Compactness and convergence rates in the combinatorial integral approximation decomposition

The combinatorial integral approximation decomposition splits the optimization of a discrete-valued control into two steps: solving a continuous relaxation of the discrete control problem, and computing a discrete-valued approximation of the relaxed control. Different algorithms exist for the second step to construct piecewise constant discrete-valued approximants that are defined on given decompositions of the domain. It is known that the resulting discrete controls can be constructed such that they converge to a relaxed control in the \(\hbox {weak}^*\) topology of \(L^\infty \) if the grid constant of this decomposition is driven to zero. We exploit this insight to formulate a general approximation result for optimization problems, which feature discrete and distributed optimization variables, and which are governed by a compact control-to-state operator. We analyze the topology induced by the grid refinements and prove convergence rates of the control vectors for two problem classes. We use a reconstruction problem from signal processing to demonstrate both the applicability of the method outside the scope of differential equations, the predominant case in the literature, and the effectiveness of the approach.

     

Sur les surfaces lisses de ℙ4

Sans résuméEspace projectif sur un corps algébriquement clos de caractéristique zéro     

Towards molecular-scale electronics and biomolecular self-assembly

This paper provides an overview of recent research developments in the field of nanoelectronics with organic materials such as carbon nanotubes and DNA-templated nanowires. Carbon nanotubes and gold electrodes are chemically functionalized in order to contact carbon nanotubes by self-assembly. The transport properties of these nanotubes are dominated by charging effects and display clear Coulomb blockade behaviour. A different approach towards nanoscale electronics is based on the molecular recognition properties of biomolecules such as DNA. As an example, DNA is stretched between electrodes using a molecular combing technique. A two-step metallization procedure leads to the formation of highly conductive gold nanowires.     

Molecular dynamics and information on possible sites of interaction of intramyocellular metabolites in vivo from resolved dipolar couplings in localized H NMR spectra

Proton NMR resonances of the endogenous metabolites creatine and phosphocreatine ((P)Cr), taurine (Tau), and carnosine (Cs, β-alanyl-l-histidine) were studied with regard to residual dipolar couplings and molecular mobility. We present an analysis of the direct ¹H–¹H interaction that provides information on motional reorientation of subgroups in these molecules in vivo. For this purpose, localized ¹H NMR experiments were performed on m. gastrocnemius of healthy volunteers using a 1.5-T clinical whole-body MR scanner. We evaluated the observable dipolar coupling strength SD₀ (S = order parameter) of the (P)Cr-methyl triplet and the Tau-methylene doublet by means of the apparent line splitting. These were compared to the dipolar coupling strength of the (P)Cr-methylene doublet. In contrast to the aliphatic protons of (P)Cr and Tau, the aromatic H2 (δ = 8 ppm) and H4 (δ = 7 ppm) protons of the imidazole ring of Cs exhibit second-order spectra at 1.5 T. This effect is the consequence of incomplete transition from Zeeman to Paschen-Back regime and allows a determination of SD₀ from H2 and H4 of Cs as an alternative to evaluating the multiplet splitting which can be measured directly in high-resolution ¹H NMR spectra. Experimental data showed striking differences in the mobility of the metabolites when the dipolar coupling constant D₀ (calculated with the internuclear distance known from molecular geometry in the case of complete absence of molecular dynamics and motion) is used for comparison. The aliphatic signals involve very small order parameters S ≈ (1.4 − 3) × 10⁻⁴ indicating rapid reorientation of the corresponding subgroups in these metabolites. In contrast, analysis of the Cs resonances yielded S ≈ (113 − 137) × 10⁻⁴. Thus, the immobilization of the Cs imidazole ring owing to an anisotropic cellular substructure in human m. gastrocnemius is much more effective than for (P)Cr and Tau subgroups. Furthermore, ¹H NMR experiments on aqueous model solutions of histidine and N-acetyl-l-aspartate (NAA) enabled the assignment of an additional signal component at δ = 8 ppm of Cs in vivo to the amide group at the peptide bond. The visibility of this proton could result from hydrogen bonding which would agree with the anticipated stronger motional restriction of Cs. Referring to the observation that all dipolar-coupled multiplets resolved in localized in vivo ¹H NMR spectra of human m. gastrocnemius collapse simultaneously when the fibre structure is tilted towards the magic angle (θ ≈ 55°), a common model for molecular confinement in muscle tissue is proposed on the basis of an interaction of the studied metabolites with myocellular membrane phospholipids.     

Announcement of Proficiency Testing Schemes

Accreditation and Quality Assurance -     

Metallo‐supramolecular block copolymer micelles: Improved preparation and characterization

Micelles prepared from amphiphilic block copolymers in which a poly(styrene) segment is connected to a poly(ethylene oxide) block via a bis‐(2,2′:6′,2″‐terpyridine‐ruthenium) complex have been intensely studied. In most cases, the micelle populations were found to be strongly heterogeneous in size because of massive micelle/micelle aggregation. In the study reported in this article we tried to improve the homogeneity of the micelle population. The variant preparation procedure developed, which is described here, was used to prepare two “protomer”‐type micelles: PS₂₀‐[Ru]‐PEO₇₀ and PS₂₀‐[Ru]‐PEO₃₇₅. The dropwise addition of water to a solution of the compounds in dimethylformamide was replaced by the controlled addition of water by a syringe pump. The resulting micelles were characterized by sedimentation velocity and sedimentation equilibrium analyses in an analytical ultracentrifuge and by transmission electron microscopy of negatively stained samples. Sedimentation analysis showed virtually unimodal size distributions, in contrast to the findings on micelles prepared previously. PS₂₀‐[Ru]‐PEO₇₀ micelles were found to have an average molar mass of 318,000 g/mol (corresponding to 53 protomers per micelle, which is distinctly less than after micelle preparation by the standard method) and an average hydrodynamic diameter (d_h) of 18 nm. For PS₂₀‐[Ru]‐PEO₃₇₅ micelles, the corresponding values were M = 603,000 g/mol (31 protomers per micelle) and d_h = 34 nm. The latter particles were found to be identical to the “equilibrium” micelles prepared in pure water. Both micelle types had a very narrow molar mass distribution but a much broader distribution of s values and thus of hydrodynamic diameters. This indicates a conformational heterogeneity that is stable on the time scale of sedimentation velocity analysis. The findings from electron microscopy were in disagreement with those from the sedimentation analysis both in average micelle diameter and in the width of the distributions, apparently because of imperfections in the staining procedure. The preparation procedure described also may be useful in micelle formation from other types of protomers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 4458–4465, 2004     

Kinetic Models for Chemotaxis and their Drift-Diffusion Limits

Kinetic models for chemotaxis, nonlinearly coupled to a Poisson equation for the chemo-attractant density, are considered. Under suitable assumptions on the turning kernel (including models introduced by Othmer, Dunbar and Alt), convergence in the macroscopic limit to a drift-diffusion model is proven. The drift-diffusion models derived in this way include the classical Keller-Segel model. Furthermore, sufficient conditions for kinetic models are given such that finite-time-blow-up does not occur. Examples are given satisfying these conditions, whereas the macroscopic limit problem is known to exhibit finite-time-blow-up. The main analytical tools are entropy techniques for the macroscopic limit as well as results from potential theory for the control of the chemo-attractant density.Present address: Centro de Matemática e Aplicações Fundamentais, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003, Lisboa, Portugal     

An Overview of Scheduling Problems Arising in Satellite Communications

Satellite communications, like batches of work in a job shop, need to be scheduled in order to use their resources as efficiently as possible. The most common satellite communications system in use today is known as Time Division Multiple Access (TDMA), in which data from earth stations is buffered before being transmitted to the appropriate receiver on a satellite. Cycles of transmission are fixed for all stations. Since the same satellite will be used for routeing data in several different ways, a schedule must be devised to use the receivers, repeaters and transmitters on board to minimize the time needed for completion of a batch of work. This paper is a survey of current scheduling algorithms used for optimizing satellite communications resources. Apart from telecommunications, the methods presented here could be applied to more general scheduling problems with renewable resources but without precedence constraints.     

Determination of total ammonium-nitrogen and free ammonia in a fermentation medium by sequential injection analysis

Summary Automated methods for the determination of ammonium and ammonia are reviewed, and techniques based on gas diffusion using a semi-permeable membrane were selected for the determination of both total ammonium-nitrogen and free ammonia in fermentation samples. A simple and robust instrument based on sequential injection analysis (SIA) consisting of a piston pump and two selector valves was used. Two different methods of ammonia detection, the Berthelot method and detection using pH-indicators, have been evaluated and compared. The indicator method showed higher reproducibility and the range of determination could easily be adjusted to match the concentrations of the samples. The range of determination could be adjusted from 0.05 mmol/l to 350 mmol/l, depending on choice of acceptor solution. This method has been evaluated with fermentation medium samples and tested on-line in a yeast fermentation process.Dedicated to Professor Dr. Wilhelm Fresenius on the occasion of his 80th birthday