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A New Family Of Elliptic Curves With Positive Rank arising from Pythagorean Triples
elliptic curves rank pythagorean triples
2011/2/28
The aim of this paper is to introduce a new family of elliptic curves in the form of y2 = x(x−a2)(x−b2) that have positive ranks. We first generate a list of pythagorean triples (a, b, c) ...
Log del Pezzo Surfaces of Rank 2 and Cartier Index 3 with a Unique Singularity
Log del Pezzo surfaces Quotient singularities
2011/1/18
Log del Pezzo surfaces play the role of the opposite of surfaces of general type. We will completely classify all the log del Pezzo surfaces of rank 2 and Cartier index 3 with a unique singularity.
A maximum rank problem for degenerate elliptic fully nonlinear equations
degenerate elliptic fully nonlinear equations
2010/12/9
The solutions to the Dirichlet problem for two degenerate elliptic fully nonlinear equations in n + 1 dimensions, namely the real Monge-Amp`ere equation and the Donaldson equation, are shown to have m...
Hyperexponential Solutions of Finite-rank Ideals in Orthogonal Ore Rings
Linear partial differential systems Linear partial difference systems Ore rings Hyperexponential solutions
2013/9/3
An orthogonal Ore ring is an abstraction of common properties of linear partial differential, shift and q-shift operators.Using orthogonal Ore rings, we present an algorithm for finding hyperexponenti...