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Given a finitely generated Z-graded module M over a graded ring R (finitely generated over R_0, which is an Artinian local ring), the Hilbert function of M is the map ...

cos(pi/(16)) = 1/2sqrt(2+sqrt(2+sqrt(2))) (1) cos((3pi)/(16)) = 1/2sqrt(2+sqrt(2-sqrt(2))) (2) cos((5pi)/(16)) = 1/2sqrt(2-sqrt(2-sqrt(2))) (3) cos((7pi)/(16)) = ...

A homework problem proposed in Steffi's math class in January 2003 asked students to prove that no ratio of two unequal numbers obtained by permuting all the digits 1, 2, ...

A set of positive integers is called weakly triple-free if, for any integer x, the set {x,2x,3x} !subset= S. For example, all subsets of {1,2,3,4,5} are weakly triple-free ...

An octic graph is a regular graph of degree eight. The numbers of simple octic graphs on n=9, 10, 11, ... nodes are 1, 6, 94, 10786, 3459386, ... (OEIS A014378). Examples are ...

The term isocline derives from the Greek words for "same slope." For a first-order ordinary differential equation y^'=f(t,y) is, a curve with equation f(t,y)=C for some ...

The angles mpi/n (with m,n integers) for which the trigonometric functions may be expressed in terms of finite root extraction of real numbers are limited to values of m ...

The inverse sine is the multivalued function sin^(-1)z (Zwillinger 1995, p. 465), also denoted arcsinz (Abramowitz and Stegun 1972, p. 79; Harris and Stocker 1998, p. 307; ...

The Klein graph is a weakly regular graph that is the dual graph of the cubic symmetric graph F_(056)B. The Klein graph is illustrated above in four order-4 LCF notations. ...

An ordinary double point of a plane curve is point where a curve intersects itself such that two branches of the curve have distinct tangent lines. Ordinary double points of ...