scholarly journals Fuzzy Random Walkers with Second Order Bounds: An Asymmetric Analysis

Algorithms ◽  
2017 ◽  
Vol 10 (2) ◽  
pp. 40 ◽  
Author(s):  
Georgios Drakopoulos ◽  
Andreas Kanavos ◽  
Konstantinos Tsakalidis
Keyword(s):  
Second Order ◽  
Random Walkers ◽  
Order Bounds ◽  
Fuzzy Random

scholarly journals Improved second-order bounds for prediction with expert advice

2006 ◽  
Vol 66 (2-3) ◽  
pp. 321-352 ◽  
Author(s):  
Nicolò Cesa-Bianchi ◽  
Yishay Mansour ◽  
Gilles Stoltz
Keyword(s):  
Second Order ◽  
Expert Advice ◽  
Prediction With Expert Advice ◽  
Order Bounds

scholarly journals Best second order bounds for two-terminal network reliability with dependent edge failures

1999 ◽  
Vol 96-97 ◽  
pp. 375-393 ◽  
Author(s):  
Pierre Hansen ◽  
Brigitte Jaumard ◽  
Guy-Blaise Douanya Nguetse
Keyword(s):  
Network Reliability ◽  
Second Order ◽  
Order Bounds

First-and second-order bounds on terminal reliability

Networks ◽  
1986 ◽  
Vol 16 (3) ◽  
pp. 319-329 ◽  
Author(s):  
J. Yael Assous
Keyword(s):  
Second Order ◽  
Terminal Reliability ◽  
Order Bounds

The overall constitutive behaviour of nonlinearly elastic composites

1989 ◽  
Vol 422 (1862) ◽  
pp. 147-171 ◽  
Keyword(s):  
Composite Materials ◽  
Nonlinear Problems ◽  
Second Order ◽  
Consistent Estimate ◽  
First Order ◽  
Variational Structure ◽  
Constitutive Assumption ◽  
Order Bounds ◽  
Definition Of ◽  
Nonlinearly Elastic

This work uses the general framework of Hill for the definition of overall mechanical properties of composite materials undergoing large deformations, together with Ball’s constitutive assumption of polyconvexity, and ideas based on a Hashin–Shtrikman variational structure developed recently by Talbot & Willis for nonlinear problems, to obtain rigorous first-order (depending only on the initial volume fractions of the phases) and second-order (depending also on the overall isotropy of the composite) bounds on the overall properties of composite materials with nonlinearly elastic phases. Although the proposed first-order upper bound, or Voigt bound, agrees with a previous result, the corresponding lower bound, or Reuss bound, is significantly tighter than the previously available result. The proposed second-order bounds are completely new, and are of course tighter than the first-order bounds. Additionally, a ‘self-consistent’ estimate is given for the case when the phases are neo-hookean.

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