The number of rational numbers determined by large sets of integers

When $A$ and $B$ are subsets of the integers in $[1,X]$ and $[1,Y]$ respectively, with $|A| \geq \alpha X$ and $|B| \geq \beta X$, we show that the number of rational numbers expressible as $a/b$ with $(a,b)$ in $A \times B$ is $\gg (\alpha \beta)^{1+\epsilon}XY$ for any $\epsilon > 0$, where the implied constant depends on $\epsilon$ alone. We then construct examples that show that this bound cannot in general be improved to $\gg \alpha \beta XY$. We also resolve the natural generalisation of our problem to arbitrary subsets $C$ of the integer points in $[1,X] \times [1,Y]$. Finally, we apply our results to answer a question of S\'ark\"ozy concerning the differences of consecutive terms of the product sequence of a given integer sequence.Comment: 11 page

Experimental Evidence of Time Delay Induced Death in Coupled Limit Cycle Oscillators

Experimental observations of time delay induced amplitude death in a pair of coupled nonlinear electronic circuits that are individually capable of exhibiting limit cycle oscillations are described. In particular, the existence of multiply connected death islands in the parameter space of the coupling strength and the time delay parameter for coupled identical oscillators is established. The existence of such regions was predicted earlier on theoretical grounds in [Phys. Rev. Lett. 80, 5109 (1998); Physica 129D, 15 (1999)]. The experiments also reveal the occurrence of multiple frequency states, frequency suppression of oscillations with increased time delay and the onset of both in-phase and anti-phase collective oscillations.Comment: 4 aps formatted RevTeX pages; 6 figures; to appear in Phys. Rev. Let

Case Report: Ocular Toxocariasis: A Report of Three Cases from the Mississippi Delta

Ocular toxocariasis can be vision threatening, and is commonly reported from tropical or subtropical regions. Knowledge of clinical manifestations from the United States, particularly in underserved areas such as the American South, is lacking. We report three cases of ocular toxocariasis in individuals from the Mississippi Delta, a rural community with prevalent poverty. Visual acuity was severely affected in two of the three cases. Increased awareness of ocular toxocariasis, which may have under-recognized frequency, will contribute to prompt diagnosis and treatment, which will ultimately improve patient health in the region

Characteristics of VHF radiowave scintillations over a solar cycle (1983?1993) at a low-latitude station: Waltair (17.7°N, 83.3°E)

International audienceThe characteristics of VHF radiowave scintillations at 244 MHz (FLEETSAT) during a complete solar cycle (1983?93) at a low-latitude station, Waltair (17.7°N, 83.3°E), are presented. The occurrence of night-time scintillations shows equinoctial maxima and summer minima in all the epochs of solar activity, and follows the solar activity. The daytime scintillation occurrence is negatively correlated with the solar activity and shows maximum occurrence during the summer months in a period of low solar activity. The occurrence of night-time scintillations is inhibited during disturbed days of high solar activity and enhanced during low solar activity