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A Montgomery curve of equation = + +. A Montgomery curve over a field K is defined by the equation,: = + + for certain A, B ∈ K and with B(A 2 − 4) ≠ 0.. Generally this curve is considered over a finite field K (for example, over a finite field of q elements, K = F q) with characteristic different from 2 and with A ≠ ±2 and B ≠ 0, but they are also considered over the rationals with ...
Elliptic curve scalar multiplication is the operation of successively adding a point along an elliptic curve to itself repeatedly. It is used in elliptic curve cryptography (ECC). The literature presents this operation as scalar multiplication, as written in Hessian form of an elliptic curve. A widespread name for this operation is also ...
The Montgomery form of the residue class a with respect to R is aR mod N, that is, it is the representative of the residue class aR. For example, suppose that N = 17 and that R = 100. The Montgomery forms of 3, 5, 7, and 15 are 300 mod 17 = 11, 500 mod 17 = 7, 700 mod 17 = 3, and 1500 mod 17 = 4.
Drainage density is a quantity used to describe physical parameters of a drainage basin. First described by Robert E. Horton, drainage density is defined as the total length of channel in a drainage basin divided by the total area, represented by the following equation: [ 1] The quantity represents the average length of channel per unit area of ...
Van der Pauw method. The van der Pauw Method is a technique commonly used to measure the resistivity and the Hall coefficient of a sample. Its strength lies in its ability to accurately measure the properties of a sample of any arbitrary shape, as long as the sample is approximately two-dimensional (i.e. it is much thinner than it is wide ...
B. Riemann used the Riemann–Siegel formula (unpublished, but reported in Siegel 1932). 1903 15 J. P. Gram (1903) used Euler–Maclaurin formula and discovered Gram's law. He showed that all 10 zeros with imaginary part at most 50 range lie on the critical line with real part 1/2 by computing the sum of the inverse 10th powers of the roots he ...
DFFITS. In statistics, DFFIT and DFFITS ("difference in fit (s)") are diagnostics meant to show how influential a point is in a linear regression, first proposed in 1980. [ 1] DFFIT is the change in the predicted value for a point, obtained when that point is left out of the regression: where and are the prediction for point i with and without ...
The basic quantities describing a sphere (meaning a 2-sphere, a 2-dimensional surface inside 3-dimensional space) will be denoted by the following variables . is the radius,