10,973 research outputs found
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 , quaternions all of modulus , so that the
-spheres determined by each point do not intersect and for , and quaternions , we wish to find a slice
hyperholomorphic Schur function so that and
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
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