It is known that in PG(3, q), q > 19, a partial flock of a quadratic cone with q − ε planes, can be extended to a unique flock if ε < 14 √ q, and a similar and slightly stronger theorem holds for the case q even. In this paper we prove the analogue of this result for cones with base curve of higher degree.

We show that there is essentially a unique elliptic curve $E$ defined over cubic Galois extension $K$ of $\mathbb Q$ with $K$-rational point order 13 and such not Q$.

Motivated by the work of Zargar and Zamani, we introduce a family elliptic curves containing several one- (respectively two-) parameter subfamilies high rank over function field $\mathbb{Q}(t)$ $\mathbb{Q}(t,k)$). Following approach Moody, construct two infinitely many at least 5 $\mathbb{Q}(t,k)$. Secondly, deduce other this family, induced edges rational cuboid five independent $\mathbb{Q}(t)...

Let Ω be a regular triangulation of a two dimensional domain and S n(Ω) be a vector space of functions in C r whose restriction to each small triangle in Ω is a polynomial of total degree at most n. Dimensions of bivariate spline spaces S n(Ω) over a special kind of triangulation, called the unconstricted triangulation, were given by Farin in the paper [J. Comput. Appl. Math. 192(2006), 320-327...

(1) Beginning of Section 5: We write that every genus g hyperelliptic curve over a perfect field k is birationally equivalent (over k) to a curve of the form y + q(x)y = p(x) where p(x), q(x) ∈ k[x] satisfy 2 deg q(x) ≤ deg p(x) and deg p(x) ∈ {2g + 1, 2g + 2}. This is false for (and only for) k = F2. Namely, this will fail for any hyperelliptic curve C over k = F2 for which the degree 2 morphi...

The discrete logarithm problem forms the basis of numerous cryptographic systems. The most eeective attack on the discrete logarithm problem in the multiplicative group of a nite eld is via the index calculus, but no such method is known for elliptic curve discrete logarithms. Indeed, Miller 23] has given a brief heuristic argument as to why no such method can exist. IN this note we give a deta...