SpringerIranian Journal of Science2731-809534120100920STUDY OF BIFURCATION AND HYPERBOLICITY IN DISCRETE DYNAMICAL SYSTEMS112216010.22099/ijsts.2010.2160ENL. M. SAHAMathematical Sciences Foundation, N-91, Greater Kailash I, New Delhi-110048, IndiaL. M. BHARTIShyam Lal College (Evening), University of Delhi, Delhi-110032, IndiaR. K. MOHANTYDeparment of Mathematics, University of Delhi, Delhi-110007, IndiaJournal Article20090921Bifurcations 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, self-similarity, has also been observed for chaotic regions within the bifurcation diagram. The results of numerical calculations assume significant values.SpringerIranian Journal of Science2731-809534120100920HIGH SPIN STATES IN DEEP-INELASTIC AND COMPOUND-NUCLEUS REACTIONS1318216110.22099/ijsts.2010.2161ENS. MOHAMMADIPhysics Department, Payame Noor University, Mashad, 91735, I. R. of IranJournal Article20081026Compound-nucleus reactions provide the standard mechanism to populate states with high angular<br />momentum in neutron deficient nuclei. Neutron-rich nuclei with mass Aand induced fission. Projectile fragmentation has proven to be an efficient method of populating nuclei far<br />from the valley of stability. However, in the case of heavy nuclei this method is still limited to species with<br />isomeric states. Deep-inelastic reactions are another reaction mechanism which can be used to study neutronrich nuclei and are able to populate relatively high-spin states. In this article we compare the advantages and disadvantages of each method.SpringerIranian Journal of Science2731-809534120100920CYCLIC SURFACES IN E51 GENERATED BY HOMOTHETIC MOTIONS1926216210.22099/ijsts.2010.2162END. SAGLAMDepartment of Mathematics, Faculty of Art and Sciences, University of Afyon
Kocatepe, ANS Campus, 03200, Afyon, TurkeyH. KABADAYIDepartment of Mathematics, Faculty of Sciences, University of Ankara,
Tandogan, 06100, Ankara, TurkeyY. YAYLIDepartment of Mathematics, Faculty of Sciences, University of Ankara,
Tandogan, 06100, Ankara, TurkeyJournal Article20070415In this paper, we study cyclic surfaces in 5 1 E generated by homothetic motions of a Lorentzian<br />circle. The properties of these cyclic surfaces up to first order are investigated. We show that, as it is shown in<br />E5 , cyclic 2-surfaces in 5 1 E , in general, are contained in canal hypersurfaces. Finally, we give an example.SpringerIranian Journal of Science2731-809534120100920a -MINIMAL SETS AND THEIR PROPERTIES2735216310.22099/ijsts.2010.2163ENF. AYATOLLAH ZADEH SHIRAZIFaculty of Mathematics, Statistics and Computer Science,
College of Science, University of Tehran, I. R. of IranJournal Article20090202a minimal sets' approach introduced some closed right ideals of the Ellis semigroup of a<br />transformation semigroup which behave like minimal right ideals of an Ellis semigroup in some senses. From<br />1997 till now they have caused some new ideas in distality, proximal relation, transformed dimension, Here<br />we will compare the above mentioned ideas and will improve them.SpringerIranian Journal of Science2731-809534120100920SIMULTANEOUS CONTROL OF THE SOURCE TERMS IN A VIBRATIONAL STRING PROBLEM3746216410.22099/ijsts.2010.2164ENT. YELOGLUMustafa Kemal University, Faculty of Science and Literature, Department of Mathematics, Hatay, TurkeyM. SUBASIAtaturk University, Faculty of Science, Department of Mathematics, 25240, Erzurum, TurkeyJournal Article20100503In this paper, simultaneous control of source terms is considered in a vibrational string problem.<br />In the considered problem, the terms to be controlled are the force and the initial velocity functions. We state<br />the generalized (weak) solution about the considered problem. The existence and uniqueness of the solution<br />for optimal control problem is investigated. The Frechet derivative of the functional and the Lipschitz<br />continuity of the gradient are investigated. Minimizing sequence is obtained by the method of the projection<br />of the gradient.SpringerIranian Journal of Science2731-809534120100920A GEOMETRIC-BASED NUMERICAL SOLUTION OF EIKONAL EQUATION OVER A CLOSED LEVEL CURVE4758216510.22099/ijsts.2010.2165ENM. JAHANANDISHDept. of Civil Eng., School of Eng., Shiraz University, Shiraz, I. R. of IranJournal Article20080909This paper presents a new numerical method for solution of eikonal equation in two dimensions.<br />In contrast to the previously developed methods which try to define the solution surface by its level sets<br />(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 importantSpringerIranian Journal of Science2731-809534120100920APPLICATION OF DIFFERENTIAL TRANSFORMS FOR SOLVING THE VOLTERRA INTEGRO-PARTIAL DIFFERENTIAL EQUATIONS5970216610.22099/ijsts.2010.2166ENM. MOHSENI MOGHADAM1Center of Excellence of Linear Algebra and Optimization, Shahid Bahonar University of Kerman, Kerman, I. R. of Iran, 76169-14111H. SAEEDIDepartment of Mathematics, Faculty of Mathematics and Computer Science, Shahid
Bahonar University of Kerman, Kerman, I. R. of Iran, 76169-14111Journal Article20090512In this paper, first the properties of one and two-dimensional differential transforms are presented.<br />Next, by using the idea of differential transform, we will present a method to find an approximate solution for<br />a Volterra integro-partial differential equations. This method can be easily applied to many linear and<br />nonlinear problems and is capable of reducing computational works. In some particular cases, the exact<br />solution may be achieved. Finally, the convergence and efficiency of this method will be discussed with some<br />examples which indicate the ability and accuracy of the method.SpringerIranian Journal of Science2731-809534120100920ON THE CANONICAL SOLUTION AND DUAL EQUATIONS OF STURM-LIOUVILLE PROBLEM WITH SINGULARITY AND TURNING POINT7188216710.22099/ijsts.2010.2167ENA. NEAMATYDepartment of Mathematics, University of Mazandaran, Babolsar, I. R. of IranMOSAZADEH S.Department of Mathematics, University of Mazandaran, Babolsar, I. R. of IranJournal Article20081108In this paper, we investigate the canonical property of solutions of a system of differential<br />equations having a singularity and turning point of even order. First, by a replacement, we transform the<br />system to the Sturm-Liouville equation with a turning point. Using the asymptotic estimates for a special<br />fundamental system of solutions of Sturm-Liouville equation, we study the infinite product representation of<br />solutions of the system and investigate the uniqueness of the solution for the dual equations of the Sturm-<br />Liouville equation. Then, we transform the Sturm-Liouville equation with a turning point to the equation with<br />a singularity, and study the asymptotic behavior of its solutions. Such representations are relevant to the<br />inverse spectral problem.