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 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 sequencespaces 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 theZakharove-Kuznetsov equations (ZK-equations). The aim of this paper is to present an efficient and reliabletreatment 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-Kowalevskayatheorem of differential equations with analytical vector field.

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

Let , be a graph with vertex set of order and edge set . A -dominating set of is a subset such that each vertex in has at least neighbors in . If is a vertex of a graph , the open -neighborhood of , denoted by , is the set , . is the closed -neighborhood of . A function 1, 1 is a signed distance- dominating function of , if for every vertex , Σ 1. The signed distance--domination number, denoted by ,, is the minimum weight of a signed distance--dominating function of . In this paper, we give lower and upper bounds on , of graphs. Also, we determine the signed distance--domination number of graph , (the graph obtained from the disjoint union by adding the edges , ) when 2.

The compact operators on the Riesz sequence space 1 ∞ have been studied by Başarır and Kara, “IJST (2011) A4, 279-285”. In the present paper, we will characterize some classes of compact operators on the normed Riesz sequence spaces and by using the Hausdorff measure of noncompactness.

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 everylocally 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 have generalized the concepts of ,q-fuzzy ideals, ,q-fuzzy quasi-ideals and,q-fuzzy bi-ideals by introducing the concepts of k ,q -fuzzy ideals, k ,q -fuzzy quasiideals and k ,q -fuzzy bi-ideals in ternary semigroups and several related properties are investigated. Different characterizations of regular and weakly regular ternary semigroups by the properties of these ideals are given.

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.