Functions: a modelling tool in mathematics and science

It is difficult for the students to transfer concepts, ideas and procedures learned in mathematics to a new and unanticipated situation in science. An alternative to this traditional transfer method stresses the importance of modelling activities in an interdisciplinary context between mathematics and science. In the paper we introduce a modelling approach to the concept of function in upper secondary school is introduced. We discuss pedagogical and didactical issues concerning the interplay between mathematics and science. The discussion is crystallized into a didactical model for interdisciplinary instruction in mathematics and science. The model is considered as an iterative movement with two phases: (1) the horizontal linking of the subjects: Situations from science are embedded in contexts which are mathematized by the students, (2) the vertical structuring in the subjects: The conceptual anchoring of the students' constructs from the horizontal linking in the systematic and framework of mathematics and science respectively.     

Synthesis and Inclusion Properties of the Host Compound 1,3-Dihydro-1,1,3,3-tetraphenylisobenzofuran. X-Ray Crystal Structures of the Free Host and of an Inclusion Compound with 1,4-Dioxane

A novel host molecule, 1, suitable for crystalline lattice-type inclusion, has been synthesized, and its cocrystal formation ability has been investigated. Host 1 proved to be of potential use for organic solvent separation and retrieval, and a promising auxiliary for solidification of certain odorous substances. The crystal structures of the solvent-free host 1, and its complex with 1,4-dioxane (1 : 1), have been determined by single crystal X-ray diffraction. The structure of 1 (guest-free) is triclinic, P , with a = 9.452(2), b = 10.359(3), c = 13.116(3) Å, = 101.80(2), = 106.53(1) and = 104.32(1)°. The spacious, propeller-like molecules are held together by weak van der Waals' forces. The dioxane inclusion compound is monoclinic, P21/a, with a = 15.050(1), b = 8.641(1) and c = 20.658(1) Å, and = 94.56(1)°, and contains two crystallographically independent guest molecules, both located around symmetry centres. The molecular packing seems to be governed by C—H···O type bonds (C···O = 3.31 and 3.48 Å) from the host to the dioxane oxygens.     

Massenspektrometrische Untersuchung aromatischer Halogenide der Summenformel C9H11Cl: Mechanismus der Äthylen-Abspaltung aus dem Ion [M ? Cl]+˙

By investigation of isomeric ²H- and ¹³C-labelled C₉H₁₁ Cl-compounds it has been shown that the ion [M ? Cl]⁺ is transformed mainly to the ion [C₇H₇]⁺ via C₂H₄-elimination from alkyl-substituted tropylium-ions. Phenyl-cyclopropane-cations play only a small part, if at all, in this fragmentation process.     

Zusammenhängende Untergruppen von pro-Lieschen Gruppen

In this paper we consider the lattice G of all closed connected subgroups of pro-Lie groups G, which seems to have in some sense a more geometric nature than the full lattice of all closed subgroups. We determine those pro-Lie groups whose lattice shares one of the elementary geometric lattice properties, such as the existence of complements and relative complements, semi-modularity and its dual, the chain condition, self-duality and related ones. Apart from these results dealing with subgroup lattices we also get two structure theorems, one saying that maximal closed analytic subgroups of Lie groups actually are maximal among all analytic subgroups, the other that each connected abelian pro-Lie group is a direct product of a compact group with copies of the reals.     

Design,synthesis, and evaluation of 6-carboxyalkyl and 6-phosphonoxyalkyl derivatives of 7-oxo-8-ribitylaminolumazines as inhibitors of riboflavin synthase and lumazine synthase

A series of 6-carboxyalkyl and 6-phosphonoxyalkyl derivatives of 7-oxo-8-D-ribityllumazine were synthesized as inhibitors of both Escherichia coli riboflavin synthase and Bacillus subtilis lumazine synthase. The compounds were designed to bind to both the ribitylpurine binding site and the phosphate binding site of lumazine synthase. In the carboxyalkyl series, maximum activity against both enzymes was observed with the 3'-carboxypropyl compound 22. Lengthening or shortening the chain linking the carboxyl group to the lumazine by one carbon resulted in decreased activity. In the phosphonoxyalkyl series, the 3'-phosphonoxypropyl compound 33 was more potent than the 4'-phosphonoxybutyl derivative 39 against lumazine synthase, but it was less potent against riboflavin synthase. Molecular modeling suggested that the terminal carboxyl group of 6-(3'-carboxypropyl)-7-oxo-8-D-ribityllumazine (22) may bind to the side chains of Arg127 and Lys135 of the enzyme. A hypothetical molecular model was also constructed for the binding of 6-(2'-carboxyethyl)-7-oxolumazine (15) in the active site of E. coli riboflavin synthase, which demonstrated that the active site could readily accommodate two molecules of the inhibitor.     

Zur direkten ma?analytischen Bestimmung von Carbamaten als sehr schwache S?uren

Zusammenfassung Eine direkte maßanalytische Methode zur Bestimmung diverser Carbamate wird beschrieben. Die potentiometrische Titration mit käuflicher Tetra-n-butylammoniumhydroxid-Lösung, verdünnt mit Propanol-(2), ist bequem durchzuführen, und die erhaltenen Titrationskurven gestatten eine korrekte Auswertung.

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Direct volumetric determination of carbamates as very weak acids

Summary A volumetric procedure for the determination of some carbamates is described. The potentiometric titration with commercial tetra-n-butylammonium hydroxide solution diluted with propanol-(2) is convenient and the obtained titration curves permit a correct calculation.

     

Thiol- and disulfide-modified oligonucleotide monolayer structures on polycrystalline and single-crystal Au(111) surfaces

We provide a comprehensive study of single- (ss) and double-strand (ds) oligonucleotides with either 25 or 10 bases or base pairs (bp) immobilized on polycrystalline and single-crystal Au(111) surfaces. The study is based on X-ray photoelectron spectroscopy, cyclic and differential pulse voltammetry, interfacial capacitance data, and electrochemical scanning tunnelling microscopy (in situ STM). The sequences used were the 25-bp sequence from the BRCA1 gene (25-mer), while the 10-bp oligonucleotides contained solely linear adenine and thymine sequences. The oligonucleotides were modified by the dimethoxytrityl group (DMT) via a disulfide group [DMT-S-S-ss25-mer and DMT-S-S-ds(AT)₁₀], a pure disulfide group (A₁₀-S-S-T₁₀), or a thiol group [HS-ss25-mer and HS-ds-(AT)₁₀], all via a hexamethylene linker. The overall pattern suggests strategies for controlled adsorption of DNA-based molecules and recognition of complementary strands or other molecules.