Host (dealuminated Y zeolite)–guest (zirconium tetraphenylporphyrin) nanocomposite materials. An efficient catalyst in the oximation of aldehydes

In this research, zirconium tetraphenylporphyrin encapsulated into dealuminated Y zeolite (ZrTPP–DAZY) was prepared through a template synthesis method. This heterogeneous catalyst was characterized by XRD, FT-IR, DRS, UV–Vis, EDX and FESEM techniques. The amount of ZrTPP in the nanocage of dealuminated Y zeolite was estimated to be 0.0156 g/g of support. This catalytic system was employed for an efficient oximation of aldehydes under magnetic stirring conditions at room temperature and the corresponding products were obtained in 50–90% yields. This catalytic system also indicated good shape selectivity towards linear aldehydes. ZrTPP–DAZY was reused several times without any significant loss in catalytic activity.     

Photoinduced electron transfer in a triarylamine-organoboron-Ru(2,2′-bipyridine)32+ compound

Long-range electron transfer reactions play a key role in biological photosynthesis, and they are likely to play an important role for future artificial photosynthetic endeavors as well. The possibility to control the rates for long-range electron transfer with external stimuli is of particular interest in this context. In the work presented herein, we explored a donor–bridge–acceptor compound in which intramolecular electron transfer from a triarylamine donor to a photoexcited Ru(bpy)₃²⁺ (bpy = 2,2′-bipyridine) acceptor occurs across an organoboron bridge over a distance of approximately 22 Å. Fluoride has a high binding affinity to the organoboron bridge in apolar solutions, and the resulting organofluoroborate has a significantly different electronic structure. We explored to what extent the change from an electron-deficient organoboron wire to an electron-rich organofluoroborate bridge affects long-range electron transfer between the distant triarylamine donor and the Ru(bpy)₃²⁺ acceptor.     

Error estimates for space–time discontinuous Galerkin formulation based on proper orthogonal decomposition

In this study, proper orthogonal decomposition (POD) method is applied to diffusion–convection–reaction equation, which is discretized using space–time discontinuous Galerkin (dG) method. We provide estimates for POD truncation error in dG-energy norm, dG-elliptic projection, and space–time projection. Using these new estimates, we analyze the error between the dG and the POD solution, and the error between the exact and the POD solution. Numerical results, which are consistent with theoretical convergence rates, are presented.     

Study on convergence and error of a numerical method for solving systems of nonlinear Fredholm–Volterra integral equations of Hammerstein type

The aim of this paper is to present an efficient analytical and numerical procedure for solving systems of nonlinear Fredholm–Volterra integral equations of the Hammerstein type with the aid of fixed point techniques and the usual Schauder basis in an adequate Banach space.     

Polarization tensors of planar domains as functions of the admittivity contrast

(Electric) polarization tensors describe part of the leading order term of asymptotic voltage perturbations caused by low volume fraction inhomogeneities of the electrical properties of a medium. They depend on the geometry of the support of the inhomogeneities and on their admittivity contrast. Corresponding asymptotic formulas are of particular interest in the design of reconstruction algorithms for determining the locations and the material properties of inhomogeneities inside a body from measurements of current flows and associated voltage potentials on the body’s surface. In this work, we consider the two-dimensional case only and provide an analytic representation of the polarization tensor in terms of spectral properties of the double layer integral operator associated with the support of simply connected conductivity inhomogeneities. Furthermore, we establish that an (infinitesimal) simply connected inhomogeneity has the shape of an ellipse, if and only if the polarization tensor is a rational function of the admittivity contrast with at most two poles whose residues satisfy a certain algebraic constraint. We also use the analytic representation to provide a proof of the so-called Hashin–Shtrikman bounds for polarization tensors; a similar approach has been taken previously by Golden and Papanicolaou and Kohn and Milton in the context of anisotropic composite materials.     

Full Bayesian analysis of claims reserving uncertainty

We revisit the gamma–gamma Bayesian chain-ladder (BCL) model for claims reserving in non-life insurance. This claims reserving model is usually used in an empirical Bayesian way using plug-in estimates for the variance parameters. The advantage of this empirical Bayesian framework is that allows us for closed form solutions. The main purpose of this paper is to develop the full Bayesian case also considering prior distributions for the variance parameters and to study the resulting sensitivities.     

Capital allocation for portfolios with non-linear risk aggregation

Existing risk capital allocation methods, such as the Euler rule, work under the explicit assumption that portfolios are formed as linear combinations of random loss/profit variables, with the firm being able to choose the portfolio weights. This assumption is unrealistic in an insurance context, where arbitrary scaling of risks is generally not possible. Here, we model risks as being partially generated by Lévy processes, capturing the non-linear aggregation of risk. The model leads to non-homogeneous fuzzy games, for which the Euler rule is not applicable. For such games, we seek capital allocations that are in the core, that is, do not provide incentives for splitting portfolios. We show that the Euler rule of an auxiliary linearised fuzzy game (non-uniquely) satisfies the core property and, thus, provides a plausible and easily implemented capital allocation. In contrast, the Aumann–Shapley allocation does not generally belong to the core. For the non-homogeneous fuzzy games studied, Tasche’s (1999) criterion of suitability for performance measurement is adapted and it is shown that the proposed allocation method gives appropriate signals for improving the portfolio underwriting profit.