Osculating Circle with Microscopes Within Microscopes

Classically, an osculating circle at a point of a planar curve is introduced technically, often with formula giving its radius and the coordinates of its center. In this note, we propose a new and intuitive definition of this concept: among all the circles which have, on the considered point, the same tangent as the studied curve and thus seem equal to the curve through a microscope, the osculating circle is this that seems equal to the curve through a microscope within microscope.     

Effects of watershed alteration on the brook trout population of a small Black Hills stream

The impacts of adjacent landscaping activity and livestock presence on the brook trout ( Salvelinus fontinalis ) population of a small Black Hills stream were evaluated. Moderate changes in temperature, turbidity, and fecal coliform numbers did not influence brook trout densities. Stream morphometry, particularly factors affecting stream cover, appeared to have the greatest impact on numbers of trout. Brook trout were poor indicators of moderate changes in water quality, but they were adequate indicators of the physical perturbations within the stream.      

The career of continental drift theory: An application of Imre Lakatos' analysis of scientific growth to the rise of drift theory

The continental drift research programme reigns supreme within the geological community. The programme achieved its regal status only within the last decade. Its ascension to the summit took over fifty years, and required numerous switchbacks. Although its climb may seem haphazard, I argue that there is an overall rationale to its development which is partially elucidated by the account of scientific growth and change as put forth by Imre Lakatos. However, at least two alterations must be made in Lakatos' analysis. One concerns his analysis of ‘novel fact’, and the other is concerned with his thesis that the hard core of a research programme remains the same throughout the programme's lifetime. I consider and reject Elie Zahar's notion of ‘novel fact’, introduce an alternative notion of ‘novel fact’, and argue that Lakatos and his followers must abandon the thesis that a research programme's hard core is immune from change, but that they can do so without endangering Lakatos' overall account of scientific growth and change.     

Brevetoxicosis: red tides and marine mammal mortalities

Potent marine neurotoxins known as brevetoxins are produced by the 'red tide' dinoflagellate Karenia brevis. They kill large numbers of fish and cause illness in humans who ingest toxic filter-feeding shellfish or inhale toxic aerosols. The toxins are also suspected of having been involved in events in which many manatees and dolphins died, but this has usually not been verified owing to limited confirmation of toxin exposure, unexplained intoxication mechanisms and complicating pathologies. Here we show that fish and seagrass can accumulate high concentrations of brevetoxins and that these have acted as toxin vectors during recent deaths of dolphins and manatees, respectively. Our results challenge claims that the deleterious effects of a brevetoxin on fish (ichthyotoxicity) preclude its accumulation in live fish, and they reveal a new vector mechanism for brevetoxin spread through food webs that poses a threat to upper trophic levels.