Building on previous work of Di Nasso and Luperi Baglini, we provide general necessary conditions for a Diophantine equation to be partition regular. These conditions are inspired by Rado's characterization of partition regular linear homogeneous equations. We conjecture that these conditions are also ...
A Method of Solving Certain Nonlinear Diophantine EquationsIn this paper we propose a method of solving a Nonlinear Diophantine Equation by converting it into a System of Diophantine Linear Equations.doi:http://dx.doi.org/Florentin Smarandache
A note on the ternary Diophantine equation x2 y2m = zn Let be the set of all positive integers. In this paper, using some known results on various types of Diophantine equations, we solve a couple of special cases of the ternary equation x2 y2m = zn, x, y, z, m, n ∈ , gcd...
Diophantine Equations and Inequalities in Algebraic Number Fields We owe to Siegel the formulation of Waring's problem in an algebraic number field, and the generalisation of the most efficient technique for its solution ... W Yuan - 《Bulletin of the London Mathematical Society》 被引量: 17发表...
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Nontrivial zeros of weight 1 3j and 6j coefficients: Relation to Diophantine equations of equal sums of like powers The nontrivial zeros of weight 1 3jand 6jcoefficients given previously are shown to be the set of all such zeros. The relation of these zeros to the soluti... S Brudno,JD...
The purpose of this exposé is to present a summary of some new developments in the theory of Hamiltonian nonlinear evolution equations, more specifically, nonlinear Schrdinger equations. The themes and methods discussed are closely related to classical mechanics. The first topic is the existence of...
Diophantine conditionMajorant seriesThis paper is concerned with a second-order nonlinear iterated differential equation of the form c 0 x ″ ( z ) + c 1 x ′ ( z ) + c 2 x ( z ) = x ( p ( z ) + b x ( z ) ) + h ( z ) . By constructing a convergent power series ...
iut−△u+Mξu+f(ω¯t)|u|2u=0,t∈R,x∈Td where Mξ is a real Fourier multiplier,f(θ¯)(θ¯=ω¯t) is real analytic and the forced frequencies ω¯ are fixed Diophantine vectors.This is a preview of subscription content, log in via an institution to check access. Si...