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The second-order ordinary differential equation y^('')-[(m(m+1)+1/4-(m+1/2)cosx)/(sin^2x)+(lambda+1/2)]y=0.

A polynomial with matrix coefficients. An nth order matrix polynomial in a variable t is given by P(t)=A_0+A_1t+A_2t^2+...+A_nt^n, where A_k are p×p square matrices.

The second-order ordinary differential equation y^('')+[alpha/(cosh^2(ax))+betatanh(ax)+gamma]y=0.

An octic curve is an algebraic curve of order eight. The pear curve is an example of an octic curve.

A relation "<=" is called a preorder (or quasiorder) on a set S if it satisfies: 1. Reflexivity: a<=a for all a in S. 2. Transitivity: a<=b and b<=c implies a<=c. A preorder ...

An Abelian planar difference set of order n exists only for n a prime power. Gordon (1994) has verified it to be true for n<2000000.

The coloring red of two complete subgraphs of n/2 points (for even n) in order to generate a blue-empty graph.

A method for constructing magic squares of odd order, also called de la Loubere's method.

A Skolem sequence of order n is a sequence S={s_1,s_2,...,s_(2n)} of 2n integers such that 1. For every k in {1,2,...,n}, there exist exactly two elements s_i,s_j in S such ...

The sporadic groups are the 26 finite simple groups that do not fit into any of the four infinite families of finite simple groups (i.e., the cyclic groups of prime order, ...