Numerical representation of interval orders on a topological space

1986 ◽  
Vol 38 (1) ◽  
pp. 160-166 ◽  
Author(s):  
Douglas S Bridges
Keyword(s):  
Topological Space ◽  
Numerical Representation ◽  
Interval Orders

scholarly journals Continuous Representability of Interval Orders: The Topological Compatibility Setting

2015 ◽  
Vol 23 (03) ◽  
pp. 345-365 ◽  
Author(s):  
G. Bosi ◽  
A. Estevan ◽  
J. Gutiérrez García ◽  
E. Induráin
Keyword(s):  
Topological Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Interval Order ◽  
Topological Spaces ◽  
Interval Orders ◽  
Finite Support ◽  
Order Representation ◽  
Necessary And Sufficient ◽  
The Given

In this paper, we go further on the problem of the continuous numerical representability of interval orders defined on topological spaces. A new condition of compatibility between the given topology and the indifference associated to the main trace of an interval order is introduced. Provided that this condition is fulfilled, a semiorder has a continuous interval order representation through a pair of continuous real-valued functions. Other necessary and sufficient conditions for the continuous representability of interval orders are also discussed, and, in particular, a characterization is achieved for the particular case of interval orders defined on a topological space of finite support.

scholarly journals Numerical representation of PQI interval orders

2005 ◽  
Vol 147 (1) ◽  
pp. 125-146 ◽  
Author(s):  
An Ngo The ◽  
Alexis Tsoukiàs
Keyword(s):  
Numerical Representation ◽  
Interval Orders

Fatigue Investigation of Elastomeric Structures

2010 ◽  
Vol 38 (3) ◽  
pp. 194-212 ◽  
Author(s):  
Bastian Näser ◽  
Michael Kaliske ◽  
Will V. Mars
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
Material Behavior ◽  
Period Effect ◽  
Numerical Representation ◽  
Material Force ◽  
Strain Behavior ◽  
Dissipative Effects ◽  
Elastomeric Materials

Abstract Fatigue crack growth can occur in elastomeric structures whenever cyclic loading is applied. In order to design robust products, sensitivity to fatigue crack growth must be investigated and minimized. The task has two basic components: (1) to define the material behavior through measurements showing how the crack growth rate depends on conditions that drive the crack, and (2) to compute the conditions experienced by the crack. Important features relevant to the analysis of structures include time-dependent aspects of rubber’s stress-strain behavior (as recently demonstrated via the dwell period effect observed by Harbour et al.), and strain induced crystallization. For the numerical representation, classical fracture mechanical concepts are reviewed and the novel material force approach is introduced. With the material force approach at hand, even dissipative effects of elastomeric materials can be investigated. These complex properties of fatigue crack behavior are illustrated in the context of tire durability simulations as an important field of application.

On the Positivity of $\mathbf{{a}}$-Linear with Random Finitely

2020 ◽  
Author(s):  
Amanda Bolton
Keyword(s):  
Representation Theory ◽  
Central Problem ◽  
Numerical Representation

Let $\rho$ be an ultra-unique, reducible topos equipped with a minimal homeomorphism. We wish to extend the results of \cite{cite:0} to trivially Cartan classes. We show that $d$ is comparable to $\mathcal{{M}}$. This leaves open the question of uniqueness. Moreover, a central problem in numerical representation theory is the description of irreducible, orthogonal, hyper-unique graphs.

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