Results 251 to 260 of about 513,946 (293)

Ovoids and Translation Planes

Canadian Journal of Mathematics, 1982
An ovoid in an orthogonal vector space V of type Ω+(2n, q) or Ω(2n – 1, q) is a set Ω of qn–1 + 1 pairwise non-perpendicular singular points. Ovoids probably do not exist when n > 4 (cf. [12], [6]) and seem to be rare when n = 4. On the other hand, when n = 3 they correspond to affine translation planes of order q2, via the Klein correspondence ...
openaire   +1 more source

The translation planes of order 49

Designs, Codes and Cryptography, 1995
The authors determine the quantity of classes of isomorphic translation planes of order 49. They report on the computer search for spreads in \(PG (3,7)\) and on classifying the spreads with the computer program NAUTY that looks for graph isomorphisms. The search results in a list of 1347 translation planes in which known planes formerly given by other
Rudolf Mathon, Gordon F. Royle
openaire   +1 more source

A characterization of «likeable» translation planes

Rendiconti del Circolo Matematico di Palermo, 1983
A translation plane of order \(q^ 2\) is said to be 'likeable' when it has kern \(GF(q)\) and when its linear translation complement contains a group of order \(q^ 2\) whose elation subgroup consists of elements, which, when the plane is constructed from a spread in \(PG(3,q)\), fix a regulus. Such planes are studied in this paper, mostly in terms of \(
Fink, J. B., Johnson, N. L., Wilke, F. W.   +2 more
openaire   +2 more sources

Doubly β-Derived Translation Planes

Designs, Codes and Cryptography, 2003
Let \(q>3\) be an odd prime power. A chain of circles in the Miquelian inversive plane \(M(q)\) is a collection of \({1\over 2}(q+3)\) circles such that every point covered by some circle in this set lies on exactly two circles from the collection. Using the correspondence between points and circles of \(M(q)\) and lines and reguli of a regular spread \
Abatangelo, V., Larato, Bambina
openaire   +1 more source

Pencils of translation ovals in translation planes

Geometriae Dedicata, 1994
Let \({\mathcal T}\) be a translation plane of even order \(q\) with translation line \(I_ \infty\). An oval \({\mathcal O}\) in \({\mathcal T}\) is called a translation oval if \(I_ \infty\) is a tangent at a point \(a\) and if the stabilizer of \({\mathcal O}\) in the translation group acts transitively on \({\mathcal O}\setminus\{a\}\).
Glynn, D. G., Steinke, G. F.
openaire   +2 more sources

Translation planes of order 27

Designs, Codes and Cryptography, 1994
Up to isomorphism there are exactly seven, already known translation planes of order 27. The author shows this with the help of a computer and describes the seven types by invariants that play an important role in the computer search. Independently of the computer proof it is shown which of these types occur in the case that there is an elation in the ...
openaire   +1 more source

On Translations in General Plane Geometries

American Journal of Mathematics, 1938
In a well-known paper, Hilbelt 1 has characterized the Euclidean and hyperbolic plane geometries by mere group and continuity axioms. He gets all the motions at once by requiring the existence of sufficiently many rotations. The present paper tries to point out how the existence of more and more translations gradually specializes the rather general ...
openaire   +1 more source

A Classification of Semi-Translation Planes

Canadian Journal of Mathematics, 1969
The classification of certain types of projective planes has recently been of considerable interest to both geometers and group theorists. Due in part to the current general interest in finite mathematics and the developments connecting group theory and finite geometry, the Lenz-Barlotti classification of finite projective planes (2; 10), in particular,
openaire   +2 more sources

Quasigroups and translation planes

Journal of Geometry, 1992
A quasigroup \((Q,\cdot)\) is said to be medial if \((x\cdot y)\cdot(z\cdot t)=(x\cdot z)\cdot(y\cdot t)\) for all \(x,y,z,t\in Q\), and is called idempotent if \(x\cdot x=x\) for all \(x\in Q\). If \((R,+,\cdot)\) is the coordinatizating ring of a translation plane and the kernel of \(R\) contains at least one element \(k\) distinct from 0 and 1, then
openaire   +2 more sources

Propagating Plane-Wave Fast Multipole Translation Operators Revisited—Standard, Windowed, Gaussian Beam

IEEE Transactions on Antennas and Propagation, 2021
Thomas F Eibert, Thorkild B Hansen
exaly