Matrix-convex set theory reveals non-classical behavior of quantum magic squares

Scilight ◽  
2020 ◽  
Vol 2020 (47) ◽  
pp. 471101
Author(s):  
Matthew Ishimaru
Keyword(s):  
Set Theory ◽  
Convex Set ◽  
Magic Squares ◽  
Classical Behavior

ASSESSMENT OF DAMAGE AND LOSS OF SEISMICALLY EXCITED STRUCTURES BASED ON CONVEX ANALYSIS

2011 ◽  
Vol 05 (02) ◽  
pp. 101-118
Author(s):  
H. LI ◽  
L. Z. JIA
Keyword(s):  
Set Theory ◽  
Convex Analysis ◽  
Convex Set ◽  
Southern China ◽  
Estimation Method ◽  
Critical Factor ◽  
Loss Estimation ◽  
Convex Model ◽  
Damage State ◽  
Fragility Function

Probabilistic results drawn upon inadequate information are suspicious. The convex set theory, which requires much less information, is employed to model the uncertainties of the spectral displacement and damage state medians. Furthermore, a convex model of fragility function is established based on the envelope bound convex models of the spectral displacement and damage state medians. A bound loss estimation method is derived by integrating HAZUS-AEBM module with the convex set theory. The loss bounds of a hotel in southern China are obtained and compared to the loss calculated by HAZUS-AEBM method, which locates in the lower half interval of convex analysis results. The uncertainty propagation is analyzed and damage state medians are found to be the most critical factor to the loss. Finally, the PEER's probabilistic loss estimation methodology is also applied to this example to deduce the probability of loss exceeding the bound values of convex analysis results.

A Bound Fragility Analysis Methodology Based on Convex Model

2011 ◽  
Vol 243-249 ◽  
pp. 4017-4020
Author(s):  
Li Zhe Jia ◽  
Zhong Dong Duan
Keyword(s):  
Set Theory ◽  
Damage Assessment ◽  
Convex Set ◽  
Southern China ◽  
Uncertain Variable ◽  
Fragility Analysis ◽  
Convex Model ◽  
Damage State ◽  
Historical Material ◽  
Analysis Methodology

The spectral displacement and the damage state medians were assumed as deterministic parameters in HAZUS-Advanced Engineering Building Module (AEBM). As the historical material and experimental data were insufficient to establish an exactly probability density function model of uncertain variable, the damage assessment results by probabilistic model derived from many assumptions and simplification were unreliable. The uncertainties of the spectral displacement and damage state medians were modeled by the Envelope Bound Convex Model. Furthermore, a bound fragility analysis methodology is derived by integrating HAZUS-AEBM module with the convex set theory. The fragility of a hotel in southern China are calculated and compared to the damage derived by HAZUS-AEBM method, and the results of fragility analysis are more sensitive to the spectral displacement and the damage state medians.

scholarly journals Directional End of a Convex Set: Theory and Applications

2001 ◽  
Vol 110 (2) ◽  
pp. 389-411 ◽  
Author(s):  
M. A. Goberna ◽  
V. Jornet ◽  
M. Rodríguez
Keyword(s):  
Set Theory ◽  
Convex Set

A Course on Set Theory

2009 ◽  
Author(s):  
Ernest Schimmerling
Keyword(s):  
Set Theory
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