arXiv subjects
Publications and source records attributed to R. Hernandez.
We introduce a new definition of pre-Schwarzian derivative for logharmonic mappings and basic properties such as the chain rule, multiplicative invariance and affine invariance are proved for these operators. It is shown that the pre-Schwarzain is stable only with respect to rotations of the identity. A characterization is given for the case when the pre-Schwarzian derivative is holomorphic.
We report the results of an experimental study of thermal and magnetic properties of nanostructured ferrimagnetic iron oxide composites with graphene and graphite fillers synthesized via the current activated pressure assisted densification. The thermal conductivity was measured using the laser-flash and transient plane source techniques. It was demonstrated that addition of 5 wt. % of equal mixture of graphene and graphite flakes to the composite results in a factor of x2.6 enhancement of the thermal conductivity without significant degradation of the saturation magnetization. The microscopy and spectroscopic characterization reveal that sp2 carbon fillers preserve their crystal structure and morphology during the composite processing. The strong increase in the thermal conductivity was attributed to the excellent phonon heat conduction properties of graphene and graphite. The results are important for energy and electronic applications of the nanostructured permanent magnets.
Lorentzian signature D-branes of all dimensions for the Nappi-Witten string are constructed. This is done by rewriting the gluing condition $J_+=FJ_-$ for the model chiral currents on the brane as a well posed first order differential problem and by solving it for Lie algebra isometries $F$ other than Lie algebra automorphisms. By construction, these D-branes are not twined conjugacy classes. Metrically degenerate D-branes are also obtained.
We report on novel ferrogels derived from polysaccharides (sodium alginate and chitosan) with embedded iron oxide nanoparticles synthesized in situ and their combination with thermally responsive poly (N-isopropylacrylamide) for externally-driven drug release using AC magnetic fields. Samples were characterized by Raman spectroscopy, transmission electron microscopy (TEM) and magnetic measurements. The obtained nanoparticles were found to be of ca. 10 nm average size, showing magnetic properties very close to those of the bulk material. The thermal response was measured by power absorption experiments, finding specific power absorption (SPA) values between 100-300 W/g, which was enough for attaining the lower critical solution temperature (LCST) of the polymeric matrix within few minutes. This fast response makes these materials good candidates for externally controlled drug release.
We present a Tight-Binding Molecular Dynamics investigation of the stability, the geometrical and the electronic structure of suspended monatomic transition metal chains. We show that linear and stable monatomic chains are formed at temperature equal or smaller than 500 K for Au, 200 K for Ag and 4 K for Cu. We also evidence that such stability is associated with the persisting sd orbital hybridization along the chains. The study highlight fundamental limitations of conductance measurement experiments to detect these chains in the breaking process of nanowires.
We investigate the relationship between the univalence of $f$ and of $h$ in the decomposition $f=h+\bar{g}$ of a sense-preserving harmonic mapping defined in the unit disk $\mathbb{D}\subset\mathbb{C}$. Among other results, we determine the holomorphic univalent maps $h$ for which there exists $c>0$ such that every harmonic mapping of the form $f=h+\bar{g}$ with $|g'|< c|h'|$ is univalent. The notion of a linearly connected domain appears in our study in a relevant way.
Lecture notes reviewing most recent developments in string/M/brane theory given by C. G. at the CIME Summer International Center of Mathematics at Cetraro. July 1997.
Global geometry of $K3$-fibration Calabi-Yau threefolds, with Hodge number $h_{2,1}=r+1$, is used to define $N=4$ softly broken $SU(r+1)$ gauge theories, with the bare coupling constant given by the dual heterotic dilaton, and the mass of the adjoint hypermultiplet given by the heterotic string tension. The $U(r+1)$ Donagi-Witten integrable model is also derived from the $K3$-fibration structure, with the extra $U(1)$ associated to the heterotic dilaton. The case of $SU(2)$ gauge group is analyzed in detail. String physics beyond the heterotic point particle limit is partially described by the $N=4$ softly broken theory.
The integrable systems associated with Seiberg-Witten geometry are considered both from the Hitchin-Donagi-Witten gauge model and in terms of intermediate Jacobians of Calabi-Yau threefolds. Dual pairs and enhancement of gauge symmetries are discussed on the basis of a map from the Donagi-Witten ``moduli'' into the moduli of complex structures of the Calabi-Yau threefold.
In these notes evidence is presented for intepreting the moduli space of the integrable model associated to $N\!=\!2$ gauge theories with $N\!=\!4$ matter content, in terms of Calabi-Yau manifolds. We restrict to the case of gauge group $SU(2)$, which is compared with the moduli space of the Calabi-Yau manifold $WP_{11226}^{12}$ appearing in the rank three dual pair $(K^{3}\times T^{2} / WP_{11226}^{12})$. The singularity loci of both spaces are maped in a one to one way and, in the weak coupling limit, $N\!=\!2$ $SU(2)$ pure Yang-Mills is obtained in both cases by the same type of blow up. Comments on the interpretation of the strong coupling locus from the perspective of the integrable system are done.
The action of the $S$-duality $Sl(2,Z)$ group on the moduli of the Calabi-Yau manifold $W\IP^{12}_{11226}$ appearing in the rank two dual pair $(K^{3}\times T^{2}/W\IP^{12}_{11226})$ is defined by interpreting the $N\!=\!4$ to $N\!=\!2$ flow, for $SU(2)$ supersymmetric Yang-Mills, in terms of the Calabi-Yau moduli. The different singularity loci are mapped in a one to one way, and the ($N\!=\!2$ limit/point particle limit) is obtained in both cases by the same type of blow up. Moreover, it is shown that the $S$-duality group permutes the different singularity loci of the moduli of $W\IP^{12}_{11226}$. We study the transformation under $S$-duality of the Calabi-Yau Yukawa couplings.