A Family of Ovals with Few Collineations

A recently discovered [1] family of ovals in PG(2, q), q = 2e, e odd, is shown to have a cyclic collineation group of order 2e

Recommendations for cubicle separation in large-scale explosive arena trials

In large-scale arena blast testing, a common and economical practice undertaken is to position several cubicle targets radially around a central charge. To gain maximal benefit from this, targets should be positioned at their minimum permissible separation at which no blast wave interference is sustained from neighbouring obstructions. This interference typically occurs either when targets positioned at the same stand-off range are too close creating an amplification effect where a superposition forms between the incident blast wave and the reflected wave off the cubicle, or, where a target is positioned in the region behind another target, which causes a shadowing effect with decreased magnitudes of pressure and impulse. A comprehensive computational modelling study was undertaken using the hydrocode Air3D to examine the influence of cubicle positioning at different ranges on the surrounding blast wave pressure-time fields. A systematic series of simulations were conducted to show the differences in incident peak overpressure and positive phase impulse between free-field and obstructed-field simulation configurations. The predictions from the modelling study indicated that the presence of cubicle target obstructions resulted in differences in peak incident overpressure and positive phase impulse in nearby pressure waves. In all cases, at close separation distances, there were greater differences in peak pressure than positive phase impulse. However, with increased separation, peak pressure returned to free-field conditions sooner whilst differences in impulse remained significant, thus governing separation distance recommendations. The simulations showed that, for targets at the same stand-off range, clear separations of between 3.88 m and 6.92 m were required to achieve free-field equivalency, depending on the distance from the charge to the target. For targets at different stand-off ranges an angle greater than 54.2° from the front corner of the cubicle has been shown to ensure free-field equivalent conditions. A bespoke recommendation table has been generated to provide precise positioning for cubicles at different stand-off ranges in a look-up matrix format that can be readily used by engineers in the field

On large maximal partial ovoids of the parabolic quadric \q(4,q)

We use the representation $T_2(O)$ for \q(4,q) to show that maximal partial ovoids of \q(4,q) of size $q^2-1$, $q=p^h$, $p$ odd prime, $h > 1$, do not exist. Although this was known before, we give a slightly alternative proof, also resulting in more combinatorial information of the known examples for $q$ prime.Comment: 11 p

Multi-Line Geometry of Qubit-Qutrit and Higher-Order Pauli Operators

The commutation relations of the generalized Pauli operators of a qubit-qutrit system are discussed in the newly established graph-theoretic and finite-geometrical settings. The dual of the Pauli graph of this system is found to be isomorphic to the projective line over the product ring Z2xZ3. A "peculiar" feature in comparison with two-qubits is that two distinct points/operators can be joined by more than one line. The multi-line property is shown to be also present in the graphs/geometries characterizing two-qutrit and three-qubit Pauli operators' space and surmised to be exhibited by any other higher-level quantum system.Comment: 8 pages, 6 figures. International Journal of Theoretical Physics (2007) accept\'

On the order of a non-abelian representation group of a slim dense near hexagon

We show that, if the representation group $R$ of a slim dense near hexagon $S$ is non-abelian, then $R$ is of exponent 4 and $|R|=2^{\beta}$, $1+NPdim(S)\leq \beta\leq 1+dimV(S)$, where $NPdim(S)$ is the near polygon embedding dimension of $S$ and $dimV(S)$ is the dimension of the universal representation module $V(S)$ of $S$. Further, if $\beta =1+NPdim(S)$, then $R$ is an extraspecial 2-group (Theorem 1.6)

Hemisystems of small flock generalized quadrangles

In this paper, we describe a complete computer classification of the hemisystems in the two known flock generalized quadrangles of order $(5^2,5)$ and give numerous further examples of hemisystems in all the known flock generalized quadrangles of order $(s^2,s)$ for $s \le 11$. By analysing the computational data, we identify two possible new infinite families of hemisystems in the classical generalized quadrangle $H(3,q^2)$.Comment: slight revisions made following referee's reports, and included raw dat

Geometric Hyperplanes of the Near Hexagon L_3 times GQ(2, 2)

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 space of the quadrangle in question.Comment: 10 pages, 5 figures and 2 tables; Version 2 - more detailed discussion of the properties of hyperplane