منابع مشابه
A New Family of Somos-like Recurrences
We exhibit a three parameter infinite family of quadratic recurrence relations inspired by the well known Somos sequences. For one infinite subfamily we prove that the recurrence generates an infinite sequence of integers by showing that the same sequence is generated by a linear recurrence (with suitable initial conditions). We also give conjectured relations among the three parameters so that...
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In his ‘Memoir on Elliptic Divisibility Sequences’, Morgan Ward’s definition of the said sequences has the remarkable feature that it does not become at all clear until deep into the paper that there exist nontrivial such sequences. Even then, Ward’s proof of coherence of his definition relies on displaying a sequence of values of quotients of Weierstraß σ -functions. We give a direct proof of ...
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In nine years the Combinatorics Initiative between San Francisco State University (SFSU) and the nation of Colombia has built an active community of more than two hundred mathematicians, most of whom are members of underrepresented groups in mathematics. More than fifty have pursued PhDs in mathematics, while others continue to be mathematics users, enthusiasts, and ambassadors in other fields ...
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Chronic kidney disease is among the fastest growing causes of death worldwide. An increased risk of all-cause and cardiovascular death is thought to depend on the accumulation of uremic toxins when glomerular filtration rate falls. In addition, the circulating levels of several markers of inflammation predict mortality in patients with chronic kidney disease. Indeed, a number of cytokines are l...
متن کاملHyperelliptic curves, continued fractions, and Somos sequences
We detail the continued fraction expansion of the square root of a monic polynomials of even degree. We note that each step of the expansion corresponds to addition of the divisor at infinity, and interpret the data yielded by the general expansion. In the quartic and sextic cases we observe explicitly that the parameters appearing in the continued fraction expansion yield integer sequences def...
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ژورنال
عنوان ژورنال: Mosaic
سال: 2007
ISSN: 1696-3296
DOI: 10.7238/m.n53.0701