Given a hyperplane arrangement in a complex vector space of dimension l, there is a natural associated arrangement of codimension k subspaces in a complex vector space of dimension kl. Topological invariants of the complement of this subspace arrangement are related to those of the complement of the original hyperplane arrangement. In particular, if the hyperplane arrangement is fiber-type, the...

The hyperplane approximation technique is a recent popular approach to motion estimation applied to a range of computer vision techniques such as active appearance models and template matching. Simply, the method learns a linear relationship between artificially applied parametric motion perturbations and the consequent induced pixel greylevel differences. Once trained, solving for any new moti...

The nonrelativistic Schrödinger equation for motion of a structureless particle in four-dimensional space-time entails a well-known expression for the conserved four-vector field of local probability density and current that are associated with a quantum state solution to the equation. Under the physical assumption that each spatial, as well as the temporal, component of this current is observa...

This paper contains four main results associated with an attractor of a projective iterated function system (IFS). The first theorem characterizes when a projective IFS has an attractor which avoids a hyperplane. The second theorem establishes that a projective IFS has at most one attractor. In the third theorem the classical duality between points and hyperplanes in projective space leads to c...

We consider the linear classification method consisting of separating two sets of points in d-space by a hyperplane. We wish to determine the hyperplane which minimises the sum of distances from all misclassified points to the hyperplane. To this end two local descent methods are developed, one grid-based and one optimisation-theory based, and are embedded in several ways into a VNS metaheurist...

For solving linear inequality constrained optimization, a new hyperplane method is introduced. The trust region approach for unconstraint optimization is used to minimize objective function on the hyperplane defined by the current iterative point. If a separate indicator shows that it is not worthwhile to find a better point in the current hyperplane. Then a line search along a chopped directio...

This paper contains four main results associated with an attractor of a projective iterated function system (IFS). The first theorem characterizes when a projective IFS has an attractor which avoids a hyperplane. The second theorem establishes that a projective IFS has at most one attractor. In the third theorem the classical duality between points and hyperplanes in projective space leads to c...

In this paper we study the linear series |L − 3p| of hyperplane sections with a triple point p of a surface S embedded via a very ample line bundle L for a general point p. If this linear series does not have the expected dimension we call (S, L) triplepoint defective. We show that on a triple-point defective regular surface through a general point every hyperplane section has either a triple c...

Early type galaxies (ETGs) are known to possess a number of quite useful scaling relations among their photometric and/or kinematical quantities. We propose a unified picture reducing both the fundamental plane and the photometric plane to suitable projections of a single relation. Modelling the ETG as a two component system, made out of a luminous Sersic profile and a NFW dark halo, and applyi...