Applications of Approximation Theory to thermographic images in earthquake engineering

In this paper we show some new applications of the approximation theory, by means of the multivariate sampling Kantorovich operators, to thermographic images in seismic engineering. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Quasi-martingales with a linearly ordered index set

We consider quasi-martingales indexed by a linearly order set. We show that such processes are isomorphic to a given class of (finitely additive) measures. From this result we easily derive the classical theorem of Stricker as well as the decompositions of Riesz, Rao and the supermartingale decomposition of Doob and Meyer.     

Exponential self-similar mixing and loss of regularity for continuity equations

We consider the mixing behavior of the solutions to the continuity equation associated with a divergence-free velocity field. In this Note, we sketch two explicit examples of exponential decay of the mixing scale of the solution, in case of Sobolev velocity fields, thus showing the optimality of known lower bounds. We also describe how to use such examples to construct solutions to the continuity equation with Sobolev but non-Lipschitz velocity field exhibiting instantaneous loss of any fractional Sobolev regularity.     

On Nonlinear Integro-differential Operators in Generalized Orlicz–Sobolev Spaces

A nonlinear integral operator T of the form (Tf)(s)=∫_G K(t, f (σ(s, t))) dμ(t), for sG, is defined and investigated in the measure space (G, Σ, μ), where f and K are vector-valued functions with values in normed linear spaces E and F, respectively. The results are applied to the case of integro-differential operators in generalized Orlicz–Sobolev spaces. There are studied problems of existence, embeddings, and approximation by means of T.     

Improved synthesis of polyfluorinated l-lysine for 19F NMR-based screening

Polyfluorinated N-α-Fmoc--Boc-l-lysine represents the best-in-class among a set of polyfluorinated amino acids (PFAs) which are useful tools for ¹⁹F NMR-Based Screening. In this communication, optimized reaction conditions that allowed for the multi-gram preparation of this unnatural amino acid are reported.     

Theoretical evaluation of zirconia and hafnia as gate oxides for si microelectronics

Parameters determining the performance of the crystalline oxides zirconia (ZrO2) and hafnia (HfO2) as gate insulators in nanometric Si electronics are estimated via ab initio calculations of the energetics, dielectric properties, and band alignment of bulk and thin-film oxides on Si (001). With their large dielectric constants, stable and low-formation-energy interfaces, large valence offsets, and reasonable (though not optimal) conduction offsets (electron injection barriers), zirconia and hafnia appear to have considerable potential as gate oxides for Si electronics.     

Super-accelerating bouncing cosmology in asymptotically free non-local gravity

Application of the effective action approach to amplitudes with loop integration is studied for collisions on two and three centers with possible gluon emission. A rule is formulated for the integration around pole singularities in the induced vertices which brings the results in agreement with the QCD. It is demonstrated that the amplitudes can be restored from the purely transverse picture by introducing the standard Feynman propagators for intermediate gluons and quarks.