Finite-dimensional distribution

Data Sources and Models

Published in Yuri S. Popkov, Alexey Yu. Popkov, Yuri A. Dubnov, Alexander Yu. Mazurov, Entropy Randomization in Machine Learning, 2023

Yuri S. Popkov, Alexey Yu. Popkov, Yuri A. Dubnov, Alexander Yu. Mazurov

A set of functions Pt1,…,tn(η1,…,ηn) is called finite-dimensional distributions of a random function x(t).

Nonlocal strain gradient beam model for nonlinear secondary resonance analysis of functionally graded porous micro/nano-beams under periodic hard excitations

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Journal Information

Published in Mechanics Based Design of Structures and Machines, 2020

A. M. Fattahi, S. Sahmani, N. A. Ahmed

On the basis of the Gaussian random field scheme (Roberts and Garboczi 2001), all finite dimensional distributions are supposed to be multivariate normal distributions for any number of coordinates. Therefore, the mass density coefficient () can be introduced as a function of the porosity coefficient () as below

Finite-dimensional distribution

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Data Sources and Models

Nonlocal strain gradient beam model for nonlinear secondary resonance analysis of functionally graded porous micro/nano-beams under periodic hard excitations