4,448 research outputs found
President\u27s Address
Delivered at the Bellingham meeting, August, 1937
Primitive divisors of elliptic divisibility sequences
Silverman proved the analogue of Zsigmondy's Theorem for elliptic divisibility sequences. For elliptic curves in global minimal form, it seems likely this result is true in a uniform manner. We present such a result for certain infinite families of curves and points. Our methods allow the first explicit examples of the elliptic Zsigmondy Theorem to be exhibited. As an application, we show that every term beyond the fourth of the Somos-4 sequence has a primitive divisor
Enzyme activity in terrestrial soil in relation to exploration of the Martian surface
Urease activity in soil is persistent for long periods under low water, low temperature, and sterile regimes, and it was suggested that some form of enzyme-protective mechanism exists in soil. Dublin soil was extracted by sonication in water followed by adding a mixture of salts. Urease activity is associated with the organo-mineral complex thus obtained and is resistant to the activities of proteolytic enzymes. Clay free soil organic matter prepared subsequently by filtration also exhibits urease activity which is resistant to proteolysis. Models consisting of enzymes with bentonite and lignin were found to mimic this resistance to proteolysis. A model system is presented which suggests both the origin and location of soil ureases and a reason for their persistence in nature
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