Apatite type lanthanum silicate and composite anode half cells

Apatite type rare earth silicates are being extensively studied as electrolyte material for intermediate temperature solid oxide fuel cells (SOFC). In this paper we presents results on synthesis of Al and/or Fe-doped ATLS, the design of compatible anode materials, thermal expansion properties and co-sintering of half-cells from expansion matched materials using the advanced pulsed electric current sintering (PECS) technique. The issues related to the co-sintering of half cells have been addressed successfully by the combined use of nano powders and PECS.     

Ultrafast and bias-free all-optical wavelength conversion using III-V-on-silicon technology

Using a 7.5 μm diameter disk fabricated with III-V-on-silicon fabrication technology, we demonstrate bias-free all-optical wavelength conversion for non-return-to-zero on-off keyed pseudorandom bit sequence (PRBS) data at the speed of 10 Gbits/s with an extinction ratio of more than 12 dB. The working principle of such a wavelength converter is based on free-carrier-induced refractive index modulation in a pump-probe configuration. We believe it to be the first bias-free on-chip demonstration of all-optical wavelength conversion using PRBS data. All-optical gating measurements in the pump-probe configuration with the same device have revealed that it is possible to achieve wavelength conversion beyond 20 Gbits/s.     

Synthesis and characterization of doped apatite-type lanthanum silicates for SOFC applications

A series of iron- and/or aluminium-doped apatite-type lanthanum silicates (ATLS) La_9.83Si_{6 ‐ x ‐ y}Al_xFe_yO_26 ± δ (x = 0, 0.25, 0.75, and 1.5, y = 0, 0.25, 0.75, and 1.5) were synthesized using the mechanochemical activation (MA), solid state reaction (SSR), Pechini (Pe) and sol-gel (SG) methods. The total conductivity of the prepared materials was measured under air in the temperature range 600-850 °C using 4-probe AC impedance spectroscopy. Its dependence on composition, synthesis method, sintering conditions and powder particle size was investigated. It was found that for electrolytes of the same composition, those prepared via mechanochemical activation exhibited the highest total specific conductivity, which was improved with increasing Al- and decreasing Fe-content. The highest conductivity value at 700 °C, equal to 2.04 × 10^− 2 S cm^− 1, was observed for the La_9.83Si₅Al_0.75Fe_0.25O_26 ± δ electrolyte. La_9.83Si_4.5Fe_1.5O_26 ± δ electrolyte samples synthesized using the Pechini method exhibited higher conductivity when sintered conventionally than when spark-plasma sintering (SPS) was used.     

Paper coatings with multi-scale roughness evaluated at different sampling sizes

Papers have a complex hierarchical structure and the end-user functionalities such as hydrophobicity are controlled by a finishing layer. The application of an organic nanoparticle coating and drying of the aqueous dispersion results in an unique surface morphology with microscale domains that are internally patterned with nanoparticles. Better understanding of the multi-scale surface roughness patterns is obtained by monitoring the topography with non-contact profilometry (NCP) and atomic force microscopy (AFM) at different sampling areas ranging from 2000 μm × 2000 μm to 0.5 μm × 0.5 μm. The statistical roughness parameters are uniquely related to each other over the different measuring techniques and sampling sizes, as they are purely statistically determined. However, they cannot be directly extrapolated over the different sampling areas as they represent transitions at the nano-, micro-to-nano and microscale level. Therefore, the spatial roughness parameters including the correlation length and the specific frequency bandwidth should be taken into account for each measurement, which both allow for direct correlation of roughness data at different sampling sizes.     

Monotonicity of the reflected Bessel transition density on the diagonal

For α∈R$\alpha \in \mathbb{R}$, let p^R(t,x,x)$p^R(t,x,x)$ denote the diagonal of the transition density of the α$\alpha$-Bessel process in (0,1]$(0,1]$, killed at 0 and reflected at 1. As a function of x$x$, if either α≥3$\alpha \ge 3$ or α=1$\alpha =1$, then for t>0$t>0$, the diagonal is nondecreasing. This monotonicity property fails if 1≠α<3$1\ne \alpha <3$.     

Dimensional variance inequalities of Brascamp–Lieb type and a local approach to dimensional Prékopaʼs theorem

We give a new approach, inspired by Hörmander?s L²$L^2$-method, to weighted variance inequalities which extend results obtained by Bobkov and Ledoux. It provides in particular a local proof of the dimensional functional forms of the Brunn–Minkowski inequalities. We also present several applications of these variance inequalities, including reverse Hölder inequalities for convex functions, weighted Brascamp–Lieb inequalities and sharp weighted Poincaré inequalities for generalized Cauchy measures.     

On optimality conditions for vector variational inequalities

Optimality conditions for weak efficient, global efficient and efficient solutions of vector variational inequalities with constraints defined by equality, cone and set constraints are derived. Under various constraint qualifications, necessary optimality conditions for weak efficient, global efficient and efficient solutions in terms of the Clarke and Michel–Penot subdifferentials are established. With assumptions on quasiconvexity of constraint functions sufficient optimality conditions are also given.     

Varieties of wonder:: John Wilkins' mathematical magic and the perpetuity of invention

Akin to the mathematical recreations, John Wilkins' Mathematicall Magick ( 1648) elaborates the pleasant, useful and wondrous part of practical mathematics, dealing in particular with its material culture of machines and instruments. We contextualize the Mathematicall Magick by studying its institutional setting and its place within changing conceptions of art, nature, religion and mathematics. We devote special attention to the way Wilkins inscribes mechanical innovations within a discourse of wonder. Instead of treating ‘wonder’ as a monolithic category, we present a typology, showing that wonders were not only recreative, but were meant to inspire Wilkins' readers to new mathematical inventions.     

The Penalty Functions Method and Multiplier Rules Based on the Mordukhovich Subdifferential

We show that the finite-dimensional Fritz John multiplier rule, which is based on the limiting/Mordukhovich subdifferential, can be proved by using differentiable penalty functions and the basic calculus tools in variational analysis. The corresponding Kuhn–Tucker multiplier rule is derived from the Fritz John multiplier rule by imposing a constraint qualification condition or the exactness of an ?₁ penalty function. Complementing the existing proofs, our proofs provide another viewpoint on the fundamental multiplier rules employing the Mordukhovich subdifferential.