On the existence of fractal strings whose set of dimensions of fractality is not perfect

In this paper we give an example of a nonlattice self-similar fractal string such that the set of real parts of their complex dimensions has an isolated point. This proves that, in general, the set of dimensions of fractality of a fractal string is not a perfect set.

On the existence of exponential polynomials with prefixed gaps

This paper shows that the conjecture of Lapidus and Van Frankenhuysen on the set of dimensions of fractality associated with a nonlattice fractal string is true in the important special case of a generic nonlattice self-similar string, but in general is false. The proof and the counterexample of this have been given by virtue of a result on exponential polynomials P(z), with real frequencies linearly independent over the rationals, that establishes a bound for the number of gaps of RP, the closure of the set of the real projections of its zeros, and the reason for which these gaps are produced.

Analysis of the colorimetric properties of goniochromatic colors using the MacAdam limits under different light sources

Technological innovation in all areas has led to the appearance in recent years of new metallic and pearlescent materials, yet no exhaustive studies have been conducted to assess their colorimetric capabilities. The chromatic variability of these special-effect pigments may largely be due to the three-dimensional effect of their curved shapes and orientations when they are directionally or diffusely illuminated. Our study examines goniochromatic colors using the optimal colors (MacAdam limits) associated with normal colors (photometric scale of relative spectral reflectance from 0 to 1) under certain conventional illuminants and other light sources. From a database of 91 metallic and interference samples and using a multi-gonio-spectrophotometer, we analyzed samples with lightness values of more than 100 and others with lightness values of less than 100, but with higher chromaticities than optimal colors, which places them beyond the MacAdam limits. Our study thus demonstrates the existence of chromatic perceptions beyond the normal solid color associated with these materials and independent of the light source. The challenge for future research, therefore, is to replicate and render these color appearances in current and future color reproduction technologies for computer graphics.

Plastisol foaming process. Decomposition of the foaming agent, polymer behavior in the corresponding temperature range and resulting foam properties

The decomposition of azodicarbonamide, used as foaming agent in PVC—plasticizer (1/1) plastisols was studied by DSC. Nineteen different plasticizers, all belonging to the ester family, two being polymeric (polyadipates), were compared. The temperature of maximum decomposition rate (in anisothermal regime at 5 K min−1 scanning rate), ranges between 434 and 452 K. The heat of decomposition ranges between 8.7 and 12.5 J g−1. Some trends of variation of these parameters appear significant and are discussed in terms of solvent (matrix) and viscosity effects on the decomposition reactions. The shear modulus at 1 Hz frequency was determined at the temperature of maximum rate of foaming agent decomposition, and differs significantly from a sample to another. The foam density was determined at ambient temperature and the volume fraction of bubbles was used as criterion to judge the efficiency of the foaming process. The results reveal the existence of an optimal shear modulus of the order of 2 kPa that corresponds roughly to plasticizer molar masses of the order of 450 ± 50 g mol−1. Heavier plasticizers, especially polymeric ones are too difficult to deform. Lighter plasticizers such as diethyl phthalate (DEP) deform too easily and presumably facilitate bubble collapse.

Population synthesis of isolated neutron stars with magneto-rotational evolution

We revisit the population synthesis of isolated radio-pulsars incorporating recent advances on the evolution of the magnetic field and the angle between the magnetic and rotational axes from new simulations of the magneto-thermal evolution and magnetosphere models, respectively. An interesting novelty in our approach is that we do not assume the existence of a death line. We discuss regions in parameter space that are more consistent with the observational data. In particular, we find that any broad distribution of birth spin periods with P0 ≲ 0.5 s can fit the data, and that if the alignment angle is allowed to vary consistently with the torque model, realistic magnetospheric models are favoured compared to models with classical magneto-dipolar radiation losses. Assuming that the initial magnetic field is given by a lognormal distribution, our optimal model has mean strength 〈log B0[G]〉 ≈ 13.0–13.2 with width σ(log B0) = 0.6–0.7. However, there are strong correlations between parameters. This degeneracy in the parameter space can be broken by an independent estimate of the pulsar birth rate or by future studies correlating this information with the population in other observational bands (X-rays and γ-rays).