Light scattering modeling of small feldspar aerosol particles using polyhedral prisms and spheroids

The use of simplified particle shapes for modeling scattering by irregularly shaped mineral-dust particles is studied using polyhedral prisms and spheroids as model particles. Simulated phase matrices averaged over shape and size distributions at wavelength 633 nm are compared with a laboratory-measured phase matrix of feldspar particles with known size distribution with effective radius of . When an equi-probable shape distribution is assumed, prisms and oblate spheroids agree with measurements to a similar degree, whereas prolate spheroids perform markedly better. Both spheroids and prisms perform much better than spheres. When an automatic fitting method is applied for finding optimal shape distributions, it is found that the most elongated spheroids are most important for good fits, whereas nearly-spherical spheroids are generally of very little importance. The phase matrices for the different polyhedral prisms, on the other hand, are found to be similar, thus their shape-averaged phase matrices are insensitive to the shape distribution assumed. For spheroids, a simple parameterization for the shape distribution, where weights increase with increasing departure from spherical shape, is proposed and tested. This parameterization improves the fit of most phase matrix elements attained with an equi-probable shape distribution, and it performs particularly well for reproducing the measured phase function.     

Diffraction of compatible random substitutions in one dimension

As a guiding example, the diffraction measure of a random local mixture of the two classic Fibonacci substitutions is determined and reanalysed via self-similar measures of Hutchinson type, defined by a finite family of contractions. Our revised approach yields explicit formulas for the pure point and the absolutely continuous parts, as well as a proof for the absence of singular continuous components. This approach is then extended to the family of random noble means substitutions and, as an example with an underlying 2-adic structure, to a locally randomised version of the period doubling chain. As a first step towards a more general approach, we interpret our findings in terms of a disintegration over the Kronecker factor, which is the maximal equicontinuous factor of a covering model set.     

Hierarchies from D-brane instantons in globally defined Calabi-Yau orientifolds

We construct the first globally consistent semirealistic type I string vacua on an elliptically fibered manifold where the zero modes of the Euclidean D1-instanton sector allow for the generation of nonperturbative Majorana masses of an intermediate scale. In another class of global models, a D1-brane instanton can generate a Polonyi-type superpotential breaking supersymmetry at an exponentially suppressed scale.     

Active Molybdenum‐Based Anode for Dehydrogenative Coupling Reactions

A new and powerful active anode system that can be operated in 1,1,1,3,3,3‐hexafluoro‐2‐propanol (HFIP) has been discovered. In HFIP the molybdenum anode forms a compact, conductive, and electroactive layer of higher‐valent molybdenum species. This system can replace powerful but stoichiometrically required Mo^V reagents for the dehydrogenative coupling of aryls. This electrolytic reaction is more sustainable and allows the conversion of a broad scope of activated arenes.     

Combining Deep Eutectic Solvents with TEMPO-based Polymer Electrodes: Influence of Molar Ratio on Electrode Performance**

For sustainable energy storage, all-organic batteries based on redox-active polymers promise to become an alternative to lithium ion batteries. Yet, polymers contribute to the goal of an all-organic cell as electrodes or as solid electrolytes. Here, we replace the electrolyte with a deep eutectic solvent (DES) composed of sodium bis(trifluoromethanesulfonyl)imide (NaTFSI) and N-methylacetamide (NMA), while using poly(2,2,6,6-tetramethylpiperidin-1-yl-oxyl methacrylate) (PTMA) as cathode. The successful combination of a DES with a polymer electrode is reported here for the first time. The electrochemical stability of PTMA electrodes in the DES at the eutectic molar ratio of 1 : 6 is comparable to conventional battery electrolytes. More viscous electrolytes with higher salt concentration can hinder cycling at high rates. Lower salt concentration leads to decreasing capacities and faster decomposition. The eutectic mixture of 1 : 6 is best suited uniting high stability and moderate viscosity.     

Instability of the Al4(2-) "all-metal aromatic" ion and its implications

Al42 - is a prototype structural unit of a new class of "all-metal aromatic" molecules. Without stabilizing counterions this species is unstable with respect to electron autodetachment in the gas phase. We estimated the height of the repulsive Coulomb barrier to approximately 2.7 eV and calculated a lifetime of 9 fs. This is a short lifetime: The only way to study the isolated dianion experimentally is to use electron scattering techniques. Investigations of the validity of bound-state quantum chemical calculations on the isolated species show that the results suffer from significant admixture of continuum states to the bound-state wave function depending on the basis set. Calculations of molecular properties can therefore give essentially arbitrary results for this ill-defined system, as is demonstrated for the energy and nuclear magnetic shieldings. This substantiates that results from calculations on the isolated dianion should be approached with caution.     

Nucleophilic additions to alkylidene bis(sulfoxides): stereoelectronic effects in vinyl sulfoxides

Conjugate additions of nucleophiles (e.g. enolates, amines and malonate anions) to bis(p-tolylsulfinyl)alkenes, alkylidene-1,3-dithiane-1,3-dioxides and alkylidene-1,3-dithiolane-1,3-dioxides have recently been published. Reasons for different selectivities and reaction rates will be discussed by consideration of steric and electronic effects. The preferred mode of attack can be explained by stereoelectronic effects (hyperconjugation) in the primarily carbanion, which is stabilized by n-->S-O-sigma* interaction with an antiperiplanar S=O group. Calculation of the transition states [BP86/aug-TZVP] for the addition of acetone enolate to the dithiane-derived alkylidene bis(sulfoxide) revealed that 6.6-7.3 kJ mol(-1) more energy is needed for an attack leading to a less-stabilized carbanion. Two axial S=O groups in dithiolane-derived alkylidene bis(sulfoxides) lead to a higher reactivity towards nucleophiles.     

A structure‐preserving doubling algorithm for Lur'e equations

We introduce a numerical method for the numerical solution of the Lur'e equations, a system of matrix equations that arises, for instance, in linear‐quadratic infinite time horizon optimal control. We focus on small‐scale, dense problems. Via a Cayley transformation, the problem is transformed to the discrete‐time case, and the structural infinite eigenvalues of the associated matrix pencil are deflated. The deflated problem is associated with a symplectic pencil with several Jordan blocks of eigenvalue 1 and even size, which arise from the nontrivial Kronecker chains at infinity of the original problem. For the solution of this modified problem, we use the structure‐preserving doubling algorithm. Implementation issues such as the choice of the parameter γ in the Cayley transform are discussed. The most interesting feature of this method, with respect to the competing approaches, is the absence of arbitrary rank decisions, which may be ill‐posed and numerically troublesome. The numerical examples presented confirm the effectiveness of this method. Copyright © 2015 John Wiley & Sons, Ltd.     

Inductive and Deductive Justification of Knowledge: Flexible Judgments Underneath Stable Beliefs in Teacher Education

Personal epistemological beliefs are considered to play an important role for processes of learning and teaching. However, research on personal epistemology is confronted with theoretical issues as there is conflicting evidence regarding the structure, stability, and context-dependence of epistemological beliefs. We give evidence how theoretical and methodological issues can partly be resolved by distinguishing between relatively stable “epistemological beliefs” and situation-specific “epistemological judgments.” A qualitative content analysis of a series of semistructured interviews (study 1) with pre-service teachers, teachers, and teacher educators as well as a statistical analysis of pre-service teachers’ extensive answers in questionnaires (study 2), both on the topic of “mathematical discovery,” reveal not only beliefs of the participants but also different qualities of judgments. Therefore, in further research both aspects of beliefs should be considered in a more differentiated manner when categorizing belief structures.