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A predictor-corrector method for solution of ordinary differential equations. The third-order equations for predictor and corrector are y_(n+1) = ...

Let f:A->B be a map between sets A and B. Let Y subset= B. Then the preimage of Y under f is denoted by f^(-1)(Y), and is the set of all elements of A that map to elements in ...

Any ideal of a ring which is strictly smaller than the whole ring. For example, 2Z is a proper ideal of the ring of integers Z, since 1 not in 2Z. The ideal <X> of the ...

The pseudosmarandache function Z(n) is the smallest integer such that sum_(k=1)^(Z(n))k=1/2Z(n)[Z(n)+1] is divisible by n. The values for n=1, 2, ... are 1, 3, 2, 7, 4, 3, 6, ...

If alpha is any number and m and n are integers, then there is a rational number m/n for which |alpha-m/n|<=1/n. (1) If alpha is irrational and k is any whole number, there ...

A generalization of the binomial coefficient whose notation was suggested by Knuth, |_n; k]=(|_n]!)/(|_k]!|_n-k]!), (1) where |_n] is a Roman factorial. The above expression ...

Define f(x_1,x_2,...,x_n) with x_i positive as f(x_1,x_2,...,x_n)=sum_(i=1)^nx_i+sum_(1<=i<=k<=n)product_(j=i)^k1/(x_j). (1) Then minf=3n-C+o(1) (2) as n increases, where the ...

An s-route of a graph G is a sequence of vertices (v_0,v_1,...,v_s) of G such that v_iv_(i+1) in E(G) for i=0, 1, ..., s-1 (where E(G) is the edge set of G) and ...

For the parametric representation x = (2t^2)/(1+t^2) (1) y = (2t^3)/(1+t^2), (2) the catacaustic of this curve from the radiant point (8a,0) is given by x = ...

E(a,b)/p denotes the elliptic group modulo p whose elements are 1 and infty together with the pairs of integers (x,y) with 0<=x,y<p satisfying y^2=x^3+ax+b (mod p) (1) with a ...