Linear Diophantine equation (LDE) decoder: A training‐free decoding algorithm for multifrequency SSVEP with reduced computation cost

Short solutions for a linear Diophantine equation

It is known that finding the shortest solution for a linear Diophantine equation is a NP problem. In this paper we have devised a method, based upon the basis reduction algorithm, to obtain short solutions to a linear Diophantine equation. By this method we can obtain a short solution (not necessarily the shortest one) in a polynomial time. Numerical experiments show superiority to other method...

On Solving Linear Diophantine Systems Using Generalized Rosser's Algorithm

Diophantine Equations Related with Linear Binary Recurrences

In this paper we find all solutions of four kinds of the Diophantine equations begin{equation*} ~x^{2}pm V_{t}xy-y^{2}pm x=0text{ and}~x^{2}pm V_{t}xy-y^{2}pm y=0, end{equation*}% for an odd number $t$, and, begin{equation*} ~x^{2}pm V_{t}xy+y^{2}-x=0text{ and}text{ }x^{2}pm V_{t}xy+y^{2}-y=0, end{equation*}% for an even number $t$, where $V_{n}$ is a generalized Lucas number. This pape...

a new type-ii fuzzy logic based controller for non-linear dynamical systems with application to 3-psp parallel robot

abstract type-ii fuzzy logic has shown its superiority over traditional fuzzy logic when dealing with uncertainty. type-ii fuzzy logic controllers are however newer and more promising approaches that have been recently applied to various fields due to their significant contribution especially when the noise (as an important instance of uncertainty) emerges. during the design of type- i fuz...

Polyhedral Omega: A New Algorithm for Solving Linear Diophantine Systems

Polyhedral Omega is a new algorithm for solving linear Diophantine systems (LDS), i.e., for computing a multivariate rational function representation of the set of all non-negative integer solutions to a system of linear equations and inequalities. Polyhedral Omega combines methods from partition analysis with methods from polyhedral geometry. In particular, we combine MacMahon’s iterative appr...