The dynamics of the second order rational difference equation in the title with complex parameters and arbitrary complex initial conditions is investigated. Two associated difference equations are also studied. The solutions in the complex plane of s
uch equations exhibit many rich and complicated asymptotic behavior. The analysis of the local stability of these three difference equations and periodicity have been carried out. We further exhibit several interesting characteristics of the solutions of this equation, using computations, which does not arise when we consider the same equation with positive real parameters and initial conditions. Many interesting observations led us to pose several open problems and conjectures of paramount importance regarding chaotic and higher order periodic solutions and global asymptotic convergence of such difference equations. It is our hope that these observations of these complex difference equations would certainly be new add-ons to the present art of research in rational difference equations in understanding the behavior in the complex domain.
This paper presents a spatial encryption technique for secured transmission of data in networks. The algorithm is designed to break the ciphered data packets into multiple data which are to be packaged into a spatial template. A secure and efficient
mechanism is provided to convey the information that is necessary for obtaining the original data at the receiver-end from its parts in the packets. An authentication code (MAC) is also used to ensure authenticity of every packet.
Ligands for only two human olfactory receptors are known. One of them, OR1D2, binds to Bourgeonal [Malnic B, Godfrey P-A, Buck L-B (2004) The human olfactory receptor gene family. Proc. Natl. Acad. Sci U. S. A. 101: 2584-2589 and Erratum in: Proc Nat
l Acad Sci U. S. A. (2004) 101: 7205]. OR1D2, OR1D4 and OR1D5 are three full length olfactory receptors present in an olfactory locus in human genome. These receptors are more than 80% identical in DNA sequences and have 108 base pair mismatches among them. We have used L-system mathematics and have been able to show a closely related subfamily of OR1D2, OR1D4 and OR1D5.
In this paper we have defined one function that has been used to construct different fractals having fractal dimensions between 1.58 and 2. Also, we tried to calculate the amount of increment of fractal dimension in accordance with the base of the nu
mber systems. Further, interestingly enough, these very fractals could be a frame of lyrics for the musicians, as we know that the fractal dimension of music is around 1.65 and varies between a high of 1.68 and a low of 1.60. Further, at the end we conjecture that the switching from one music fractal to another is nothing but enhancing a constant amount fractal dimension which might be equivalent to a kind of different sets of musical notes in various orientations.
In this paper we have used one 2 variable Boolean function called Rule 6 to define another beautiful transformation named as Extended Rule-6. Using this function we have explored the algebraic beauties and its application to an efficient Round Robin
Tournament (RRT) routine for 2k (k is any natural number) number of teams. At the end, we have thrown some light towards any number of teams of the form nk where n, k are natural numbers.
