منابع مشابه
Euler’s Concordant Forms
If EQ(M,N) has positive rank, then there are infinitely many primitive integer solutions to (1); but if EQ(M,N) has rank 0, then there may be a non-trivial solution. Such a solution exists if and only if the torsion group is Z2×Z8 or Z2×Z6.We classify all such cases, thereby reducing Euler’s problem to a question of ranks. In some cases, the ranks of quadratic twists of EQ(M,N) are described by...
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* Contributions from the Scripps Institution of Oceanography, New Series, No. 324. 'Ekman, V. W., Annalen Hydrographie u. Mar. Met., 34, 423-430 (1906). 2Stockmann, W., Comptes rendus (Doklady) l'Acad. sci. I'U.R.S.S., 52, 309-312 (1946). Fjeldstad, J. E., Archiv Math. Naturvid., 48, no. 6 (1946). 4 Montgomery, R. B., and Palmen, E., Jour. Marine Research, 3, 112-133 (1940). 6 Ekman, V. W., Ger...
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We propose a variable metric framework for minimizing the sum of a self-concordant function and a possibly non-smooth convex function, endowed with an easily computable proximal operator. We theoretically establish the convergence of our framework without relying on the usual Lipschitz gradient assumption on the smooth part. An important highlight of our work is a new set of analytic step-size ...
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We describe a large class of chemical reaction networks, those endowed with a subtle structural property called concordance. We show that the class of concordant networks coincides precisely with the class of networks which, when taken with any weakly monotonic kinetics, invariably give rise to kinetic systems that are injective - a quality that, among other things, precludes the possibility of...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1996
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-78-2-101-123