On the approximation of continuous nonlinear operators in normed spaces by polynomial operators

Zusammenfassung Für eine sehr allgemeine Klasse von Funktionen, die eine kompakte TeilmengeX eines BanachraumesE stetig inE abbilden, wird gezeigt, dass sich jede dieser Funktionen aufX beliebig genau gleichmässig durch entartete Polynomoperatoren approximieren lässt.     

Contamination of some important kinds of plants by fission products

Quantitative data for some of the radionuclides, most important because of their intensity and radiotoxicity, present in the biosphere after the Chernobyl accident are given for a selected number among numerous plant and food samples analyzed before and after the accident.     

Radionuclides in sediments of the Danube river

The trend of variation of sediment radiocontamination, expressed as a function of space and time, and specific accumulation of particular radionuclides in some investigated localities, are discussed on the basis of experimental results of gamma spectrometric analyses of artificial radionuclide contents.     

AC transport and magnetic characterisation of multifilamentary Ag-BSCCO(2223) tapes with different filament arrangements

AC losses in multifilamentary tapes depend on various parameters. Among them, geometrical factors such as overall tape width and thickness as well as the precise arrangement of the filaments are expected to have an important influence. Several theoretical models describe this dependency. In order to study these geometrical effects experimentally, we prepared a series of Bi(2223)/Ag tapes with gradually changing filament arrangements and tape aspect ratio, and characterised them by AC transport and magnetic measurements. The results are compared to model predictions.     

Relation between algebraic and geometric view on nurbs tensor product surfaces

NURBS (Non-Uniform Rational B-Splines) belong to special approximation curves and surfaces which are described by control points with weights and B-spline basis functions. They are often used in modern areas of computer graphics as free-form modelling, modelling of processes. In literature, NURBS surfaces are often called tensor product surfaces. In this article we try to explain the relationship between the classic algebraic point of view and the practical geometrical application on NURBS.     

Robust Optimal Trajectory Planning for Robots by Stochastic Optimization

In the optimal control of industrial, field or service robots, the standard procedure is to determine first offline a reference trajectory and a feedforward control, based on some selected nominal values of the unknown stochastic model parameters, and to correct then the inevitable and increasing deviation of the state or performance of the robot from the prescribed state or performance of the system by online measurement and control actions. Due to the stochastic variations of the model parameters, increasing measurement and correction actions are needed during the process. By optimal stochastic trajectory planning (OSTP), based on stochastic optimization methods, the available a priori and sample information about the robot and its working environment is incorporated into the control process. Consequently, more robust reference trajectories and feedforward controls are obtained which cause much less online control actions. In order to maintain a high quality of the guiding functions, the reference trajectory and the feedforward control can be updated at some later time points such that additional information about the control process is available. After the presentation of the Adaptive Optimal Stochastic Trajectory Planning (AOSTP) procedure based on stochastic optimization methods, several numerical techniques for the computation of robust reference trajectories and feedforward controls under real-time conditions are presented. Additionally, numerical examples for a Manutec r3 industrial robot are discussed. The first one demonstrates real-time solutions of (OSTP) based on a sensitivity analysis of a before-hand calculated reference trajectory. The second shows the differences between reference trajectories based on deterministic methods and the stochastic methods introduced in this paper. Based on simulations of the robots behavior, the increased robustness of stochastic reference trajectories is demonstrated.     

Plastic Structural Analysis Under Stochastic Uncertainty

Problems from limit load or shakedown analysis are based on the convex, linear or linearized yield/strength condition and the linear equilibrium equation for the generic stress vector. Having to take into account, in practice, stochastic variations of the model parameters (e.g., yield stresses, plastic capacities) and external loadings, the basic stochastic plastic analysis problem must be replaced by an appropriate deterministic substitute problem. Instead of calculating approximatively the probability of failure based on a certain choice of failure modes, here, a direct approach is presented based on the costs for missing carrying capacity and the failure costs (e.g., costs for damage, repair, compensation for weakness within the structure, etc.). Based on the basic mechanical survival conditions, the failure costs may be represented by the minimum value of a convex and often linear program. Several mathematical properties of this program are shown. Minimizing then the total expected costs subject to the remaining (simple) deterministic constraints, a stochastic optimization problem is obtained which may be represented by a “Stochastic Convex Program (SCP) with recourse”. Working with linearized yield/strength conditions, a “Stochastic Linear Program (SLP) with complete fixed recourse” is obtained. In case of a discretely distributed probability distribution or after the discretization of a more general probability distribution of the random structural parameters and loadings as well as certain random cost factors one has a linear program (LP) with a so-called “dual decomposition data” structure. For stochastic programs of this type many theoretical results and efficient numerical solution procedures (LP-solver) are available. The mathematical properties of theses substitute problems are considered. Furthermore approximate analytical formulas for the limit load factor are given.     

Stabilization of self‐assembled microdroplets using short chain alcohols

The condensation of water vapor on a volatile polymeric solution leads to a porous surface after evaporation of both solvent and water. However, the stabilization of the water microdroplet is of great importance, which can be achieved using specific polymer or adding a third substance to the polymer solution. Short chain alcohols (methanol, ethanol, and n‐propanol) are utilized to fabricate a self‐assembled porous honeycomb film of linear, low molecular weight polystyrene using the breath figure technique. A combination of breath figure processing and the effect of alcohol on a water droplet can stabilize the pattern and make pores on the surface of the polymer film. The quality of the porous honeycomb film is strongly dependent on the type of alcohols and the concentration of polymer. In a specific range of polymer and alcohol concentration, pores cover all the surface of the polymer film. This method offers the possibility of producing a honeycomb structure with no trace of additive residual after the fabrication process and avoiding polymer modification. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 709–718     

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