Search Results for ""

A map u:M->N, between two compact Riemannian manifolds, is a harmonic map if it is a critical point for the energy functional int_M|du|^2dmu_M. The norm of the differential ...

There are several types of numbers that are commonly termed "lucky numbers." The first is the lucky numbers of Euler. The second is obtained by writing out all odd numbers: ...

Roman (1984, p. 2) describes umbral calculus as the study of the class of Sheffer sequences. Umbral calculus provides a formalism for the systematic derivation and ...

Linnik's constant L is the constant appearing in Linnik's theorem. Heath-Brown (1992) has shown that L<=5.5, and Schinzel, Sierpiński, and Kanold (Ribenboim 1989) have ...

In 1891, Chebyshev and Sylvester showed that for sufficiently large x, there exists at least one prime number p satisfying x<p<(1+alpha)x, where alpha=0.092.... Since the ...

A manifold possessing a metric tensor. For a complete Riemannian manifold, the metric d(x,y) is defined as the length of the shortest curve (geodesic) between x and y. Every ...

The branch of geometry dealing with the properties and invariants of geometric figures under projection. In older literature, projective geometry is sometimes called "higher ...

The following vector integrals are related to the curl theorem. If F=cxP(x,y,z), (1) then int_CdsxP=int_S(daxdel )xP. (2) If F=cF, (3) then int_CFds=int_Sdaxdel F. (4) The ...

When n is an integer >=0, then J_n(z) and J_(n+m)(z) have no common zeros other than at z=0 for m an integer >=1, where J_n(z) is a Bessel function of the first kind. The ...

The totient function phi(n), also called Euler's totient function, is defined as the number of positive integers <=n that are relatively prime to (i.e., do not contain any ...