The mentioned estimators are computationally heavy because of the required multi-dimensional systems resolution.
The elucidation of multi-dimensional systems will be investigated in another paper.
The numerical methods utilized appear to be applicable to complex multi-dimensional systems.
PSS are complex, dynamic, and multi-dimensional systems, which are supported by appropriate infrastructure and networks.
Stochastic particle-resolved methods have proven useful for simulating multi-dimensional systems such as composition-resolved aerosol size distributions.
However, its numerical solution in multi-dimensional systems is intractable due to the large number of independent variables.
Our framework applies from one-dimensional scalar cases all the way to multi-dimensional systems of conservation laws.
Several examples are given and show clearly the effects of the non-linearities and of the random parametric excitation for multi-dimensional systems.
In this paper, the fourth in a series, the spectral volume (SV) method is extended to multi-dimensional systems – the 2D Euler equations.
Another approach to finding the escape times of dynamical systems under small noise is the Eyring-Kramer (EK) equation, which has been rigorously proved for multi-dimensional systems [26].
Multi-dimensional systems (Husserl 1913/1962, §10; Ingarden 1960/1964, Chapter 2; Thomasson 1999, Chapter 8; Smith forthcoming, Chapter 8) address the second worry to some extent by acknowledging that the different dimensions of categorization are possible, and that no one-dimensional list can purport to completeness.
