Comparing German and Taiwanese secondary school students’ knowledge in solving mathematical modelling tasks requiring their assumptions

Mathematization is critical in providing students with challenges for solving modelling tasks. Inadequate assumptions in a modelling task lead to an inadequate situational model, and to an inadequate mathematical model for the problem situation. However, the role of assumptions in solving modelling problems has been investigated only rarely. In this study, we intentionally designed two types of assumptions in two modelling tasks, namely, one task that requires non-numerical assumptions only and another that requires both non-numerical and numerical assumptions. Moreover, conceptual knowledge and procedural knowledge are also two factors influencing students’ modelling performance. However, current studies comparing modelling performance between Western and non-Western students do not consider the differences in students’ knowledge. This gap in research intrigued us and prompted us to investigate whether Taiwanese students can still perform better than German students if students’ mathematical knowledge in solving modelling tasks is differentiated. The results of our study showed that the Taiwanese students had significantly higher mathematical knowledge than did the German students with regard to either conceptual knowledge or procedural knowledge. However, if students of both countries were on the same level of mathematical knowledge, the German students were found to have higher modelling performance compared to the Taiwanese students in solving the same modelling tasks, whether such tasks required non-numerical assumptions only, or both non-numerical and numerical assumptions. This study provides evidence that making assumptions is a strength of German students compared to Taiwanese students. Our findings imply that Western mathematics education may be more effective in improving students’ ability to solve holistic modelling problems.     

Formation of amyloid-like aggregates through the attachment of protein molecules to a Congo red scaffolding framework ordered under the influence of an electric field

This study describes a technique which makes it possible to introduce the amyloid-like order to protein aggregates by using the scaffolding framework built from supramolecular, fibrillar Congo red structures arranged in an electric field. The electric field was used not only to obtain a uniform orientation of the charged dye fibrils, but also to make the fibrils long, compact and rigid due to the delocalization of pi electrons, which favors ring stacking and, as a consequence, results in an increased tendency to self-assemble. The protein molecules (immunoglobulin L chain lambda, ferritin) attached to this easily adsorbing dye framework assume its ordered structure. The complex precipitating as plate-like fragments shows birefringence in polarized light. The parallel organization of fibrils can be observed with an electron microscope. The dye framework may be removed via reduction with sodium dithionite, leaving the aggregated protein molecules in the ordered state, as confirmed by X-ray diffraction studies.      

Stilbene-Like Molecules as Fluorescent Probes Applied for Monitoring of Polymerization Process

2-(p-N,N-dimethylaminostyryl)benzoxazole (OS), 2-(p-N,N-dimethylaminostyryl)-benzothiazole (SS) and 2-(p-N,N-dimethylaminostyryl)naphtiazole (PS) were prepared and their absorption and fluorescence spectra were measured in various solvents at room temperature. On the basis of the solvatochromic behavior the ground state (μ_g) and excited state (μ_e) dipole moments of these pN,N-dimethylaminostyryl derivatives were evaluated. The dipole moments (μ_g and μ_e) were estimated from solvatochromic shifts of absorption and fluorescence spectra as function of the dielectric constant (ɛ) and refractive index (n) of applied solvents. The absorption spectra only slightly are affected by the solvent polarity in contrast to the fluorescence spectra that are highly solvatochromic and display a large Stokes shift. The analysis of the solvatochromic behavior of the fluorescence spectra as function of Δf (ɛ, n) revealed that the emission occurs from a high polarity excited state. The large dipole moment change along with the strongly red-shifted fluorescence, as the solvent polarity is increased, demonstrate the formation of an intramolecular charge transfer state (ICT). Compounds under the study were used as fluorescence probes for monitoring the kinetics of polymerization. The study on the changes in fluorescence intensity and spectroscopic shifts of studied compounds were carried out during thermally initiated polymerization of methyl methacrylate (MMA) and during photoinitiated polymerization of 2-ethyl-2-(hydroxymethyl)propane-1,3-diol triacrylate (TMPTA).     

Klein-Gordon thermal equation for a planck gas

In this paper the quantum hyperbolic equation formulated in our earlier paper [Found. Phys. Lett. 10, 599 (1997)] is applied to the study of the propagation of the initial thermal state of the universe. It is shown that the propagation depends on the barrier height. The Planck wall potential is introduced,V _P = ħ/8t_P = 1.125 10¹⁸ GeV, wheret _P is a Planck time. For the barrier heightV <V _P , the master thermal equation isthe modified telegrapher’sequation, and for barrier heightV >V _P the master equation is theKlein- Gordon equation. The solutions of both type equations for Cauchy boundary conditions are discussed.     

Über das unterschiedliche katalytische Verhalten von stellungs-isomeren organischen Verbindungen

Ohne Zusammenfassung     

Hausdorff Dimension and Hausdorff Measures of Julia Sets of Elliptic Functions

It is proved here that if is an elliptic function and q is the maximal multiplicity ofall poles of f, then the Hausdorff dimension of the Julia setof f is greater than 2 q/(q + 1), and the Hausdorff dimensionof the set of points that escape to infinity is less than orequal to 2q/(q + 1). In particular, the area of this latterset is equal to 0. 2000 Mathematics Subject Classification 37F35(primary); 37F10, 30D30 (secondary).     

Influence of electric field on photoluminescence of lanthanide-doped nematic liquid crystal

Highly resolved luminescence and luminescence excitation spectra of recently synthesized LnL₃bpy complexes, where Ln=Eu³⁺, Tb³⁺, bpy=2,2′- bipyridyne and L=phosphoroazo derivative of β-diketone: CCl₃C(O)NP(O)(OCH₃)₂, in solid state and dissolved in nematic liquid crystal 6CHBT [4-(isothiocyanatophenyl)-1-(trans-4-hexyl)cyclohexane] were measured. The photoluminescence intensity of the complexes dissolved in 6CHBT was found to exhibit a strong dependence on the electric field. The mechanism of the effect and reason of its asymmetry with respect to the sign of electric field are discussed in the paper. Luminescence decay time in various environments and experimental quantum yields of the luminescence of these compounds in CDCl₃ and CHCl₃ solutions were measured.     

Miniaturized free-flow electrophoresis: production,optimization, and application using 3D printing technology

The increasing resolution of three-dimensional (3D) printing offers simplified access to, and development of, microfluidic devices with complex 3D structures. Therefore, this technology is increasingly used for rapid prototyping in laboratories and industry. Microfluidic free flow electrophoresis (μFFE) is a versatile tool to separate and concentrate different samples (such as DNA, proteins, and cells) to different outlets in a time range measured in mere tens of seconds and offers great potential for use in downstream processing, for example. However, the production of μFFE devices is usually rather elaborate. Many designs are based on chemical pretreatment or manual alignment for the setup. Especially for the separation chamber of a μFFE device, this is a crucial step which should be automatized. We have developed a smart 3D design of a μFFE to pave the way for a simpler production. This study presents (1) a robust and reproducible way to build up critical parts of a μFFE device based on high-resolution MultiJet 3D printing; (2) a simplified insertion of commercial polycarbonate membranes to segregate separation and electrode chambers; and (3) integrated, 3D-printed wells that enable a defined sample fractionation (chip-to-world interface). In proof of concept experiments both a mixture of fluorescence dyes and a mixture of amino acids were successfully separated in our 3D-printed μFFE device.     

First N‐Heterocyclic Carbenes Relying on the Triazolone Structural Motif: Syntheses,Modifications and Reactivity

4‐Phenylsemicarbazide and 1,5‐diphenylcarbazide are suitable starting materials for the syntheses of N‐heterocyclic carbene (NHC) compounds with new backbone structures. In the first case, cyclisation and subsequent methylation leads to a cationic precursor whose deprotonation affords the triazolon‐ylidene 2 , which was converted to the corresponding sulfur and selenium adducts and a range of metal complexes. In contrast, cyclisation of diphenylcarbazide affords a neutral betain‐type NHC‐precursor 7 , which is not in equilibrium with its carbene tautomer 7a . Precursor 7 can either be deprotonated to give the anionic NHC 8 or methylated at the N or O atom of the backbone resulting in two isomeric cationic species 16 and 20 . Deprotonation of the latter two provides neutral NHC compounds with a carboxamide or carboximidate backbone, respectively. The ligand properties of the new NHC compounds were evaluated by IR and ⁷⁷Se NMR spectroscopy. Tolman electronic parameter (TEP) values range from 2050 to 2063 cm^?1 with the anionic NHC 8 being the best overall donor.