Search Results for ""

A semiperfect magic cube, sometimes also called an "Andrews cube" (Gardner 1976; Gardner 1988, p. 219) is a magic cube for which the cross section diagonals do not sum to the ...

A differential equation or system of ordinary differential equations is said to be autonomous if it does not explicitly contain the independent variable (usually denoted t). ...

The upper and lower hinges are descriptive statistics of a set of N data values, where N is of the form N=4n+5 with n=0, 1, 2, .... The hinges are obtained by ordering the ...

Solution of a system of second-order homogeneous ordinary differential equations with constant coefficients of the form (d^2x)/(dt^2)+bx=0, where b is a positive definite ...

There are essentially three types of Fisher-Tippett extreme value distributions. The most common is the type I distribution, which are sometimes referred to as Gumbel types ...

Denote the nth derivative D^n and the n-fold integral D^(-n). Then D^(-1)f(t)=int_0^tf(xi)dxi. (1) Now, if the equation D^(-n)f(t)=1/((n-1)!)int_0^t(t-xi)^(n-1)f(xi)dxi (2) ...

Given a homogeneous linear second-order ordinary differential equation, y^('')+P(x)y^'+Q(x)y=0, (1) call the two linearly independent solutions y_1(x) and y_2(x). Then ...

Every finite Abelian group can be written as a group direct product of cyclic groups of prime power group orders. In fact, the number of nonisomorphic Abelian finite groups ...

A set of n distinct numbers taken from the interval [1,n^2] form a magic series if their sum is the nth magic constant M_n=1/2n(n^2+1) (Kraitchik 1942, p. 143). The numbers ...

1. Find a complete system of invariants, or 2. Decide when two metrics differ only by a coordinate transformation. The most common statement of the problem is, "Given metrics ...