Appropriate problems for learning and for performing—an issue for teacher training

Selecting, modifying or creating appropriate problems for mathematics class has become an activity of increaing importance in the professional development of German mathematics teachers. But rather than asking in general: “What is a good problem?” there should be a stronger emphasis on considering the specific goal of a problem, e.g.: “What are the ingredients that make a problem appropriate for initiating a learning process” or “What are the characteristics that make a problem appropriate for its use in a central test?” We propose a guiding scheme for teachers that turns out to be especially helpful, since the newly introduced orientation on outcome standards a) leads to a critical predominance of test items and b) expects teachers to design adequate problems for specific learning processes (e.g. problem solving, reasoning and modelling activities).     

Singlet versus triplet dynamics of β-carotene studied by quantum control spectroscopy

Biomolecules very often present complex energy deactivation networks with overlapping electronic absorption bands, making their study a difficult task. This can be especially true in transient absorption spectroscopy when signals from bleach, excited state absorption and stimulated emission contribute to the signal. However, quantum control spectroscopy can be used to discriminate specific electronic states of interest by applying specifically designed laser pulses. Recently, we have shown the control of energy flow in bacterial light-harvesting using shaped pump pulses in the visible and the selective population of pathways in carotenoids using an additional depletion pulse in the transient absorption technique. Here, we apply a closed-loop optimization approach to β-carotene using a spatial light modulator to decipher the energy flow network after a multiphoton excitation with a shaped ultrashort pulse in the near-IR. After excitation, two overlapping bands were detected and identified as the S₁ state and the first triplet state T₁. Using the transient absorption signal at a specific probe delay as feedback, the triplet signal could be optimized over the singlet contribution.     

Parametric multiple sequence alignment and phylogeny construction

Bounds are given on the size of the parameter-space decomposition induced by multiple sequence alignment problems where phylogenetic information may be given or inferred. It is shown that many of the usual formulations of these problems fall within the same integer parametric framework, implying that the number of distinct optima obtained as the parameters are varied across their ranges is polynomially bounded in the length and number of sequences.     

Anomalous capacitance of quantum well double-barrier diodes

The S-parameters of several different quantum well double barrier diodes have been measured. A technique has been developed for measuring whisker contacted diodes with and HP 8510B automatic network analyzer. Special coaxial mounts using K-connectors were designed to enable measurements up to 20 GHz. The voltage-dependent conductance and capacitance were derived from the measured reflection coefficient of each device. The C/V characteristics were observed to exhibit an anomalous increase at voltages corresponding the the negative differential resistance region (NDR). These are the first reported S-parameter measurements in the negative differential resistance region of quantum well double barrier diodes. A theory is presented that explains, in part, the observed results.     

Comparing adult mathematical literacy with PISA students: results of a pilot study

In Germany, very little empirical data about the mathematical competence of adults is available. The aim of this study is to test the level of mathematical competence in an adult sample. For this purpose, a mathematics test was constructed using the PISA mathematics framework as a guideline. The test consisted of fourteen public items from the mathematics test in PISA 2000. The study was implemented by carrying out house visits (Germany). The sample was comprised of 64 adults (90% women, age: 41 years). The test results were scaled in the metric of PISA 2000. Compared with the average German student competencies in PISA 2000, the average competency in the adult sample was on the same level as the fifteen-year-old comprehensive secondary school student (at a German Gymnasium). Further analysis shows that the mathematics competency level in the adult sample is positively connected to the individual vocational education degree.     

The Random Average Process and Random Walk in a Space-Time Random Environment in One Dimension

We study space-time fluctuations around a characteristic line for a one-dimensional interacting system known as the random average process. The state of this system is a real-valued function on the integers. New values of the function are created by averaging previous values with random weights. The fluctuations analyzed occur on the scale n ^1/4, where n is the ratio of macroscopic and microscopic scales in the system. The limits of the fluctuations are described by a family of Gaussian processes. In cases of known product-form invariant distributions, this limit is a two-parameter process whose time marginals are fractional Brownian motions with Hurst parameter 1/4. Along the way we study the limits of quenched mean processes for a random walk in a space-time random environment. These limits also happen at scale n ^1/4 and are described by certain Gaussian processes that we identify. In particular, when we look at a backward quenched mean process, the limit process is the solution of a stochastic heat equation.     

What do multistep methods approximate?

Summary Standard analysis of multistep methods for ODE's assumes the application of an initialization routine that generates the starting points. Here ak-step method is considered directly as a mappingR ^kn R ⁿ . It is shown to approximate a mapping which is expressible directly in terms of the flow of the vector field. Some useful properties of that mapping are shown and for strictly stable methods these are applied to the question of invariant circles near a hyperbolic periodic solution.     

Solution-phase, triangular ag nanotriangles fabricated by nanosphere lithography

A novel method to produce solution-phase triangular silver nanoparticles is presented. Ag nanoparticles are prepared by nanosphere lithography and are subsequently released into solution. The resulting nanoparticles are asymmetrically functionalized to produce either single isolated nanoparticles or dimer pairs. The structural and optical properties of Ag nanoparticles have been characterized. Mie theory and the Discrete Dipole Approximation method (DDA) have been used to model and interpret the optical properties of the released Ag nanoparticles.     

Transparent conducting oxides: texture and microstructure effects on charge carrier mobility in MOCVD-derived CdO thin films grown with a thermally stable, low-melting precursor

A series of low-melting, thermally stable cadmium metal-organic chemical vapor deposition (MOCVD) precursors have been synthesized, structurally and spectroscopically characterized, and implemented in growth of highly conductive and transparent CdO thin films. One member of the series, bis(1,1,1,5,5,5-hexafluoro-2,4-pentanedionato)(N,N-diethyl-N',N'-dimethyl-ethylenediamine)cadmium(II), Cd(hfa)(2)()(N,N-DE-N',N'-DMEDA), represents a particularly significant improvement over previously available Cd precursors, owing to the low melting point and robust thermal stability. High-quality CdO films were grown by MOCVD on glass and single-crystal MgO(100) between 300 and 412 degrees C. Film growth parameters and substrate surface have large effects on microstructure and electron carrier transport properties. Enhanced mobilities observed for highly biaxially textured films grown on MgO(100) vs glass are attributed, on the basis of DC charge transport and microstructure analysis, to a reduction in neutral impurity scattering and/or to a more densely packed grain microstructure. Although single-grained films grown on MgO(100) exhibit greater mobilities than analogues with discrete approximately 100 nm grains and similar texture, this effect is attributed, on the basis of charge transport and Hall effect measurements as well as optical reflectivity analysis, to differences in carrier concentration rather than to reduced grain boundary scattering. Unprecedented conductivities and mobilities as high as 11,000 S/cm and 307 cm(2)/V.s, respectively, are obtained for epitaxial single-grained films (X-ray diffraction parameters: fwhm(omega) = 0.30 degrees, fwhm(phi) = 0.27 degrees ) grown in situ on MgO(100) at a relatively low temperature (400 degrees C).