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A connection on a vector bundle pi:E->M is a way to "differentiate" bundle sections, in a way that is analogous to the exterior derivative df of a function f. In particular, ...

In practice, the vertical offsets from a line (polynomial, surface, hyperplane, etc.) are almost always minimized instead of the perpendicular offsets. This provides a ...

Nonparametric estimation is a statistical method that allows the functional form of a fit to data to be obtained in the absence of any guidance or constraints from theory. As ...

The function defined by y=ab^(q^x). It is used in actuarial science for specifying a simplified mortality law (Kenney and Keeping 1962, p. 241). Using s(x) as the probability ...

Exponential decay is the decrease in a quantity N according to the law N(t)=N_0e^(-lambdat) (1) for a parameter t and constant lambda (known as the decay constant), where e^x ...

In combinatorial logic minimization, a device known as a Karnaugh map is frequently used. It is similar to a truth table, but the various variables are represented along two ...

A function f is said to be an entire modular form of weight k if it satisfies 1. f is analytic in the upper half-plane H, 2. f((atau+b)/(ctau+d))=(ctau+d)^kf(tau) whenever [a ...

The mean of a distribution with probability density function P(x) is the first raw moment mu_1^', defined by mu=<x>, (1) where <f> is the expectation value. For a continuous ...

The logarithm log_bx for a base b and a number x is defined to be the inverse function of taking b to the power x, i.e., b^x. Therefore, for any x and b, x=log_b(b^x), (1) or ...

P(Z)=Z/(sigma^2)exp(-(Z^2+|V|^2)/(2sigma^2))I_0((Z|V|)/(sigma^2)), where I_0(z) is a modified Bessel function of the first kind and Z>0. For a derivation, see Papoulis ...