104 research outputs found
A new one parameter deformation of the exponential function
Recently, in the ref. Physica A \bfm{296} 405 (2001), a new one parameter
deformation for the exponential function , which presents a power law
asymptotic behaviour, has been proposed. The statistical distribution
, has been obtained
both as stable stationary state of a proper non linear kinetics and as the
state which maximizes a new entropic form. In the present contribution,
starting from the -algebra and after introducing the -analysis,
we obtain the -exponential as
the eigenstate of the -derivative and study its main mathematical
properties.Comment: 5 pages including 2 figures. Paper presented in NEXT2001 Meetin
Clifford Algebras and Possible Kinematics
We review Bacry and Levy-Leblond's work on possible kinematics as applied to
2-dimensional spacetimes, as well as the nine types of 2-dimensional
Cayley-Klein geometries, illustrating how the Cayley-Klein geometries give
homogeneous spacetimes for all but one of the kinematical groups. We then
construct a two-parameter family of Clifford algebras that give a unified
framework for representing both the Lie algebras as well as the kinematical
groups, showing that these groups are true rotation groups. In addition we give
conformal models for these spacetimes.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA
One-Parameter Homothetic Motion in the Hyperbolic Plane and Euler-Savary Formula
In \cite{Mul} one-parameter planar motion was first introduced and the
relations between absolute, relative, sliding velocities (and accelerations) in
the Euclidean plane were obtained. Moreover, the relations
between the Complex velocities one-parameter motion in the Complex plane were
provided by \cite{Mul}. One-parameter planar homothetic motion was defined in
the Complex plane, \cite{Kur}. In this paper, analogous to homothetic motion in
the Complex plane given by \cite{Kur}, one-parameter planar homothetic motion
is defined in the Hyperbolic plane. Some characteristic properties about the
velocity vectors, the acceleration vectors and the pole curves are given.
Moreover, in the case of homothetic scale identically equal to 1, the
results given in \cite{Yuc} are obtained as a special case. In addition, three
hyperbolic planes, of which two are moving and the other one is fixed, are
taken into consideration and a canonical relative system for one-parameter
planar hyperbolic homothetic motion is defined. Euler-Savary formula, which
gives the relationship between the curvatures of trajectory curves, is obtained
with the help of this relative system
Numerical Palindromes: Part 1
At first sight, RESEDACEAE (the plant family to which the mignonette belongs) is not a palindrome. But it is--in disguise! When its ten letters are split into two equal groups of five letters each, and the letter assigned the values A=1, B=2, ... RESED- totals 51 whilst -ACEAE totals 15
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