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F_x[1/pi(1/2Gamma)/((x-x_0)^2+(1/2Gamma)^2)](k)=e^(-2piikx_0-Gammapi|k|). This transform arises in the computation of the characteristic function of the Cauchy distribution.

A frustum (unfortunately commonly misspelled "frustrum") is that portion of a solid which lies between two parallel planes cutting the solid. Degenerate cases are obtained ...

Two unit-speed plane curves which have the same curvature differ only by a Euclidean motion.

A G-space is a special type of T1-Space. Consider a point x and a homeomorphism of an open neighborhood V of x onto an open set of R^n. Then a space is a G-space if, for any ...

A transformation from one reference frame to another moving with a constant velocity v with respect to the first for classical motion. However, special relativity shows that ...

A perspective collineation in which the center and axis are not incident. The term was first used by Poncelet (Cremona 1960, p. ix).

The determinant G(f_1,f_2,...,f_n)=|intf_1^2dt intf_1f_2dt ... intf_1f_ndt; intf_2f_1dt intf_2^2dt ... intf_2f_ndt; | | ... |; intf_nf_1dt intf_nf_2dt ... intf_n^2dt|.

Let the vertices of a graph G be numbered with distinct integers 1 to |G|. Then the dilation of G is the maximum (absolute) difference between integers assigned to adjacent ...

Harmonic coordinates satisfy the condition Gamma^lambda=g^(munu)Gamma_(munu)^lambda=0, (1) or equivalently, partial/(partialx^kappa)(sqrt(g)g^(lambdakappa))=0. (2) It is ...

The partial differential equation u_t=u_(xxx)u^3.