Describing the set of words generated by interval exchange transformation

Let $W$ be an infinite word over finite alphabet $A$. We get combinatorial criteria of existence of interval exchange transformations that generate the word W.Comment: 17 pages, this paper was submitted at scientific council of MSU, date: September 21, 200

Spatially dispersive finite-difference time-domain analysis of sub-wavelength imaging by the wire medium slabs

In this paper, a spatially dispersive finite-difference time-domain (FDTD) method to model wire media is developed and validated. Sub-wavelength imaging properties of the finite wire medium slabs are examined. It is demonstrated that the slab with its thickness equal to an integer number of half-wavelengths is capable of transporting images with sub-wavelength resolution from one interface of the slab to another. It is also shown that the operation of such transmission devices is not sensitive to their transverse dimensions, which can be made even comparable to the wavelength. In this case, the edge diffractions are negligible and do not disturb the image formation.Comment: 14 pages, 13 figures, submitted to Optics Expres

State-Selective High-Energy Excitation of Nuclei by Resonant Positron Annihilation

In the annihilation of a positron with a bound atomic electron, the virtual gamma photon created may excite the atomic nucleus. We put forward this effect as a spectroscopic tool for an energy-selective excitation of nuclear transitions. This scheme can efficiently populate nuclear levels of arbitrary multipolarities in the MeV regime, including monopole transitions and giant resonances. In certain cases, it may have a higher cross sections than the conventionally used Coulomb excitation

On Shirshov bases of graded algebras

We prove that if the neutral component in a finitely-generated associative algebra graded by a finite group has a Shirshov base, then so does the whole algebra.Comment: 4 pages; v2: minor corrections in English; to appear in Israel J. Mat

Geometrical Description of the Local Integrals of Motion of Maxwell-Bloch Equation

We represent a classical Maxwell-Bloch equation and related to it positive part of the AKNS hierarchy in geometrical terms. The Maxwell-Bloch evolution is given by an infinitesimal action of a nilpotent subalgebra $n_+$ of affine Lie algebra $\hat {sl}_2$ on a Maxwell-Bloch phase space treated as a homogeneous space of $n_+$. A space of local integrals of motion is described using cohomology methods. We show that hamiltonian flows associated to the Maxwell-Bloch local integrals of motion (i.e. positive AKNS flows) are identified with an infinitesimal action of an abelian subalgebra of the nilpotent subalgebra $n_+$ on a Maxwell- Bloch phase space. Possibilities of quantization and latticization of Maxwell-Bloch equation are discussed.Comment: 16 pages, no figures, plain TeX, no macro