In this paper we present a simple method for efficient modeling of the tunneling effect in a non-homogeneous epsilon-near-zero (ENZ) waveguide, using an equivalent circuit approach. ENZ waveguide consists of rectangular waveguides filled with two-layered dielectric, E-step, and a narrow channel. It was shown that the E-step in a non-homogenous structure can be modeled rather simply using a shun...

We establish multiple recurrence and convergence results for pairs of zero entropy measure preserving transformations that do not satisfy any commutativity assumptions. Our cover the case where iterates two are n $n$ k $n^k$ , respectively, ⩾ 2 $k\geqslant 2$ = 1 $k=1$ remains an open problem. starting point is based on observation Furstenberg systems sequences form ( f T x ) $(f(T^{n^k}x))$ ha...

We apply the dressing method to a string solution given by a static string wrapped around the equator of a three-sphere and find that the result is the single spike solution recently discussed in the literature. Further application of the method allows the construction of solutions with multiple spikes. In particular we construct the solution describing the scattering of two single spikes and c...

In this paper we give a complete classification of two-step nilpotent Leibniz algebras in terms Kronecker modules associated with pairs bilinear forms. particular, describe the complex and real case indecomposable Heisenberg as generalization classical $(2n+1)-$dimensional Lie algebra $\mathfrak{h}_{2n+1}$. Then use - local racks correspondence proposed by S. Covez to show that have always glob...