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The curl of a vector field, denoted curl(F) or del xF (the notation used in this work), is defined as the vector field having magnitude equal to the maximum "circulation" at ...

In hexagonal close packing, layers of spheres are packed so that spheres in alternating layers overlie one another. As in cubic close packing, each sphere is surrounded by 12 ...

A Kähler structure on a complex manifold M combines a Riemannian metric on the underlying real manifold with the complex structure. Such a structure brings together geometry ...

A Lorentz transformation is a four-dimensional transformation x^('mu)=Lambda^mu_nux^nu, (1) satisfied by all four-vectors x^nu, where Lambda^mu_nu is a so-called Lorentz ...

The real projective plane is the closed topological manifold, denoted RP^2, that is obtained by projecting the points of a plane E from a fixed point P (not on the plane), ...

Given the closed interval [0,x] with x>1, let one-dimensional "cars" of unit length be parked randomly on the interval. The mean number M(x) of cars which can fit (without ...

Transitivity is a result of the symmetry in the group. A group G is called transitive if its group action (understood to be a subgroup of a permutation group on a set Omega) ...

The number of representations of n by k squares, allowing zeros and distinguishing signs and order, is denoted r_k(n). The special case k=2 corresponding to two squares is ...

An Abelian integral, are also called a hyperelliptic integral, is an integral of the form int_0^x(dt)/(sqrt(R(t))), where R(t) is a polynomial of degree >4.

In an additive group G, the additive inverse of an element a is the element a^' such that a+a^'=a^'+a=0, where 0 is the additive identity of G. Usually, the additive inverse ...