On the Result of Invariance of the Closure Set of the Real Projections of the Zeros of an Important Class of Exponential Polynomials

In this paper we provide the proof of a practical point-wise characterization of the set RP defined by the closure set of the real projections of the zeros of an exponential polynomial P(z) = Σn j=1 cjewjz with real frequencies wj linearly independent over the rationals. As a consequence, we give a complete description of the set RP and prove its invariance with respect to the moduli of the c′ js, which allows us to determine exactly the gaps of RP and the extremes of the critical interval of P(z) by solving inequations with positive real numbers. Finally, we analyse the converse of this result of invariance.

Characterisation of montmorillonites simultaneously modified with an organic dye and an ammonium salt at different dye/salt ratios. Properties of these modified montmorillonites EVA nanocomposites

In this work, a sodium montmorillonite (Na+-Mt) was modified with two molecules simultaneously, an organic dye, methylene blue (MB), and ethyl hexadecyl dimethyl ammonium (EHDDMA). The synthesised organo-montmorillonites (OMt) combining different proportions of the two molecules were thoroughly characterised and mixed with ethylene vinyl acetate copolymer (EVA) in order to check the ability of these OMt as pigments and reinforcing additives. The synthesised OMt combining both surfactants, MB and EHDDMA, present higher interlayer distances than those with only MB, which were employed in previous works as nanopigments. When these OMt were incorporated in the EVA matrix, the obtained clay polymer nanocomposites (CPN) showed a high exfoliation degree of the OMt in the polymer, in such a way that at 80% of the cationic exchange capacity (CEC) of the Mt exchanged with EHDDMA, most of the OMt was exfoliated. Moreover, all the obtained CPN showed an increase in the Young's Moduli compared to the EVA reference, and especially those containing higher amounts of MB. The thermal stability of the CPN also increases with the MB content, compared to other CPN including conventional surfactants. The hiding power and colouring power achieved in the CPN are higher even with a much lower load of MB when EHDDMA is exchanged in the Mt.

Estimation of Time-Limited Channel Spectra From Nonuniform Samples

This paper deals with the estimation of a time-invariant channel spectrum from its own nonuniform samples, assuming there is a bound on the channel’s delay spread. Except for this last assumption, this is the basic estimation problem in systems providing channel spectral samples. However, as shown in the paper, the delay spread bound leads us to view the spectrum as a band-limited signal, rather than the Fourier transform of a tapped delay line (TDL). Using this alternative model, a linear estimator is presented that approximately minimizes the expected root-mean-square (RMS) error for a deterministic channel. Its main advantage over the TDL is that it takes into account the spectrum’s smoothness (time width), thus providing a performance improvement. The proposed estimator is compared numerically with the maximum likelihood (ML) estimator based on a TDL model in pilot-assisted channel estimation (PACE) for OFDM.

A simple method to predict elastic settlements in foundations resting on two soils of differing deformability

This paper shows the analysis results obtained from more than 200 finite element method (FEM) models used to calculate the settlement of a foundation resting on two soils of differing deformability. The analysis considers such different parameters as the foundation geometry, the percentage of each soil in contact with the foundation base and the ratio of the soils’ elastic moduli. From the described analysis, it is concluded that the maximum settlement of the foundation, calculated by assuming that the foundation is completely resting on the most deformable soil, can be correlated with the settlement calculated by FEM models through a correction coefficient named “settlement reduction factor” (α). As a consequence, a novel expression is proposed for calculating the real settlement of a foundation resting on two soils of different deformability with maximum errors lower than 1.57%, as demonstrated by the statistical analysis carried out. A guide for the application of the proposed simple method is also explained in the paper. Finally, the proposed methodology has been validated using settlement data from an instrumented foundation, indicating that this is a simple, reliable and quick method which allows the computation of the maximum elastic settlement of a raft foundation, evaluates its suitability and optimises its selection process.