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F_x[sin(2pik_0x)](k) = int_(-infty)^inftye^(-2piikx)((e^(2piik_0x)-e^(-2piik_0x))/(2i))dx (1) = 1/2iint_(-infty)^infty[-e^(-2pii(k-k_0)x)+e^(-2pii(k+k_0)x)]dx (2) = ...

A one-dimensional map whose increments are distributed according to a normal distribution. Let y(t-Deltat) and y(t+Deltat) be values, then their correlation is given by the ...

The solution to the differential equation [D^(2v)+alphaD^v+betaD^0]y(t)=0 (1) is y(t)={e_alpha(t)-e_beta(t) for alpha!=beta; ...

An occurrence of a variable in a logic formula which is not inside the scope of a quantifier.

Two closed simply connected 4-manifolds are homeomorphic iff they have the same bilinear form beta and the same Kirby-Siebenmann invariant kappa. Any beta can be realized by ...

Pick any point P on a conic section, and draw a series of right angles having this point as their vertices. Then the line segments connecting the rays of the right angles ...

A smooth curve which corresponds to the limiting case of a histogram computed for a frequency distribution of a continuous distribution as the number of data points becomes ...

A distribution of values of a discrete variate represented graphically by plotting points (x_1,f_1), (x_2,f_2), ..., (x_k,f_k), and drawing a set of straight line segments ...

The permanent of an n×n integer matrix with all entries either 0 or 1 is 0 iff the matrix contains an r×s submatrix of 0s with r+s=n+1. This result follows from the ...

rho_(n+1)(x)=intrho_n(y)delta[x-M(y)]dy, where delta(x) is a delta function, M(x) is a map, and rho is the natural invariant.