch units surrounding a central core. Topological indices are numbers associated with molecular graphs for the purpose of allowing quantitative structure-activity relationships. These topological indices correlate certain physico-chemical properties such as the boiling point, stability, strain energy, and others, of chemical compounds. In this article, we determine hyper-Zagreb index, first multiple Zagreb index, second multiple Zagreb index, and Zagreb polynomials for hetrofunctional dendrimers, triangular benzenoids, and nanocones.

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