Enforced stability of a simple eigenvalue in the continuous spectrum of a waveguide

It is shown in the paper that, under several orthogonality and normalization conditions and a proper choice of accessory parameters, a simple eigenvalue lying between thresholds of the continuous spectrum of the Dirichlet problem in a domain with a cylindrical outlet to infinity is not taken out from the spectrum by a small compact perturbation of the Helmholtz operator. The result is obtained by means of an asymptotic analysis of the augmented scattering matrix.     

Residual‐based artificial viscosity for simulation of turbulent compressible flow using adaptive finite element methods

In this paper, we present a finite element method with a residual‐based artificial viscosity for simulation of turbulent compressible flow, with adaptive mesh refinement based on a posteriori error estimation with sensitivity information from an associated dual problem. The artificial viscosity acts as a numerical stabilization, as shock capturing, and as turbulence capturing for large eddy simulation of turbulent flow. The adaptive method resolves parts of the flow indicated by the a posteriori error estimates but leaves shocks and turbulence under‐resolved in a large eddy simulation. The method is tested for examples in 2D and 3D and is validated against experimental data. Copyright © 2012 John Wiley & Sons, Ltd.     

Expedient Strategy for the Synthesis of 5-Acylethynylpyrrole-2-carbaldehydes

5-Acylethynylpyrrole-2-carbaldehydes have been synthesized from the protected pyrrole-2-carbaldehydes by their transition-metal-free topochemical mechanoactivated ethynylation with acylbromoacetylenes in a solid Al₂O₃ medium (room temperature, 6 h, 41–54% yields).     

Bäcklund transformations between four Lax-integrable 3D equations

Recently a classification of contactly-nonequivalent three-dimensional linearly degenerate equations of the second order was presented by E.V. Ferapontov and J. Moss. The equations are Lax-integrable. In our paper we prove that all these equations are connected with each other by appropriate Bäcklund transformations.