
International Journal of Research and Reviews in Applied Sciences
ISSN: 2076734X, EISSN: 20767366
Volume 6, Issue 3 (February, 2011)
Special Issue on "Science and Mathematics with Applications"
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1. 
ON SOME FRACTIONAL PARABOLIC EQUATIONS DRIVEN BY FRACTIONAL GAUSSIAN NOISE 
by Mahmoud M. ElBorai & Khairia ElSaid ElNadi 
Abstract 
Some fraction parabolic partial differential equations driven
by fraction Gaussian noise are considered. Initialvalue problems for these equations
are studied. Some properties of the solutions are given under suitable conditions and with Hurst parameter less than half.



2. 
INVERSE CAUCHY PROBLEMS FOR NONLINEAR FRACTIONAL PARABOLIC EQUATIONS IN HILBERT SPACE 
by Mahmoud M. ElBorai

Abstract 
This note is devoted to study an inverse Cauchy problem in a Hilbert space for fractional
abstract differential equations.



3. 
BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS ON A FIXED FINITE TIME INTERVAL 
by Mahmoud M.ElBorai, Khairia ElSaid ElNadi & Hoda A. Fouad 
Abstract 
This paper deals with a class of backward stochastic differential
equations (BSDE in short) under Lipschitz and monotonicity coefficients, the authors
obtain the existence and uniqueness of solution to BSDE and estimate the difference
between two solutions in terms of the difference between the data (Comparison theorem).



4. 
A THERMOELASTIC HALF SPACE PROBLEM UNDER THE ACTION OF HEAT SOURCES AND BODY FORCES WITH TWO RELAXATION TIMES 
by A.A. AbdelHalim 
Abstract 
The twodimensional problem for a half space is considered within the context of the theory of thermoelasticity
with two relaxation times under the action of body forces and heat sources that
permeate the
medium. Laplace and exponential Fourier transform techniques
are used to obtain the solution in the transformed domain by a direct approach.
The inverse double transform is evaluated numerically. Numerical results are computed for the temperature, displacement and stress distributions then presented graphically.



5. 
AN INVESTIGATION ON FIBER OPTICAL SOLITON IN MATHEMATICAL PHYSICS AND ITS APPLICATION TO COMMUNICATION ENGINEERING 
by Md. Haider Ali Biswas, Md. Ashikur Rahman & Tapasi Das 
Abstract 
Solitons
are selflocalized wave packets arising from a robust balance between dispersion
and nonlinearity. Soliton is the physics
of wave, acting upon wave. In mathematics and physics, a
soliton is a selfreinforcing solitary wave that maintains its shape
while it travels at constant speed. They are a universal phenomenon, exhibiting
properties typically associated with particles.
Optical soliton in media with quadratic nonlinearity and frequency dispersion are
theoretically analyzed. Our aim is to discuss the behavior of soliton solutions to
the KdV equation and their interactions and applications are then investigated in
the fiber optics solitons theory in communication engineering.
In this study optical soliton is studied
with illustrated graphical representation.



6. 
APPLICATION OF CONIC OPTIMIZATION AND SEMIDEFINITE PROGRAMMING IN CLASSIFICATION 
by AbdelKarim S.O. Hassan, Mohamed A. ElGamal & Ahmad A.I. Ibrahim 
Abstract 
In this paper, Conic optimization and semidefinite programming (SDP)
are utilized and applied in classification problem. Two new classification algorithms
are proposed and completely described. The new algorithms are; the Voting Classifier
(VC) and the Nellipsoidal Classifier (NEC). Both are built on solving a Semidefinite
Quadratic Linear (SQL) optimization problem of dimension n where n is the number
of features describing each pattern in the classification problem. The voting classifier
updates usage of ellipsoids in separating N different classes instead of only binary
classification by using a voting unit. The Nellipsoidal classifier makes the separation
by means of N separating ellipsoids each contains one of the N learning sets of
the classes intended to be separated. Experiments are performed on some data sets
from UCI machine learning repository. Results are compared with several wellknown
classification algorithms, and the proposed approaches are shown to provide more
accurate and less complex classification systems with competitive error rates.




7. 
A NOTE ON SMOOTH GONJUGACY OF NODE MANIFOLDS 
by Fatma M. Kandil 
Abstract 
It
was shown that there exists a unique C' smooth invariant manifold for a given dynamical
system.



8. 
NUMERICAL ANALYSIS FOR SOME AUTONOMOUS STOCHASTIC DELAY DIFFERENTIAL EQUATIONS 
by Hamdy M.Ahmed 
Abstract 
Numerical solution of stochastic delay differential equations
is studied by using explicit onestep methods. Onestep method is asymptotically
zerostable in the quadratic mean square sense.



9. 
POSSIBILITY OF A PHYSICAL CONNECTION BETWEEN SOLAR VARIABILITY AND GLOBAL TEMPERATURE CHANGE THROUGHOUT THE PERIOD 19702008 
by M.A. ElBorie, A.A. AbdelHalim,
E. Shafik & S.Y. ElMonier 
Abstract 
The present work introduces a correlative
study to investigate the possible effect of some geomagnetic and solar parameters
on global surface temperature anomalies (GST). Monthly averages of GST
anomalies through the period from 1970 till 2008 and four solargeomagnetic activity
indices have been used. The indices are the geomagnetic activity (aa), the
sunspot number (Rz), and the dynamic pressure (nv^{2}) throughout
a period of 39 years (19702008) and total solar irradiance (TSI) throughout
a period of 24 years (19792003). Scatter plots are used to show the association
between GST and each of the solargeomagnetic activity indices at zero lag.
Running cross correlation analyses were applied between GST and each of these
indices at different lags. Finally a series of power spectral densities (PSD) have
been obtained. Our results reveal increase in GSTsolar variability correlations
indicated that 4050% of this increase in GST is due to solar forcing. It
is also found from correlation analysis that the change of nv^{2}
over GST carries a phase shift of about 47 months (~4 yrs), with the change of Rz
and TSI while it experiences a phase shift of 35 months (3 yrs) with the
change of aa. Similarities between sets of significant peaks in the spectra
of GST and solar geomagnetic activities have revealed from power spectra
analyses.



10. 
TWO DIMENSIONAL UNSTEADY MOTION OF MICROPOLAR FLUID IN THE HALFPLANE WHEN THE VELOCITY ARE GIVEN ON THE BOUNDARY 
by Ibrahim H.Elsirafy & Aly M. AbdelMoneim 
Abstract 
The object of this work is to investigate the unsteady
two dimensional motion of micropolar fluid within the halfplane (∞< x <∞,
y>0  t>0) due to the sudden motion of its horizontal boundary. Using the
technique of LaplaceFourier transform, numerical results of velocities, pressure,
microrotation, stream function, stresses and moments are obtained and illustrated
graphically. The classical problem of viscous fluid is included as special case
and compared numerically with its
analytical solution.



11. 
MEASUREMENT OF WELDING INDUCED DISTORTIONS IN FABRICATION OF A PROTOTYPE DRAGLINE JOINT: A CASE STUDY 
by Suraj Joshi & Abdulkareem S. Aloraier 
Abstract 
Discontinuous welding of hollow tubular members is an important joining process in structural applications like dragline booms, cranes, pipelines, ships and bridges. The nonuniform temperature fields generated by the plume of heat energy emanating from the weld torch invariably create undesired distortions in the parent metal that negatively influence the fabrication accuracy and physical appearance. The load bearing ability and effective strength of members is further compromised by the unmitigated residual stresses that are usually left untreated owing to huge costs, long timeframes and the general infeasibility of post weld heat treatment processes. This paper presents a case study reporting the measurements of welding induced distortions in a fourmember, circular hollow section tubular joint fabricated as a prototype cluster of a much larger dragline boom. Measurements were taken in a workshop setting with a coordinate measuring laser machine and were collated and analysed for predictions about the overall effect and implications of distortions. It was concluded that in welding of members of very large structures such as dragline booms, welding induced distortions produce negligible dimensional inaccuracies which could safely be left out in the overall design process.



12. 
ON STABILITY OF POPULATION SYSTEM 
by Fatma M. Kandil 
Abstract 
By
using the spectral properties of population operator, we investigated the existence
and asymptotic behavior of the population system.



13. 
GAURSAT FUNCTION FOR AN ELASTIC PLATE WEAKENED BY A CURVILINEAR HOLE IN THE PRESENCE OF HEAT 
by Y.A. Jaha & M.A. Abdou 
Abstract 
In this work, Complex Variable method is used to obtain the complex
potential functions, Goursat functions, for an infinite elastic plate weakened by
a curvilinear hole.



14. 
ADOMIAN AND BLOCKBYBLOCK METHODS TO SOLVE NONLINEAR TWODIMENSIONAL VOLTERRA INTEGRAL EQUATION 
by I.L. ElKalla & A.M. AlBugami 
Abstract 
In
this paper, the existence of a unique solution of a nonlinear twodimensional Volterra
integral equation (NTDVIE)
with continuous kernel is discussed. Adomian Decomposition Method (ADM) and
Block by block method (B by BM) are used to solve this type of NT–DVIE.
Numerical examples are considered to illustrate the effectiveness of the proposed
methods and the error is estimated.





15. 
FREDHOLMVOLTERRA INTEGRAL EQUATION WITH A GENERALIZED SINGULAR KERNEL AND ITS NUMERICAL SOLUTIONS 
by I.L. ElKalla & A.M. AlBugami 
Abstract 
In
this paper, the existence and uniqueness of solution of the FredholmVolterra integral
equation (FVIE), with a generalized singular kernel, are discussed
and proved in the space L2(Ω) X C(O,T)
The Fredholm integral term (FIT) is considered in position while the
Volterra integral term (VIT) is considered in time. Using a numerical technique
we have a system of Fredholm integral equations (SFIEs). This system of integral
equations can be reduced to a linear algebraic system (LAS) of equations
by using two different methods. These methods are: Toeplitz matrix method and Product
Nyström method. A numerical examples are considered when the generalized kernel
takes the following forms: Carleman
function, logarithmic form, Cauchy kernel, and Hilbert kernel.



16. 
AN INTEGRAL METHOD TO DETERMINE THE STRESS COMPONENTS OF STRETCHED INFINITE PLATE WEAKENED BY A CURVILINEAR HOLE 
by M.A. Abdou & S.J. Monaquel 
Abstract 
An integral method, complex variable method,
is used to obtain exact and closed expressions for Goursat functions for the stretched
infinite plate weakened by a hole having arbitrary shape. The inner of
the infinite plate is free from stresses. The plates considered
are conformally mapped on the area of the right half – plane.
The interesting cases of an infinite plate
weakened by a crescent like hole or by a cut having the shape of a circular arc
, also when the hole takes the form of hypotrochoidal with four round corners, are
included as special cases.



17. 
GOURSAT FUNCTIONS OF THE THERMOELASTIC PROBLEM OF AN INFINITE PLATE WITH HYPITROCHOIDAL HOLE 
by Ibrahim H. ElSirafy 
Abstract 
Complex
variable methods are used to solve the thermoelastic problem of the infinite isotropic homogeneous plate with a hypitrochoidal
hole with multi round corners conformally mapped on the domain outside a unit circle
by means of a rational mapping function .The thermoelastic problem is equivalent
to finding two analytic functions(Goursat functions)at any point
z =x + iy
within the region of the plate . The problem is transformed to solve
an integrodifferential equation, in the complex plane, with singular kernel. Closed expressions for the Goursat function
and consequently the tangential thermoelastic stresses on the boundary of the hole
are obtained in quadrature in the presence of a uniform heat stream.



18. 
DESIGN CENTERING AND REGION APPROXIMATION USING SEMIDEFINITE PROGRAMMING 
by AbdelKarim S.O. Hassan & Ahmed AbdelNaby 
Abstract 
The design centering problem seeks for the optimal values for the system designable
parameters that maximize the production yield (probability of satisfying the design
specifications by the manufactured systems).A
new method for design centering and region approximation for a convex and bounded
feasible region is introduced. The method finds iteratively a sequence of increasingvolume
ellipsoids enclosing tightly selective sets of feasible points. These ellipsoids
are found using semidefinite programming problem and known as LöwnerJohn ellipsoids.
The sequence of LöwnerJohn ellipsoids is well definedin the method to converge
to the minimum volume ellipsoid containing the feasible region. The center of the
final ellipsoiddefines a design center for the proposed design problem and the ellipsoid
itself is considered as a region approximation for the feasible region. Areuse
of system simulations is performedin order to minimize the overall computational
effort. Numerical and practical examples are considered to show the effectiveness
of the new method.



19. 
PROJECTIONITERATION METHOD FOR SOLVING NONLINEAR INTEGRAL EQUATION OF MIXED TYPE 
by W.G. ElSayed, M.A. Seddeek & F.M. ElSaedy 
Abstract 
In this paper, the existence of a unique solution of
VolterraHammerstein integral equation of the second kind (VHIESK)
is proved by using Banach fixed point
theorem (BFPT) in the space L2(Ω) X C[O,T]
,
where
represents the domain of integration
of the variable space and
is the time. Then, different
kinds of projectioniteration methods (PIMs) for solving this integral equation
in the space
L2(Ω) X C[O,T]
are introduced. Finally, we deduced that: this method is quick convergent
and the estimating error is better than the approximate error in the method of successive
approximation for solving the integral equation numerically.


