Die Reaktionen von Eisen(III)-chlorid mit Trithiazylchlorid. Die Kristallstruktur von [S4N4Cl]+[FeCl4]⊖

Reactions of Iron Trichloride with Trithyazyl Chloride. Crystal Structure of [S₄N₄Cl]⁺[FeCl₄]^? Iron trichloride reacts with (NSCl)₃ yielding S₄N₄[FeCl₄]₂, S₃N₃Cl₂[FeCl₄] or S₄N₄Cl[FeCl₄], depending on the reaction conditions. The i.r. spectra prove the presence of [FeCl₄]^? ions for all three compounds. The ⁵⁷Fe-Mössbauer spectra show a slight quadrupole splitting at 80 K for S₃N₃Cl₂[FeCl₄] (ΔE^Q = 0.42 mm · s^?1) and S₄N₄Cl[FeCl₄] (ΔE^Q = 0.23 mm · s^?1), which indicates a slight deformation of the FeCl₄^? tetrahedra. The crystal structure of S₄N₄Cl[FeCl₄] was determined and refined with X-ray diffraction data (2549 independent reflexions, R = 0.026). S₄N₄Cl[FeCl₄] crystallizes in the triclinic space group P1 with two formula units per unit cell. The lattice constants are a = 712, b = 911, c = 1006 pm, α = 76.5°, β = 83.8° and γ = 80.5°. The structure consists of the so far unknown [S₄N₄Cl]^⊕ cations and slightly deformed FeCl₄^? ions. The [S₄N₄Cl]^⊕ ion consists of a S₄N₄ ring built up of two nearly planar S₃N₂ fragments having a dihedral angle of 136°. The average SN bond length is 157 pm, the SCI bond length 214 pm.     

Subdivision Strategies for Boxes in Branch-and-Bound Nonlinear Solvers and Verification

Most verified solvers for nonlinear interval systems of equations comprise two strategies: a branch-and-bound-type “location” phase for excluding regions that cannot contain a solution, and a “verification” phase for proving that the remaining regions do indeed contain solutions. In the first phase, subdivision is crucial for the efficiency of the solvers. We discuss several ways for subdivision and present robust strategies that are suited for a variety of nonlinear systems. Particular focus is on the choice of subdivision directions, subdivision points and the handling of unbounded intervals. Furthermore we discuss a method to discard parts of a box within subdivision. Numerical evaluations are given based on the nonlinear interval solver SONIC. In the verification phase, further subdivision can increase the strength of the verification tests. In this paper, we address methods for the rigorous implementation of symmetrical subdivision which is needed, e.g., in existence tests based on Borsuk’s theorem.     

Long-term characteristics of analogical processing in high-school students with high fluid intelligence: an fMRI study

Intelligence is known to predict scholastic achievement and enables high performance in cognitive tasks. Fluid intelligence is strongly related to analogical reasoning abilities, which are fundamental to mathematical thinking. Geometric analogical reasoning is a prototypical measure of fluid intelligence. However, the cerebral correlates of geometric analogical reasoning and their developmental modulation over time are still rarely investigated. We report a 1-year follow-up functional magnetic resonance imaging study of a geometric analogical reasoning task in high fluid intelligence high-school students. This study was designed to characterise the cerebral correlates of geometric analogical reasoning and to improve our knowledge about the impact of general cognitive development on behavioural performance and on cerebral mechanisms underlying geometric analogical reasoning in adolescents. Our data indicate that a fronto-parietal network comprising the left and right parietal lobes and the left middle frontal gyrus was equally modulated by task difficulty at both measuring time points. At the behavioural level, however, participants showed improvements in performance at the second measuring time point. The behavioural improvements point to a more efficient task processing. As this is not accompanied by differential recruitment of fronto-parietal brain regions, the data suggest an increase in neural efficiency for these brain regions.     

Weighted Composition Operators Between Weighted Bloch Type Spaces and Weighted Banach Spaces of Holomorphic Functions

Let φ: 𝔻 → 𝔻 and ψ: 𝔻 → ? be analytic maps. They induce a weighted composition operator ψ C _φ acting between weighted Bloch type spaces and weighted Banach spaces of holomorphic functions. Under some assumptions on the weights, we give a necessary as well as a sufficient condition when such an operator is bounded resp. compact.     

Topological Structure of the Set of Weighted Composition Operators on Weighted Bergman Spaces of Infinite Order

We consider the topological space of all weighted composition operators on weighted Bergman spaces of infinite order endowed with the operator norm. We show that the set of compact weighted composition operators is path connected. Furthermore, we find conditions to ensure that two weighted composition operators are in the same path connected component if the difference of them is compact. Moreover, we compare the topologies induced by L(H^∞) and L(H^∞_v) on the space of bounded composition operators and give a sufficient condition for a composition operator to be isolated.     

Comparing adult mathematical literacy with PISA students: results of a pilot study

In Germany, very little empirical data about the mathematical competence of adults is available. The aim of this study is to test the level of mathematical competence in an adult sample. For this purpose, a mathematics test was constructed using the PISA mathematics framework as a guideline. The test consisted of fourteen public items from the mathematics test in PISA 2000. The study was implemented by carrying out house visits (Germany). The sample was comprised of 64 adults (90% women, age: 41 years). The test results were scaled in the metric of PISA 2000. Compared with the average German student competencies in PISA 2000, the average competency in the adult sample was on the same level as the fifteen-year-old comprehensive secondary school student (at a German Gymnasium). Further analysis shows that the mathematics competency level in the adult sample is positively connected to the individual vocational education degree.