Numerical integration based on trivariate C 2 quartic spline quasi-interpolants

In this paper we consider the space generated by the scaled translates of the trivariate C ² quartic box spline B defined by a set X of seven directions, that forms a regular partition of the space into tetrahedra. Then, we construct new cubature rules for 3D integrals, based on spline quasi-interpolants expressed as linear combinations of scaled translates of B and local linear functionals. We give weights and nodes of the above rules and we analyse their properties. Finally, some numerical tests and comparisons with other known integration formulas are presented.     

Position and flux stabilization of X‐ray beams produced by double‐crystal monochromators for EXAFS scans at the titanium K‐edge

The simultaneous and active feedback stabilization of X‐ray beam position and monochromatic beam flux during EXAFS scans at the titanium K‐edge as produced by a double‐crystal monochromator beamline is reported. The feedback is generated using two independent feedback loops using separate beam flux and position measurements. The flux is stabilized using a fast extremum‐searching algorithm that is insensitive to changes in the synchrotron ring current and energy‐dependent monochromator output. Corrections of beam height are made using an innovative transmissive beam position monitor instrument. The efficacy of the feedback stabilization method is demonstrated by comparing the measurements of EXAFS spectra on inhomogeneous diluted Ti‐containing samples with and without feedback applied.     

Measurements of Deflection and Residual Stress in Thin Films Utilizing Coherent Light Reflection/Projection Moiré Interferometry

Thin film technology is an area of great importance in current applications of opto-electronics, electronics, MEMS and computer technology. A critical issue in thin film technology is residual stresses that arise when the coating is deposited onto a substrate. Residual stresses can be very large in magnitude and have detrimental effects on the role that the thin film must play. To save development time on coating deposition processes it is important to perform accurate residual stresses measurements in situ in real time where the deposition is made. A novel optical set up is developed in this study to measure deflections and residual stresses generated in coated specimens that can be applied directly in the reactor utilized in the deposition process. Experimental results are in good agreement with other measurements carried out independently and other data reported in literature for thin films like those tested in the experiments.     

Imaging cytoplasmic cAMP in mouse brainstem neurons

Background  

cAMP is an ubiquitous second messenger mediating various neuronal functions, often as a consequence of increased intracellular Ca²⁺ levels. While imaging of calcium is commonly used in neuroscience applications, probing for cAMP levels has not yet been performed in living vertebrate neuronal tissue before.     

Ti‐Based Catalysts and Photocatalysts: Characterization and Modeling

This perspective article aims to underline how cutting‐edge synchrotron radiation spectroscopies such as extended X‐ray absorption spectroscopy (EXAFS), X‐ray absorption near edge structure (XANES), high resolution fluorescence detected (HRFD) XANES, X‐ray emission spectroscopy (XES) and resonant inelastic X‐ray scattering (RIXS) have played a key role in the structural and electronic characterization of Ti‐based catalysts and photocatalysts, representing an important additional value to the outcomes of conventional laboratory spectroscopies (UV‐Vis, IR, Raman, EPR, NMR etc.). Selected examples are taken from the authors research activity in the last two decades, covering both band‐gap and shape engineered TiO₂ materials and microporous titanosilicates (ETS‐10, TS‐1 and Ti?AlPO‐5). The relevance of the state of the art simulation techniques as a support for experiments interpretation is underlined for all the reported examples.     

An approximated 3-d model of the Langevin transducer and its experimental validation

In this work, an approximated 3-D analytical model of the Langevin transducer is proposed. The model, improving the classical 1-D approach describing the thickness extensional mode, allows us to predict also the radial modes of both the piezoelectric ceramic disk and the loading masses; furthermore, it is able to describe the coupling between radial and thickness extensional modes. In order to validate the model, the computed frequency spectrum is compared with that obtained by measurements carried out on 13 manufactured samples of different thicknesses to diameter ratios. The comparison shows that the model predicts with quite good accuracy the resonance frequencies of the two lowest frequency modes, i.e., those of practical interest, all over the explored range. Finally, the coupling effect between thickness and radial modes on the frontal displacement is measured and discussed.     

Counterrotating disks of collisionless particles and the hoop conjecture

We construct solutions to the Einstein equations and their sources with a high asphericity using kinetic theory. In particular, we consider all the solutions associated with disk like sources of counter rotating collisionless particles, and find that the hoop conjecture is satisfied.     

A Real Analyticity Result for Symmetric Functions of the Eigenvalues of a Domain-Dependent Neumann Problem for the Laplace Operator

Let Ω be an open connected subset of for which the imbedding of the Sobolev space W ^1,2(Ω) into the space L ²(Ω) is compact. We consider the Neumann eigenvalue problem for the Laplace operator in the open subset (Ω) of , where is a Lipschitz continuous homeomorphism of Ω onto (Ω). Then we prove a result of real analytic dependence for symmetric functions of the eigenvalues upon variation of . This paper represents an extension of a part of the work performed by P.D. Lamberti in his PhD Thesis at the University of Padova under the guidance of M. Lanza de Cristoforis.     

Quasi-interpolation based on bivariate quadratic B-splines with multiple knots

Taking into account the results given in [1, 3, 4] on bivariate spline quasi-interpolation and in [5] on the effects of multiple knots, in this paper we consider local quadratic spline quasi-interpolants on criss-cross triangulations of a rectangular domain Ω, with possible multiple knots inside Ω and/or on the boundary ∂Ω. Such splines can be particularly useful in mechanics and engineering applications, since they can model constrained surfaces with different kind of smoothness in Ω. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)