A first step towards variational methods in engineering

In this paper, a didactical proposal is presented to introduce the variational methods for solving boundary value problems to engineering students. Starting from a couple of simple models arising in linear elasticity and heat diffusion, the concept of weak solution for these models is motivated and the existence, uniqueness and continuous dependence on the initial data for these solutions are proved. Finally, the solutions of the above mentioned problems are numerically evaluated by the finite element method.     

Accurate calculation of the eigenvalues of a new simple class of superpotentials in SUSY quantum mechanics

We obtain accurate eigenvalues for two recently derived SUSY partner Hamiltonians. We improve the Rayleigh-Ritz variational method proposed by the authors and show how to apply the Riccati-Padé method to those particular partner potentials.     

Pointwise Fourier Inversion on Rank 1 Symmetric Spaces with Cesaro Means

Conditions for pointwise Fourier inversion using spherical Cesàromeans of a given degree are established on rank 1 noncompactsymmetric spaces.     

On disjoint function systems and complemented subspaces

A sufficient condition for the complementability of subspaces generated by disjoint function systems in rearrangement invariant spaces is given. Orthogonal projections in L _p -spaces are extended to certain rearrangement invariant spaces. Applications to Lorentz spaces are given.     

New basic catalysts obtained from layered double hydroxides nanocomposites

A new route for the preparation of basic mixed oxides using nanocomposite precursors obtained from layered double hydroxides (LDH) was investigated. These nanocomposites have been prepared by intercalation of negatively charged guest entities containing Ca²⁺, Sr²⁺, Ba²⁺ or La³⁺ cations in the interlayer space of host Mg/Al LDH by anionic exchange. The guest entities have been previously prepared by complexation of the required cations in the presence of edta or citrate chelating anions. Intercalation of [Mⁿ⁺(edta)]^(4?n)? or [La(cit)OH]^? complexes is proved by elemental analysis, XRD analysis and FT-IR spectroscopy. However, in order to satisfy the charge equilibrium in the materials, (edta)^4? and (citrate)^3? species are also co-intercalated in the nanocomposites. The basic properties of the mixed oxides obtained after thermal decomposition of the nanocomposites precursors were evaluated in the disproportionation of 2-methyl-3-butyn-2-ol (MBOH) and the transesterification of 1-phenylethanol with diethylcarbonate (DEC). The Sr- and Ba-containing mixed oxides exhibit basicity close to the one of MgO and Mg(La)O mixed oxides. A comparative study of the reactivity of La-containing mixed oxides obtained following different preparation routes, i.e. coprecipitation or anionic exchange, allows to conclude that the nanocomposite route led to the most active samples.     

Roughness-induced effects on the thermomicropolar fluid flow through a thin domain

In this paper, we study the asymptotic behavior of the thermomicropolar fluid flow through a thin channel with rough boundary. The flow is governed by the prescribed pressure drop between the channel's ends and the heat exchange through the rough wall is allowed. Depending on the limit of the ratio between channel's thickness and the wavelength of the roughness, we rigorously derive different asymptotic models clearly showing the roughness-induced effects on the average velocity and microrotation. To accomplish that, we employ the adaptation of the unfolding method to a thin-domain setting.     

MISTRAL: a transmission soft X‐ray microscopy beamline for cryo nano‐tomography of biological samples and magnetic domains imaging

The performance of MISTRAL is reported, the soft X‐ray transmission microscopy beamline at the ALBA light source (Barcelona, Spain) which is primarily dedicated to cryo soft X‐ray tomography (cryo‐SXT) for three‐dimensional visualization of whole unstained cells at spatial resolutions down to 30 nm (half pitch). Short acquisition times allowing for high‐throughput and correlative microscopy studies have promoted cryo‐SXT as an emerging cellular imaging tool for structural cell biologists bridging the gap between optical and electron microscopy. In addition, the beamline offers the possibility of imaging magnetic domains in thin magnetic films that are illustrated here with an example.     

On a ‐Kirchhoff equation with critical exponent and an additional nonlocal term via truncation argument

We study existence and multiplicity of solutions of the following nonlocal ‐Kirchhoff equation with critical exponent, via truncation argument on the Sobolev space with variable exponent, where Ω is a bounded smooth domain of , , M, f are continuous functions, , and are real parameter.