Towards the Design of Optically Active Thiophene S-Oxides using Quantum Chemistry

The importance of axially chiral biaryls has risen steeply in the recent decades. This structural motif proved to be successful in catalytic asymmetric synthesis and the configuration of the biaryl axis is decisive for the biological activity. A new approach for the atroposelective synthesis of biaryls would be through a cycloaddition between an enantiopure phenyl-substituted thiophene S-oxide and an alkyne. Importantly, the chiral center of the thiophene S-oxide needs to be stable enough to avoid pyramidal inversion during the cycloaddition. Considering that the racemization of thiophene monoxides has been scarcely investigated so far, we perform a thorough quantum chemical study on the inversion barriers of a large number of chiral thiophene S-oxide derivatives. Our main goal is to identify substitution patterns leading to stable atropisomers at room temperature. Appealingly, the role of stereoelectronic effects and the position of the substituents as well as the importance of aromaticity on the pyramidal inversion barrier are elucidated for the first time.     

Perylene polyphenylmethylsiloxanes for optoelectronic applications

The incorporation of fluorescent organic dyes in an encapsulating matrix represents a route to generate stable and processable materials for optoelectronic devices. Here, we present a method to embed perylene dyes into a high refractive index (HRI) polysiloxane matrix applying an allyl functionalized perylene dye and hydrosilylation chemistry. In a first approach, the dye molecules were covalently integrated into the backbone of linear polyphenylmethylsiloxane chains. The fluorescent and liquid polymers were synthesized with molecular weights from 5660 up to 8400 g mol^?1. In a second approach, the dye itself was used as a cross‐linking agent between linear polyphenylmethylsiloxane chains. These preformed fluorescent batch polymers are liquids with dye concentrations between 0.025 and 8 wt %. The applied synthetic methods incorporated the dye covalently into the polymer structure and avoided the crystallization of the dye molecules and thus the formation of excimers, which would reduce the optical emission. The resulting products can be easily incorporated into curable commercially available HRI polyphenylmethylsiloxane resins. The formed materials are ideal LED encapsulants with a solid and flexible consistency, a uniform dispersion of the dyes, and adjustable mechanical properties, realized by changing the amount of perylene polymers. Further properties of the obtained materials are thermal stabilities up to 478 °C, quantum yields larger than 0.97, and high photostabilities. Thus, the covalent integration of dyes into polyphenylsiloxane structures represents a possible route for the stabilization of the organic dyes against the extreme irradiance and thermal conditions in LED applications. © 2019 The Authors. Journal of Polymer Science Part B: Polymer Physics published by Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1062–1073     

Reference priors for exponential families with simple quadratic variance function

Reference analysis is one of the most successful general methods to derive noninformative prior distributions. In practice, however, reference priors are often difficult to obtain. Recently developed theory for conditionally reducible natural exponential families identifies an attractive reparameterization which allows one, among other things, to construct an enriched conjugate prior. In this paper, under the assumption that the variance function is simple quadratic, the order-invariant group reference prior for the above parameter is found. Furthermore, group reference priors for the mean- and natural parameter of the families are obtained. A brief discussion of the frequentist coverage properties is also presented. The theory is illustrated for the multinomial and negative-multinomial family. Posterior computations are especially straightforward due to the fact that the resulting reference distributions belong to the corresponding enriched conjugate family. A substantive application of the theory relates to the construction of reference priors for the Bayesian analysis of two-way contingency tables with respect to two alternative parameterizations.     

From holes to sponge at irradiated Ge surfaces with increasing ion energy—an effect of defect kinetics?

We show that hole patterns and sponge-like layers at irradiated Ge surfaces originate from the same driving force, namely the kinetics of ion beam induced defects in the amorphous Ge surface layer. Ge hole patterns reported earlier for irradiation with low energy (5 keV) Ga⁺ ions were reproduced for low energy Bi⁺ but also for Ge⁺ self-irradiation, which proves that the dominating driving force for morphology evolution cannot originate from the implanted impurities. At higher ion energies the well-known formation of sponge-like Ge surface layers after heavy ion irradiation was found for Bi⁺ irradiation and Ge⁺ self-irradiation, also. The transition from smooth surfaces via hole patterns to sponge-like morphologies with increasing ion energies was studied in detail. A model based on the kinetics of ion beam induced defects was developed and implemented in 3D kinetic Monte Carlo simulations, which reproduce the transition from hole patterns to sponge-like layers with increasing ion energy.     

Periodic Solutions for Completely Resonant Nonlinear Wave Equations with Dirichlet Boundary Conditions

We consider the nonlinear string equation with Dirichlet boundary conditions u_tt–u_xx=(u), with (u)=u³+O(u⁵) odd and analytic, 0, and we construct small amplitude periodic solutions with frequency for a large Lebesgue measure set of close to 1. This extends previous results where only a zero-measure set of frequencies could be treated (the ones for which no small divisors appear). The proof is based on combining the Lyapunov-Schmidt decomposition, which leads to two separate sets of equations dealing with the resonant and non-resonant Fourier components, respectively the Q and the P equations, with resummation techniques of divergent powers series, allowing us to control the small divisors problem. The main difficulty with respect to the nonlinear wave equations u_tt–u_xx+Mu=(u), M0, is that not only the P equation but also the Q equation is infinite-dimensional.     

An efficient solution method for Weber problems with barriers based on genetic algorithms

In this paper we consider the problem of locating one new facility with respect to a given set of existing facilities in the plane and in the presence of convex polyhedral barriers. It is assumed that a barrier is a region where neither facility location nor travelling are permitted. The resulting non-convex optimization problem can be reduced to a finite series of convex subproblems, which can be solved by the Weiszfeld algorithm in case of the Weber objective function and Euclidean distances. A solution method is presented that, by iteratively executing a genetic algorithm for the selection of subproblems, quickly finds a solution of the global problem. Visibility arguments are used to reduce the number of subproblems that need to be considered, and numerical examples are presented.     

The Existence of Bifurcating Invariant Tori in a Spatially Extended Reaction-Diffusion-Convection System with Spatially Localized Amplification

We consider a spatially extended reaction-diffusion-convection system with a marginally stable ground state and a spatially localized amplification. We are interested in solutions bifurcating from the spatially homogeneous ground state in the case when pairs of imaginary eigenvalues simultaneously cross the imaginary axis. For this system we prove the bifurcation of a family of invariant tori which may contain quasiperiodic solutions. There is a serious difficulty in obtaining this result, because the linearization at the ground state possesses an essential spectrum up to the imaginary axis for all values of the bifurcation parameter. To construct the invariant tori, we use their invariance under the flow which manifests in a condition in PDE form. The nonlinear terms of this resulting PDE exhibit a loss of regularity. Since the linear part of this PDE is not smoothing, an adaption of the hard implicit function theorem (or Nash-Moser scheme) and energy estimates will be used to prove our result.