Mathematics achievement and interest in mathematics from a differential perspective

In this article, we present results of an empirical study with 500 German students of grades 7 and 8. The study focussed on students' mathematics achievement and their interest in mathematics as well as on the relation between these two constructs. In particular, the results show that the development of an individual student's achievement between grade 7 and grade 8 depends on the achievement level of the specific classroom and therefore on the specific mathematics instruction Interest in mathematics could be regarded a predictor for mathematics achievement Moreover, our findings suggest that the students show hardly any fear of mathematics independent of their achievement level.     

Negatively charged hyperbranched polyether-based polyelectrolytes

The preparation of carboxylated hyperbranched polyglycerols of narrow polydispersity was achieved by modification (78–90%) of the hydroxyl end groups via Michael addition of acrylonitrile, followed by hydrolysis. High conversion could only be achieved for low molecular weight starting materials (520 and 1,030 g mol⁻¹). The solution properties of the resulting materials were investigated by dynamic light scattering (DLS), showing the formation of large aggregates with size depending on the pH value. After deposition on a negatively charged mica surface, the structures observed by atomic force microscope (AFM) show the coexistence of aggregates and single macromolecules. Most interesting, in the case of the lower molecular weight sample (PG 520 g mol⁻¹), extended and ordered terrace structures were formed, which are unprecedented for hyperbranched polymers and are of interest for surface modification in general.     

First organophosphorus radical-mediated cyclisations to afford medium-sized rings: eight-membered lactones and seven- and eight-membered lactams

The phosphorus based radical precursors N-ethylpiperidine hypophosphite (EPHP) and diethylphosphine oxide (DEPO) are efficient reagents for carrying out the formation of seven- and eight-membered rings. Esters and amides were successfully converted into the corresponding eight-membered lactones and seven- and eight-membered lactams in good to excellent yields.     

Die Undecaarsenide A3As11 (A = Rb,Cs) — Synthesen und Kristallstrukturen

Alkaline Metal Arsenides A₃As₁₁ (A = Rb, Cs): Preparation and Crystal Structures Rb₃As₁₁ and Cs₃As₁₁ were synthesized from the elements and the crystal structures of the ordered room temperature form were characterized via single crystal x‐ray studies. In the Zintl phases the As atoms form chiral ufosan‐anions As with As‐As distances ranging from 238 to 248 pm. Like K₃As₁₁ Rb₃As₁₁ crystallizes with the Na₃P₁₁ structure type (orthorhombic, space group Pbcn, a = 1108.2(2), b = 1533.5(3), c = 1060.1(2) pm, Z = 4), whereas the Cs compound (monoclinic, space group C2/c, a = 1324.5(7), b = 1524.5(9), c = 1937.2(11) pm, β = 95.29(1)°, Z = 8) forms a new structure type. The crystallographic relationship between the two structure types and the anion packings in the plastic crystalline high temperature forms are discussed.     

Transition probabilities of Lévy‐type processes: Parametrix construction

We present an existence result for Lévy‐type processes which requires only weak regularity assumptions on the symbol with respect to the space variable x. Applications range from existence and uniqueness results for Lévy‐driven SDEs with Hölder continuous coefficients to existence results for stable‐like processes and Lévy‐type processes with symbols of variable order. Moreover, we obtain heat kernel estimates for a class of Lévy and Lévy‐type processes. The paper includes an extensive list of Lévy(‐type) processes satisfying the assumptions of our results.     

Oxidative addition transition states of Pd(0) complexes in polar solvent—a DFT study involving implicit and explicit solvation

Previous reports in the literature have suggested that concerted transition states for oxidative addition would not exist in solution. By contrast, this report describes the successful location of transition states for the oxidative addition of monoligated Pd(P^tBu₃), bisligated Pd(P^tBu₃)(MeCN), and anionic Pd(P^tBu₃)F^? complexes to C–Cl and C–OTf of an aryl chloro triflate in polar solvent (MeCN). Optimizations were done with implicit solvation and a combined implicit/explicit solvation approach in which six acetonitrile molecules were additionally involved in the optimization. The geometries obtained from optimizations employing an implicit solvation model are structurally largely analogous to those found using a combination of implicit and explicit solvation.     

N-CF3 Imidazolidin-2-one Derivatives via Photocatalytic and Silver-Catalyzed Cyclizations

While the N-trifluoromethylation of cyclic ureas is of interest for the potential to fundamentally change the properties of these biologically relevant moieties, the single synthetic procedure known to date describing their access only gives 4,4-disubstituted or fused aromatic cyclic N-CF₃ urea derivatives. We herein report an alternative approach to unleash access to the 4-monosubstituted imidazolidinone motif. The strategy relies on straightforward cyclization of readily accessible acyclic ureas, enabled by Ag-catalysis or light-assisted proton coupled electron transfer. The cyclic core is shown to be highly robust and amenable to various derivatizations, such as tandem Ni-catalysis, C−B, C−N, C−C cross couplings or C−H functionalizations, tolerating basic, nucleophilic and/or oxidizing conditions.     

Temperature and Composition Dependent Optical Properties of CdSe/CdS Dot/Rod-Based Aerogel Networks

Employing nanocrystals (NCs) as building blocks of porous aerogel network structures allows the conversion of NC materials into macroscopic solid structures while conserving their unique nanoscopic properties. Understanding the interplay of the network formation and its influence on these properties like size-dependent emission is a key to apply techniques for the fabrication of novel nanocrystal aerogels. In this work, CdSe/CdS dot/rod NCs possessing two different CdSe core sizes were synthesized and converted into porous aerogel network structures. Temperature-dependent steady-state and time-resolved photoluminescence measurements were performed to expand the understanding of the optical and electronic properties of these network structures generated from these two different building blocks and correlate their optical with the structural properties. These investigations reveal the influence of network formation and aerogel production on the network-forming nanocrystals. Based on the two investigated NC building blocks and their aerogel networks, mixed network structures with various ratios of the two building blocks were produced and likewise optically characterized. Since the different building blocks show diverse optical response, this technique presents a straightforward way to color-tune the resulting networks simply by choosing the building block ratio in connection with their quantum yield.