A flexible control of wave scattering in complex media is relevance different areas classical and quantum physics. Recently, great interest has been devoted to engineering non-Hermitian systems, with the prediction demonstration new classes potentials unique properties, such as transparent invisible or one-way reflectionless potentials. Such have found for both continuous discrete (lattice) sys...

Sampling properties of some three-dimensional lattices are examined. The Cartesian cubic lattice is compared with the non-Cartesian faceand body-centered cubic lattices. Numerical computations using analytical functions are used to compare rotational dependency and aliasing effects.

We show that a natural hybridation construction of lattices in SU(n, 1) to produce (non-arithmetic) lattices in SU(n + 1, 1) fails when n = 1 for most triangle groups in SU(1, 1).

We consider models of random Schrr odinger operators which exist thanks to a cohomological theorem in ergodic theory. Examples are ergodic Schrr odinger operators with random magnetic uxes on discrete two-dimensional lattices or non-periodic situations like Penrose lattices.

In this paper we investigate the atomic level in the lattice of subvarieties of residuated lattices. In particular, we give infinitely many commutative atoms and construct continuum many non-commutative, representable atoms that satisfy the idempotent law; this answers Problem 8.6 of [12]. Moreover, we show that there are only two commutative idempotent atoms and only two cancellative atoms. Fi...

Rectangular lattices are special planar semimodular lattices introduced by G. Grätzer and E. Knapp in 2009. By a patch lattice we mean a rectangular lattice whose weak corners are coatoms. As a sort of gluings, we introduce the concept of a patchwork system. We prove that every glued sum indecomposable planar semimodular lattice is a patchwork of its maximal patch lattice intervals “sewn togeth...

Two-dimensional films of semiconductors can be patterned into super-lattices with nanoscale periodicity, using top-down (lithography) or bottom-up approaches. In particular, square and honeycomb lattices of semiconductor nanocrystals have been recently synthesized using oriented attachment. We have performed atomistic tight-binding calculations of the conduction bands of super-lattices of CdSe....