The square root law and structure of finite rings

Let $R$ be a finite ring and define the hyperbola $H=\{(x,y) \in R \times R: xy=1 \}$. Suppose that for a sequence of finite odd order rings of size tending to infinity, the following "square root law" bound holds with a constant $C>0$ for all non-trivial characters $\chi$ on $R^2$: $$\left| \sum_{(x,y)\in H}\chi(x,y)\right|\leq C\sqrt{|H|}.$$ Then, with a finite number of exceptions, those rings are fields. For rings of even order we show that there are other infinite families given by Boolean rings and Boolean twists which satisfy this square-root law behavior. We classify the extremal rings, those for which the left hand side of the expression above satisfies the worst possible estimate. We also describe applications of our results to problems in graph theory and geometric combinatorics. These results provide a quantitative connection between the square root law in number theory, Salem sets, Kloosterman sums, geometric combinatorics, and the arithmetic structure of the underlying rings

High-altitude plume computer code development

The flowfield codes that have been developed to predict rocket motor plumes at high altitude were used to predict plume properties for the RCS motor which show reasonable agreement with experimental data. A systematic technique was established for the calculation of high altitude plumes. The communication of data between the computer codes was standardized. It is recommended that these outlined procedures be more completed, documented and updated as the plume methodology is applied to the varied problems of plume flow and plume impingement encountered by space station design and operation

B-52 control configured vehicles: Flight test results

Recently completed B-52 Control Configured Vehicles (CCV) flight testing is summarized, and results are compared to analytical predictions. Results are presented for five CCV system concepts: ride control, maneuver load control, flutter mode control, augmented stability, and fatigue reduction. Test results confirm analytical predictions and show that CCV system concepts achieve performance goals when operated individually or collectively

A constraint on a varying proton--electron mass ratio 1.5 billion years after the Big Bang

A molecular hydrogen absorber at a lookback time of 12.4 billion years, corresponding to 10$\%$ of the age of the universe today, is analyzed to put a constraint on a varying proton--electron mass ratio, $\mu$. A high resolution spectrum of the J1443$+$2724 quasar, which was observed with the Very Large Telescope, is used to create an accurate model of 89 Lyman and Werner band transitions whose relative frequencies are sensitive to $\mu$, yielding a limit on the relative deviation from the current laboratory value of $\Delta\mu/\mu=(-9.5\pm5.4_{\textrm{stat}} \pm 5.3_{\textrm{sys}})\times 10^{-6}$.Comment: Accepted for publication in PRL. Includes supplemental materia

Enhancing Consultants' IT Skills: A Reverse Mentoring Project

13-16 July 2002 Many medical students arrive with excellent IT skills and experience of mentoring their peers in secondary school. Senior clinicians, by contrast, did not grow up with the technology and often feel left behind by the IT revolution. This generation gap is often seen as a threat to the authority of clinical tutors. We have set up a reverse mentoring scheme to help consultants develop their IT skills. With a grant from the post graduate dean, we have recruited thirty medical students to act as personal trainers to thirty consultants and specialist registrars. Each participant is issued with a set of learning vouchers which enables them to purchase four hours of training and a password to access the learning resources from the project website. This paper will describe the methods used, and report on the results of this unique reverse mentoring scheme

Solar flare gamma-ray line spectroscopy

The techniques and the results of solar elemental abundance determinations using observations of gamma ray lines from the April 27 1981 olar flare were outlined. The techniques are elaborated on and observed and the best-fitting theoretical spectra are presented. Numerical values for the photon fluences and the total number of protons involved in the thick-target production of these gamma rays are derived

Hydrocarbons in the banana leaf, Musa sapientum

Mass spectrometry, spectroscopy, and thin layer and gas chromatography studies of hydrocarbons in banana leave

Abundances from solar-flare gamma-ray line spectroscopy

Elemental abundances of the ambient gas at the site of gamma ray line production inthe solar atmosphere are deduced using gamma ray line observations from a solar flare. The resultant abundances are different from local galactic abundances which are thought to be similar to photospheric abundances

The stratigraphy and depositional environment of Upper Ordovician to Lower Devonian rocks in the Antigonish Highlands, Nova Scotia

Upper Ordovician to lower Devonian rocks in the Antigonish Highlands, Nova Scotia, consist of biinodal volcanics and redbeds at the base overlain by a thick sequence of fossiliferous marine slliciclastic rocks. These rocks belong to the Arisaig Group and correlate well with coeval rocks to the north of the Antigonish Highlands. The definition of the Arisaig Group is revised to Include the uppermost Ordovician-lowermost Silurian Bears Brook Formation which occurs at the base, and the lower Devonian Knoydart Formation which occurs at the top of the succession. The sequence as a whnle is probably related to a local rifting event. The Bears Brook Formation consists of continental redbeds and biinodal rift-related volcanic rocks. A marine transgression at. the base of the Silurian is indicated by the first appearance of marine fossiliferous rocks and by the overstep relations exhibited by Silurian strata onto Precambrian basement. The marine transgression may have been associated with a world-wide eustatic rise in sea level and with local rifting. The Knoydart Formation is dominated by fluviatile redbeds indicating a return to subaerial conditions. The distribution of the Arisaig Group rocks around the southern and western margins of the Highlands together with the overstep relationships indicate that the Antigonish Highlands became progressively submerged during the Silurian. This was followed by a return to subaerial conditions In the Early Devonian. RÉSUMÉ Dans les Monts Antigonish, les roches de l'Ordovicien supérieur au Dévonien inférieur comprennent un ensemble inférieur de volcanites bimodales et de lits rouges sur lequel repose une puissante assise de roches fosslliferes marines silicoclastiques. Ces roches appartiennent au Groupe d'Arisaig et peuvent aiseraent être corrélées avec leurs bomologues au nord des Monts Antigonish. On redèfinit le Groupe d'Arisaig pour y inclure la Formation de Bears Brook. présente en sa base et s'étageant du sommet de l'Ordovicien au Silurien basal, ainsi que la Formation de Knoydart, du Dévonien inférieur et répartie au sommet de la succession. Dans son ensemble, la séquence correspond probablement à un épisode local de rifting. La Formation de Bears Brook comprend des lits rouges contiuentaux et des volcanites bimodales spparentées au rift. La première apparition de roches marines fossillferes et la discordance fondaraentale entre les strates sliuriennes et le bati précambrien teraoignent d'une transgression marine à l’amorce du Silurien. Cette incursion marine apparalt reliée à une remontée du niveau marin global ainsi qu'a un rifting local. L'importance des lits rouges fluviatlles dans la de Knoydart y atteste d'un rétour à des conditions subaerlennes. La distribution des roches du Groupe en bordures méridionale et occidentale des Monts ainsi que leur contact en discordance indiquent une progressive des Monts Antigonish au cours du Silurlen. L'Eodévonien marque un rétour aux conditions eustatique Formation d'Arisaig submersion subaériennes [Traduit par le journal