2010
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STUDY OF BIFURCATION AND HYPERBOLICITY IN DISCRETE DYNAMICAL SYSTEMS
2
2
Bifurcations leading to chaos have been investigated in a number of one dimensional dynamical
systems by varying the parameters incorporated within the systems. The property hyperbolicity has been studied in detail in each case which has significant characteristic behaviours for regular and chaotic evolutions. In the process, the calculations for invariant set have also been carried out. A broad analysis of bifurcations and hyperbolicity provide some interesting results. The fractal property, selfsimilarity, has also been observed for chaotic regions within the bifurcation diagram. The results of numerical calculations assume significant values.
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12


L. M.
SAHA
Mathematical Sciences Foundation, N91, Greater Kailash I, New Delhi110048, India
Mathematical Sciences Foundation, N91, Greater
India
lmsaha.msf@gmail.com


L. M.
BHARTI
Shyam Lal College (Evening), University of Delhi, Delhi110032, India
Shyam Lal College (Evening), University of
India


R. K.
MOHANTY
Deparment of Mathematics, University of Delhi, Delhi110007, India
Deparment of Mathematics, University of Delhi,
India
Hyperbolicity
invariant set
chaos
nonlinearity
HIGH SPIN STATES IN DEEPINELASTIC AND COMPOUNDNUCLEUS REACTIONS
2
2
Compoundnucleus reactions provide the standard mechanism to populate states with high angularmomentum in neutron deficient nuclei. Neutronrich nuclei with mass Aand induced fission. Projectile fragmentation has proven to be an efficient method of populating nuclei farfrom the valley of stability. However, in the case of heavy nuclei this method is still limited to species withisomeric states. Deepinelastic reactions are another reaction mechanism which can be used to study neutronrich nuclei and are able to populate relatively highspin states. In this article we compare the advantages and disadvantages of each method.
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18


S.
MOHAMMADI
Physics Department, Payame Noor University, Mashad, 91735, I. R. of Iran
Physics Department, Payame Noor University,
Iran
mohammadi@pnu.ac.ir
Compoundnucleus
deepinelastic
reaction mechanisms
neutronrich nuclei
High Spin States
CYCLIC SURFACES IN E51 GENERATED BY HOMOTHETIC MOTIONS
2
2
In this paper, we study cyclic surfaces in 5 1 E generated by homothetic motions of a Lorentziancircle. The properties of these cyclic surfaces up to first order are investigated. We show that, as it is shown inE5 , cyclic 2surfaces in 5 1 E , in general, are contained in canal hypersurfaces. Finally, we give an example.
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26


D.
SAGLAM
Department of Mathematics, Faculty of Art and Sciences, University of Afyon
Kocatepe, ANS Campus, 03200, Afyon, Turkey
Department of Mathematics, Faculty of Art
Turkey
dryilmaz@aku.edu.tr


H.
KABADAYI
Department of Mathematics, Faculty of Sciences, University of Ankara,
Tandogan, 06100, Ankara, Turkey
Department of Mathematics, Faculty of Sciences,
Turkey


Y.
YAYLI
Department of Mathematics, Faculty of Sciences, University of Ankara,
Tandogan, 06100, Ankara, Turkey
Department of Mathematics, Faculty of Sciences,
Turkey
Minkowski space
cyclic surfaces
homothetic motions
a MINIMAL SETS AND THEIR PROPERTIES
2
2
a minimal sets' approach introduced some closed right ideals of the Ellis semigroup of atransformation semigroup which behave like minimal right ideals of an Ellis semigroup in some senses. From1997 till now they have caused some new ideas in distality, proximal relation, transformed dimension, Herewe will compare the above mentioned ideas and will improve them.
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35


F.
AYATOLLAH ZADEH SHIRAZI
Faculty of Mathematics, Statistics and Computer Science,
College of Science, University of Tehran, I. R. of Iran
Faculty of Mathematics, Statistics and Computer
Iran
Almost periodicity
a minimal set
transformation group
transformation semigroup
SIMULTANEOUS CONTROL OF THE SOURCE TERMS IN A VIBRATIONAL STRING PROBLEM
2
2
In this paper, simultaneous control of source terms is considered in a vibrational string problem.In the considered problem, the terms to be controlled are the force and the initial velocity functions. We statethe generalized (weak) solution about the considered problem. The existence and uniqueness of the solutionfor optimal control problem is investigated. The Frechet derivative of the functional and the Lipschitzcontinuity of the gradient are investigated. Minimizing sequence is obtained by the method of the projectionof the gradient.
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46


T.
YELOGLU
Mustafa Kemal University, Faculty of Science and Literature, Department of Mathematics, Hatay, Turkey
Mustafa Kemal University, Faculty of Science
Turkey
tyeloglu@mku.edu.tr


M.
SUBASI
Ataturk University, Faculty of Science, Department of Mathematics, 25240, Erzurum, Turkey
Ataturk University, Faculty of Science, Department
Turkey
Optimal control problem
frechet derivative
projection of the gradient
A GEOMETRICBASED NUMERICAL SOLUTION OF EIKONAL EQUATION OVER A CLOSED LEVEL CURVE
2
2
This paper presents a new numerical method for solution of eikonal equation in two dimensions.In contrast to the previously developed methods which try to define the solution surface by its level sets(contour curves), the developed methodology identifies the solution surface by resorting to its characteristics. The suggested procedure is based on the geometric properties of the solution surface and does not require any mesh for computation. It works well in finding the ridge of the solution surface as well. In addition, the area of the surface and its corresponding volume can be easily determined via this method. Three examples have been provided to demonstrate the capability of the suggested method in presenting these important features of the solution. The issue of convergence has also been investigated. It has been concluded that the suggested method works well in solving the eikonal equation in problems for which the direction of characteristics of the solution surface, and its area or volume underneath are quite important
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58


M.
JAHANANDISH
Dept. of Civil Eng., School of Eng., Shiraz University, Shiraz, I. R. of Iran
Dept. of Civil Eng., School of Eng., Shiraz
Iran
jahanand@shirazu.ac.ir
Eikonal equation
characteristics
nonlinear partial differential equations
APPLICATION OF DIFFERENTIAL TRANSFORMS FOR SOLVING THE VOLTERRA INTEGROPARTIAL DIFFERENTIAL EQUATIONS
2
2
In this paper, first the properties of one and twodimensional differential transforms are presented.Next, by using the idea of differential transform, we will present a method to find an approximate solution fora Volterra integropartial differential equations. This method can be easily applied to many linear andnonlinear problems and is capable of reducing computational works. In some particular cases, the exactsolution may be achieved. Finally, the convergence and efficiency of this method will be discussed with someexamples which indicate the ability and accuracy of the method.
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70


M.
MOHSENI MOGHADAM1
Center of Excellence of Linear Algebra and Optimization, Shahid Bahonar University of Kerman, Kerman, I. R. of Iran, 7616914111
Center of Excellence of Linear Algebra and
Iran
mohseni@mail.uk.ac.ir


H.
SAEEDI
Department of Mathematics, Faculty of Mathematics and Computer Science, Shahid
Bahonar University of Kerman, Kerman, I. R. of Iran, 7616914111
Department of Mathematics, Faculty of Mathematics
Iran
Volterra
integropartial differential equations
differential transforms
ON THE CANONICAL SOLUTION AND DUAL EQUATIONS OF STURMLIOUVILLE PROBLEM WITH SINGULARITY AND TURNING POINT
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2
In this paper, we investigate the canonical property of solutions of a system of differentialequations having a singularity and turning point of even order. First, by a replacement, we transform thesystem to the SturmLiouville equation with a turning point. Using the asymptotic estimates for a specialfundamental system of solutions of SturmLiouville equation, we study the infinite product representation ofsolutions of the system and investigate the uniqueness of the solution for the dual equations of the SturmLiouville equation. Then, we transform the SturmLiouville equation with a turning point to the equation witha singularity, and study the asymptotic behavior of its solutions. Such representations are relevant to theinverse spectral problem.
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88


A.
NEAMATY
Department of Mathematics, University of Mazandaran, Babolsar, I. R. of Iran
Department of Mathematics, University of
Iran
namaty@umz.ac.ir


MOSAZADEH
S.
Department of Mathematics, University of Mazandaran, Babolsar, I. R. of Iran
Department of Mathematics, University of
Iran
Turning point
singularity
sturmliouville
infinite products
hadamard's theorem
dual equations
eigenvalues