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The Diophantine equation x^2+y^2=p can be solved for p a prime iff p=1 (mod 4) or p=2. The representation is unique except for changes of sign or rearrangements of x and y. ...

For a unit speed curve on a surface, the length of the surface-tangential component of acceleration is the geodesic curvature kappa_g. Curves with kappa_g=0 are called ...

If F is a family of more than n bounded closed convex sets in Euclidean n-space R^n, and if every H_n (where H_n is the Helly number) members of F have at least one point in ...

If R is a Noetherian ring, then S=R[X] is also a Noetherian ring.

Any complex measure lambda decomposes into an absolutely continuous measure lambda_a and a singular measure lambda_c, with respect to some positive measure mu. This is the ...

Multivariable calculus is the branch of calculus that studies functions of more than one variable. Partial derivatives and multiple integrals are the generalizations of ...

The Pontryagin number is defined in terms of the Pontryagin class of a manifold as follows. For any collection of Pontryagin classes such that their cup product has the same ...

The Stiefel-Whitney number is defined in terms of the Stiefel-Whitney class of a manifold as follows. For any collection of Stiefel-Whitney classes such that their cup ...

A fundamental system of logic based on the concept of a generalized function whose argument is also a function (Schönfinkel 1924). This mathematical discipline was ...

The Euler formula, sometimes also called the Euler identity (e.g., Trott 2004, p. 174), states e^(ix)=cosx+isinx, (1) where i is the imaginary unit. Note that Euler's ...