If b and d are given positive integers with b > 1, then we show that the equation of the title possesses at most one solution in positive integers X; Y. Moreover, we give an explicit characterization of this solution, when it exists, in terms of fundamental units of associated quadratic elds. The proof utilizes estimates for linear forms in logarithms of algebraic numbers in conjunction with pr...

A new physics package solves radiation transport equations in one space dimension, multiple energy groups and directions. A discontinuous finite element method discretizes radiation intensity with respect to space and angle, and a continuous finite element method discretizes electron temperature in space. A splitting method solves the resulting linear equations. This is a one-dimensional analog...

in this paper, the temperature distribution around a moving heat source had been investigated including the phase change and non phase change . in non-phase change state, the governing equation was converted to finite difference equation by finite volume method and the equation was solved by alternating direction implicit method. this method was unconditionally stable . in phase change state, t...

in this paper, the (m+1)-step adams-bashforth, adams-moulton, and predictor-correctormethods are used to solve rst-order linear fuzzy ordinary dierential equations. the conceptsof fuzzy interpolation and generalised strongly dierentiability are used, to obtaingeneral algorithms. each of these algorithms has advantages over current methods. moreover,for each algorithm a convergence formula can b...

If b and d are given positive integers with b > 1, then we show that the equation of the title possesses at most one solution in positive integers X, Y . Moreover, we give an explicit characterization of this solution, when it exists, in terms of fundamental units of associated quadratic fields. The proof utilizes estimates for linear forms in logarithms of algebraic numbers in conjunction with...

In this paper we study symmetries in polynomial equation systems and how they can be integrated into the action matrix method. The main contribution is a generalization of the partial p-fold symmetry and we provide new theoretical insights as to why these methods work. We show several examples of how to use this symmetry to construct more compact polynomial solvers. As a second contribution we ...