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A compact manifold admits a Lorentzian structure iff its Euler characteristic vanishes. Therefore, every noncompact manifold admits a Lorentzian structure.

A group in which the elements are square matrices, the group multiplication law is matrix multiplication, and the group inverse is simply the matrix inverse. Every matrix ...

The maximum degree, sometimes simply called the maximum degree, of a graph G is the largest vertex degree of G, denoted Delta.

Somewhere on the Earth, there is a pair of antipodal points having simultaneously the same temperature and pressure.

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

A necessary and sufficient condition that [alpha^'] should be comparable with [alpha] for all positive values of the a is that one of (alpha^') and (alpha) should be ...

An algebraic expression containing more than one term (cf., binomial). The term is also used to refer to a polynomial.

Let S_N(s)=sum_(n=1)^infty[(n^(1/N))]^(-s), (1) where [x] denotes nearest integer function, i.e., the integer closest to x. For s>3, S_2(s) = 2zeta(s-1) (2) S_3(s) = ...

A group or other algebraic object is called non-Abelian if the law of commutativity does not always hold, i.e., if the object is not Abelian. For example, the group of ...

A ruled surface parameterization x(u,v)=b(u)+vg(u) is called noncylindrical if gxg^' is nowhere 0. A noncylindrical ruled surface always has a parameterization of the form ...