On delta spaces satisfying Pasch's axiom

We consider partial linear spaces all of whose lines contain at least three points and in which every pair of intersecting lines generates a subspace isomorphic to a projective or dual affine plane. In particular, we classify in this paper those spaces that contain a projective plane.     

The geometry of k-transvection groups

Let k be a (commutative) field and G a group, then a conjugacy class of Abelian subgroups of G is called a class of k-transvection subgroups in G if and only if it generates G and any two elements of the class either commute or are full unipotent subgroups of the group they generate and which is isomorphic to (P)SL₂(k).In this paper we study the geometry of k-transvection groups. Given a class of k-transvection groups Σ, we consider a partial linear space whose points are the elements of Σ, and whose lines correspond to the groups generated by two noncommuting elements from Σ. We derive several properties of this partial linear space. These properties are used to give a characterization of the geometries of k-transvection groups and provide a classification of groups generated by k-transvection subgroups.     

Electrical model of a liquid crystal pixel with dynamic, voltage history-dependent capacitance value

The voltage history-dependent nature of a liquid crystal pixel capacitance becomes an important issue in active matrix addressing as large storage capacitors are replaced with more intelligent circuitry such as in-pixel frame buffers. In this paper, a simple but flexible Spice macro model is introduced that allows accurate simulations of the electrical behaviour of a nematic liquid crystal pixel capacitance. The model correctly predicts voltage drops caused by the increasing dielectric constant when liquid crystal molecules align themselves to the electric field. An internal node of the macro model represents the average director orientation and can also be used to predict the optical response. In its basic embodiment, the model uses a first-order, low pass RMS filter to implement the dynamic behaviour of the pixel, which suffices to predict response delays and asymmetric rise and fall times. However, the model also supports more elaborated filters that offer more control over the simulated dynamic behaviour. A number of simulations are performed that illustrate the usefulness of the new model during the design of novel 'smart' pixel architectures.     

One dimensional stationary states with constant electrical induction in ferroelectric liquid crystals

In a ferroelectric liquid crystal, it is the electrical induction, D, and not the electric field, E, which is independent of the space coordinate in a one dimensional analysis. This causes, at small applied voltages, stationary states which have a homogeneous orientation and are field free over most of the liquid crystal. At higher voltages homogeneous field states with zero, one or two surface layers may exist.     

A characterization of the symplectic and unitary 3-transposition groups

Let D be a normal set of 3-transpositions in a group G. For each d ∈ D, let D_d be the set of elements ε in D such that the order of de equals 2. Then we can define an equivalence relation ? on D by dre if and only if D_d ? {d} = D_e ? {ε}.

We characterize the symplectic and unitary groups over GF(2), respectively, GF(4) generated by their transvections as groups generated by a class D of 3-transposition with r trivial on D, but not when restricted to D_d for some d ∈ D.