Conceptualizations of slope in Mexican intended curriculum

Slope is a fundamental mathematics concept in middle and high school that transcends to the university level. An understanding of slope is needed at the university level since slope plays an important role in understanding problems involving variation and change. In this study Mexican curricula documents were examined to determine which conceptualizations of slope are addressed in the intended mathematics curriculum. To explain the results, we use conceptualizations of slope identified in previous research. Our findings reveal that, to a certain extent, the conceptualizations proposed in the Mexican intended mathematics curriculum differ slightly in terms of the emphasis and timing of instruction from what others have identified in the U.S., with slope as a geometric ratio receiving less emphasis in the Mexican curriculum. There was also noted discontinuity within the Mexican curriculum in introducing slope in grade 9 and subsequently introducing of linear functions in grade 10 without explicit mention of slope. Suggestions are made for future studies, both to consider the conceptualizations of slope promoted in the Mexican textbooks and the impact they have in classroom instruction and student learning of slope.     

The 48 bp centromeric repeat is a functionally conserved motif in great apes and man showing protein-binding properties

The centromere-kinetochore complex is a chromosomal assembly site including repeat motifs and protein binding properties thus mediating chromosome motility and mitotic regulation. Next to the alpha-satellite DNA family as well as human satellite III DNA, contribution of other repetitive sequences has to be strongly considered in centromere function. Here, we report the identification of centromeric 48 bp motifs, isolated from chimpanzee and orang-utan using an orthologous human DNA probe. Applying Southern hybridization we show that these sequences are restricted to hominoid species. Diminishing hybrid formation in gibbons suggested that the 48 bp repeat originated approximately 25-20 million years ago. Consistently, both chimpanzee as well as human repeat probes failed to generate any hybridization signal with the monkey species Cercopithecus aethiops and Aotes trivirgatus. Sequence deviations from the consensus of human repeat monomers of 6% and 10.4% in chimpanzee and orang-utan, respectively, were found within a 16 bp region of the 48 bp repeat units. Gel mobility shift assays using chimpanzee repeat dimers as probes revealed peptide-binding properties with human and chimpanzee nuclear extracts. Species-specific DNA-protein complexes remained unaffected by competition studies and indicated the presence of at least one novel interacting protein consisting of two subunits with 90 and 95 kDa. Our data suggest that the 48 bp repeat, next to alpha-satellite DNA, provides essential sequence information for specific DNA-protein interaction and they imply phylogenetic conservation of these binding properties in primates. The complex is likely involved in the proper formation and/or function of mammalian centromeres.     

Frequency-locking phenomena of propagating wave fronts in reaction-diffusion systems

We observe N:(N-1)(N>/=2) frequency-locking phenomena of propagating wave fronts when increasing the light intensity in a spatially extended system. The experiments were carried out using the light-sensitive form of the Belousov-Zhabotinsky reaction with Ru(bpy)(2+)3 as a catalyst. By constructing a mapping function, the characteristic devil's staircase can be reproduced when plotting wave period versus light intensity, in agreement with the experimental data.     

α-SUBSTITUIERTE PHOSPHONATE 52.1 SYNTHESE UND REAKTIONEN VON 1- ACETOXY-1-METHYLTHIOMETHAN PHOSPHORYLVERBINDUNGEN

Abstract

The 1-acetoxy-1-methylthiomethanephosphoryl compounds (4) are prepared from methylthiomethanephosphoryl derivatives (1) by electrolysis in 0.6 molar sodium acetate/acetic acid solution. The reaction of 1-acetoxy compounds (4) with halogen carriers gives the 1-halogen-1-methylthiomethane-phosphoryl derivatives 5, 7 and 8. The reaction of 4a under PTC-conditions results in cleavage of the P-C-bond.

Die 1-Acetoxy-1-methylthiomethanphosphoryl-Verbindungen (4) wurden aus Methylthiomethanphos-phorylderivaten (1) durch Elektrolyse in 0.6 molarer Na-acetat/Essigsäure-Lösung dargestellt. Die Reaktion der 1-Acetoxyverbindungen mit Halogenüberträgern führt zu den 1-Halogen-1-methyl-thiomethanphosphorylderivaten 5, 7 und 8. Bei Reaktion von 4a unter PTC-Bedingungen beobachtet man eine Spaltung der P-C-Bindung.     

Methyl methacrylate polymerization at samarium(II)-grafted MCM-41

Sm(II)-modified periodic mesoporous silica (PMS), Sm[N(SiHMe₂)₂]₂(THF)_x@MCM-41, was used for the synthesis of Sm(II) alkyl, alkoxide, and indenyl surface species via secondary ligand exchange. The performance of the novel Sm(II)-based organometallic–inorganic hybrid materials as initiators for the graft polymerization of methyl methacrylate (MMA) is reported. All of the Sm(II) hybrid materials including the new PMMA–PMS composites were characterized via N₂ physisorption, elemental analysis, FTIR spectroscopy, and scanning electron microscopy (SEM). The organic–inorganic composites revealed complete pore blockage as well as enrichment and strong adhesion of the polymer at the exterior of the porous silica material.