Students' mental prototypes for functions and graphs

This research study investigates the concept of function developed by students studying English A-level mathematics. It shows that, while students may be able to use functions in their practical mathematics, their grasp of the theoretical nature of the function concept may be tenuous and inconsistent. The hypothesis is that students develop prototypes for the function concept in much the same way as they develop prototypes for concepts in everyday life. The definition of the function concept, though given in the curriculum, is not stressed and proves to be inoperative, with their understanding of the concept reliant on properties of familiar prototype examples: those having regular shaped graphs, such as x2 or sin*, those often encountered (possibly erroneously), such as a circle, those in which y is defined as an explicit formula in x, and so on. Investigations reveal significant misconceptions. For example, threequarters of a sample of students starting a university mathematics course considered that a constant function was not a function in either its graphical or algebraic forms, and threequarters thought that a circle is a function. This reveals a wide gulf between the concepts as perceived to be taught and as actually learned by the students

The Two Roads to "Intrinsic Charm" in B Decays

We describe two complementary ways to show the presence of higher order effects in the 1/m_Q expansion for inclusive B decays that have been dubbed "Intrinsic Charm". Apart from the lessons they can teach us about QCD's nonperturbative dynamics their consideration is relevant for precise extractions of |V_{cb}|: for they complement the estimate of the potential impact of 1/m_Q^4 contributions. We draw semiquantitative conclusions for the expected scale of Weak Annihilation in semileptonic B decays, both for its valence and non-valence components.Comment: 17 pages, 3 figure

Observation of single collisionally cooled trapped ions in a buffer gas

Individual Ba ions are trapped in a gas-filled linear ion trap and observed with a high signal-to-noise ratio by resonance fluorescence. Single-ion storage times of ~5 min (~1 min) are achieved using He (Ar) as a buffer gas at pressures in the range 8e-5 - 4e-3 torr. Trap dynamics in buffer gases are experimentally studied in the simple case of single ions. In particular, the cooling effects of light gases such as He and Ar and the destabilizing properties of heavier gases such as Xe are studied. A simple model is offered to explain the observed phenomenology.Comment: 5 pages, 4 figures, accepted for publication in Phys. Rev. A. Minor text and figure change

Minkowski Tensors of Anisotropic Spatial Structure

This article describes the theoretical foundation of and explicit algorithms for a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, the so-called Minkowski tensors. Minkowski tensors are generalisations of the well-known scalar Minkowski functionals and are explicitly sensitive to anisotropic aspects of morphology, relevant for example for elastic moduli or permeability of microstructured materials. Here we derive explicit linear-time algorithms to compute these tensorial measures for three-dimensional shapes. These apply to representations of any object that can be represented by a triangulation of its bounding surface; their application is illustrated for the polyhedral Voronoi cellular complexes of jammed sphere configurations, and for triangulations of a biopolymer fibre network obtained by confocal microscopy. The article further bridges the substantial notational and conceptual gap between the different but equivalent approaches to scalar or tensorial Minkowski functionals in mathematics and in physics, hence making the mathematical measure theoretic method more readily accessible for future application in the physical sciences

Peculiarities of the function of cardiomyocytes in patients with ischemic heart disease associated with diabetes mellitus type 2

The functional activity of myocardium in patients with type 2 diabetes mellitus(T2DM) and coronary heart disease (CAD) was studied. The study included patients with CAD with T2DM as representatives of the main group, the comparison group consisted of patients with univariant course of ischemic heart disease without violation of carbohydrate metabolism. Contractile activity of the myocardium was evaluated by the inotroic reaction of isolated trabeculae of patients according to the Protocol tests "Post-rest" and "Ekstrasistoliei test". As a result, it was found that rhythm-inotropic myocardial response in patients with comorbid pathology persists to a greater extent than in the one-dimensional flow of CAD

Local Anisotropy of Fluids using Minkowski Tensors

Statistics of the free volume available to individual particles have previously been studied for simple and complex fluids, granular matter, amorphous solids, and structural glasses. Minkowski tensors provide a set of shape measures that are based on strong mathematical theorems and easily computed for polygonal and polyhedral bodies such as free volume cells (Voronoi cells). They characterize the local structure beyond the two-point correlation function and are suitable to define indices $0\leq \beta_\nu^{a,b}\leq 1$ of local anisotropy. Here, we analyze the statistics of Minkowski tensors for configurations of simple liquid models, including the ideal gas (Poisson point process), the hard disks and hard spheres ensemble, and the Lennard-Jones fluid. We show that Minkowski tensors provide a robust characterization of local anisotropy, which ranges from $\beta_\nu^{a,b}\approx 0.3$ for vapor phases to $\beta_\nu^{a,b}\to 1$ for ordered solids. We find that for fluids, local anisotropy decreases monotonously with increasing free volume and randomness of particle positions. Furthermore, the local anisotropy indices $\beta_\nu^{a,b}$ are sensitive to structural transitions in these simple fluids, as has been previously shown in granular systems for the transition from loose to jammed bead packs

Mobility of thorium ions in liquid xenon

We present a measurement of the $^{226}$Th ion mobility in LXe at 163.0 K and 0.9 bar. The result obtained, 0.240$\pm$0.011 (stat) $\pm$0.011 (syst) cm$^{2}$/(kV-s), is compared with a popular model of ion transport.Comment: 6.5 pages,