Relative embeddings of discs into convex domains

Dedicated to the memory of my father     

Structure of minimizers in linear-quadratic Bolza problems of optimal control

In this paper, we study intersections of extremals in a linear-quadratic Bolza problem of optimal control. The structure of the inter-sections is described. We show that this structure implies the semipositive definiteness of the quadratic cost functional. In addition, we derive necessary and sufficient conditions for the existence of minimizers.     

High pressure mössbauer studies of magnetic actinide systems

Due to the wider radial extent of 5f electrons when compared to their 4f counterparts, intermetallics of the light actinides show a broad spectrum of magnetic properties ranging from the localized magnetism of the lanthanides to the itinerant magnetism often found in transition metal compounds. One parameter which strongly influences the magnetic character of the compound is the actinide-actinide separation which can experimentally be varied by the application of high pressure. The question of 5f electron delocalization will be reviewed with respect to Moesshauer high pressure data on NpCo₂si₂, NpAl₂, NpOs₂ and new results will be presented of NpAs. The connection of hyperfine parameters with results of X-ray diffraction studies will be discussed.Work supported by the Bundesministerium für Forschung und Technologie, Federal Republic of Germany     

The high-T c superconductor Sr0.2Lai1.8CuO4: A direct and inverse-photoemission study

We have measured ultraviolet and inverse-photoemission spectra of the novel superconductor Sr₀₂La_1.8CuO₄. Our results compare favorably with recent band-structure calculations for La₂CuO₄.A full account of this work will be published elsewhere [1]     

Pushing Squares Around

We study dynamic self-reconfiguration of modular metamorphic systems. We guarantee the feasibility of motion planning in a rectangular model consisting of square modules that are allowed to slide along or rotate about one another. That is, we show that any two connected configurations of the same number of modules can be transformed into each other by a sequence of moves so that all intermediate configurations are connected. This settles a conjecture formulated in [6].     

Slow positron beam study of corrosion-related defects in pure iron

Corrosion-related defects of pure iron were investigated by measuring Doppler broadening energy spectra (DBES) of positron annihilation and positron annihilation lifetime (PAL). Defect profiles of the S-parameter from DBES as a function of positron incident energy up to 30 keV (i.e. ∼1 μm depth) were analyzed. The DBES data show that S-parameter increases as a function of positron incident energy (mean depth) after corrosion, and the increase in the S-parameter is larger near the surface than in the bulk due to corrosion. Furthermore, information on defect size from PAL data as a function of positron incident energy up to 10 keV (i.e. ∼0.2 μm depth) was analyzed. In the two-state trapping model, the lifetime τ₂ = 500 ps is ascribed to annihilation of positrons in voids with a size of the order of nanometer. τ₁, which decreases with depth from the surface to the bulk, is ascribed to the annihilation of positrons in dislocations and three-dimensional vacancy clusters. The corroded samples show a significant increase in τ₁ and the intensity I₂, and near the surface the corroded iron introduces both voids and large-size three-dimensional vacancy clusters. The size of vacancy clusters decreases with depth.     

Decay Rates in Probability Metrics Towards Homogeneous Cooling States for the Inelastic Maxwell Model

We quantify the long-time behavior of solutions to the nonlinear Boltzmann equation for spatially uniform freely cooling inelastic Maxwell molecules by means of the contraction property of a suitable metric in the set of probability measures. Existence, uniqueness, and precise estimates of overpopulated high energy tails of the self-similar profile proved in ref. 9 are revisited and derived from this new Liapunov functional. For general initial conditions the solutions of the Boltzmann equation are then proved to converge with computable rate as t → ∞ to the self-similar solution in this distance, which metrizes the weak convergence of measures. Moreover, we can relate this Fourier distance to the Euclidean Wasserstein distance or Tanaka functional proving also its exponential convergence towards the homogeneous cooling states. The findings are relevant in the understanding of the conjecture formulated by Ernst and Brito in refs. 15, 16, and complement and improve recent studies on the same problem of Bobylev and Cercignani⁽⁹⁾ and Bobylev, Cercignani and one of the authors.⁽¹¹⁾     

New hearing threshold measurements for pure tones under free-field listening conditions.

Hearing thresholds for pure tones were measured under free-field listening conditions in the frequency range of 40 Hz-15 kHz. Results are consistent with the standard threshold specified in ISO 226 for frequencies up to 250 Hz, but a few dB below the ISO curve at higher frequencies. Thresholds are distributed normally on a logarithmic level scale with a standard deviation of approximately 5 dB. No significant differences between thresholds of male and female subjects were observed.