Power system stability is quantified as the ability to regain an equilibrium state after being subjected to perturbations. We start by investigating the global basin stability of a single machine bus-bar system and then extend it to two and four oscillators. We calculate the basin stability of the stable fixed point over the whole parameter space, in which different parameter combinations give ...

We investigate the convergence of the self-consistent field (SCF) iteration used to solve a class of nonlinear eigenvalue problems. We show that for the class of problem considered, the SCF iteration produces a sequence of approximate solutions that contain two convergent subsequences. These subsequences may converge to two different limit points, neither of which is the solution to the nonline...

Asynchronous computing environments provide an ideal framework for conceptual modeling and simulation of large scale, distributed discrete event systems. Such environments may, however, exhibit an aperiodic oscillatory behavior referred to as “computational chaos”, which impedes the correct processing of quantities of interest. In this paper, we illustrate the emergence of computational chaos f...

In this paper, we report the existence of twelve small limit cycles in a planar system with 3rd-degree polynomial functions. The system has Z2symmetry, with a saddle point, or a node, or a focus point at the origin, and two focus points which are symmetric about the origin. It is shown that such a Z2-equivariant vector field can have twelve small limit cycles. Fourteen or sixteen small limit cy...

We study the scaling limit of a model of a tethered crumpled D-dimensional random surface interacting through an exclusion condition with a fixed impurity in d-dimensional Euclidean space by the methods of Wilson's renormalization group. In this paper we consider a hierarchical version of the model and we prove rigorously the existence of the scaling limit and convergence to a non-Gaussian fixe...

For any lacunary sequence $theta = (k_{r})$, we define the concepts of $S_{theta}-$limit point and $S_{theta}-$cluster point of a sequence of fuzzy numbers $X = (X_{k})$. We introduce the new sets  $Lambda^{F}_{S_{theta}}(X)$, $Gamma^{F}_{S_{theta}}(X)$ and prove some inclusion relaions between these and the sets $Lambda^{F}_{S}(X)$, $Gamma^{F}_{S}(X)$ introduced in ~cite{Ayt:Slpsfn} by Aytar [...

In this paper, by using C-class functions, we will present a coupled …xed problem in b-metric space for the single-valued operators satisfying a generalized contraction condition. First part of the paper is related to some …xed point theorems, the second part presents the uniqueness and existence for the solution of the coupled …xed point problem and in the third part we...

In this article, we consider a sequence (Nn)n≥1 of point processes, whose points lie in a subset E of R\{0}, and satisfy an asymptotic independence condition. Our main result gives some necessary and sufficient conditions for the convergence in distribution of (Nn)n≥1 to an infinitely divisible point process N . As applications, we discuss the exceedance processes and point processes based on r...

In this paper, the authors consider both the forced and unforced versions of a second order nonlinear differential equation with a p-Laplacian. They give sufficient conditions as well as necessary and sufficient conditions for the unforced equation to be of the strong nonlinear limit-circle type, and they give sufficient conditions for the forced equation to be of the strong nonlinear limit-cir...

We discuss a Penrose limit of an elliptic brane configuration withN1 NS5 andN2 D4 branes. This background is T-dual to N1 D3 branes at a fixed point of aC /ZN2 singularity and the T-duality survives the Penrose limit. The triple scaling limit of N1 and N2 gives rise to IIA pp-wave solution with a space-like compact direction. We identify the quiver gauge theory operators and argue that upon exc...