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The principal value of an analytic multivalued function is the single value chosen by convention to be returned for a given argument. Complex multivalued functions have ...

A proof by contradiction establishes the truth of a given proposition by the supposition that it is false and the subsequent drawing of a conclusion that is contradictory to ...

A pseudoinverse is a matrix inverse-like object that may be defined for a complex matrix, even if it is not necessarily square. For any given complex matrix, it is possible ...

A mathematical problem, usually not requiring advanced mathematics, to which a solution is desired. Puzzles frequently require the rearrangement of existing pieces (e.g., 15 ...

Pythagoras's theorem states that the diagonal d of a square with sides of integral length s cannot be rational. Assume d/s is rational and equal to p/q where p and q are ...

The signature of a non-degenerate quadratic form Q=y_1^2+y_2^2+...+y_p^2-y_(p+1)^2-y_(p+2)^2-...-y_r^2 of rank r is most often defined to be the ordered pair (p,q)=(p,r-p) of ...

A groupoid S such that for all a,b in S, there exist unique x,y in S such that ax = b (1) ya = b. (2) No other restrictions are applied; thus a quasigroup need not have an ...

Let the two-dimensional cylinder function be defined by f(x,y)={1 for r<R; 0 for r>R. (1) Then the Radon transform is given by ...

The ramp function is defined by R(x) = xH(x) (1) = int_(-infty)^xH(x^')dx^' (2) = int_(-infty)^inftyH(x^')H(x-x^')dx^' (3) = H(x)*H(x), (4) where H(x) is the Heaviside step ...

It is possible to find six points in the plane, no three on a line and no four on a circle (i.e., none of which are collinear or concyclic), such that all the mutual ...