Abstract:
Synthesis of highly $^{13}$C isotope enriched azafullerene, C$_{59}$N embedded in C$_{60}$ is reported. $^{13}$C enriched fullerenes, produced with the Kr\"{a}tschmer-Huffmann process, were subject to a N$_{2}$ discharge that produces C$_{59}$N with a low probability. Raman spectroscopy indicates a homogeneous $^{13}$C distribution. Electron spin resonance measurement (ESR) proves that the C$_{59}$N concentration, 0.2 %, is similar as in non-enriched fullerenes. The ESR spectrum is simulated accurately with the known $^{14}$N and $^{13}$C hyperfine coupling constants. The material enables the nuclear spin-labelling of heterofullerene complexes with a potential for biological applications. It might also find applications as a building element for quantum computation.

Abstract:
We studied the temperature stability of the endohedral fullerene molecule, N@C60, inside single-wall carbon nanotubes using electron spin resonance spectroscopy. We found that the nitrogen escapes at higher temperatures in the encapsulated material as compared to its pristine, crystalline form. The temperature dependent spin-lattice relaxation time, T_1, of the encapsulated molecule is significantly shorter than that of the crystalline material, which is explained by the interaction of the nitrogen spin with the conduction electrons of the nanotubes.

Abstract:
Temperature dependent electron spin resonance (ESR) measurements are reported on stage 1 potassium doped graphite, a model system of biased graphene. The ESR linewidth is nearly isotropic and although the g-factor has a sizeable anisotropy, its majority is shown to arise due to macroscopic magnetization. Albeit the homogeneous ESR linewidth shows an unusual, non-linear temperature dependence, it appears to be proportional to the resistivity which is a quadratic function of the temperature. These observations suggests the validity of the Elliott-Yafet relaxation mechanism in KC8 and allows to place KC8 on the empirical Beuneu-Monod plot among ordinary elemental metals.

Abstract:
C59N magnetic fullerenes were formed inside single-wall carbon nanotubes by vacuum annealing functionalized C59N molecules encapsulated inside the tubes. A hindered, anisotropic rotation of C59N was deduced from the temperature dependence of the electron spin resonance spectra near room temperature. Shortening of spin-lattice relaxation time, T_1, of C59N indicates a reversible charge transfer toward the host nanotubes above $\sim 350$ K. Bound C59N-C60 heterodimers are formed at lower temperatures when C60 is co-encapsulated with the functionalized C59N. In the 10-300 K range, T_1 of the heterodimer shows a relaxation dominated by the conduction electrons on the nanotubes.

Abstract:
High filling of single wall carbon nanotubes (SWCNT) with C$_{60}$ and C$_{70}$ fullerenes in solvent is reported at temperatures as low as 69 $^{o}$C. A 2 hour long refluxing in n-hexane of the mixture of the fullerene and SWCNT results in a high yield of C$_{60}$,C$_{70}$@SWCNT, fullerene peapod, material. The peapod filling is characterized by TEM, Raman and electron energy loss spectroscopy and X-ray scattering. We applied the method to synthesize the temperature sensitive (N@C$_{60}$:C$_{60}$)@SWCNT as proved by electron spin resonance spectroscopy. The solvent prepared peapod samples can be transformed to double walled nanotubes enabling a high yield and industrially scalable production of DWCNT.

Abstract:
The set S_{F}(x_{0};T) of states y reachable from a given state x_{0} at time T under a set-valued dynamic x’(t)∈F(x (t)) and under constraints x(t)∈K where K is a closed set, is also the capture-viability kernel of x_{0} at T in reverse time of the target {x_{0}} while remaining in K. In dimension up to three, Saint-Pierre’s viability algorithm is well-adapted; for higher dimensions, Bonneuil’s viability algorithm is better suited. It is used on a large-dimensional example.

The introduction of an exponential or power law gradient
in the interstellar medium (ISM) allows to produce an asymmetric
evolution of the supernova remnant (SNR) when the framework of the thin layer
approximation is adopted. Unfortunately both the exponential and power law
gradients for the ISM do not have a well defined physical meaning. The physics
conversely is well represented by an isothermal self-gravitating disk of
particles whose velocity is everywhere Maxwellian. We derived a law of motion
in the framework of the thin layer approximation with a control parameter of
the swept mass. The photon’s losses, which are often neglected in the thin layer
approximation, are modeled trough velocity dependence. The developed framework
is applied to SNR 1987A and the three observed rings are simulated.

Abstract:
A first new luminosity function of galaxies can be built starting from a left truncated beta probability density function, which is characterized by four parameters. In the astrophysical conversion, the number of parameters increases by one, due to the addition of the overall density of galaxies. A second new galaxy luminosity function is built starting from a left truncated beta probability for the mass of galaxies once a simple nonlinear relationship between mass and luminosity is assumed; in this case the number of parameters is six because the overall density of galaxies and a parameter that regulates mass and luminosity are added. The two new galaxy luminosity functions with finite boundaries were tested on the Sloan Digital Sky Survey (SDSS) in five different bands; the results produce a “better fit” than the Schechter luminosity function in two of the five bands considered. A modified Schechter luminosity function with four parameters has been also analyzed.

Abstract:
We argued that the standard field scalar potential couldn’t be widely used for getting the adequate galaxies’ curve lines and determining the profiles of dark matter their halo. For discovering the global properties of scalar fields that can describe the observable characteristics of dark matter on the cosmological space and time scales, we propose the simplest form of central symmetric potential celestial-mechanical type, i.e. U(φ) = –μ/φ. It was shown that this potential allows get rather satisfactorily dark matter profiles and rotational curves lines for dwarf galaxies. The good agreement with some previous results, based on the N-body simulation method, was pointed out. A new possibility of dwarf galaxies’ masses estimation was given, also.

Abstract:
We study the classical dynamics of binary stars when there is an interchange of mass between them. Assuming that one of
the stars is more massive than others, the dynamics of the lighter one is analyzed as a function of its time
depending mass variation. Within our approximations and models for mass
transference, we obtain a general result which establishes that if the lightest
star looses mass, its period increases. If the lightest star wins mass, its period decreases.