منابع مشابه
Rational points on diagonal quartic surfaces
We searched up to height 107 for rational points on diagonal quartic surfaces. The computations fill several gaps in earlier lists computed by Pinch, Swinnerton-Dyer, and Bright.
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Let a, b, c, d be nonzero rational numbers whose product is a square, and let V be the diagonal quartic surface in P defined by ax + by + cz + dw = 0. We prove that if V contains a rational point that does not lie on any of the 48 lines on V or on any of the coordinate planes, then the set of rational points on V is dense in both the Zariski topology and the real analytic
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Up to now the maximal number of smooth conics, that can lie on a smooth quartic surface, seems not to be known. So our number 352 should be compared with 64, the maximal number of lines that can lie on a smooth quartic [S]. We construct the surfaces as Kummer surfaces of abelian surfaces with a polarization of type (1, 9). Using Saint-Donat’s technique [D] we show that they embed in IP3. In thi...
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Dynamical systems, whether continuous or discrete, are used by physicists in order to study non-linear phenomena. In the case of discrete dynamical systems, one of the most used is the quadratic map depending on a parameter. However, some phenomena can depend alternatively of two values of the same parameter. We use the quadratic map xn+1 = 1 − axn when the parameter alternates between two valu...
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ژورنال
عنوان ژورنال: Nature
سال: 1917
ISSN: 0028-0836,1476-4687
DOI: 10.1038/098367a0