J-Class Weighted Shifts on the Space of Bounded Sequences of Complex Numbers

We provide a characterization of J-class and J ^mix-class unilateral weighted shifts on in terms of their weight sequences. In contrast to the previously mentioned result we show that a bilateral weighted shift on cannot be a J-class operator. During this research the second author was fully supported by SFB 701 “Spektrale Strukturen und Topologische Methoden in der Mathematik" at the University of Bielefeld, Germany. He would also like to express his gratitude to Professor H. Abels for his support.     

Alteration of biological samples in speciation analysis of metalloproteins

For investigations of metalloproteins by speciation analysis, the integrity of the protein–metal complexes before and during separation is crucial. Knowledge about potential alterations of the samples is thus essential to avoid misinterpretations of the analytical results. Chromatographic element profiles of different cytosolic samples from animal tissues were measured repeatedly to estimate the sample stability. The dependence of the signals on the dwell time of the sample in an autosampling device at 4 °C for a period of 10 h was observed. Alterations in the element content of different metal-containing fractions were quantified by means of recovery values. Some metalloprotein fractions (e.g. ≈27-kDa arsenic, ≈27-kDa iron and different zinc fractions) were stable or only minor alterations were observed and for their investigation an autosampling device is therefore suitable. However, most of the other metalloprotein fractions, especially nickel-containing proteins, showed major alterations: these samples should therefore be analysed immediately after preparation or directly after thawing. Figure Chromatographic manganese-profiles of 11 repeated SEC-ICP-MS-separations of rat brain cytosol. The first sample at time 0 h was the run immediately started after thawing of the prepared cytosol; the other samples were measured hourly, taken from the same sample vial. In addition to the time axis the estimated molecular mass axis is plotted Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

A theoretical approach to the interpretation of the transient data in scanning laser ablation inductively coupled plasma mass spectrometry: Consideration of the geometry of the scanning area

This paper represents a further development of the theoretical basis for the interpretation of transient data obtained by scanning laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) to overcome the non-linear distortion of the transient signal as well as to improve spatial resolution. The reconstruction of the relative concentration profile from transient data is suggested in terms of simple models of analytical information gathering for extreme cases of depth distribution of the analyte. The main attention is focused on the geometry of the overlap between the laser spot and the concentration profile, the consideration of which allows defining explicitly the response function necessary for the deconvolution procedure. The profile of the transient signal simulated according the proposed model for a real system (copper conductor lines in polymer matrix) is in good agreement with the measured data. The feasibility of the deconvolution procedure to reconstruct the relative concentration profile for a model system is demonstrated. The suggested analytical framework is intended to overcome certain limitations of scanning LA-ICP-MS which are caused by the measuring process independently from the optimization of hardware and experimental conditions.     

Local Lower Norm Estimates for Dyadic Maximal Operators and Related Bellman Functions

We provide lower \(L^{q}\) and weak \(L^{q}\)-bounds for the localized dyadic maximal operator on \(\mathbb {R}^{n}\), when the local \(L^{1}\) and the local \(L^{p}\) norms of the function are given. We actually do that in the more general context of homogeneous trees in probability spaces.     

Sharp Lorentz Estimates for Dyadic-like Maximal Operators and Related Bellman Functions

We precisely evaluate Bellman-type functions for the dyadic maximal operator on \(\mathbb {R}^{n}\) and of maximal operators on martingales related to local Lorentz-type estimates. Using a type of symmetrization principle, introduced for the dyadic maximal operator in earlier works of the authors, we precisely evaluate the supremum of the Lorentz quasinorm of the maximal operator on a function \(\phi \) when the integral of \(\phi \) is fixed and also the same Lorentz quasinorm of \(\phi \) is fixed. Also we find the corresponding supremum when the integral of \(\phi \) is fixed and several weak type conditions are given.     

Linear conic formulations for two-party correlations and values of nonlocal games

In this work we study the sets of two-party correlations generated from a Bell scenario involving two spatially separated systems with respect to various physical models. We show that the sets of classical, quantum, no-signaling and unrestricted correlations can be expressed as projections of affine sections of appropriate convex cones. As a by-product, we identify a spectrahedral outer approximation to the set of quantum correlations which is contained in the first level of the Navascués, Pironio and Acín (NPA) hierarchy and also a sufficient condition for the set of quantum correlations to be closed. Furthermore, by our conic formulations, the value of a nonlocal game over the sets of classical, quantum, no-signaling and unrestricted correlations can be cast as a linear conic program. This allows us to show that a semidefinite programming upper bound to the classical value of a nonlocal game introduced by Feige and Lovász is in fact an upper bound to the quantum value of the game and moreover, it is at least as strong as optimizing over the first level of the NPA hierarchy. Lastly, we show that deciding the existence of a perfect quantum (resp. classical) strategy is equivalent to deciding the feasibility of a linear conic program over the cone of completely positive semidefinite matrices (resp. completely positive matrices). By specializing the results to synchronous nonlocal games, we recover the conic formulations for various quantum and classical graph parameters that were recently derived in the literature.     

Computational modeling of domain wall interactions with dislocations in ferroelectric crystals

This paper provides a theoretical and numerical framework to investigate the interactions between domain walls and arrays of dislocations in ferroelectric single crystals. A phase-field approach is implemented in a non-linear finite element method to determine equilibrium solutions for the coupled electromechanical interactions between a domain wall and a dislocation array. The numerical simulations demonstrate the effect of the relative size and orientation of dislocations on 180° and 90° domain wall configurations. In addition, results for the pinning strength of dislocations in the case that domain walls move due the application of external electric field and shear stress are computed. The presented numerical results are compared with the findings reported for charged defects and it is shown that non-charged defects, such as dislocations, can also interact strongly with domain walls, and therefore affect the ferroelectric material behavior.     

Dipolar gradient elasticity of cables

The increasing structural use of cables and cable-systems has given rise to a substantial technical literature concerning their static and dynamic response. However, the majority of these works is based on classical elasticity theory, according to which the rigidity of the cable is neglected. The present work re-examines in detail the behavior of steel cables under in-plane loading, taking into account the effect of the material microstructure on the overall stiffness, on the basis of the well-established simplified gradient elasticity theory. Accounting for two-dimensional deformations the generalized equilibrium equations under dipolar action are assessed and the corresponding boundary value problem is solved. Numerical results obtained for a characteristic cable segment indicate a much stiffer behavior than the one predicted by classical elasticity theory. This phenomenon is observed in the rod or cable-actuated braking mechanism of bicycles and can be used in novel structural applications.     

Implementation Issues of the Conditional Moment Closure Model in Large Eddy Simulations

Different ways of transferring information regarding the mixture fraction, its sub-grid scale variance and the scalar dissipation rate are examined in terms of a Large Eddy Simulation (LES)/Conditional Moment Closure (CMC) calculation. In such a simulation, information must be transferred from a fine LES grid to a usually coarser CMC grid. Different options of calculating conditional and unconditional quantities in the CMC resolution are assessed by filtering experimental mixture fraction and scalar dissipation rate data at various resolutions. It was found that when a presumed shape for the Filtered Density Function at the CMC resolution is used, special care must be given to the mixture fraction variance. It was also found that the Amplitude Mapping Closure model can be used for the conditional scalar dissipation rate. LES/CMC with detailed chemistry of a bluff-body stabilised burner was performed using two different ways of calculating the turbulent diffusivity. The structure of the flame is realistic, with little difference noticed when using the two diffusivities.