The Fourier–Stieltjes transform of Minkowskiʼs ?(x) function and an affirmative answer to Salemʼs problem

By using structural and asymptotic properties of the Kontorovich–Lebedev transform associated with Minkowski?s question mark function, we give an affirmative answer to the question posed by R. Salem (Trans. Amer. Math. Soc. 53 (3) (1943) 439) whether its Fourier–Stieltjes transform vanishes at infinity.     

Integral transformations by the index of Lommel's function

In this paper we study a class of integral transformations with kernels consisting of Lommel's functions of a certain index. Boundedness properties, Parseval type formula, inversion theorem are proved in Lebesgue spaces of integrable functions. This revised version was published online in August 2006 with corrections to the Cover Date.     

Future teachers’ competence to plan a lesson: first results of a six-country study on the efficiency of teacher education

The study "Mathematics Teaching in the 21st Century (MT21)" focuses beyond others on the measurement of teachers’ general pedagogical knowledge (GPK). GPK is regarded as a latent construct embedded in a larger theory of teachers’ professional competence. It is laid out how GPK was defined and operationalized. As part of an international comparison GPK was measured with several complex vignettes. In the present paper, the results of future mathematics teachers’ knowledge from four countries (Germany, South Korea, Taiwan, and the US) with very different teacher-education systems are presented. Significant and relevant differences between the four countries as well as between future teachers at the beginning and at the end of teacher education were found. The results are discussed with reference to cultural discourses about teacher education.     

Stokes flow solutions in infinite and semi-infinite porous channels

We derive a class of exact solutions for Stokes flow in infinite and semi-infinite channel geometries with permeable walls. These simple, explicit, series expressions for both pressure and Stokes flow are valid for all permeability values. At the channel walls, we impose a no-slip condition for the tangential fluid velocity and a condition based on Darcy's law for the normal fluid velocity. Fluid flow across the channel boundaries is driven by the pressure drop between the channel interior and exterior; we assume the exterior pressure to be constant. We show how the ground state is an exact solution in the infinite channel case. For the semi-infinite channel domain, the ground-state solutions approximate well the full exact solution in the bulk and we derive a method to improve their accuracy at the transverse wall. This study is motivated by the need to quantitatively understand the detailed fluid dynamics applicable in a variety of engineering applications including membrane-based water purification, heat and mass transfer, and fuel cells.     

A robust model-based test planning procedure

A wide variety of model-based optimal test design methodologies have been developed in the past decade using deterministic approaches. This means that the test planning is based on a single-nominal model and an optimal design is obtained for precisely this model. Needless to say, the deterministic approach can lead to an ineffective distribution of sensors and poorly defined excitation points due to the presence of epistemic modelling errors. In this article, a robust-satisficing design approach to test planning is proposed based on info-gap decision theory. This methodology provides a decision-making tool for better understanding the trade-off between an optimal test design with no robustness to modelling uncertainties and a sub-optimal design which satisfies a less demanding level of performance while remaining maximally robust with respect to a given horizon of info-gap model uncertainty. The proposed strategy is illustrated using an aerospace application under base excitation conditions.     

Vibrational control of systems with Arrhenius dynamics

A nonlinear system with S-shape steady state characteristic is referred to as a system with Arrhenius dynamics. The negative slope part of the S-shape curve represents a set of unstable steady states. Using two examples of Arrhenius systems (catalytic reactor and continuous stirred tank reactor), it is shown that introduction of sufficiently fast oscillations in the parameters of the system generates a new Arrhenius system, the steady state characteristic of which has a smaller negative slope part. Results of analytical investigation as well as numerical simulation are presented. It is shown that vibrational stabilization of Arrhenius systems gives an increase in productivity of the plants.     

Electrical conduction in Fe2O3 and Cr2O3

The influence of some impurities on the conduction properties of Cr₂O₃ and Fe₂O₃ are examined and contrasted. A mechanism is proposed to account for the effect of Ti in Cr₂O₃.     

Photophysics of (1-butyl-4-(1H-inden-1-ylidene)-1,4-dihydropyridine (BIDP): an experimental test for conical intersections

Fluorescence experiments on (1-butyl-4-(1H-inden-1-ylidene)-1,4-dihydropyridine (BIDP) are reported in liquid and glassy solutions. The data indicate a fast decay in the fluid nonpolar, nonprotic solutions (decay times approximately 10(-12) s) and rapid but considerably slower decay in polar ones. In frozen solutions (polar and nonpolar), the fluorescence quantum yield is much higher (near 0.5 and around 0.1 in polar and nonpolar glasses, respectively). The rapid nonradiative transitions in fluid solutions are assigned to internal conversion in both solvent classes, as intersystem crossing is much slower and no net reaction is observed. These results are in agreement with predictions made for the closely related (in terms of electronic structure) but simpler molecule cyclopentadienyl-1,4-dihydropyridine (CPDHP) for which an S1/S0 conical intersection was recently proposed [Int. J. Quant. Chem. 2005, 102, 961]. The crossing of the two lowest singlet states is calculated to vanish in polar solvents such as methyl cyanide, leading to longer lifetime of S1 of CPDHP. As BIDP has a very similar electronic structure, the model predicts a corresponding change in this larger molecule. The strong fluorescence observed in the glassy environments is rationalized by the hindering of the internal torsion required to reach the geometry of the conical intersection.