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Each iteration of the Sierpinski triangle contains triangles related to the next iteration by a scale factor of 1/2. In affine geometry, uniform scaling (or isotropic scaling [1]) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale factor that is the same in all directions (isotropically).
Scale analysis (or order-of-magnitude analysis) is a powerful tool used in the mathematical sciences for the simplification of equations with many terms. First the approximate magnitude of individual terms in the equations is determined. Then some negligibly small terms may be ignored.
In mathematics and physics, multiple-scale analysis (also called the method of multiple scales) comprises techniques used to construct uniformly valid approximations to the solutions of perturbation problems, both for small as well as large values of the independent variables. This is done by introducing fast-scale and slow-scale variables for ...
Fouling, i.e., formation of a deposit layer (scale) on a solid surface, e.g., in a boiler; in particular, a kind of micro fouling as crystallization of salts; Scaling rock, the removal of loose rock from a rock wall after blasting; Scaling of innovations, a process that leads to widespread use of an innovation
In the simplest cases, normalization of ratings means adjusting values measured on different scales to a notionally common scale, often prior to averaging. In more complicated cases, normalization may refer to more sophisticated adjustments where the intention is to bring the entire probability distributions of adjusted values into alignment.
Multidimensional scaling (MDS) is a means of visualizing the level of similarity of individual cases of a data set. MDS is used to translate distances between each pair of n {\textstyle n} objects in a set into a configuration of n {\textstyle n} points mapped into an abstract Cartesian space .
In operations research, multiscale modeling addresses challenges for decision-makers that come from multiscale phenomena across organizational, temporal, and spatial scales. This theory fuses decision theory and multiscale mathematics and is referred to as multiscale decision-making. Multiscale decision-making draws upon the analogies between ...
Dynamic scaling (sometimes known as Family–Vicsek scaling [1] [2]) is a litmus test that shows whether an evolving system exhibits self-similarity. In general a function is said to exhibit dynamic scaling if it satisfies: