(i) [F.sub.E] [equivalent to] {[[0].sub.E], [[1].sub.E], [[[infinity]].sub.E]} for projective frames of the real

projective line P[R.sup.1], and

Then, X is either a

projective line bundle over [bar.X] or the direct product of [bar.X] and a fiber of [[phi].sub.R].

(i) So F = [[theta].sub.u] ([V.sub.2]), [V.sub.2] [subset] [V.sub.3], where the

projective line L = [PV.sub.2] is of kind [[LAMBDA].sub.3], with line pattern (0,3,1,0).

Coverage includes a guide to closure operations in commutative algebra, a survey of test ideals, finite-dimensional vector spaces with Frobenius action, finiteness and homological conditions in commutative group rings, regular pullbacks, noetherian rings without finite normalization, Krull dimension of polynomial and power series rings, the

projective line over the integers, on zero divisor graphs, and a closer look at non-unique factorization via atomic decay and strong atoms.

A line in P is given by an equation {(x, y, z)|ax + by + cz = 0}, that is, a

projective line corresponds to a plane in [F.sup.3] containing the origin.

His condition is as follows: if each

projective line has at least three points of intersection with hyperplanes in H, then [P.sup.n](C) - [absolute value of H] is Brody hyperbolic.

The

projective line [P.sup.1.sub.K] over K is defined as the quotient space ([K.sup.2]\{0})/ ~ where ~ is the equivalence relation defined by: ([z.sub.0], [z.sub.1]) ~ ([w.sub.0], [w.sub.1]) if there exists a non-zero element c in K such that ([z.sub.0], [z.sub.1]) = (c X [w.sub.0], c X [w.sub.j]).

Topics of the 13 papers include products and powers of linear codes under component wise multiplication, the geometry of efficient arithmetic on elliptic curves, 2-2-2 isogenics between Jacobians of hyperelliptic curves, a point counting algorithm for cyclic covers of the

projective line, genetics of polynomials over local fields, and smooth embeddings for the Suzuki and Ree curves.

over the regular bipyramid over Q is a direct product with the

projective line [P.sub.1] [??] [X.sub.[-1,1]].

We project from a

projective line intersecting X in two points x and y onto a 3-dimensional space [GAMMA] skew to this line.

Potential theory and dynamics on the Berkovich

projective line.

An edge with its two vertices is a combinatorial

projective line over [F.sub.1], and more generally, any subset of vertices together with the induced graph structure defines a linear subspace.