On the uniform domination number of a finite simple group

Let $G$ be a finite simple group. By a theorem of Guralnick and Kantor, $G$ contains a conjugacy class $C$ such that for each non-identity element $x \in G$, there exists $y \in C$ with $G = \langle x,y\rangle$. Building on this deep result, we introduce a new invariant $\gamma_u(G)$, which we call the uniform domination number of $G$. This is the minimal size of a subset $S$ of conjugate elements such that for each $1 \ne x \in G$, there exists $s \in S$ with $G = \langle x, s \rangle$. (This invariant is closely related to the total domination number of the generating graph of $G$, which explains our choice of terminology.) By the result of Guralnick and Kantor, we have $\gamma_u(G) \leqslant |C|$ for some conjugacy class $C$ of $G$, and the aim of this paper is to determine close to best possible bounds on $\gamma_u(G)$ for each family of simple groups. For example, we will prove that there are infinitely many non-abelian simple groups $G$ with $\gamma_u(G) = 2$. To do this, we develop a probabilistic approach, based on fixed point ratio estimates. We also establish a connection to the theory of bases for permutation groups, which allows us to apply recent results on base sizes for primitive actions of simple groups.Comment: 35 pages; to appear in Trans. Amer. Math. So

A semibuoyant vehicle for general transportation missions

The concept of a small, semibuoyant, lifting-body airship with either a disposable or nondisposable buoyant fluid is discussed. Estimations of fuel consumption, payload capability, power requirements and productivity are made and compared to other flight systems. Comparisons are made on the basis of equal cost vehicles. The assumption is made that, to a first-order approximation, the costs of developing, procuring, and operating a commercial air transport vehicle are proportional to vehicle empty weight. It must be noted that no historical cost data exist for the lifting-body airship and therefore these comparisons must be considered preliminary

Design, cost, and advanced technology applications for a military trainer aircraft

The potential impact is examined of advanced aerodynamic and propulsive technologies in terms of operating and acquisition costs on conceptual mission and performance requirements for a future undergraduate jet pilot trainer aircraft

The response of self-graviting protostellar discs to slow reduction in cooling timescale: the fragmentation boundary revisited

A number of previous studies of the fragmentation of self-gravitating protostellar discs have modeled radiative cooling with a cooling timescale (t_{cool}) parameterised as a simple multiple (beta_{cool}) of the local dynamical timescale. Such studies have delineated the `fragmentation boundary' in terms of a critical value of beta_{cool} (beta_{crit}), where the disc fragments if beta_{cool} < beta_{crit}. Such an approach however begs the question of how in reality a disc could ever be assembled with beta_{cool} < beta_{crit}. Here we adopt the more realistic approach of gradually reducing beta_{cool}, as might correspond to changes in thermal regime due to secular changes in the disc density profile. We find that when beta_{cool} is gradually reduced (on a timescale longer than t_{cool}), the disc is stabilised against fragmentation, compared with models in which beta_{cool} is reduced rapidly. We therefore conclude that a disc's ability to remain in a self-regulated, self-gravitating state (without fragmentation) is partly dependent on its thermal history, as well as its current cooling rate. Nevertheless, a slow reduction in t_{cool} appears only to lower the fragmentation boundary by about a factor two in t_{cool} and thus only permits maximum alpha values (parameterising the efficiency of angular momentum transfer in the disc) that are about a factor two higher than determined hitherto. Our results therefore do not undermine the notion of a fundamental upper limit to the heating rate that can be delivered by gravitational instabilities before the disc is subject to fragmentation. An important implication of this work, therefore, is that self-gravitating discs can enter into the regime of fragmentation via secular evolution and it is not necessary to invoke rapid (impulsive) events to trigger fragmentation.Comment: accepted for publication in MNRA

Study of properties of high-field superconductors at elevated temperatures Final technical report, 27 Apr. - 26 Aug. 1966

Properties of high field superconductors at high temperatures - magnetization experiments on niobium and niobium compound

Study of properties of high field superconductors, ac field induced flux jumps Technical summary report, 21 Jun. 1965 - 26 Apr. 1966

Magnetization experiments in superimposed dc and audiofrequency ac magnetic fields on cold worked NbTi alloy samples - ac field induced flux jump

Broughton Archipelago Clam Terrace Survey : final report

During a 1995 aerial video survey of the coastline of Johnstone Strait, an unusual shoreline feature was noted and termed “clam terraces” (inset) because of the terrace-type morphology and the apparent association with high clam productivity on the sandflats. Typical alongshore lengths of the terrace ridges are 20-50m, and across-shore widths are typically 20-40m. An area with an especially high density of clam terraces was noted in the Broughton Archipelago, between Broughton and Gilford Islands of southeastern Queen Charlotte Strait. Clam terraces in this area were inventoried from the aerial video imagery to quantify their distribution. The terraces accounted for over 14 km of shoreline and 365 clam terraces were documented. A three-day field survey by a coastal geomorphologist, archeologist and marine biologist was conducted to document the features and determine their origin. Nine clam terraces were surveyed. The field observations confirmed that: the ridges are comprised of boulder/cobblesized material, ridge crests are typically in the range of 1-1.5m above chart datum, sandflats are comprised almost entirely of shell fragments (barnacles and clams) and sandflats have very high shellfish production. There are an abundance of shell middens in the area (over 175) suggesting that the shellfish associated with the terraces were an important food source of aboriginal peoples. The origin of the ridges is unknown; they appear to be a relict feature in that they are not actively being modified by present-day processes. The ridges may be a relict sea-ice feature, although the mechanics of ridge formation is uncertain. Sand accumulates behind the ridge because the supply rate of the shell fragments exceeds the dispersal rate in these low energy environments. The high density areas of clam terraces correspond to high density areas of shell middens, and it is probable that the clam terraces were subjected to some degree of modification by aboriginal shellfish gatherers over the thousands of years of occupation in the region. (Document contains 39 pages