The Hartman-Grobman and Poincaré-Bendixon Theorems are two of the most powerful tools used in dynamical systems. The Hartman-Grobman theorem allows us to represent the local phase portrait about certain types of equilibria in a nonlinear system by a similar, simpler linear system that we can find by computing the system’s Jacobian matrix at the equilibrium point. The Poincaré-Bendixon theorem g...

A harmonic balance based identification algorithm was applied to the simulated single pendulum with horizontal base-excitation. The purpose of this simulation was to examine the applicability of the algorithm on parametrically excited, whirling chaotic systems. Modifications were adopted to adapt to the whirling systems. The system was supposed to be unknown except only the excitation frequency...

In the book Birth of a Theorem: A Mathematical Adventure, Cédric Villani paints portrait himself, from (dare I say) obsessed mathematician who works until wee hours night, to ordinary citizen, enjoying an impressive variety music, slightly odd man sporting ornamental spider daily. From Lyon Paris, through despair not being able eat quality cheese, takes us on journey, revisiting path that led h...

In this paper we consider a system of two reaction-diffusion equations that models diffusional-thermal combustion with stepwise ignition-temperature kinetics and fractional reaction order 0<α<1. We turn the free interface problem into scalar boundary coupled an integral equation. The main intermediary step is to reduce study non-Lipschitz vector field in dimension 2. latter treated by qualitati...

the aim of this paper is to show the importance of analytic hyperbolic geometry introduced in [9]. in [1], ungar and chen showed that the algebra of the group sl(2,c) naturally leads to the notion of gyrogroups and gyrovector spaces for dealing with the lorentz group and its underlying hyperbolic geometry. they defined the chen addition and then chen model of hyperbolic geometry. in this paper,...

Sculpting various 3D facial expressions from a static 3D face model is a process with intensive manual tuning efforts. In this paper, we present an interactive 3D facial expression posing system through 2D portrait manipulation, where a manipulated 2D portrait serves a metaphor for automatically inferring its corresponding 3D facial expression with fine details. Users either rapidly assemble a ...

The paper looks at the digital portrait used in the form of avatars in various online worlds and communication networks. It describes an ongoing modal shift from an ontological understanding of the portrait towards the portrait as performative

Born in 1944, I grew up in a world in which polio was both a gripping fear and real threat. Then in a matter of a few years-polio was eradicated by a vaccine developed by Jonas Salk. Later I learned that Salk's efforts were built on pioneering work of many others, including John Enders, Thomas Weller and Frederick Robbins (Nobelists, 1954), and David Bodian, who pioneered studies of polio patho...

Chaotic analysis has been shown to be useful in a variety of medical applications, particularly in cardiology. Chaotic parameters have shown potential in the identification of diseases, especially in the analysis of biomedical signals like electrocardiogram (ECG). In this work, underlying chaos in ECG signals has been analyzed using various non-linear techniques. First, the ECG signal is proces...

Surprisingly, an utterly imaginative "portrait" has become synonymous with Maimonides forever. How and when did this particular portrait become associated with Maimonides? This and many other intriguing questions regarding this portrait are systematically addressed, and its origins, possible inspiration, and hidden objectives are revealed.