In-depth study of fixed point theory is to solve the existence of the equation Tx = x (or x ∈ T (x)), where T is a self-map or a non-self-map. However, as we know, the equation Tx = x (or x ∈ T (x)) is not necessarily to have a solution. So, we turn to explore the best approximation of the existence of solutions. In 2003, Kirk-Srinavasan-Veeramani [1] introduced cyclic maps and best proximity p...

Two experiments were conducted. The first experiment compared cyclic and hierarchical concept maps, and measured the impact of concept quantification on the construction of both types of maps. The second experiment examined the preference for the two concept map structures. The results showed that structure does have a significant effect on the extent to which propositions imply a dynamic relat...

Several chaotic properties of cyclic permutation maps are considered. Cyclic refer to p-dimensional dynamical systems the form φ(b1,b2,⋯,bp)=(up(bp),u1(b1),⋯,up−1(bp−1)), where bj∈Hj (j∈{1,2,⋯,p}), p≥2 is an integer, and Hj (j∈{1,2,⋯,p}) compact subintervals real line R=(−∞,+∞). uj:Hj→Hj+1(j=1,2,…,p−1) up:Hp→H1 continuous maps. Necessary sufficient conditions for a class have Li–Yorke chaos, di...

A regular map M is a cellular decomposition of a surface such that its automorphism group Aut(M) acts transitively on the flags of M. It can be shown that if a Sylow subgroup P ≤ Aut(M) has order coprime to the Euler characteristic of the supporting surface, then P is cyclic or dihedral. This observation motivates the topic of the current paper, where we study regular maps whose automorphism gr...

Abstract We study the plane-symmetric collision of two gravitational waves and describe global spacetime geometry generated by this collision. formulate characteristic initial value problem for Einstein equations, when Goursat data describing incoming are prescribed on null hypersurfaces. construct a solution representing cyclic based junction conditions associated with singularity scattering m...

Task-specific focal dystonia is thought to have a neurological basis where stereotypical synchronous inputs and maladaptive plasticity play a role. As afferent input is a powerful driver of cortical reorganization, we propose that a period of asynchronous afferent stimulation may reverse maladaptive cortical changes and alleviate symptoms. Using transcranial magnetic stimulation (TMS), 3 hand m...