Attention to meaning by algebra teachers

Non-attendance to meaning by students is a prevalent phenomenon in school mathematics. Our goal is to investigate features of instruction that might account for this phenomenon. Drawing on a case study of two high school algebra teachers, we cite episodes from the classroom to illustrate particular teaching actions that de-emphasize meaning. We categorize these actions as pertaining to (a) purpose of new concepts, (b) distinctions in mathematics, (c) mathematical terminology, and (d) mathematical symbols. The specificity of the actions that we identify allows us to suggest several conjectures as to the impact of the teaching practices observed on student learning: that students will develop the belief that mathematics involves executing standard procedures much more than meaning and reasoning, that students will come to see mathematical definitions and results as coincidental or arbitrary, and that students’ treatment of symbols will be largely non-referential.     

Classical Invariants for Global Actions and Groupoid Atlases

A global action is the algebraic analogue of a topological manifold. This construction was introduced in first place by A. Bak as a combinatorial approach to K-Theory and the concept was later generalized by Bak, Brown, Minian and Porter to the notion of groupoid atlas. In this paper we define and investigate homotopy invariants of global actions and groupoid atlases, such as the strong fundamental groupoid, the weak and strong nerves, classifying spaces and homology groups. We relate all these new invariants to classical constructions in topological spaces, simplicial complexes and simplicial sets. This way we obtain new combinatorial formulations of classical and non classical results in terms of groupoid atlases.      

Stiefel-Whitney classes and toral actions

Certain Stiefel-Whitney classes of manifolds with smooth, effective toral actions are shown to be computable in terms of Poincare duals of fixed point sets of isotropy subgroups. As an application the toral degrees of symmetry of certain Dold manifolds are determined.     

Topological,affine and isometric actions on flat riemannian manifolds II

Explicit examples of finite subgroups of the group of homotopy classes of self-homotopy equivalences of some flat Riemannian manifolds which cannot be lifted to effective actions are given. It is also shown that no finite subgroups of the kernel of π₀(Homeo(M))→Out π₁(M) can be lifted back to Homeo(M), for a large class of flat manifolds M. Some results of an earlier paper by the authors are refined and related to recent work of R. Schoen and S.T. Yau.     

On Completely Integrable Systems with Local Torus Actions

This paper concerns with symplectic topology of compact completely integrable Hamiltonian systems with only stable nondegenerate elliptic singularities. We describe all systems whose universal coverings admit actian-angle coordinates and, in particular, prove that some finite cover of a base space is diffeomorphic to a product of a convex polytope and a solvmanifold. We also construct an obstruction, vanishing of which guarantees splitting of some finite cover of a phase space as a toric variety and a torus fibering over a solvmanifold.     

The Uniqueness of the Actions of Certain Branch Groups on Rooted Trees

It is proved that in many cases of interest the actions of groups on rooted trees can be recovered from the structure of the groups. The results apply to most of the groups introduced by the first author and to the Gupta–Sidki groups; they are proved in the wider context of branch groups satisfying two natural conditions.     

Systematic Construction of <Emphasis Type="Italic">q</Emphasis>-Analogs of <Emphasis Type="Italic">t</Emphasis>−(<Emphasis Type="Italic">v</Emphasis>,<Emphasis Type="Italic">k</Emphasis>,λ)-Designs

In the present paper we consider a q-analog of t–(v,k,)-designs. It is canonic since it arises by replacing sets by vector spaces over GF(q), and their orders by dimensions. These generalizations were introduced by Thomas [Geom.Dedicata vol. 63, pp. 247–253 (1996)] they are called t –(v,k,;q)- designs. A few of such q-analogs are known today, they were constructed using sophisticated geometric arguments and case-by-case methods. It is our aim now to present a general method that allows systematically to construct such designs, and to give complete catalogs (for small parameters, of course) using an implemented software package. &nbsp; In order to attack the (highly complex) construction, we prepare them for an enormous data reduction by embedding their definition into the theory of group actions on posets, so that we can derive and use a generalization of the Kramer-Mesner matrix for their definition, together with an improved version of the LLL-algorithm. By doing so we generalize the methods developed in a research project on t –(v,k,)-designs on sets, obtaining this way new results on the existence of t–(v,k,;q)-designs on spaces for further quintuples (t,v,k,;q) of parameters. We present several 2–(6,3,;2)-designs, 2–(7,3,;2)-designs and, as far as we know, the very first 3-designs over GF(q).classification 05B05     

The interaction of an atmospheric pressure plasma jet using argon or argon plus hydrogen peroxide vapour addition with bacillus subtilis

This paper reports that an atmospheric pressure dielectric barrier discharge plasma jet, which uses argon or argon + hydrogen peroxide vapour as the working gas, is designed to sterilize the bacillus subtilis. Compared with the pure argon plasma, the bacterial inactivation efficacy has a significant improvement when hydrogen peroxide vapour is added into the plasma jet. In order to determine which factors play the main role in inactivation, several methods are used, such as determination of optical emission spectra, high temperature dry air treatment, protein leakage quantification, and scanning electron microscope. These results indicate that the possible inactivation mechanisms are the synergistic actions of chemically active species and charged species.     

Topological obstructions to certain Lie group actions on manifolds

Given a smooth closed -manifold , this article studies the extent to which certain numbers of the form are determined by the fixed-point set , where classifies the universal cover of , , is a polynomial in the Pontrjagin classes of , and is in the subalgebra of generated by . When , various vanishing theorems follow, giving obstructions to certain fixed-point-free actions. For example, if a fixed-point-free -action extends to an action by some semisimple compact Lie group , then . Similar vanishing results are obtained for spin manifolds admitting certain -actions.

     

Topology of generalized complex quotients

Consider the Hamiltonian action of a torus on a compact twisted generalized complex manifold M$M$. We first observe that Kirwan injectivity and surjectivity hold for ordinary equivariant cohomology in this setting. Then we prove that these two results hold for the twisted equivariant cohomology as well.