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

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

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

Regular Moebius transformations of the space of quaternions

Let H be the real algebra of quaternions. The notion of regular function of a quaternionic variable recently presented by G. Gentili and D. C. Struppa developed into a quite rich theory. Several properties of regular quaternionic functions are analogous to those of holomorphic functions of one complex variable, although the diversity of the quaternionic setting introduces new phenomena. This paper studies regular quaternionic transformations. We first find a quaternionic analog to the Casorati-Weierstrass theorem and prove that all regular injective functions from H to itself are affine. In particular, the group Aut(H) of biregular functions on H coincides with the group of regular affine transformations. Inspired by the classical quaternionic linear fractional transformations, we define the regular fractional transformations. We then show that each regular injective function from the Alexandroff compactification of H to itself is a regular fractional transformation. Finally, we study regular Moebius transformations, which map the unit ball B onto itself. All regular bijections from B to itself prove to be regular Moebius transformations.Comment: 12 page

Simulation of the heat recovery use of R744 systems in a supermarket

This paper describes the outcomes a research project that investigate the improvement in the COP of an enhanced booster R744 refrigeration system that provided MT cooling for chilled food cabinets and LT cooling for cold room/frozen food cabinets by recovering the heat rejected and using it more for other building services applications in the supermarket. For instance, the heat reclaimed can be used for heating, HWS or to drive absorption chillers, either in whole or in part. To demonstrate the potential of the heat reclaimed within the supermarket and its impact on the store’s CO2e emissions, a feasibility study has been performed to examine the innovative system compared to of the existing conventional system which will cover the cooling demands of an existing supermarket. In order to achieve this, the data collected by a smart energy monitoring system will be used to examine the working of the novel system when covering the cooling demands of the store. The energy consumption of the novel system will be analyzed according to thermodynamic theory. Using an Excel model, the potential heat reclaimed will be mathematically investigated for best practice applications of heat recovery. The energy saved and CO2e emission reduction achieved in apply the novel system will be determined and analysed