7,243 research outputs found
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
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
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