Dynamical Systems Gradient method for solving nonlinear equations with monotone operators

A version of the Dynamical Systems Gradient Method for solving ill-posed nonlinear monotone operator equations is studied in this paper. A discrepancy principle is proposed and justified. A numerical experiment was carried out with the new stopping rule. Numerical experiments show that the proposed stopping rule is efficient. Equations with monotone operators are of interest in many applications.Comment: 2 figure

High frequency limit of the Transport Cross Section and boundedness of the Total Cross Section in scattering by an obstacle with impedance boundary conditions

The scalar scattering of the plane wave by a strictly convex obstacle with impedance boundary conditions is considered. The uniform boundedness of the Total Cross Section for all values of frequencies is proved. The high frequency limit of the Transport Cross Section is founded and presented as a classical functional of the variational theory

Resonance regimes of scattering by small bodies with impedance boundary conditions

The paper concerns scattering of plane waves by a bounded obstacle with complex valued impedance boundary conditions. We study the spectrum of the Neumann-to-Dirichlet operator for small wave numbers and long wave asymptotic behavior of the solutions of the scattering problem. The study includes the case when $k=0$ is an eigenvalue or a resonance. The transformation from the impedance to the Dirichlet boundary condition as impedance grows is described. A relation between poles and zeroes of the scattering matrix in the non-self adjoint case is established. The results are applied to a problem of scattering by an obstacle with a springy coating. The paper describes the dependence of the impedance on the properties of the material, that is on forces due to the deviation of the boundary of the obstacle from the equilibrium position

Detection of protein glycosylation using tip enhanced Raman scattering

The correct glycosylation of biopharmaceutical glycoproteins and their formulations is essential for them to have the desired therapeutic effect on the patient. It has recently been shown that Raman spectroscopy can be used to quantify the proportion of glycosylated protein from mixtures of native and glycosylated forms of bovine pancreatic ribonuclease (RNase). Here we show the first steps towards not only the detection of glycosylation status, but the characterisation of glycans themselves from just a few protein molecules at a time using tip-enhanced Raman scattering (TERS). Whilst this technique generates complex data that are very dependent on the protein orientation, with the careful development of combined data preprocessing, univariate and multivariate analysis techniques, we have shown that we can distinguish between the native and glycosylated forms of RNase. Many glycoproteins contain populations of subtly different glycoforms, therefore with stricter orientation control, we believe this has the potential to lead to further glycan characterisation using TERS, which would have use in biopharmaceutical synthesis and formulation research

Timber gridshells: beyond the drawing board

In March 2011, a week-long workshop that invited participation from all architecture and architectural technology students at Sheffield Hallam University, UK was organised with the objective of enhancing students’ thinking and experience by construction thinking. It was aimed at creating a sense of realness to realise a design project collectively. Timber was set as the material of exploration. The students had to make use of bending to design and create a timber gridshell structure. This made use of a quality traditionally felt to be a structural weakness of the material. To do this, students form-found non-mathematically and non-digitally using paper gridmats. This paper describes the aims, activity and outcome of the timber gridshell workshop as a way of preparing architects and technologists of the future and introducing the challenges of architectural design in terms of economics and construction process, aesthetics, effective communication and structural intuition by working with a given material – all important aspects in achieving effective architecture