Kyungpook Mathematical Journal 

Abstract: In this paper, global chaos synchronization is investigated for WINDMI (J. C. Sprott, 2003) and Coullet (P. Coullet et al, 1979) chaotic systems using adaptive backstep- ping control design based on recursive feedback control. Our theorems on synchronization for WINDMI and Coullet chaotic systems are established using Lyapunov stability the- ory. The adaptive backstepping control links the choice of Lyapunov function with the design of a controller and guarantees global stability performance of strict-feedback chaotic systems. The adaptive backstepping control maintains the parameter vector at a predeter- mined desired value. The adaptive backstepping control method is efiective and convenient to synchronize and estimate the parameters of the chaotic systems. Mainly, this technique gives the ∞exibility to construct a control law and estimate the parameter values. Numeri- cal simulations are also given to illustrate and validate the synchronization results derived in this paper.

Abstract: In this paper we introduce the concept of lacunary statistical and lacunary strongly convergence of generalized difference sequence of fuzzy real numbers. We prove some inclusion relations and also study some of their properties.

Abstract: In this research work, a seven-term 3-D novel jerk chaotic system with two quadratic nonlinearities has been proposed. The basic qualitative properties of the novel jerk chaotic system have been described in detail. Next, an adaptive backstepping controller is designed to stabilize the novel jerk chaotic system with two unknown parameters. Moreover, an adaptive backstepping controller is designed to achieve complete chaos synchronization of the identical novel jerk chaotic systems with two unknown parameters. MATLAB simulations have been shown in detail to illustrate all the main results developed for the 3-D novel jerk chaotic system.

Abstract: K1: Find necessary and sufficient conditions under which every preopen set is open. K2: Find conditions under which every dense-in-itself set is preopen. K3: Find conditions under which the intersection of any two preopen sets preopen. K4: If (X, τ) is a topological space, let τ ∗ denote the topology on X obtained by taking the collection of all preopen sets of (X, τ) as a subbase. Find conditions under which τ ∗ is discrete. ∗AMS Subject Classification : 54 A 05, 54 A 10;

Abstract: The object of the present paper is to study a type of Riemannian manifold called generalized quasi Einstein manifold