A detailed understanding of the avalanche phenomena is required to construct hazard scenarios which involve the careful specification of initial conditions (release zone location and dimensions) and definition of appropriate friction parameters.
The description of the dimension and definition of competency was systematically developed for the specific context and translated in measurable terms to create an instrument similar to those in previous studies [ 5, 31].
Some common computer aided geometry constraints and dimension driving techniques and definitions for designing the simulation mechanisms are presented.
Besides, the Fourier transform is extended to infinite dimensions and a new definition of the composition of a tempered distribution with the Brownian motion is given.
Researchers could investigate whether commonly agreed upon dimensions relate to factor perception and definitions of network risk.
Instead of presenting here our initial definitions and reformulations at every step of this process, we refer to the detailed, resulting dimensions and sub-domains with their definitions in the following section.
In order to obtain a correct system embedding dimension, starting from the time series, it is necessary to estimate the attractor dimension D. Among the different dimension definitions, correlation dimension discovered by Grassberger and Procaccia in 1983 [19], is the most popular one due to its calculation simplicity.
Detailed definitions of dimensions and subscales and information on theory development have previously been described [ 15], as have the methods for calculating instrument outcome scores [ 20].
Collating the main overlapping dimensions, definitions, and their measurement scales, a recent systematic review proposed that mood instability is 'rapid oscillations of intense affect, with a difficulty in regulating these oscillations or their behavioural consequences'.
The macroscale parameters consist of structural dimensions, layup definition, and an imperfection scale factor.
