Discrete approximations, relaxation, and optimization of one-sided Lipschitzian differential inclusions in Hilbert spaces

We study discrete approximations of nonconvex differential inclusions in Hilbert spaces and dynamic optimization/optimal control problems involving such differential inclusions and their discrete approximations. The underlying feature of the problems under consideration is a modified one-sided Lipschitz condition imposed on the right-hand side (i.e., on the velocity sets) of the differential inclusion, which is a significant improvement of the conventional Lipschitz continuity. Our main attention is paid to establishing efficient conditions that ensure the strong approximation (in the W^1,p-norm as p1) of feasible trajectories for the one-sided Lipschitzian differential inclusions under consideration by those for their discrete approximations and also the strong convergence of optimal solutions to the corresponding dynamic optimization problems under discrete approximations. To proceed with the latter issue, we derive a new extension of the Bogolyubov-type relaxation/density theorem to the case of differential inclusions satisfying the modified one-sided Lipschitzian condition. All the results obtained are new not only in the infinite-dimensional Hilbert space framework but also in finite-dimensional spaces.     

Regularity and Integration of Set-Valued Maps Represented by Generalized Steiner Points

A family of probability measures on the unit ball in generates a family of generalized Steiner (GS-)points for every convex compact set in . Such a “rich” family of probability measures determines a representation of a convex compact set by GS-points. In this way, a representation of a set-valued map with convex compact images is constructed by GS-selections (which are defined by the GS-points of its images). The properties of the GS-points allow to represent Minkowski sum, Demyanov difference and Demyanov distance between sets in terms of their GS-points, as well as the Aumann integral of a set-valued map is represented by the integrals of its GS-selections. Regularity properties of set-valued maps (measurability, Lipschitz continuity, bounded variation) are reduced to the corresponding uniform properties of its GS-selections. This theory is applied to formulate regularity conditions for the first-order of convergence of iterated set-valued quadrature formulae approximating the Aumann integral.      

The directed and Rubinov subdifferentials of quasidifferentiable functions, Part II: Calculus

We continue the study of the directed subdifferential for quasidifferentiable functions started in [R. Baier, E. Farkhi, V. Roshchina, The directed and Rubinov subdifferentials of quasidifferentiable functions, Part I: Definition and examples (this journal)]. Calculus rules for the directed subdifferentials of sum, product, quotient, maximum and minimum of quasidifferentiable functions are derived. The relation between the Rubinov subdifferential and the subdifferentials of Clarke, Dini, Michel-Penot, and Mordukhovich is discussed. Important properties implying the claims of Ioffe’s axioms as well as necessary and sufficient optimality conditions for the directed subdifferential are obtained.     

Moduli of smoothness of vector valued functions of a real variable and applications

Moduli of smoothness of Banach space valued functions of a real argument are defined and studied. The classical Whitney's theorem on the error of polynomial approximation [7] is extended to this case. Estimates for quadrature formulae and numerical treatment of abstract differential equations are presented.

Applications to the numerical analysis of set-valued maps, differential inclusions and interval functions are made.     

Electrodeposition and stripping voltammetry of arsenic(III) and arsenic(V) on a carbon black–polyethylene composite electrode in the presence of iron ions

In this work, a new sensor is proposed for the stripping voltammetric determination (anodic stripping voltammetry—ASV) of total arsenic(V) or arsenic(III). The sensor is based on an Fe-modified carbon composite electrode containing 30 % carbon black–high-pressure polyethylene (CB/PE). The modification with iron is achieved by the addition of Fe(III) or Fe(II) ions to the sample solution and co-electrodeposition of iron and arsenic on the CB/PE electrode. In anodic stripping voltammetry, two peaks are observed: an Fe peak at ?0.45 or ?0.29 V and a peak at 0.12?±?0.07 V which depends on the arsenic concentration and corresponds to the As(0) → As(III) oxidation, as is the case with other solid electrodes. The optimum conditions proposed for ASV determination of As(V) and As(III) in solutions in the presence of dissolved oxygen are the following: the background electrolyte is 0.005 M HCl containing 0.5–1 mg/?L Fe(III) for As(V) and containing 1.0–1.5 mg/?L Fe(III) for As(III), respectively; E _dep?=??2.3 V; rest period at ?0.10 V for 3–5 s before the potential sweep from ?0.2 to +0.4 V; scan rate is 120 mV/?s. The detection limit (LOD, t?=?120 s) for As(III) and As(V) is 0.16 and 0.8 μg/?L, respectively. Various hypotheses on the effect of Fe ions and atoms on the electrodeposition and dissolution of arsenic are considered. The new method of determination of As(III) and As(V) differs from known analogues by its simplicity, low cost, and easy accessibility of the electrode material. It allows the voltammetric determination of total arsenic after chemical reduction of all its forms to As(III) or after their oxidation to As(V).     

Investigations into beam monitors at the AEg ̄ IS experiment

Detailed diagnostic of antiproton beams at low energies is required for essentially all experiments at the Antiproton Decelerator (AD), but will be particularly important for the future Extra Low ENergy Antiproton ring (ELENA) and its keV beam lines to the different experiments. Many monitors have been successfully developed and operated at the AD, but in particular beam profile monitoring remains a challenge. A dedicated beam instrumentation and detector test stand has recently been setup at the AE \(\bar {g}\) IS experiment (Antimatter Experiment: Gravity, Interferometry, Spectroscopy). Located behind the actual experiment, it allows for parasitic use of the antiproton beam at different energies for testing and calibration. With the aim to explore and validate different candidate technologies for future low energy beam lines, as well as the downstream antihydrogen detector in AE \(\bar {g}\) IS, measurements have been carried out using Silicon strip and pixel detectors, a purpose-built secondary emission monitor and emulsions. Here, results from measurements and characterization of the different detector types with regard to their future use at the AD complex are presented.     

Monitoring selectivity in kinase-promoted phosphorylation of densely packed peptide monolayers using label-free electrochemical detection

This paper describes remarkably high sensitivities in the label-free detection of kinase-promoted phosphorylation for 14 different peptide substrates on electrode-immobilized monolayers (gold or nitride) using serine/threonine kinases PKA, PKC, and CaMK2. Peptide substrates were preselected using (33)P-labeling in a microarray of 1024 substrates. The three most active peptides (A1-A3, C1-C3, and M1-M3) were investigated using electrochemical impedance spectroscopy (EIS) and ion-sensitive field effect transistors (ISFETs). Some of the peptide substrates, for example, the PKC-specific substrate PPRRSSIRNAH (C1), showed a remarkably high sensitivity in the EIS-based sensor measurements. Our studies revealed that this high sensitivity is primarily due to the monolayer's packing density. Nanoscopic studies demonstrated a distinct disordering of the C1-monolayer upon phosphorylation, while phosphatase-promoted dephosphorylation regenerated the highly ordered peptide monolayer. As a matter of fact, the initial surface packing of the peptide monolayer mainly determined the level of sensitivity, whereas electrostatic repulsion of the redox-active species was found to be much less important.     

Advanced X-Ray Laboratory Microbeam Techniques Applied to Metallurgy

X-ray experiments with a spatial resolution of lower then 1 μm have been achieved with microfocus sources by means of high brilliance 3^rd generation synchrotrons. Recently the availability of high-sensitivity, high-resolution and large area detectors, as for example image plate, has allowed the analysis of samples with a spatial resolution of few tens of micrometers also with conventional laboratory sources. X-ray microdiffraction (μXRD) experiments have also been considered with increasing interest for phase identification and to evaluate the crystallite size distribution and preferred orientation. Coupled with X-ray microfluorescence (μXRF), this technique allows a complete characterisation of very small samples and/or with complex geometry. In this paper interesting applications of these laboratory techniques for the characterisation of deposits from superheater tubes of solid waste incinerator are shown. The high resolution of the probe allows the precise determination of the mixture of salts and oxides forming the deposits. This information is mandatory for the understanding of corrosion mechanisms which take place in the tubes. The results obtained by μXRD and μXRF are integrated by others techniques, such as Scanning Electron Microscopy (SEM) and Energy Dispersive X-ray Spectroscopy (EDXS).