Exploring mathematical connections of pre-university students through tasks involving rates of change

This paper reports the results of a research exploring the mathematical connections of pre-university students while they solving tasks which involving rates of change. We assume mathematical connections as a cognitive process through which a person finds real relationships between two or more ideas, concepts, definitions, theorems, procedures, representations or meanings or with other disciplines or the real-world. Four tasks were proposed to the 33 pre-university students that participated in this research; the central concept of the first task is the slope, the last three tasks contain concepts like velocity, speed and acceleration. Task-based interviews were conducted to collect data and later analysed with thematic analysis. Results showed most of the students made mathematical connections of the procedural type, the mathematical connections of the common features type are made in smaller quantities and the mathematical connection of the generalization type is scarcely made. Furthermore, students considered slope as a concept disconnected from velocity, speed and acceleration.     

Characterization of Commercial Amylases for the Removal of Filter Cake on Petroleum Wells

Drilling fluid has many functions, such as carry cuttings from the hole permitting their separation at the surface, cool and clean the bit, reduce friction between the drill pipe and wellbore, maintain the stability of the wellbore, and prevent the inflow of fluids from the wellbore and form a thin, low-permeable filter cake. Filter cake removal is an important step concerning both production and injection in wells, mainly concerning horizontal completion. The drilling fluids are typically comprised of starch, the most important component of the filter cake. A common approach to remove this filter cake is the use of acid solutions. However, these are non-specific reactants. A possible alternative is the use of enzymatic preparations, like amylases, that are able to hydrolyze starch. Wells usually operate in drastic conditions for enzymatic preparations, such as high temperature, high salt concentration, and high pressure. Thus, the main objective of this work was to characterize four enzymatic preparations for filter cake removal under open hole conditions. The results showed that high salt concentrations (204,000 ppm NaCl) in completion fluid decreased amylolytic activity. All enzymatic preparations were able to catalyze starch hydrolysis at all temperatures tested (30, 65, 80, and 95 °C). An increase of amylolytic activity was observed with the increase of pressure (100, 500 and 1,000 psi) for one commercial amylase.     

Relations on the period mapping giving extensions of mixed hodge structures on compact Riemann surfaces

We consider a period map from Teichmüller space to , which is a real vector bundle over the Siegel upper half space. This map lifts the Torelli map. We study the action of the mapping class group on this period map. We show that the period map from Teichmüller space modulo the Johnson kernel is generically injective. We derive relations that the quadratic periods must satisfy. These identities are generalizations of the symmetry of the Riemann period matrix. Using these higher bilinear relations, we show that the period map factors through a translation of the subbundle and is completely determined by the purely holomorphic quadratic periods. We apply this result to strengthen some theorems in the literature. One application is that the quadratic periods, along with the abelian periods, determine a generic marked compact Riemann surface up to an element of the kernel of Johnson's homomorphism. Another application is that we compute the cocycle that exhibits the mapping class group modulo the Johnson kernel as an extension of the group SP _g () by the group .     

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.     

Slopes of integral lattices

We use the dyadic trace to define the concept of slope for integral lattices. We present an introduction to the theory of the slope invariant. The main theorem states that a Siegel modular cusp form f of slope strictly less than the slope of an integral lattice with Gram matrix s satisfies f(sτ)=0 for all τ in the upper half plane. We compute the dyadic trace and the slope of each root lattice and we give applications to Siegel modular cusp forms.     

Stereoselective intramolecular nicholas reaction using epoxides as nucleophiles

[reaction: see text] The intramolecular nucleophilic attack of the epoxides on the exo-Co(2)(CO)(6)-propargylic cations provided cyclic ethers in good yields. The use of substrates with stereochemically defined oxiranes provided polysubstituted tetrahydropyrans and oxepanes with a high degree of stereocontrol. The cyclization is sensitive to the nature of the protecting group used at the primary alcohol, the use of tert-butyl carbonates being highly effective in terms of regioselectivity and yields.