INTRODUCTION Precambrian rocks in the Tusas Mountains range from nearly monomineralic quartzite, in which the principal result of metamorphism has been simple recrystallization, through locally metasomatized schist and gneiss profoundly modified by potash-rich fluids during the intrusion of pegmatite. Texturally, the rocks range from schist and phyllite containing penetrative and pervasive clea...

By Florian Libisch, Jin Cheng, and Emily A. Carter3,∗ 1 Department for Mechanical and Aerospace Engineering, Princeton University, Engineering Quadrangle, Olden Street, NJ, 08540 Princeton, USA 2 Department of Chemistry, Princeton University, Washington Road, NJ, 08544 Princeton, USA 3 Department for Mechanical and Aerospace Engineering, Program in Applied and Computational Mathematics, and And...

Having in mind their potential quantum physical applications, we classify all geometric hyperplanes of the near hexagon that is a direct product of a line of size three and the generalized quadrangle of order two. There are eight different kinds of them, totalling to 1023 = 2 10 − 1 = |PG(9, 2)|, and they form two distinct families intricately related with the points and lines of the Veldkamp s...

Given a finite generalized quadrangle Q, an extended generalized quadrangle is called an extension of Q if each point-residue is isomorphic to Q. There are several known examples of extended generalized quadrangles [4, §1.1], among which those admitting flag-transitive automorphism groups have been extensively studied in their close relations with group theory. Those flag-transitive geometries ...

This article is about ovoids of the generalised quadrangle O(5, q) and, equivalently, spreads of the generalised quadrangle Sp(4, q). In a less than conventional way the quadrangles are represented in the field GF (q) which allows some amount of computation to be done. It is shown that an ovoid of O(5, q) meets an elliptic quadric in 1 modulo p points.

The concept of a tight set of points of a generalised quadrangle was introduced by S. E. Payne in 1987, and that of an m-ovoid of a generalised quadrangle was introduced by J. A. Thas in 1989, and we unify these two concepts by defining intriguing sets of points. We prove that every intriguing set of points in a generalised quadrangle is an m-ovoid or a tight set, and we state an intersection r...

Let 0 be a finite generalized quadrangle of order (q, q2), and suppose that it has a subquadrangle 1 isomorphic to Q(4, q). We show that 0 is isomorphic to the classical generalized quadrangle Q(5, q) if at least one of the following holds: (1) all linear collineations of 1 extend to 0; (2) all subtended ovoids are classical (and we present a uniform proof independent of the characteristic). Fu...