Uniqueness of dilation invariant norms

Let be a nontrivial dilation. We show that every complete norm on that makes from into itself continuous is equivalent to . also determines the norm of both and with in a weaker sense. Furthermore, we show that even all the dilations do not determine the norm on .

     

Enhancement of surface mechanical properties by using TiN[BCN/BN]n/c-BN multilayer system

The aim of this work is to improve the mechanical properties of AISI 4140 steel substrates by using a TiN[BCN/BN]_n/c-BN multilayer system as a protective coating. TiN[BCN/BN]_n/c-BN multilayered coatings via reactive r.f. magnetron sputtering technique were grown, systematically varying the length period (Λ) and the number of bilayers (n) because one bilayer (n = 1) represents two different layers (t_BCN + t_BN), thus the total thickness of the coating and all other growth parameters were maintained constant. The coatings were characterized by Fourier transform infrared spectroscopy showing bands associated with h-BN bonds and c-BN stretching vibrations centered at 1400 cm⁻¹ and 1100 cm⁻¹, respectively. Coating composition and multilayer modulation were studied via secondary ion mass spectroscopy. Atomic force microscopy analysis revealed a reduction in grain size and roughness when the bilayer number (n) increased and the bilayer period decreased. Finally, enhancement of mechanical properties was determined via nanoindentation measurements. The best behavior was obtained when the bilayer period (Λ) was 80 nm (n = 25), yielding the relative highest hardness (∼30 GPa) and elastic modulus (230 GPa). The values for the hardness and elastic modulus are 1.5 and 1.7 times greater than the coating with n = 1, respectively. The enhancement effects in multilayered coatings could be attributed to different mechanisms for layer formation with nanometric thickness due to the Hall-Petch effect; because this effect, originally used to explain increased hardness with decreasing grain size in bulk polycrystalline metals, has also been used to explain hardness enhancements in multilayered coatings taking into account the thickness reduction at individual single layers that make up the multilayered system. The Hall-Petch model based on dislocation motion within layered and across layer interfaces has been successfully applied to multilayered coatings to explain this hardness enhancement.     

Runge-Kutta schemes that maintain invariant solutions for differential algebraic systems

Implicit Runge-Kutta (IRK) methods and projected IRK methods for the solution of semiexplicit index-2 systems of differential algebraic systems (DAEs) have been proposed by several authors. In this paper we prove that if a method satisfiesBA+A ^t B–bb ^t =0, it conserves quadratic invariants of DAEs.     

Logarithmic Norms and Nonlinear DAE Stability

Logarithmic norms are often used to estimate stability and perturbation bounds in linear ODEs. Extensions to other classes of problems such as nonlinear dynamics, DAEs and PDEs require careful modifications of the logarithmic norm. With a conceptual focus, we combine the extension to nonlinear ODEs [15] with that of matrix pencils [10] in order to treat nonlinear DAEs with a view to cover certain unbounded operators, i.e. partial differential algebraic equations. Perturbation bounds are obtained from differential inequalities for any given norm by using the relation between Dini derivatives and semi-inner products. Simple discretizations are also considered.     

Optimized IR synchrotron beamline design

Synchrotron infrared beamlines are powerful tools on which to perform spectroscopy on microscopic length scales but require working with large bending‐magnet source apertures in order to provide intense photon beams to the experiments. Many infrared beamlines use a single toroidal‐shaped mirror to focus the source emission which generates, for large apertures, beams with significant geometrical aberrations resulting from the shape of the source and the beamline optics. In this paper, an optical layout optimized for synchrotron infrared beamlines, that removes almost totally the geometrical aberrations of the source, is presented and analyzed. This layout is already operational on the IR beamline of the Brazilian synchrotron. An infrared beamline design based on a SOLEIL bending‐magnet source is given as an example, which could be useful for future IR beamline improvements at this facility.     

Network DEA approach to airports performance assessment considering undesirable outputs

In this paper, a directional distance approach is proposed to deal with network DEA problems in which the processes may generate not only desirable final outputs but also undesirable outputs. The proposed approach is applied to the problem of modelling and benchmarking airport operations. The corresponding network DEA model considers two process (Aircraft Movement and Aircraft Loading) with two final outputs (Annual Passenger Movement and Annual Cargo handled), one intermediate product (Aircraft Traffic Movements) and two undesirable outputs (Number of Delayed Flights and Accumulated Flight Delays). The proposed approach has been applied to Spanish airports data for year 2008 comparing the computed directional distance efficiency scores with those obtained using a conventional, single-process directional distance function approach. From this comparison, it can be concluded that the proposed network DEA approach has more discriminatory power than its single-process counterpart, uncovering more inefficiencies and providing more valid results.     

Wavy graphene sheets from electrochemical sewing of corannulene

The presence of non-hexagonal rings in the honeycomb carbon arrangement of graphene produces rippled graphene layers with valuable chemical and physical properties. In principle, a bottom-up approach to introducing distortion from planarity of a graphene sheet can be achieved by careful insertion of curved polyaromatic hydrocarbons during the growth of the lattice. Corannulene, the archetype of such non-planar polyaromatic hydrocarbons, can act as an ideal wrinkling motif in 2D carbon nanostructures. Herein we report an electrochemical bottom-up method to obtain egg-box shaped nanographene structures through a polycondensation of corannulene that produces a new conducting layered material. Characterization of this new polymeric material by electrochemistry, spectroscopy, electron microscopy (SEM and TEM), scanning probe microscopy, and laser desorption-ionization time of flight mass spectrometry provides strong evidence that the anodic polymerization of corannulene, combined with electrochemically induced oxidative cyclodehydrogenations (Scholl reactions), leads to polycorannulene with a wavy graphene-like structure.

A bottom-up synthesis of wavy graphene structures obtained through an anodic polymerization process, combined with an electrochemically triggered oxidative cyclodehydrogenation, of the bowl-shaped polyaromatic hydrocarbon corannulene.     

Selenium speciation in animal tissues after enzymatic digestion by high-performance liquid chromatography coupled to inductively coupled plasma mass spectrometry

A procedure is described for the enzymatic digestion of tuna and mussel samples that allows the determination of selenium species by high-performance liquid chromatography in conjunction with inductively coupled plasma mass spectrometry. The species were extracted by two-step enzymatic hydrolysis with a non-specific protease (subtilisin). The selenium species were separated on a Spherisorb 5 ODS/AMINO column using two different chromatographic conditions, namely phosphate buffers at pH 2.8 and pH 6.0 as mobile phases. The method determines organic (trimethylselenonium, selenocystine, selenomethionine and selenoethionine) and inorganic selenium species (selenite and selenate), but only organic selenium species were found in the samples. The sum of identified selenium species in the sample was about 30% of the total selenium present in the enzymatic extract despite the fact that recoveries of total hydrolysed selenium were 93-102%. Trimethylselenonium ion and selenomethionine were found in both tuna and mussel samples and an unknown selenium species was also found in tuna samples.