Random Fields Related to the Symmetry Classes of Second-Order Symmetric Tensors

2018 ◽  
pp. 173-185
Author(s):  
Anatoliy Malyarenko ◽  
Martin Ostoja-Starzewski
Keyword(s):  
Random Fields ◽  
Second Order ◽  
Symmetric Tensors ◽  
Symmetry Classes

scholarly journals Characterizing sand ripples at equilibrium phases

2013 ◽  
Vol 61 (4) ◽  
pp. 293-298 ◽  
Author(s):  
Jie Qin ◽  
Deyu Zhong ◽  
Guangqian Wang
Keyword(s):  
Time Series ◽  
Random Fields ◽  
Morphological Characteristics ◽  
Structure Functions ◽  
Second Order ◽  
Order Structure ◽  
Two Dimensional ◽  
Sand Ripples ◽  
Digital Elevation ◽  
Equilibrium Phases

Abstract Morphological characteristics of ripples are analyzed considering bed surfaces as two dimensional random fields of bed elevations. Two equilibrium phases are analyzed with respect to successive development of ripples based on digital elevation models. The key findings relate to the shape of the two dimensional second-order structure functions and multiscaling behavior revealed by higher-order structure functions. Our results suggest that (1) the two dimensional second-order structure functions can be used to differentiate the two equilibrium phases of ripples; and (2) in contrast to the elevational time series of ripples that exhibit significant multiscaling behavior, the DEMs of ripples at both equilibrium phases do not exhibit multiscaling behavior.

On stationarity and second-order properties of bilinear random fields

2014 ◽  
Vol 17 (3) ◽  
pp. 221-244
Author(s):  
Abdelouahab Bibi ◽  
Karima Kimouche
Keyword(s):  
Random Fields ◽  
Second Order

scholarly journals Classification of second order symmetric tensors in five‐dimensional Kaluza–Klein‐type theories

1995 ◽  
Vol 36 (6) ◽  
pp. 3074-3084 ◽  
Author(s):  
J. Santos ◽  
M. J. Rebouças ◽  
A. F. F. Teixeira
Keyword(s):  
Second Order ◽  
Symmetric Tensors ◽  
Kaluza Klein

scholarly journals Stein's method for negatively associated random variables with applications to second-order stationary random fields

2018 ◽  
Vol 55 (1) ◽  
pp. 196-215 ◽  
Author(s):  
Nathakhun Wiroonsri
Keyword(s):  
Normal Distribution ◽  
Random Vector ◽  
Random Fields ◽  
Second Order ◽  
Multidimensional Case ◽  
Standard Normal Distribution ◽  
Smooth Functions ◽  
Negatively Associated ◽  
Standard Normal ◽  
Stationary Random Fields

Abstract Let ξ = (ξ1, . . ., ξm) be a negatively associated mean-zero random vector with components that obey the bound |ξi| ≤ B, i = 1, . . ., m, and whose sum W = ∑i=1mξi has variance 1. The bound d1(ℒ(W), ℒ(Z)) ≤ 5B - 5.2∑i≠ jσij is obtained, where Z has the standard normal distribution and d1(∙, ∙) is the L1 metric. The result is extended to the multidimensional case with the L1 metric replaced by a smooth functions metric. Applications to second-order stationary random fields with exponential decreasing covariance are also presented.

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