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The natural norm induced by the L1-norm is called the maximum absolute column sum norm and is defined by ||A||_1=max_(j)sum_(i=1)^n|a_(ij)| for a matrix A. This matrix norm ...

Let f(x) be differentiable on the open interval (a,b) and continuous on the closed interval [a,b]. Then there is at least one point c in (a,b) such that ...

The study of the inner structure of a mathematical theory considered as a whole. It deals with the general properties of the rules according to which the objects of a certain ...

The unknotting number for a torus knot (p,q) is (p-1)(q-1)/2. This 40-year-old conjecture was proved (Adams 1994) by Kronheimer and Mrowka (1993, 1995).

Let E be the largest and e the smallest power of l in the HOMFLY polynomial of an oriented link, and i be the braid index. Then the Morton-Franks-Williams inequality holds, ...

An N-cluster is a point lattice configuration in which the distance between every pair of points is an integer, no three points are collinear, and no four points are ...

If the Gauss map of a complete minimal surface omits a neighborhood of the sphere, then the surface is a plane. This was proven by Osserman (1959). Xavier (1981) subsequently ...

A geodesic on a paraboloid x = sqrt(u)cosv (1) y = sqrt(u)sinv (2) z = u (3) has differential parameters defined by P = ...

The set of all lines through a point. The term was first used by Desargues (Cremona 1960, p. x). The six angles of any pencils of four rays O{ABCD} are connected by the ...

Campbell (2022) used the WZ method to obtain the sum (pi^2)/4=sum_(n=1)^infty(16^n(n+1)(3n+1))/(n(2n+1)^2(2n; n)^3), (1) where (n; k) is a binomial coefficient. There is a ...