Search Results for ""

A polynomial discriminant is the product of the squares of the differences of the polynomial roots r_i. The discriminant of a polynomial is defined only up to constant ...

Let X be a set of urelements, and let V(X) be the superstructure with X as its set of individuals. Let kappa be a cardinal number. An enlargement V(^*X) is kappa-saturated ...

Every smooth nonzero vector field on the 3-sphere has at least one closed orbit. The conjecture was proposed in 1950 and proved true for Hopf maps. The conjecture was ...

A diagram lemma which states that the above commutative diagram of Abelian groups and group homomorphisms with exact rows gives rise to an exact sequence This commutative ...

Let (K,L) be a pair consisting of finite, connected CW-complexes where L is a subcomplex of K. Define the associated chain complex C(K,L) group-wise for each p by setting ...

Also called Macaulay ring, a Cohen Macaulay ring is a Noetherian commutative unit ring R in which any proper ideal I of height n contains a sequence x_1, ..., x_n of elements ...

Let A(n) denote the number of partitions of n into parts =2,5,11 (mod 12), let B(n) denote the number of partitions of n into distinct parts =2,4,5 (mod 6), and let C(n) ...

Let L=<L, v , ^ > and K=<K, v , ^ > be lattices, and let h:L->K. Then h is a lattice homomorphism if and only if for any a,b in L, h(a v b)=h(a) v h(b) and h(a ^ b)=h(a) ^ ...

Macdonald's constant term conjectures are related to root systems of Lie algebras (Macdonald 1982, Andrews 1986). They can be regarded as generalizations of Dyson's ...

The spherical harmonics can be generalized to vector spherical harmonics by looking for a scalar function psi and a constant vector c such that M = del x(cpsi) (1) = psi(del ...