Title:
A Cosmic Quantum Mechanics
Author:
I. Arbab
Comments:
10 pages
Abstract:
We presented a model for
unification of electricity and gravity. We
have found a consistent description of all
physical quantities pertaining to the system.
We have provided limiting values for all physical
values. These values are neither zero nor
infinity. Our universe is described at all
times by the four dimensional constants $c,
\hbar, k, G$ only. The remnant of vacuum remains
at all epochs with different values. The present
cosmological hierarchy and puzzles are justified
as due to the consequences of cosmic quantization
developed in this work. The missing energy
in the universe can be resolved if one considers
the contribution of the gravito-electromagnetic
counterparts besides the observed mass in
the universe.
Title:
Systèmes hamiltoniens complètement
intégrables et méthode de la
courbe spectrale
Author:
A. Elachab
Comments:
7 pages
Abstract:
We presented a model for unification of electricity
and gravity. We have found a consistent description
of all physical quantities pertaining to the
system. We have provided limiting values for
all physical values. These values are neither
zero nor infinity. Our universe is described
at all times by the four dimensional constants
$c, \hbar, k, G$ only. The remnant of vacuum
remains at all epochs with different values.
The present cosmological hierarchy and puzzles
are justified as due to the consequences of
cosmic quantization developed in this work.
The missing energy in the universe can be
resolved if one considers the contribution
of the gravito-electromagnetic counterparts
besides the observed mass in the universe.
Title:
Characterization of the Poisson transform
of an $L^{2}$-function on the Shilov boundary
$S$ of the Lie ball in $\bf{C}^{2}$.
Author:
Fouzia EL wassouli
Comments:
3 pages
Abstract:
Let ${\cal D}_{2}$ be the
Lie ball in $\bf{C}^{2}$ and let ${\cal H}$
be the associated Hua operator.\\The purpose
of the present work is to establish for every
number $\lambda$ such that $\mathcal{R}e(i\lambda)>0$
that every $\bf{C}-valued function $F$ on
${\cal D}_{2}$ satisfying the following ${\cal
H}F(z)=-(\lambda^{2}+1)F(z).e,$ is the Poisson
transform of an $L^{2}$-function on the Shilov
boundary $S$ of ${\cal D}_{2}$ if and only
if it satisfies a growth condition of Hardy
type.
Title:
The Non commutative Geometry of the Matrix
Algebra $M_{3}(C)$
Author:
A.E.F. Djemai
Comments:
20 pages
Abstract:
The main aim of this work
is to investigate the non--commutative differential
geometry of matrix algebras $M_{3}(C)$. Firstly,
we give a presentation of these algebras viewed
as {\em cyclic} Manin planes ${\cal M}_{3}$.
Then, the table of the Hodge-star operator
on the invariants is computed. Finally, the
quantum group $G_{3}$, its associated quantum
algebra ${\cal G}_{3}$ and the Wess--Zumino
complex $\Omega_{WZ}({\cal M}_{3};d)$ corresponding
to $M_{3}(C)$, viewed as a cyclic Manin plane,
are constructed.
Title:
Sur les symétries de l'équation
de Burgers généralisée
Author:
A. Ouhadan and E. H.
El Kinani
Comments:
6 pages
Abstract:
Nous montrons que l'éequation de Burgers
géenéeraliséee n'admet
pas des syméetries propres de Lie $B\ddot{a}cklund$
d'ordre 2 et 3. En examinant l'algèbre
constituéee des géenéerateurs
de son groupe de syméetrie à
un paramètre, on remarque qu'elle contient
une sous algèbre de dimension infinie.
Cette syméetrie infinie permet la possibilitée
de transformer l'éequation de Burgers
géenéeraliséee en une
éequation linéeaire type de
la chaleur.
Title:
Structures de Lie-Poisson sur $SU(2)$ et $SL(2,\bf{R})$
Author:
S. Benmouloud, B. Ganbouri
and SM. Sbai
Comments:
4 pages
Abstract:
We show that every multiplicativ
Poisson tensor on $Su(2)$ or $SL(2,\bf{R})$
is linearizable in a neighborhood of the identity
element.
Title:
Higher-Order Supersymmetric Quantum Mechanics
and Infinite Well Potential
Author:
J. Sadeghi, A. R. Amani
and B. Pourhassan
Comments:
4 pages
Abstract:
The higher - order supersymmetric quantum
mechanics is very important because that involves
to differential operators of order greater
than one. We use the iterations of first -
order supersymmetry transformation which are
simple way for obtaining to the higher - order
case. We use the higher order supersymmetry
and obtain the corresponding partner hamiltonian
for infinite we? g?ll potential. In order
to obtain the hamiltonian partner we introduce
the supercharges which are corresponding to
the raising and lowering operators for higher
order supersymmetry.
Title:
Polarized Poisson manifolds and its generalizations
Author:
Azzouz AWANE
Comments:
8 pages
Abstract:
We introduce and study the basic notions of
polarized Poisson manifold and the vectorial
polarized Poisson manifold which give a sense
to the Poisson structure subordinate to a
polarized manifold in the sense of P.Molino
and to a k-symplectic manifold respectively,
and which generalize the classical case of
the Poisson manifold. And also, we show that
for any vectorial polarized Hamiltonian mapping,
the associated generalized Hamilt? g?onian
system of Nambu and the polarized Hamiltonian
system are connected by relations characterizing
the mechanical aspect of the }$k-${\it symplectic
geometry.
Title:
Study of some domain decomposition strategies.
Author:
B. Radi
Comments:
5 pages
Abstract:
Two interface techniques to solve the elliptic
differential equations are considered. The
first is the Robin method. The second one
is the penalization technique which is theoritically
attractive. our objective in this paper is
to compute the performance of these two methods
for classical problem like the Poisson equation.
Numerical comparison of these two interface
techniques are given.
Title:
Almost $k-$complex structures
Author:
Azzouz AWANE and Maimouna
BENT BAH
Comments:
6 pages
Abstract:
We introduce and develop the notion of almost
$k$-complex manifolds in analogy with the
well known almost complex structure. In terms
of $G$-structure, the integrability of this
structure is equivalent to the vanishing of
the Bernard-Chern tensor.
Title:
$k-$symplectic affine Lie algebras
Author:
A. Awane, A. Chkiriba
and M. Goze
Comments:
8 pages
Abstract:
The notion of $k$-symplectic structures was
introduced by A. Awane in his dissertation
in 1984 (\cite{AWN1}, \cite{PT}). Here we
are interested by the classification of Lie
algebras provided with such a structure. We
introduce also the notion of affine structure
associated to a $k$-symplectic structure on
a Lie algebra.
Title:
Asymptotic Expansions for a General Hamiltonians
in the Born-Oppenheimer Approximation
Author:
Abderrahmane Senoussaoui
Comments:
9 pages
Abstract:
We study the discrete spectrum of a general
class of Born-Oppenheimer Hamiltonians of
the type: \begin{eqnarray*} H=-h^{2}\Delta
_{x}+P\left( x,y,D_{y}\right) \text{on }L^{2}
\left( \bf{R% }_{x}^{n}\times \bf{R}_{y}^{p}\right)
,n,p\in \bf{N}^{\ast } \end{eqnarray*}% {\small
when }$h${\small \ tends to }$0^{+}${\small
, here }$P\left( x,y,D_{y}\right) ${\small
\ is a pseudodifferential operator on }$%
L^{2}\left( \bf{R}_{y}^{p}\right) .$ {\small
In the case where the first eigenvalue }$\lambda
_{1}\left( x\right) ${\small \ of }$P\left(
x,y,D_{y}\right) ${\small \ on }$L^{2}\left(
\bf{R}_{y}^{p}\right) $% {\small \ admits
one non degenerate point-well, we obtain WKB-type
expansions for all order in }${\small h}^{{\small
1/2}}${\small \ of eigenvalues (in the interval
}$[0,C_{0}h],${\small \ }$C_{0}>0)${\small
\ and associated normalized eigenfunctions
of }$H,${\small \ and this for all orders
in }$h^{1/2}$.
Title:
Hall effect on couette flow with heat
transfer of a dusty conducting fluid in the
presenceof uniform suction and injection
Author:
Hazem A. ATTIA
Comments:
13 pages
Abstract:
In the present study, the unsteady Couette
flow with heat transfer of a dusty viscous
incompressible electrically conducting fluid
under the influence of a constant pressure
gradient is studied without neglecting the
Hall effect. The parallel plates are assumed
to be porous and subjected to a uniform suction
from above and injection from below while
the fluid is acted upon by an external uniform
magnetic field is applied perpendicular to
the plates. The governing equations are solved
numerically using finite differences to yield
the velocity and temperature distributions
for both the fluid and dust particles.
Title:
The Moyal Momentum Algebra
Author:
A. Boulahoual and M.B.Sedra
Comments:
3 pages
Abstract:
We introduce in this short note some aspects
of the Moyal momentum algebra introduced first
by Das and Popowicz and that is denoted by
Mm algebra. Our interest on this algebra is
motivated by the central role that it can
play in the formulation of integrable models
and in higher conformal spin theories.
Title:
Functional equations and $2 \times 2$-matrix
valued functions
Author:
B.Bouikhalene E.Elqorachi
and S.Kabbaj
Comments:
12pages
Abstract:
In this paper, we solve the functional equation
f(x+y)+f(x+\sigma(y))=2g_{1}(x)h_{1}(y)+2g_{2}(x)h_{2}(y),
x, y \in G, where $G$ is an abelian topological
group, $\sigma : G\longrightarrow G$ is a
continuous homomorphism such that $\sigma^{2}=I$,
and $f,g_{1},g_{2},h_{1},h_{2}$ are continuous
complex valued functions on $G$, to be determined.
Title:
Trapping of laser-vaporized silver clusters
in rare-gas matrices: Magnetic
circular dichroism (MCD) studies of silver
clusters in neon and argon matrix
Author:
J.T. Zoueu, E. Farhi
and J.C. Rivoal
Comments:
12pages
Abstract:
Silver clusters have been prepared by laser-ablation
metal clusters source, embedded in rare-gas
matrices at helium temperature (below 5 Kelvin)
and studied by magneto-optical spectroscopy.
We designed and constructed this source to
produce and trap metallic clusters (M) in
rare-gas (RG) matrices at low temperature.
Optimizing the condensation parameters (source
geometry, M-RG ratio, pulses intensities,
temperature and delay), we perform sufficient
amount of particles for optical signal detection
in rare-gas matrix at low temperature as our
results show. The magneto-optical spectra
of the obtained mixture show several distinct
bands within the range 2.48 - 4.47 eV. Silver
atom peaks can be clearly identified, allowing
the remaining bands to be assigned to larger
silver clusters sizes.
