scholarly journals AN ALGEBRAIC CHARACTERIZATION OF SIMPLE CLOSED CURVES ON SURFACES WITH BOUNDARY

2010 ◽  
Vol 02 (03) ◽  
pp. 395-417 ◽  
Author(s):  
MOIRA CHAS ◽  
FABIANA KRONGOLD
Keyword(s):  
Conjugacy Class ◽  
Fundamental Group ◽  
Intersection Number ◽  
Algebraic Characterization ◽  
Closed Curves ◽  
Curves On Surfaces

We prove that a conjugacy class in the fundamental group of a surface with boundary is represented by a power of a simple curve if and only if the Goldman bracket of two different powers of this class, one of them larger than two, is zero. The main theorem actually counts self-intersection number of a primitive class by counting the number of terms of the Goldman bracket of two distinct powers, one of them larger than two.

Algebraic characterization of simple closed curves via Turaev's cobracket

2015 ◽  
Vol 9 (1) ◽  
pp. 91-104 ◽  
Author(s):  
Moira Chas ◽  
Fabiana Krongold
Keyword(s):  
Algebraic Characterization ◽  
Closed Curves

scholarly journals Characterization of Dissipative Structures for First-Order Symmetric Hyperbolic System with General Relaxation

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 728
Author(s):  
Yasunori Maekawa ◽  
Yoshihiro Ueda
Keyword(s):  
Hyperbolic System ◽  
Dissipative Structure ◽  
Dissipative Structures ◽  
Algebraic Characterization ◽  
Symmetric Hyperbolic System ◽  
Full Generality ◽  
Order Linear ◽  
First Order

In this paper, we study the dissipative structure of first-order linear symmetric hyperbolic system with general relaxation and provide the algebraic characterization for the uniform dissipativity up to order 1. Our result extends the classical Shizuta–Kawashima condition for the case of symmetric relaxation, with a full generality and optimality.

An Axiomatic Characterization of a Class of Petri Nets

1991 ◽  
Vol 14 (4) ◽  
pp. 477-491
Author(s):  
Waldemar Korczynski
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Axiomatic Characterization ◽  
Algebraic Characterization

In this paper an algebraic characterization of a class of Petri nets is given. The nets are characterized by a kind of algebras, which can be considered as a generalization of the concept of the case graph of a (marked) Petri net.

Algebraic characterization of bridged polycyclic compounds

1981 ◽  
Vol 19 (5) ◽  
pp. 929-955 ◽  
Author(s):  
Ov. Mekenyan ◽  
D. Bonchev ◽  
N. Trinajsti?
Keyword(s):  
Algebraic Characterization ◽  
Polycyclic Compounds

scholarly journals Algebraic Characterization of Rings of Continuousp-Adic Valued Functions

2015 ◽  
Vol 44 (2) ◽  
pp. 486-499
Author(s):  
Samuel Volkweis Leite ◽  
Alexander Prestel
Keyword(s):  
Algebraic Characterization

On the Dynamic Isotropy of Mechanisms With Two Degrees of Freedom

2005 ◽  
Author(s):  
Raffaele Di Gregorio ◽  
Alessandro Cammarata ◽  
Rosario Sinatra
Keyword(s):  
Finite Number ◽  
Degrees Of Freedom ◽  
Point Of View ◽  
Closed Curves ◽  
Special Cases ◽  
Dynamic Performances ◽  
Definition Of ◽  
Geometric Locus

The comparison of mechanisms with different topology or with different geometry, but with the same topology, is a necessary operation during the design of a machine sized for a given task. Therefore, tools that evaluate the dynamic performances of a mechanism are welcomed. This paper deals with the dynamic isotropy of 2-dof mechanisms starting from the definition introduced in a previous paper. In particular, starting from the condition that identifies the dynamically isotropic configurations, it shows that, provided some special cases are not considered, 2-dof mechanisms have at most a finite number of isotropic configurations. Moreover, it shows that, provided the dynamically isotropic configurations are excluded, the geometric locus of the configuration space that collects the points associated to configurations with the same dynamic isotropy is constituted by closed curves. This results will allow the classification of 2-dof mechanisms from the dynamic-isotropy point of view, and the definition of some methodologies for the characterization of the dynamic isotropy of these mechanisms. Finally, examples of applications of the obtained results will be given.

scholarly journals SEIFERT SURFACES, COMMUTATORS AND VASSILIEV INVARIANTS

2007 ◽  
Vol 16 (10) ◽  
pp. 1295-1329
Author(s):  
E. KALFAGIANNI ◽  
XIAO-SONG LIN
Keyword(s):  
Fundamental Group ◽  
Lower Central Series ◽  
Central Series ◽  
Seifert Surface ◽  
Vassiliev Invariants ◽  
Seifert Surfaces

We show that the Vassiliev invariants of a knot K, are obstructions to finding a regular Seifert surface, S, whose complement looks "simple" (e.g. like the complement of a disc) to the lower central series of its fundamental group. We also conjecture a characterization of knots whose invariants of all orders vanish in terms of their Seifert surfaces.

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