On Septic Scrolls Having a Rectilinear Directrix

Divisors on Rational Normal Scrolls

Let A be the homogeneous coordinate ring of a rational normal scroll. The ring A is equal to the quotient of a polynomial ring S by the ideal generated by the two by two minors of a scroll matrix ψ with two rows and l catalecticant blocks. The class group of A is cyclic, and is infinite provided l is at least two. One generator of the class group is [J], where J is the ideal of A generated by t...

A NOTE ON THE UNSTEADY FLOW OF A VISCO-ELASTIC MAXWELL FLUID THROUGH A RECTILINEAR PIPE

The unsteady flow of a visco-elastic Maxwell fluid through a rectilinear pipe having its cross-section as a parallelogram under the influence of a axial pressure gradient (I) varying linearly with time , and (II) decreasing exponentially with time has been discussed in the present paper. Variables separable and Laplace transform methods have been used to solve the problem.  

On Rectilinear Link Distance

Given a simple polygon P without holes all of whose edges are axis-parallel, a rectilinear path in P is a path that consists of axis-parallel segments only and does not cross any edge of P. The length of such a path is defined as the number of segments it consists of and the rectilinear link distance between two points in P is defined as the length of the shortest path connecting the two points...

A Note on Scrolls of Smallest Embedded Codimension

The situation considered in this note is as follows. Let M be an algebraic submanifold of P with n = dimM . M is said to be a scroll over S if there is a surjective morphism π : M → S such that every fiber Fx = π (x) over x ∈ S is a linear subspace in P of dimension r − 1 = n − s, where s = dimS. This is equivalent to saying that M ∼= PS(E) for some vector bundle E of rank r = n− s+1 and the ta...

A note on approximations of rectilinear polygons