Two questions in diophantine approximation

The first question is about a possible variation on Dirichlet's approximation theorem for linear forms x+y+z, wherex,y are restricted topositive integers. The second question, which turns out to be related to the first, is about approximation to elements in a power series fieldk((t ^–1)) by solutions of first order linear differential equationsx+y+z=0, wherex,y,z are polynomials int. Dedicated to Prof. Dr. E. Hlawka on the occasion of his 60th birthday     

Mathematics Assessment: Practices and Reporting Methods

The curriculum, teaching, and assessment Standards of the National Council of Teachers of Mathematics advocate the use of various assessment techniques in mathematics, K-12. Practitioners from 35 school districts in two regions of a midwestern state completed a questionnaire and reported information about their assessment practices, reporting methods, and other issues that affect change in mathematics. The results of the survey suggest that current reporting practices are limiting the use of alternative classroom assessment practices. Delays in the use of alternative mathematics assessment practice can probably be expected until the reporting systems used in school districts become consistent with the assessment systems and teachers participate in ongoing professional development programs to learn more about alternative assessment practices.     

Spectral integral representations of volume scattering in sediments in layered waveguides

In situ measurements of scattering strength are often obtained by analyzing the early-time, high-angle reverberation from bottom and subbottom features. In order to provide insight into the mechanisms which cause bottom reverberation, and to their distinguishing characteristics, it is necessary to have a capability for modeling both the rough surface and the volume scattering mechanisms. For high-angle, early-time backscatter, the most appropriate approach is to use a spectral integral representation, which naturally includes the continuous spectrum important for this angular regime. A rough surface scattering theory developed earlier in this framework has provided important insights into wave scattering and penetration physics at the seafloor. Here a consistent representation for the subbottom scattering is developed and examples are provided which illustrate the observable differences between the two scattering mechanisms.     

Chemical, morphological and accumulation phenomena in ultrashort-pulse laser ablation of TiN in air

Ultrashort-pulse laser ablation (τ=130 fs, λ=800 nm, repetition rate 2–20 Hz) of titanium nitride was investigated for laser fluences between 0.3 and 4.5 J/cm² using the direct focusing technique in air. The influence of the laser pulse number and the peak fluence was investigated by means of several surface analytical techniques (optical microscopy, dynamic friction atomic force microscopy, scanning Auger electron microscopy and small-spot electron spectroscopy for chemical analysis). The correlation of the results about optical, physical and chemical properties of the irradiated areas allows us to propose a simple oxidation model, which explains different observed phenomena associated with surface damage such as mound formation and crater widening and clarifies the incubation behavior reported earlier for this material. Received: 8 May 2000 / Accepted: 9 May 2000 / Published online: 13 September 2000     

The REX-ISOLDE project

The Radioactive Beam Experiment REX-ISOLDE [1–3] is a pilot experiment at ISOLDE (CERN) testing the new concept of post acceleration of radioactive ion beams by using charge breeding of the ions in a high charge state ion source and the efficient acceleration of the highly charged ions in a short LINAC using modern ion accelerator structures. In order to prepare the ions for the experiments singly charged radioactive ions from the on-line mass separator ISOLDE will be cooled and bunched in a Penning trap, charge bred in an electron beam ion source (EBIS) and finally accelerated in the LINAC. The LINAC consists of a radiofrequency quadrupole (RFQ) accelerator, which accelerates the ions up to 0.3 MeV/u, an interdigital H-type (IH) structure with a final energy between 1.1 and 1.2 MeV/u and three seven gap resonators, which allow the variation of the final energy. With an energy of the radioactive beams between 0.8 MeV/u and 2.2 MeV/u a wide range of experiments in the field of nuclear spectroscopy, astrophysics and solid state physics will be addressed by REX-ISOLDE. This revised version was published online in July 2006 with corrections to the Cover Date.     

Kinetic energy spectrum and polarization of neutrons from the reaction 12C(p,n)X at 590 MeV

Abstact: The kinetic energy spectrum and the polarization of the PSI neutron beam produced in the reaction ¹²C(p,n)X at 0° with 590 MeV polarized protons were investigated. A strong energy dependence of the neutron beam polarization is observed which was not expected at the time the neutron beam was built. Received: 3 April 1998     

Fission experiments with secondary beams

Nuclear fission from excitation energies around 11 MeV was studied at GSI, Darmstadt for 76 neutron-deficient actinides and pre-actinides by use of relativistic secondary beams. The characteristics of multimodal fission of nuclei around ²²⁶Th are systematically investigated and related to the influence of shell effects on the potential-energy and on the level density between saddle point and scission. A systematic view on the large number of elemental yields measured gave rise to a new interpretation of the enhanced production of even elements in nuclear fission and allowed for a new understanding of pair breaking in fission.     

The Classical Solutions of Two-dimensional Gravity

The solutions of two-dimensional gravityfollowing from a non-linear Lagrangian =f(R)g are classified, and their symmetry andsingularity properties are described. Then a conformaltransformation is applied to rewrite these solutions as analogoussolutions of two-dimensional Einstein-dilaton gravityand vice versa.     

Intensity range as a function of task and training

This study examined intensity range as a function of elicitation task (reading and automatic speech sequences), musical training, and the interaction between task and musical training in 31 college students. The results indicated significant differences in loudness range by experiental task. Intensity range for the descending automatic sequence was significantly greater than that for the ascending and reading tasks. While the overall effect of musical training was nonsignificant, there was a significant interaction between task and training, with musicians having a significantly greater mean range on the ascending task. A comparison between ascending and descending tasks indicated a significant mean difference between lower limits and no significant mean difference between upper limits. The range for the reading probe was located approximately in the middle of the total available intensity range.     

19.4%‐efficient large‐area fully screen‐printed silicon solar cells

We demonstrate industrially feasible large‐area solar cells with passivated homogeneous emitter and rear achieving energy conversion efficiencies of up to 19.4% on 125 × 125 mm² p‐type 2–3 Ω cm boron‐doped Czochralski silicon wafers. Front and rear metal contacts are fabricated by screen‐printing of silver and aluminum paste and firing in a conventional belt furnace. We implement two different dielectric rear surface passivation stacks: (i) a thermally grown silicon dioxide/silicon nitride stack and (ii) an atomic‐layer‐deposited aluminum oxide/silicon nitride stack. The dielectrics at the rear result in a decreased surface recombination velocity of S_rear = 70 cm/s and 80 cm/s, and an increased internal IR reflectance of up to 91% corresponding to an improved J_sc of up to 38.9 mA/cm² and V_oc of up to 664 mV. We observe an increase in cell efficiency of 0.8% absolute for the cells compared to 18.6% efficient reference solar cells featuring a full‐area aluminum back surface field. To our knowledge, the energy conversion efficiency of 19.4% is the best value reported so far for large area screen‐printed solar cells. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)