In this paper, the notion of Integral Value Transformations (IVTs), a class of Discrete Dynamical Maps has been introduced. Then notion of Affine Discrete Dynamical System (ADDS) in the light of IVTs is defined and some rudimentary mathematical prope
rties of the system are depicted. Collatz Conjecture is one of the most enigmatic problems in 20th Century. The Conjecture was posed by German Mathematician L. Collatz in 1937. There are much advancement in generalizing and defining analogous conjectures, but even to the date, there is no fruitful result for the advancement for the settlement of the conjecture. We have made an effort to make a Collatz type problem in the domain of IVTs and we have been able to solve the problem in 2011 [1]. Here mainly, we have focused and inquired on Collatz-like ADDS. Finally, we have designed the Optimal Distributed and Parallel Environment (ODPE) in the light of ADDS.
Here the Integral Value Transformations (IVTs) are considered to be Discrete Dynamical System map in the spacemathbb{N}_(0). In this paper, the dynamics of IVTs is deciphered through the light of Topological Dynamics.
A simple and effective stepwise-method has been developed to remove defects from the top graphene layers of highly orientated pyrolytic graphite. Using a combination of ozone exposure and moderately high temperature we have shown that a defect-rich g
raphite surface can be modified to generate a graphene-like surface containing a negligible amount of oxygen, hydrogen and sp3 carbon. We report definitive x-ray photoelectron and x-ray absorption spectroscopy analysis after each stage of the process, suggest a mechanism by which the modification occurs and propose it as a route towards the preparation or manipulation of pristine graphene samples.
