Iranian Journal of Science
Year:2010 | Volume:34 | Issue:A1|Papers Count:11

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, self-similarity, has also been observed for chaotic regions within the bifurcation diagram. The results of numerical calculations assume significant values.

Compound-nucleus reactions provide the standard mechanism to populate states with high angular momentum in neutron deficient nuclei. Neutron-rich nuclei with mass A<150 can be studied in spontaneous and induced fission. Projectile fragmentation has proven to be an efficient method of populating nuclei far from the valley of stability. However, in the case of heavy nuclei this method is still limited to species with 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.

In this paper, we study cyclic surfaces in E15 generated by homothetic motions of a Lorentzian circle. The properties of these cyclic surfaces up to first order are investigated. We show that, as it is shown in E5, cyclic 2-surfaces in E15, in general, are contained in canal hypersurfaces. Finally, we give an example.

a- minimal sets’ approach introduced some closed right ideals of the Ellis semigroup of a transformation semigroup which behave like minimal right ideals of an Ellis semigroup in some senses. From 1997 till now they have caused some new ideas in distality, proximal relation, transformed dimension, Here we will compare the above mentioned ideas and will improve them.

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 state the generalized (weak) solution about the considered problem. The existence and uniqueness of the solution for optimal control problem is investigated. The Frechet derivative of the functional and the Lipschitz continuity of the gradient are investigated. Minimizing sequence is obtained by the method of the projection of the gradient.

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.

In this paper, first the properties of one and two-dimensional differential transforms are presented. Next, by using the idea of differential transform, we will present a method to find an approximate solution for a Volterra integro-partial differential equations. This method can be easily applied to many linear and nonlinear problems and is capable of reducing computational works. In some particular cases, the exact solution may be achieved. Finally, the convergence and efficiency of this method will be discussed with some examples which indicate the ability and accuracy of the method.

In this paper, we investigate the canonical property of solutions of a system of differential equations having a singularity and turning point of even order. First, by a replacement, we transform the system to the Sturm-Liouville equation with a turning point. Using the asymptotic estimates for a special fundamental system of solutions of Sturm-Liouville equation, we study the infinite product representation of solutions of the system and investigate the uniqueness of the solution for the dual equations of the Sturm- Liouville equation. Then, we transform the Sturm-Liouville equation with a turning point to the equation with a singularity, and study the asymptotic behavior of its solutions. Such representations are relevant to the inverse spectral problem.