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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).
With β = 1, the usual exponential function is recovered. With a stretching exponent β between 0 and 1, the graph of log f versus t is characteristically stretched, hence the name of the function. The compressed exponential function (with β > 1) has less practical importance, with the notable exception of β = 2, which gives the normal ...
ε 2: −1: 0: 1 Spacetime interpretation None: Newtonian spacetime: Minkowski spacetime Slope tan φ = m: tanp φ = u: tanh φ = v "cosine" cos φ = (1 + m 2) −1/2: cosp φ = 1: cosh φ = (1 − v 2) −1/2 "sine" sin φ = m (1 + m 2) −1/2: sinp φ = u: sinh φ = v (1 − v 2) −1/2 "secant" sec φ = (1 + m 2) 1/2: secp φ = 1: sech φ ...
In this case, the displacement is horizontal by a factor of 2 where the fixed line is the x-axis, and the signed distance is the y-coordinate. Note that points on opposite sides of the reference line are displaced in opposite directions. Shear mappings must not be confused with rotations.
Liouville's equation appears in the study of isothermal coordinates in differential geometry: the independent variables x,y are the coordinates, while f can be described as the conformal factor with respect to the flat metric. Occasionally it is the square f 2 that is referred to as the conformal factor, instead of f itself.
A quantity undergoing exponential decay. Larger decay constants make the quantity vanish much more rapidly. This plot shows decay for decay constant (λ) of 25, 5, 1, 1/5, and 1/25 for x from 0 to 5. A quantity is subject to exponential decay if it decreases at a rate proportional to its current value.
Your doctor will suspect osteoporosis if you have an overall height loss of 1.5 inches or more, or a height loss of 0.8 inches or more from your last measurement, Litt says.
The concept of unit circle (the set of all vectors of norm 1) is different in different norms: for the 1-norm, the unit circle is a square oriented as a diamond; for the 2-norm (Euclidean norm), it is the well-known unit circle; while for the infinity norm, it is an axis-aligned square.