Effects of external global harmonic influence on chimera states

Nonlinear Dynamics - The effects of the global harmonic force on an ensemble of nonlocally coupled chaotic Rössler oscillators is studied. The autonomous ensemble without external force...     

Lie point symmetries and some group invariant solutions of the quasilinear equation involving the infinity Laplacian

Using the classical Lie method we obtain the full Lie point symmetry group of the Aronsson equation in two independent variables. Some group invariant solutions of this equation are found and a conjecture on the Lie point symmetry group of the Aronsson equation in Rⁿ is presented.     

On the local asymptotics of Faber polynomials

We study a local asymptotics of the (generalized) Faber polynomials at the boundary of the associated domain, under certain mild smoothness conditions on the weight function and geometric conditions on the boundary. The main result exhibits how this asymptotics depends on the corners at the boundary. Its proof is based on the continuity properties of the Visser-Ostrowski quotient at the corners.

     

A class of dimension-skipping graphs

Forn≧6 there exists a graphG with dimG=n, dimG*≧n+2, whereG* isG with a certain edge added.     

High-frequency 263 GHz PELDOR

Pulsed electron–electron double resonance (PELDOR/DEER) at high frequencies can provide information on the relative orientation of paramagnetic centres or spin labels, if those are rigidly oriented in a host biomolecule and experiments are performed with sufficient orientation selectivity. We present the first comparative PELDOR study at 263 and 94 GHz on a model RNA system containing rigid nitroxides. We show that at 263 GHz still considerable modulation depth is observed and orientation selectivity is significant, particularly in g _x–g _y plane of the nitroxides.     

Removability of isolated singularity for anisotropic parabolic equations with absorption

We study the problem of removability of isolated singularity for general quasilinear anisotropic parabolic equations with absorption. The precise conditions on the behaviour of the absorption term that ensure the non-existence of solutions with point singularities are established.     

Practical synthesis of 1,4-dioxane derivative of the closo-dodecaborate anion and its ring opening with acetylenic alkoxides

Practical method of synthesis of the 1,4-dioxane derivative of the closo-dodecaborate anion was developed. The cleavage of the dioxonium ring in [B₁₂H₁₁O(CH₂CH₂)₂O]⁻ with acetylenic alcohols gave rise to the preparation of closo-dodecaborate derivatives with terminal acetylene group. These compounds can be introduced into click reactions with phenylazide leading to the corresponding triazoles. The structures of (Bu₄N)[B₁₂H₁₁O(CH₂CH₂)₂O] and (Bu₄N)₂[B₁₂H₁₁(OCH₂CH₂)₂OCH₂CCH] · 0.5HOCH₂CCH were determined by single-crystal X-ray diffraction.