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The sigmoid function, also called the sigmoidal curve (von Seggern 2007, p. 148) or logistic function, is the function y=1/(1+e^(-x)). (1) It has derivative (dy)/(dx) = ...

The sign of a real number, also called sgn or signum, is -1 for a negative number (i.e., one with a minus sign "-"), 0 for the number zero, or +1 for a positive number (i.e., ...

Simple harmonic motion refers to the periodic sinusoidal oscillation of an object or quantity. Simple harmonic motion is executed by any quantity obeying the differential ...

Given a simple harmonic oscillator with a quadratic perturbation, write the perturbation term in the form alphaepsilonx^2, x^..+omega_0^2x-alphaepsilonx^2=0, (1) find the ...

A simple point process (or SPP) is an almost surely increasing sequence of strictly positive, possibly infinite random variables which are strictly increasing as long as they ...

A sinusoidal spiral is a curve of the form r^n=a^ncos(ntheta), (1) with n rational, which is not a true spiral. Sinusoidal spirals were first studied by Maclaurin. Special ...

Two or more lines which have no intersections but are not parallel, also called agonic lines. Since two lines in the plane must intersect or be parallel, skew lines can exist ...

Guy's "strong law of small numbers" states that there aren't enough small numbers to meet the many demands made of them. Guy (1988) also gives several interesting and ...

Given the left factorial function Sigma(n)=sum_(k=1)^nk!, SK(p) for p prime is the smallest integer n such that p|1+Sigma(n-1). The first few known values of SK(p) are 2, 4, ...

If a random variable X has a chi-squared distribution with m degrees of freedom (chi_m^2) and a random variable Y has a chi-squared distribution with n degrees of freedom ...