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									                             ]Paper [1

                         Geometry Information
                      Distribution of Random Walk

        ) Moustafa .with Nassar H. Abdel-All and H. M(

    .)Debrecen, 63/1-2, 51-66 (2003 .Journal of Publ. Math

Nature) has emerged Information geometry (Geometry and
from the study of invariant properties of the manifold of
probability distributions.It is regarded as mathematical sciences
developing areas of applications as well as giving having vast
               .topological methods new trends in geometrical and
applications which are Information geometry has many
statistical ,treated in many different branches, for instance
inference, linear systems and time series, neural networks and
nonlinear systems, linear programing, convex analysis and
dynamical systems, quantum information completely integrable
                               .modelling geometry and geometric
information geometry and Here, we give a brief account of
and the the deep relationship between the differential geometry
statistics[1,4,5,10,11].The parameter space of the random walk
distribution using its Fisher's matrix is defined.The Riemannian
curvatues of the parameter space are calculated.The and scalar
the geodesic are obtained and differential equations of
the geodesic solved.The relations between the J-divergence and
                                   .distance in that space are found
                             ]Paper [2

          hyperbolic space Perturbations of curvatures flow in a

             ) with Nassar H. Abdel-All(

 ,Journal of App. Math. and Computation
           .)3331( 163-143 ,341
the A representation of a special type of
variational problem on a surface immersed in a
The perturbations of the .hyperbolic space is given
mean curvature functional are studied. For this
the corresponding frams are constructed and ,study
surface is established. the polar surfaces of a given
The technique adapted here is based on Cartan's
of moving frames, exterior differential methods
           .]3,4,4,2[ forms and the group of motions

                             ]Paper [3
         a hyperbolic space Deformation of a kinematic surface in

             ) with Nassar H. Abdel-All(

 Fractals, Journal of Chaos, Solitons and
           .)15, 631-638 (2003

variational We give a representation of the
problem on a time (space) like surface immersed in
space. The geometric properties of the a hyperbolic
variational deformed surfaces are given. The
problem for the Klein images of 2-parametric
line (kinematic surface) are continuous motion of a
introduced. The theory of Klein images is applied
to a time like and space like congruence. Finally,
mentioned in the concluding additional results are
remarks.The technique adapted here is based on
Cartan's methods of moving frames, exterior
motions differential forms and the group of

                             ]Paper [4

                      On The Tangential Variation
                         Surfaces Hyperruled
               ) with N. H. Abdel All(

And Computation, .App. Math Journal of
       .)149, 475-492 (2004

profound aspects One of the most interesting and
of classical differential geometry is its interplay
calculus of variations. In fact, the main with the
calculus of differential geometric ideas of the
variation occur over and over again and are
invented and rediscorered in a continually being
vast array of classical and modern differential
geometry. So the normal variational problem on
surfaces were general surfaces and hyperruled
studied by some geometers, specifically one may
regard, the works of [1-7,9,10]. The cite, in this
purpose of the present work is to study
effectiveness the tangential variation in the
base curve of direction of the tangent for the
                         .¹??hyperruled surfaces in E

                          ]Paper [5
            Distribution Geometrical Properties of Pareto

  ) A.W. Mahmoud.M and H.Abdel-All.N with(
    Soc., Accepted on .Journal of Egypt. Math
             . 1/6/2005 and to appear

for The differential-geometrical framework
analyzing statistical problems related to Pareto
classical and intuitive way distribution, is given.A
of description the relationship between the
differential geometry and the statistics, is
in a slightly introduced [2,8-12,14-16,32], but
modified manner.This is in order to provide an
for readers not familiar with easier introduction
differential geometry. Here the parameter space of
the Pareto distribution using its Fisher's matrix is
scalar curvatues to defined.The Riemannian and
parameter space are calculated.The differential
the geodesics are obtained and equations of
and solved.The J-divergence, the geodesic distance
the relations between of them in that space are
relation between the found. A development of the
J-divergence and the geodesic distance is
scalar curvature of the J-space is illustrated. The

                      ]Paper [6

                 Surfaces Motion of Tubular
                      H. N. Abd-Ellah

    Accepted on ,Mathematics Italian Journal of Pure and Applied
            .to appear 23/2/2006 and

investigate the The present paper intends to
kinematics of a particular type of linear Weingarten
namely tubular surfaces, in terms of their ,surfaces
evolution intrinsic geometric formulas. The
equations for the local frame, the first and the
quantities for the motion are second fundamental
established. The mean curvature flow is
studied.Thus the evolution equations of the
examples of tubular curvatures are obtained. Two
surfaces and their motions are considered and

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