ON COUSIN I SPACE AND NULLSTELLENSATZ

Graphene and Cousin Systems

On the finite field Nullstellensatz

Let X c pn be an irreducible projective variety defined over the finite field F q. We will say that X satisfies the property F F N (k, q) (Finite Field Nullstellensatz of degree k over F q) if every homogeneous polynomial over F q of degree k on pn vanishing on X (F q) vanishes on X, that is, it vanishes at all points of X defined over the algebraic closure of F q . We study when FFN(k,q) holds...

Hilbert’s Nullstellensatz

Let k be an algebraically closed field. We will employ the following notation. If I ⊂ k[X1, . . . , Xn] is an ideal, we let Z(I) denote the affine algebraic set in An defined by the vanishing of the polynomials in I . Conversely, if X is an affine algebraic set, I(X) denotes the ideal of polynomials in k[X1, . . . , Xn] vanishing on X . We will give a proof of the following result, called the w...

On the Twin and Cousin Primes

The computer results of the investigation of the number of pairs of primes separated by gap d = 2 (\twins") and gap d = 4 (\cousins") are reported. The number of twins and cousins turn out to be is almost the same. The plot of the function W (x) giving the diierence of the number of twins and cousins for x 2 (1; 10 12) is presented. This function has fractal properties and the fractal dimension...

Cousin Marriage

It is a great honour to be invited to contribute a lecture to this long-established series* founded to commemorate a very eminent physician of the Bristol Medical School an a member of a family distinguished for services to medicine and to the City over man/ years. I have also seen with particular pleasure that the first Long Fox lecture ^ given by John Beddoe, a pioneer of British anthropology...