An alternating potential based approach for a Cauchy problem for the Laplace equation in a planar domain with a cut

We consider a Cauchy problem for the Laplace equation in a bounded region containing a cut, where the region is formed by removing a sufficiently smooth arc (the cut) from a bounded simply connected domain D. The aim is to reconstruct the solution on the cut from the values of the solution and its normal derivative on the boundary of the domain D. We propose an alternating iterative method which involves solving direct mixed problems for the Laplace operator in the same region. These mixed problems have either a Dirichlet or a Neumann boundary condition imposed on the cut and are solved by a potential approach. Each of these mixed problems is reduced to a system of integral equations of the first kind with logarithmic and hypersingular kernels and at most a square root singularity in the densities at the endpoints of the cut. The full discretization of the direct problems is realized by a trigonometric quadrature method which has super-algebraic convergence. The numerical examples presented illustrate the feasibility of the proposed method.

An iterative method based on boundary integrals for elliptic Cauchy problems in semi-infinite domains

In this study, we investigate the problem of reconstruction of a stationary temperature field from given temperature and heat flux on a part of the boundary of a semi-infinite region containing an inclusion. This situation can be modelled as a Cauchy problem for the Laplace operator and it is an ill-posed problem in the sense of Hadamard. We propose and investigate a Landweber-Fridman type iterative method, which preserve the (stationary) heat operator, for the stable reconstruction of the temperature field on the boundary of the inclusion. In each iteration step, mixed boundary value problems for the Laplace operator are solved in the semi-infinite region. Well-posedness of these problems is investigated and convergence of the procedures is discussed. For the numerical implementation of these mixed problems an efficient boundary integral method is proposed which is based on the indirect variant of the boundary integral approach. Using this approach the mixed problems are reduced to integral equations over the (bounded) boundary of the inclusion. Numerical examples are included showing that stable and accurate reconstructions of the temperature field on the boundary of the inclusion can be obtained also in the case of noisy data. These results are compared with those obtained with the alternating iterative method.

Efficient 1,4-addition of enones and boronic acids catalyzed by a Ni-Zn hydroxyl double salt-intercalated anionic rhodium(III) complex

Intercalation of an in situ prepared [Rh(OH)6]3- complex into an anion exchangeable Ni-Zn layered hydroxy double salt (Rh/NiZn) was demonstrated. The resulting Rh/NiZn effectively catalyzed the 1,4-addition of diverse enones and phenylboronic acids to their corresponding β-substituted carbonyl compounds. In the case of 2-cyclohexen-1-one and phenylboronic acid, a turnover frequency (TOF) of 920 h-1 based on Rh was achieved. The [Rh(OH)6]3- complex maintained its original monomeric trivalent state within the NiZn interlayer following catalysis, attributable to a strong electrostatic interaction between the NiZn host and anionic Rh(III) complex.

Hydrophenylation of internal alkynes with boronic acids catalysed by a Ni–Zn hydroxy double salt-intercalated anionic rhodium(III) complex

[Rh(OH)6]3− intercalated Ni–Zn mixed basic salt (Rh/NiZn) acts as an efficient catalyst for the hydrophenylation of internal alkynes with arylboronic acids under mild conditions. The turnover number per Rh site approached 740 in the reaction between 4-octyne and phenylboronic acid. The catalytic monomeric Rh(III) complex is stabilised within the NiZn interlayers, attributable to a strong electrostatic interaction, promoting its re-use.

Disentangling Double Politikverflechtung? The implications of the federal reforms for Bund-Länder relations on Europe

The recent reforms of German federalism (Reform I) have established a new framework for Bund–Länder co-operation on EU policy. These seek to safeguard Germany's ability to co-operate in Europe by disentangling the joint roles and responsibilities bound up within the complex arrangements of the EU policy-making system, defined as a multiple framework of joint decisions, or doppelte Politikverflechtung. Whilst on the surface, the reforms enacted may be read as a success for the Länder in their bid to secure autonomy on European issues, closer analysis reveals that these changes may in fact hamper the Länder agenda on European issues, closing off new opportunities for influence.

The value of indirect ties in citation networks:SNA analysis with OWA operator weights

This paper seeks to advance the theory and practice of the dynamics of complex networks in relation to direct and indirect citations. It applies social network analysis (SNA) and the ordered weighted averaging operator (OWA) to study a patent citations network. So far the SNA studies investigating long chains of patents citations have rarely been undertaken and the importance of a node in a network has been associated mostly with its number of direct ties. In this research OWA is used to analyse complex networks, assess the role of indirect ties, and provide guidance to reduce complexity for decision makers and analysts. An empirical example of a set of European patents published in 2000 in the renewable energy industry is provided to show the usefulness of the proposed approach for the preference ranking of patent citations.