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]     

A NOVEL METHOD FOR FABRICATING COMPOSITE MOSAIC MEMBRANE WITH UNIQUE NF SELECTIVITY

A novel method of fabricating composite mosaic membranes was studied on the basis of interracial polymerization （IP） by coating a thin selective layer onto the surface of a micro-porous hollow-fiber membrane, in which, 2,5-diaminobenzene sulfonic acid was used as one monomer of the IP reaction, and a mixture of trimesoyl chloride （TMCI） and 4-（chloromethyl） benzoyl chloride as the other monomer. Through the IP reaction a thin selective layer with negatively charged groups could be first formed on the polyethersulfone （PES） support membrane. Then trimethylamine solution was introduced to modify the IP layer through a quaternization reaction. Thus the selective layer of this composite membrane contained both negatively charged and positively charged groups to perform the mosaic functionality. Characterization of the composite mosaic membranes was carried out through permeation experiments using different inorganic salts and dyes. The experimental results showed that the membranes could permeate both mono- and bi-valent inorganic salts, but reject larger organic molecules. Such a mosaic membrane is potentially useful for the separation of salts from water-soluble organics, especially in dye and textile industries.     

Dosimetric investigations of laser-induced phase transition of MX1-cell membranes by use of quantum dots

It is well known that laser scattered-light applicators when applied for laser-induced tumor therapy allow the precise thermal destruction of metastases. Using laser radiation in the NIR spectral range (usually, Nd:YAG laser systems λ = 1064 nm), a penetration depth of 5–10 cm (1/e is the decrease in radiation intensity) is achieved in biological tissues. The major tissue-optical parameters, i.e., absorption coefficient μ_a, scattering coefficient μ_s, and the anisotropy factor g, show biological tissues to be strongly scattering media which have a so-called optical window in the NIR. As a consequence, the therapeutic laser radiation is scattered and absorbed at a deeper level, leading to a virtual enlargement of the laser applicator. The thermal sclerotization and the thermal cell damage originate within the absorbing volume of the laser radiation and spread outward by thermal diffusion. There are three dosimetrically relevant zones of thermal and biological damage: (1) a zone of thermal coagulation; (2) a threshold of partial necrosis (destruction of all metabolic processes in the cell is the maintenance of essential parts of the cytoskeleton and the plasma membrane); this is characterized by a specific temperature range, the so-called phase transition, which refers to the transition from the gel phase of the biomembrane to the fluid phase; the determination of this temperature zone is an integral part of the following experimental investigations on MX1 cells; (3) an external zone of thermal effects made up of partial and multiple damage with a statistical chance of survival. This paper describes the investigations on heat stress in cancer cells to verify the maximum phase transition of the outer MX1 cell membranes and the related results. For this purpose, a novel method of quantum dot fluorescence dosimetry was developed. The evaluation of the measured laser-induced fluorescences yields a first approximation of the determination of the phase transition on MX1 cells.     

Synthesis of 2H-pyrroles via the 1,3-dipolar cycloaddition reaction of nitrile ylides with acrylamides

3,4-Dihydro-2H-pyrrole derivatives were synthesized by the 1,3-dipolar cycloaddition reaction of nitrile ylides with acrylamides. Acrylamide substitution patterns and benzimidoyl chloride equilibration were investigated.     

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⁾