Iranian Journal of science and Technology (A: Siences)
Volume:36 Issue: 3, Summer 2012

In this study the theory of strips and Joachimsthal Theorem in 􀥷􀬷 are generalized to Lorentz space 􀥷􀯡, 􁈺􀝊 􀵐 3􁈻. Furthermore, the Joachimsthal Theorem is investigated when the strip is time-like and space-like.

In this paper, solution of nonlinear optimal control problems and the controlled Duffing oscillator, as a special class of optimal control problems, are considered and an efficient algorithm is proposed. This algorithm is based on state parametrization as a polynomial with unknown coefficients. By this method, the control and state variables can be approximated as a function of time. Also, the numerical value of the performance index is obtained readily. The convergence of the algorithm is proved. To demonstrate reliability and efficiency of the proposed algorithm, the scheme is tested on some numerical examples.

In this paper, following the methods of Connor, we introduce some new generalized double difference sequence spaces using summability with respect to a two valued measure, double infinite matrix and an Orlicz function in 2- normed spaces which have unique non-linear structure and examine some of their properties.

In this paper, the variational homotopy perturbation method (VHPM) and its convergence is adopted for the Zakharove-Kuznetsov equations (ZK-equations). The aim of this paper is to present an efficient and reliable treatment of the VHPM for the nonlinear partial differential equations and show that this method is convergent. The convergence of the applied method is approved using the method of majorants from Cauchy Kowalevskaya theorem of differential equations with analytical vector field.

In this article, the modified exp-function method is used to construct many exact solutions to the nonlinear generalized K(n,n) and BBM equations with variable coefficients. Under different parameter conditions, explicit formulas for some new exact solutions are successfully obtained. The proposed solutions are found to be important for the explanation of some practical physical problems.

Dually flat Finsler metrics form a special and valuable class of Finsler metrics in Finsler information geometry, which play a very important role in studying flat Finsler information structure. In this paper, we prove that every locally dually flat generalized Randers metric with isotropic S-curvature is locally Minkowskian.

Different discrete models of population dynamics of certain insects have been investigated under various feasible conditions within the framework of nonlinear dynamics. Evolutionary phenomena are discussed through bifurcation analysis leading to chaos. Some tools of nonlinear dynamics, such as Lyapunov characteristic exponents (LCE), Lyapunov numbers, correlation dimension, etc. are calculated for numerical studies and to characterize regular and chaotic behavior. These results are produced through various graphics. Chaotic evolutions of such insect population have been discussed as the parameters attain certain set of critical values. The results obtained are informative and very significant. The correlation dimension for evolution of insect population signifies certain fractal structure.

In this paper, uniqueness theorem is studied for boundary value problem with «aftereffect» on a finite interval with discontinuity conditions in an interior point. The oscillation of the eigenfunctions corresponding to large modulus eigenvalues is established and an asymptotic of the nodal points is obtained. By using these new spectral parameters, uniqueness theorem is proved.

In this paper, we prove a common fixed point theorem for six mappings (two set valued and four single valued mappings) without assuming compatibility and continuity of any mapping on non complete metric spaces. To prove the theorem, we use a non compatible condition, that is, weak commutativity of type (KB). We show that completeness of the whole space is not necessary for the existence and uniqueness of common fixed point, and give an example to support our theorem. Also, we prove a common fixed point theorem for two self mappings and two sequences set-valued mappings by the same weaker conditions. Our results improve, extend and generalizes the corresponding results given by many authors.