This paper investigates the homography which transforms a set of points in projective space when undergoing a rigid translation, termed a projective translation. A representation with seven parameters is proposed. They represent explicitly the geometric entities constraining and defining the translation. A practical algebraic method for extracting these parameters is developed. It allows for af...

This paper presents a dependencyconstrained hierarchical machine translation model that uses Moses open-source toolkit for rule extraction and decoding. Experiments are carried out for the German-English language pair in both directions for projective and non-projective dependencies. We examine effects on SCFG size and automatic evaluation results when constraints are applied with respect to pr...

In this paper, all 16-dimensional locally compact translation planes admitting the unimodular quaternion group SL2H as a group of collineations will be determined explicitly. Besides the classical plane over the octonions there are a vast number of planes having this property, cf. the Classification Theorem (2.8). Indeed, the class of these planes covers an interesting borderline case: Among al...

We investigate generalized quadrangles Γ that admit at least two projective axes of symmetry. We show that if there are three such axes incident with a common point x, then x is a translation point of Γ. In case that Γ is moreover a compact connected quadrangle with topological parameters (p, p), p ∈ N, then Γ is a topological translation generalized quadrangle. We further investigate the case ...

Planar functions were introduced by Dembowski and Ostrom ([4]) to describe projective planes possessing a collineation group with particular properties. Several classes of planar functions over a finite field are described, including a class whose associated affine planes are not translation planes or dual translation planes. This resolves in the negative a question posed in [4]. These planar f...

Translation planes of order q and kernel containing KGGFðqÞ admitting fixedpoint-free collineation groups GK , each of whose point orbits is the set of nonzero vectors of a 2-dimensional K-subspace, are shown to permit spread-retraction and produce either Baer subgeometry or mixed partitions of a corresponding projective space. When the same translation plane or spread produces a number of part...

Evaluators and researchers often have to deal with situations in which conventional research tools are impossible to use, either because of the characteristics of a population or unclear research variables. This paper presents a technique that succeeds in overcoming this kind of problem--a projective technique, but one that differs from the usual approach to projective techniques. The approach ...