A probabilistic description of footbridges vibration serviceability

Vibration serviceability of pedestrian bridges is considered. Imperfections in the human walking force are described as changes in walking factors. Probability distributions of walking frequencies, step length, and amplitude of walking force are taken into account. The imperfections can influence the level of footbridge vibration response. The Monte Carlo method is applied. The generated realizations of the loads formulate a set of initial data for numerical calculations. The probability distribution of maximal vertical acceleration is obtained. The results are presented as a probability that the required level of vibration will not be exceeded. A reliability describing the footbridges serviceability is also estimated. The probabilistic based approach can be used for future optimalizations of footbridge design codes due to the dynamic force loads. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Measurement of particle and antiparticle elastic scattering on protons between 6 and 14 GeV

Differential cross sections in the t-range between 0.02 and 1.5 GeV² have been measured for the elastic scattering of particles and antiparticles on protons at 6.4, 10.4 and 14 GeV for K^±p and 10.4 GeV for π^±p and p^±p. Large statistics have been achieved and systematic uncertainties have been minimized. The relative systematic uncertainty between particle and antiparticle data is less than 0.5%. Accurate measurements of the position of the first crossover between particle and antiparticle differential cross sections have been performed. As the energy increases from 6.4 to 14 GeV the K^±p crossover moves to smaller values by 0.010 GeV² with a statistical error of 0.006 GeV² and a systematic uncertainty of 0.005 GeV². The crossover positions at 10.4 GeV for π^±, K^± and p^± scale approximately with the interaction radii.     

A note on jets of entire curves in semi-abelian varieties

We prove a product decomposition of the Zariski closure of every jet lift of an entire curve f:CA into a semi-abelian variety A, provided that f is of finite order. On the other hand, by giving an example of f into a three dimensional abelian variety we show that this product decomposition does not hold in general; there was a gap in the proofs of [2], Proposition 1.8 (ii) and of [6], Theorem 2.2. Mathematics Subject Classifications (2000):32H30, 14K20.     

Channeling‐enhanced EDX for polarity resolved crystal orientation determination

Using channeling‐enhanced energy‐dispersive X‐ray spectroscopy (EDX), we demonstrate polarity sensitive orientation determination of a non‐centrosymmetric crystal in the scanning electron microscope. The authors observe a characteristic asymmetry in the channeling‐enhanced, angle‐dependent EDX data of a GaAs sample, which is in good agreement to simulations using the dynamical theory of diffraction for the incident electron beam. This allows us to assign the orientation of the GaAs crystal according to the non‐centrosymmetric point group. The method shown here overcomes the limitation of a reduced point‐group sensitivity of electron backscatter diffraction patterns and electron channeling patterns for crystalline phases that contain atoms of approximately equal electron scattering cross sections.     

The impact of the computer on the teaching of analysis

The computer creates new opportunities for analysis instruction. Some traditional motivations for treating conceptually exacting analysis in school can, however, no longer be maintained without further discussion, for instance: calculations such as finding extreme values or areas can be easily programmed without analysis, and practical applications, as in physics or technology, use discrete methods in computer programs.

This results in a crisis: the legitimacy of traditional analysis in school is challenged. This challenge is analysed, consequences for goals and methods of analysis teaching at schools are named, and some initial examples are given, as to how this could be realized with the help of the computer.     

Site-specific recoil diffraction of backscattered electrons in crystals

A novel diffraction effect in high-energy electron backscattering is demonstrated: the formation of element-specific diffraction patterns via nuclear recoil. For sapphire (Al(2)O(3)), the difference in recoil energy allows us to determine if an electron scattered from aluminum or from oxygen. The angular electron distribution obtained in such measurements is a strong function of the recoiling lattice site. These element-specific recoil diffraction features are explained using the dynamical theory of electron diffraction. Our observations open up new possibilities for local, element-resolved crystallographic analysis using quasielastically backscattered electrons in scanning electron microscopy.     

Computer use in mathematics education – present situation,intentions, and problems in the Federal Republic of Germany†

Computers, and computer‐related thinking structures, are only gradually influencing mathematics education. On the one hand, there is a discrepancy between involved teachers who already have changed their own classroom teaching to a great extent, and a majority of mathematics teachers who have not yet taken notice of the computer for teaching purposes. On the other hand, knowledge of the computer and of algorithms is frequently merely added to the mathematical subject matter. As opposed to that, the authors argue that it is necessary to genuinely integrate such subject matter, and to include general topics such as social impact and changed attitudes toward application. With regard to implementation, they develop concrete ideas which are aligned in a differentiated manner to the specific situation and the opportunities offered in the Federal Republic of Germany. The rationale for that is that only such reference to a specific situation will provide an opportunity for readers abroad to usefully apply approaches and ideas to the situation given in their own cultural environment.

An abbreviated version of this paper for cursory reading or other purposes has been marked by bold lines on the margin.

     

Gender differences in the mathematics achievements of German primary school students: results from a German large-scale study

In Germany, national standards for mathematics for the end of primary school were established in 2004. In the present study, data were collected to evaluate these standards, and were used to compare the mathematical skills of girls and boys. Many studies have shown that gender differences are strongest at the highest levels of education. The findings from primary school are less consistent. Thus, in our study we analyzed achievement differences in a sample of approximately 10,000 third and fourth graders, representative of the German elementary school population. Gender-specific competencies were compared in the different content domains, both for the general mathematical competence, and for the cognitive levels of the tasks. Overall, boys outperformed girls, but substantial variation was found between the content domains and general mathematical achievement. Differences were higher in grade three than in grade four. The proportion of boys in the classroom did not appear to affect the individual level of performance. Analysis of the items on which boys or girls clearly outperformed each other reproduced a pattern of specific item characteristics predicting gender bias consistent with those reported in previous studies in other countries.