In this paper, we use the network solution of the Ar T -system to derive that of the unrestricted A∞ T -system, equivalent to the octahedron relation. We then present a method for implementing various boundary conditions on this system, which consists of picking initial data with suitable symmetries. The corresponding restricted T -systems are solved exactly in terms of networks. This gives a s...

We consider two classes of birational maps, or birational difference equations, that have structural properties defined by algebraic relations. The properties are possession of a rational integral and having a discrete time-reversal symmetry. We then consider how these algebraic structures constrain the distribution of orbit lengths of such maps when they are reduced over finite fields, giving ...

Abstract: We establish a relation between the length T of the integration window of a linear differential equation x′+Ax = b and a spectral parameter s∗. This parameter is determined by comparing the exact solution x(T ) at the end of the integration window to the solution of a linear system obtained from the Laplace transform of the differential equation by freezing the system matrix. We propo...

In this paper, we discuss the synchronization and anti-synchronization of two identical chaotic T-systems. The adaptive and nonlinear control schemes are used for the synchronization and anti-synchronization. The stability of these schemes is derived by Lyapunov Stability Theorem. Firstly, the synchronization and anti-synchronization are applied to systems with known parameters, then to systems...

abstract aims: one of the consequences of taking ground water into surface is changing its chemical quality, specially increasing the concentration of dissolved salts. this research was performed in order to analyze growth possibility of heterotrophic bacteria in the membrane of active desalination plants in kashan city, iran. instrument & methods: this descriptive cross-sectional study was don...