Linearized Asymptotic Stability for Fractional Differential Equations

We prove the theorem of linearized asymptotic stability for fractional differential equations. More precisely, we show that an equilibrium of a nonlinear Caputo fractional differential equation is asymptotically stable if its linearization at the equilibrium is asymptotically stable. As a consequence we extend Lyapunov's first method to fractional differential equations by proving that if the spectrum of the linearization is contained in the sector \{\lambda \in \C : |\arg \lambda| > \frac{\alpha \pi}{2}\} where $\alpha > 0$ denotes the order of the fractional differential equation, then the equilibrium of the nonlinear fractional differential equation is asymptotically stable

Who are the Devils Wearing Prada in New York City?

Fashion is a perpetual topic in human social life, and the mass has the penchant to emulate what large city residents and celebrities wear. Undeniably, New York City is such a bellwether large city with all kinds of fashion leadership. Consequently, to study what the fashion trends are during this year, it is very helpful to learn the fashion trends of New York City. Discovering fashion trends in New York City could boost many applications such as clothing recommendation and advertising. Does the fashion trend in the New York Fashion Show actually influence the clothing styles on the public? To answer this question, we design a novel system that consists of three major components: (1) constructing a large dataset from the New York Fashion Shows and New York street chic in order to understand the likely clothing fashion trends in New York, (2) utilizing a learning-based approach to discover fashion attributes as the representative characteristics of fashion trends, and (3) comparing the analysis results from the New York Fashion Shows and street-chic images to verify whether the fashion shows have actual influence on the people in New York City. Through the preliminary experiments over a large clothing dataset, we demonstrate the effectiveness of our proposed system, and obtain useful insights on fashion trends and fashion influence

Differential Phase-contrast Interior Tomography

Differential phase contrast interior tomography allows for reconstruction of a refractive index distribution over a region of interest (ROI) for visualization and analysis of internal structures inside a large biological specimen. In this imaging mode, x-ray beams target the ROI with a narrow beam aperture, offering more imaging flexibility at less ionizing radiation. Inspired by recently developed compressive sensing theory, in numerical analysis framework, we prove that exact interior reconstruction can be achieved on an ROI via the total variation minimization from truncated differential projection data through the ROI, assuming a piecewise constant distribution of the refractive index in the ROI. Then, we develop an iterative algorithm for the interior reconstruction and perform numerical simulation experiments to demonstrate the feasibility of our proposed approach

An empirical study on the effect of internal marketing on frontline service employees' performance

2008-2009 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Diagonally Implicit Symplectic Runge-Kutta Methods with High Algebraic and Dispersion Order

The numerical integration of Hamiltonian systems with oscillating solutions is considered in this paper. A diagonally implicit symplectic nine-stages Runge-Kutta method with algebraic order 6 and dispersion order 8 is presented. Numerical experiments with some Hamiltonian oscillatory problems are presented to show the proposed method is as competitive as the existing same type Runge-Kutta methods