8,902 research outputs found
Stochastic Stability Analysis of Discrete Time System Using Lyapunov Measure
In this paper, we study the stability problem of a stochastic, nonlinear,
discrete-time system. We introduce a linear transfer operator-based Lyapunov
measure as a new tool for stability verification of stochastic systems. Weaker
set-theoretic notion of almost everywhere stochastic stability is introduced
and verified, using Lyapunov measure-based stochastic stability theorems.
Furthermore, connection between Lyapunov functions, a popular tool for
stochastic stability verification, and Lyapunov measures is established. Using
the duality property between the linear transfer Perron-Frobenius and Koopman
operators, we show the Lyapunov measure and Lyapunov function used for the
verification of stochastic stability are dual to each other. Set-oriented
numerical methods are proposed for the finite dimensional approximation of the
Perron-Frobenius operator; hence, Lyapunov measure is proposed. Stability
results in finite dimensional approximation space are also presented. Finite
dimensional approximation is shown to introduce further weaker notion of
stability referred to as coarse stochastic stability. The results in this paper
extend our earlier work on the use of Lyapunov measures for almost everywhere
stability verification of deterministic dynamical systems ("Lyapunov Measure
for Almost Everywhere Stability", {\it IEEE Trans. on Automatic Control}, Vol.
53, No. 1, Feb. 2008).Comment: Proceedings of American Control Conference, Chicago IL, 201
Accounting and accountability in Fiji: A review and synthesis
This paper reviews accounting and accountability research in Fiji. The review is based on 41 papers which were published in accounting refereed journals, professional journals, edited book chapters and thesis and other refereed journals outside accounting. The reviews are over the years 1978 and onwards. In addition to categorization of the reviewed papers according to accounting topics, theories and methods of data collection, some themes to which the papers could be related are discussed. Financial reporting/ accountability research is the most popular research in Fiji followed by the new public management. Corporate governance research treads third. The paper findings suggest some directions for future accounting history research in Fiji and where the data can possibly be sourced for such research. We conclude that more future work is needed in the areas of accounting history which entails topics such as accounting and the state, performance auditing, indigenous accounting, financial reporting, SMEs and accountability in general
The Compression-Mode Giant Resonances and Nuclear Incompressibility
The compression-mode giant resonances, namely the isoscalar giant monopole
and isoscalar giant dipole modes, are examples of collective nuclear motion.
Their main interest stems from the fact that one hopes to extrapolate from
their properties the incompressibility of uniform nuclear matter, which is a
key parameter of the nuclear Equation of State (EoS). Our understanding of
these issues has undergone two major jumps, one in the late 1970s when the
Isoscalar Giant Monopole Resonance (ISGMR) was experimentally identified, and
another around the turn of the millennium since when theory has been able to
start giving reliable error bars to the incompressibility. However, mainly
magic nuclei have been involved in the deduction of the incompressibility from
the vibrations of finite nuclei. The present review deals with the developments
beyond all this. Experimental techniques have been improved, and new
open-shell, and deformed, nuclei have been investigated. The associated changes
in our understanding of the problem of the nuclear incompressibility are
discussed. New theoretical models, decay measurements, and the search for the
evolution of compressional modes in exotic nuclei are also discussed.Comment: Review paper to appear in "Progress in Particle and Nuclear Physics
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