Positive and generalized positive real lemma for slice hyperholomorphic functions

In this paper we prove a quaternionic positive real lemma as well as its generalized version, in case the associated kernel has negative squares for slice hyperholomorphic functions. We consider the case of functions with positive real part in the half space of quaternions with positive real part, as well as the case of (generalized) Schur functions in the open unit ball

Order-disorder phase change in embedded Si nano-particles

We investigated the relative stability of the amorphous vs crystalline nanoparticles of size ranging between 0.8 and 1.8 nm. We found that, at variance from bulk systems, at low T small nanoparticles are amorphous and they undergo to an amorphous-to-crystalline phase transition at high T. On the contrary, large nanoparticles recover the bulk-like behavior: crystalline at low T and amorphous at high T. We also investigated the structure of crystalline nanoparticles, providing evidence that they are formed by an ordered core surrounded by a disordered periphery. Furthermore, we also provide evidence that the details of the structure of the crystalline core depend on the size of the nanoparticleComment: 8 pages, 5 figure

The rotation of the planet Mercury

Rotation of planet Mercury from radar observation explained by solar gravitational torque on tidal deformation and equatorial plane asymmetr

k-Dirac operator and parabolic geometries

The principal group of a Klein geometry has canonical left action on the homogeneous space of the geometry and this action induces action on the spaces of sections of vector bundles over the homogeneous space. This paper is about construction of differential operators invariant with respect to the induced action of the principal group of a particular type of parabolic geometry. These operators form sequences which are related to the minimal resolutions of the k-Dirac operators studied in Clifford analysis

Boundary interpolation for slice hyperholomorphic Schur functions

A boundary Nevanlinna-Pick interpolation problem is posed and solved in the quaternionic setting. Given nonnegative real numbers $\kappa_1, \ldots, \kappa_N$, quaternions $p_1, \ldots, p_N$ all of modulus $1$, so that the $2$-spheres determined by each point do not intersect and $p_u \neq 1$ for $u = 1,\ldots, N$, and quaternions $s_1, \ldots, s_N$, we wish to find a slice hyperholomorphic Schur function $s$ so that $$\lim_{\substack{r\rightarrow 1\\ r\in(0,1)}} s(r p_u) = s_u\quad {\rm for} \quad u=1,\ldots, N,$$ and $$\lim_{\substack{r\rightarrow 1\\ r\in(0,1)}}\frac{1-s(rp_u)\overline{s_u}}{1-r}\le\kappa_u,\quad {\rm for} \quad u=1,\ldots, N.$$ Our arguments relies on the theory of slice hyperholomorphic functions and reproducing kernel Hilbert spaces