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When the scale factor is larger than 1, (uniform or non-uniform) scaling is sometimes also called dilation or enlargement. When the scale factor is a positive number smaller than 1, scaling is sometimes also called contraction or reduction. In the most general sense, a scaling includes the case in which the directions of scaling are not ...
In physics, mathematics and statistics, scale invariance is a feature of objects or laws that do not change if scales of length, energy, or other variables, are multiplied by a common factor, and thus represent a universality. The technical term for this transformation is a dilatation (also known as dilation).
In a scale invariant quantum field theory, by definition each operator acquires under a dilation a factor , where is a number called the scaling dimension of . This implies in particular that the two point correlation function O ( x ) O ( 0 ) {\displaystyle \langle O(x)O(0)\rangle } depends on the distance as ( x 2 ) − Δ {\displaystyle (x^{2 ...
Dilation (operator theory), a dilation of an operator on a Hilbert space; Dilation (morphology), an operation in mathematical morphology; Scaling (geometry), including: Homogeneous dilation , the scalar multiplication operator on a vector space or affine space; Inhomogeneous dilation, where scale factors may differ in different directions
Here is the ratio of magnification or dilation factor or scale factor or similitude ratio. Such a transformation can be called an enlargement if the scale factor exceeds 1. The above-mentioned fixed point S is called homothetic center or center of similarity or center of similitude.
Dilation (usually represented by ⊕) is one of the basic operations in mathematical morphology. Originally developed for binary images, it has been expanded first to grayscale images, and then to complete lattices. The dilation operation usually uses a structuring element for probing and expanding the shapes contained in the input image.
Michael Chavez found out he won $1.2 million in the California Lottery Mega Millions on Nov. 5, 2024, after a co-worker joked to him about winning the draw, reported NBC4 Los Angeles and The ...
Horizontal shear of a square into parallelograms with factors and =. In the plane =, a horizontal shear (or shear parallel to the x-axis) is a function that takes a generic point with coordinates (,) to the point (+,); where m is a fixed parameter, called the shear factor.