Fractional Hamiltonian Monodromy

We introduce fractional monodromy in order to characterize certain non-isolated critical values of the energy–momentum map of integrable Hamiltonian dynamical systems represented by nonlinear resonant two-dimensional oscillators. We give the formal mathematical definition of fractional monodromy, which is a generalization of the definition of monodromy used by other authors before. We prove that the 1:( − 2) resonant oscillator system has monodromy matrix with half-integer coefficients and discuss manifestations of this monodromy in quantum systems. Communicated by Eduard Zehnder Submitted: February 25, 2005; Accepted: November 17, 2005     

Green luminescence in diffusion-doped layers of zinc selenide

Diffusion-doped layers with a green emission band dominating in the room-temperature luminescence spectrum are obtained by annealing single-crystal zinc selenide substrates in tellurium and zinc vapors.     

On an Inverse Problem for a Parabolic Equation

In this paper, we study the inverse problem of the reconstruction of the right-hand side of special form for a parabolic equation in u in which the coefficients of u _t and u depend on u _(x,t) , with overdetermination given by the integral of the solution over time. The Fredholm property for this problem and the existence and uniqueness theorems in Sobolev spaces are established.     

Conductance of a multiterminal ballistic wire

JETP Letters - An experimental study of the two-, three-, and four-terminal resistance of a ballistic wire is carried out. The wire is fabricated on the basis of high-mobility 2D electron gas in an...     

Bounded sets in topological groups and embeddings

We show that the existence of a non-metrizable compact subspace of a topological group G often implies that G contains an uncountable supersequence (a copy of the one-point compactification of an uncountable discrete space). The existence of uncountable supersequences in a topological group has a strong impact on bounded subsets of the group. For example, if a topological group G contains an uncountable supersequence and K is a closed bounded subset of G which does not contain uncountable supersequences, then any subset A of K is bounded in G?(K?A). We also show that every precompact Abelian topological group H can be embedded as a closed subgroup into a precompact Abelian topological group G such that H is bounded in G and all bounded subsets of the quotient group G/H are finite. This complements Ursul's result on closed embeddings of precompact groups to pseudocompact groups.     

The contact problem of electroelasticity for a plane elliptic die

We obtain an exact solution of the problem of the stress-strain state of an elastic piezoelectric half-space acted on by a rigid elliptic die with a flat base. The axis of symmetry of the body coincides with the direction of the field of preliminary polarization of the body. The solution is confined to the case of translational displacement of the die. We determine the quantities that characterize the mechanical and electric fields that arise in the region of contact of the die with the half-space. Bibliography: 7 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 28, 1998, pp. 40–52.     

On variable stepsize Runge-Kutta approximations of a Cauchy problem for the evolution equation

We consider a Cauchy problem for the sectorial evolution equation with generally variable operator in a Banach space. Variable stepsize discretizations of this problem by means of a strongly A(φ)-stable Runge-Kutta method are studied. The stability and error estimates of the discrete solutions are derived for wider families of nonuniform grids than quasiuniform ones (in particular, if the operator in question is constant or Lipschitz-continuous, for arbitrary grids).     

A catalyst-free one-step synthesis of N-pyrimidinyl amidines from endocyclic enamines and 4-azidopyrimidines

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