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According to the dependence on the variable (i.e., time), these systems were classified into two types: continuous-time systems and discrete-time systems.
This method stands in contrast to the general transformation to the canonical form: it transfers the dependence on the variable x to the coefficient of ẏ, precisely the term that the canonical transformation strives to eliminate.
Sometimes we shall also consider equations with measurable coefficients, that is when the vector field a exhibits an explicit dependence on the variable x, i.e., - div a ( x, D u ) = μ.
MCAR is the assumption that there is no dependence on the variable values that are missing with any other variable in the study, including itself.
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Allometric scaling laws, which can be used to characterize many biological systems [1] [3], take the form Y = bXα, which represents the dependence of the variable Y on the variable X as a function that involves the normalization constant b and the scaling exponent a.
SAC can be a property of the variable itself (inherent or intrinsic SAC) or it can arise due to the dependence of the variable of interest on another spatially autocorrelated variable (induced SAC) (Legendre et al. 2002; Fortin and Dale 2005).
Its dependence on the variables t and x is discontinuous, since the signum function sgn, the greatest integer function, and the function h are discontinuous.
Graphical visualization of the fitted function as a function of one or more of the explanatory variables provides a comprehensive summary of its dependence on the variables, especially if the function is dominated by additive terms and/or lower-order interactions.
Regression lines were fitted to the data, showing the dependence of the variables on the number of movable items.
In the first one, the J-GL-C is employed for approximating the functional dependence on the spatial variable, using (N−1) nodes of the Jacobi Gauss Lobatto interpolation which depends upon two general Jacobi parameters.
In this article an infinite space Green's function of the time-dependent RTE is derived where the final solutions have an analytical dependence on the time variable and are well convergent due to the exponential decay of the time-dependent modes.
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