The Bogdanov-Takens system has at most one limit cycle and, in the parameter space, it exists between a Hopf and a saddle-loop bifurcation curves. The aim of this paper is to prove the Perko’s conjectures about some analytic properties of the saddle-loop bifurcation curve. Moreover, we provide sharp piecewise algebraic upper and lower bounds for this curve.

We construct vortex loop operators in the three-dimensional N = 6 supersymmetric Chern-Simons theory recently constructed by Aharony, Bergman, Jafferis and Maldacena. These disorder loop operators are specified by a vortex-like singularity for the scalar and gauge fields along a one dimensional curve in spacetime. We identify the 1/2, 1/3 and 1/6 BPS loop operators in the Chern-Simons theory wi...

Could inflated credit ratings that provide new information have adverse ex-ante real effects? If so, why? In a debt-rollover game featuring a feedback loop, we show that when the risky projects have high upside returns, the credit rating agency’s (CRA) ex-ante real effects are negative, despite of its positive informational effects. This arises from the CRAs feedback effects: it strategically a...

The Receiver Operating Characteristic (ROC) Curve originated during Second World War to analyse radar signals by observing the relationship between signal and noise [1]. The framework of ROC Curve has a wide spread of interdisciplinary applications such as human perception, decision making [2], industrial quality control [3], military monitoring [4] etc. In later years, the applications of ROC ...

In Brazil, the correct measurement of individual firm energy a plant is important, since it influences directly determination its assured which used to establish contracts between power plants and distribution companies, free consumers, traders. With increasing technological development greater reliability in use automated techniques for monitoring, Acoustic Doppler Current Profiler (ADCP), has...

modeling of stream flow–suspended sediment relationship is one of the most studied topics in hydrology due to itsessential application to water resources management. recently, artificial intelligence has gained much popularity owing toits application in calibrating the nonlinear relationships inherent in the stream flow–suspended sediment relationship. thisstudy made us of adaptive neuro-fuzzy ...

Modeling of stream flow–suspended sediment relationship is one of the most studied topics in hydrology due to itsessential application to water resources management. Recently, artificial intelligence has gained much popularity owing toits application in calibrating the nonlinear relationships inherent in the stream flow–suspended sediment relationship. Thisstudy made us of adaptive neuro-fuzzy ...