Das Wissen um Unterschiede in den kognitiven Strukturen von Schülerinnen und Schülern als Erklärung von Unterrichtsbeiträgen

It is reported about a longitudinal study run at the Institute of Cognitive Mathematics of the University of Osnabrueck, in which pupils’ verbal and text productions from mathematics lessons at a grammar school are analysed by means of cognitive theoretical methods. First of all, a teaching scene from an instruction to probability calculus and further text productions from an introductory lesson about exponential functions are analysed, in which five pupils take part whose cognitive structures have been assessed and classified in individual examinations. The characteristics brought out according to these teaching scenes indicate different ideas and thinking processes of the pupils. The second part shows that the pupils’ behaviour described is not only to be regarded in isolation but it can also be found in longitudinal examinations and can therefore be considered as a stable, typical characteristic. These results lead to consequences for the planning and design of mathematics lessons based on a well-founded theory of cognition.     

On the slow evolution of quasi-stationary shock waves

We consider the Burgers equation with a nonhomogeneous drift term, in the limit of small dissipation. A finite-dimensional manifold of slowly varying shock-like solutions is described, and a formal derivation of the dynamics on this manifold, in terms of a system of ordinary differential equations, is given. We also discuss the interpretation of the stationary solutions to the Burgers equation imbedded on the slow manifold.     

Dimorphic Modification of the Trinuclear Nickel(II) Complex [Ni3(NCS)6(pdz)6]: Synthesis,Crystal Structure,Thermal, Magnetic and Spectroscopic Properties

Reaction of nickel(II) thiocyanate and pyridazine (pdz) as organic spacer ligand leads to the formation of the ligand‐rich 1:2 (1:2 = metal to ligand ratio) trinuclear nickel(II) complex of composition [Ni₃(NCS)₆(pdz)₆]. Depending on the reaction solvent, different polymorphic modifications are obtained: Reaction in acetonitrile leads to the formation of the new modification 1I and reaction in ethanol leads to the formation of modification 1II reported recently. In their crystal structures discrete [Ni₃(NCS)₆(pdz)₆] units are found, in which each of the Ni²⁺ cations exhibits a NiN₆ distorted octahedral arrangement. The central Ni²⁺ cation is coordinated by four bridging pdz ligands and two thiocyanato anions in trans positions. Both thiocyanato anions exhibit the end‐on bridging mode. The peripheral Ni²⁺ cations are bridged by one thiocyanato anion and by two pdz ligands with the central Ni²⁺ cation. Further they are coordinated by two terminal N‐bonded thiocyanato anions and one terminal N‐bonded pdz ligand. The structure of 1I was determined by X‐ray single crystal structure investigation and emphasized by infrared spectroscopy. Magnetic measurements revealed a quasi Curie behavior with net ferromagnetic interactions for 1I and net antiferromagnetic interactions for 1II . Solvent‐mediated conversion experiments clearly show that modification 1I represents the thermodynamic most stable form at room temperature and that modification 1II is metastable. On thermal decomposition, both modification transform quantitatively in a new ligand‐deficient intermediate. Elemental analysis revealed a 3:4 compound of composition [Ni₃(NCS)₆(pdz)₄]. A structure model supported by IR spectroscopic investigations was assumed, in which three coordination modes of the thiocyanato anion exist, resulting in a 2D polymeric network.     

Die Kristallstrukturen der Cyanidofluoridoborate K[BFx(CN)4–x], x = 0–4

The crystal structure of K[BF₃(CN)] (Pbcn (Nr. 60) with a = 13.3486(15) b = 6.5239(7) c = 10.0085(11) Å, and eight formula units per unit cell) has been determined and the one of K[BF₂(CN)₂] was confirmed and improved. The different networks in the complete series of borates K[BF_x(CN)_4–x], x = 0–4 are compared and discussed.     

Study of J/psi-->pp[over],LambdaLambda[over] and observation of eta(c)-->LambdaLambda[over] at Belle

We study the baryonic charmonium decays of B mesons B+-->etacK+ and B+-->J/psiK+, where the etac and J/psi subsequently decay into a pp[over] or LambdaLambda[over] pair. We measure the J/psi-->pp[over] and LambdaLambda[over] anisotropy parameters alphaB=-0.60+/-0.13+/-0.14 (pp[over]), -0.44+/-0.51+/-0.31 (LambdaLambda[over ]) and compare to results from e;{+}e;{-}-->J/psi formation experiments. We also report the first observation of etac-->LambdaLambda[over]. The measured branching fraction is B(etac-->LambdaLambda[over ])=(0.87(+0.24)/(-0.21)(stat)(+0.09/-0.14) (syst)+/-0.27(PDG))x10-3. This study is based on a 357 fb-1 data sample recorded on the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric-energy e+ e- collider.     

Measurement of the quark mixing parameter cos2phi1 using time-dependent Dalitz analysis of B0 -->D[KS(0)pi + pi-]h0

We present a measurement of the angle phi1 of the Cabibbo-Kobayashi-Maskawa unitarity triangle using a time-dependent Dalitz analysis of D-->KS(0)pi + pi- decays produced in neutral B meson decay to a neutral D meson and a light meson (B0-->D*h0). The method allows a direct extraction of 2phi1 and, therefore, helps to resolve the ambiguity between 2phi1 and pi-2phi1 in the measurement of sin2phi1. We obtain sin2phi1= 0.78 +/- 0.44 +/- 0.22 and cos2varphi1 = 1.87(-0.53-0.32)(+0.40 + 0.22). The sign of cos2phi1 is determined to be positive at 98.3% C.L.