We consider the CSLs of 4–dimensional hypercubic lattices. In particular, we derive the coincidence index Σ and calculate the number of different CSLs as well as the number of inequivalent CSLs for a given Σ. The hypercubic face centered case is dealt with in detail and it is sketched how to derive the corresponding results for the primitive hypercubic lattice.

The coincidence site lattices of the root lattice A4 are considered, and the statistics of the corresponding coincidence rotations according to their indices is expressed in terms of a Dirichlet series generating function. This is possible via an embedding of A4 into the icosian ring with its rich arithmetic structure, which recently [6] led to the classification of the similar sublattices of A...

We discuss the possibility to measure entropy of the system created in heavy ion collisions using the Ma coincidence method.

In this paper, we prove some coupled coincidence point theorems for mappings with the mixed monotone property and obtain the uniqueness of this coincidence point. Then we providing useful examples in Nash equilibrium.

We study the existence of periodic solutions for a nonlinear system of n-th order di erential equations on time-scales. Assuming a suitable Nirenberg type condition, we prove the existence of at least one solution of the problem using Mawhin's coincidence degree.

We introduce the notion of quasi-cyclic-noncyclic pair and its relevant new notion of coincidence quasi-best proximity points in a convex metric space. In this way we generalize the notion of coincidence-best proximity point already introduced by M. Gabeleh et al cite{Gabeleh}. It turns out that under some circumstances this new class of mappings contains the class of cyclic-noncyclic mappings ...

let $p$ be a complex polynomial of the form $p(z)=zdisplaystyleprod_{k=1}^{n-1}(z-z_{k})$,where $|z_k|ge 1,1le kle n-1$ then $ p^prime(z)ne 0$. if $|z|

Computing modular coincidences can show whether a given substitution system, which is supported on a point lattice in R d , consists of model sets or not. We prove the computatibility of this problem and determine an upper bound for the number of iterations needed. The main tool is a simple algorithm for computing modular coincidences, which is essentially a generalization of Dekking coincidenc...