842 research outputs found
Hausdorff dimension of three-period orbits in Birkhoff billiards
We prove that the Hausdorff dimension of the set of three-period orbits in
classical billiards is at most one. Moreover, if the set of three-period orbits
has Hausdorff dimension one, then it has a tangent line at almost every point.Comment: 10 pages, 1 figur
Palm distributions of wave characteristics in encountering seas
Distributions of wave characteristics of ocean waves, such as wave slope,
waveheight or wavelength, are an important tool in a variety of oceanographic
applications such as safety of ocean structures or in the study of ship
stability, as will be the focus in this paper. We derive Palm distributions of
several wave characteristics that can be related to steepness of waves for two
different cases, namely for waves observed along a line at a fixed time point
and for waves encountering a ship sailing on the ocean. The relation between
the distributions obtained in the two cases is also given physical
interpretation in terms of a ``Doppler shift'' that is related to the velocity
of the ship and the velocities of the individual waves.Comment: Published in at http://dx.doi.org/10.1214/07-AAP480 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Eigenfunctions for smooth expanding circle maps
We construct a real-analytic circle map for which the corresponding
Perron-Frobenius operator has a real-analytic eigenfunction with an eigenvalue
outside the essential spectral radius when acting upon -functions.Comment: 10 pages, 2 figure
A Borel-Cantelli lemma for intermittent interval maps
We consider intermittent maps T of the interval, with an absolutely
continuous invariant probability measure \mu. Kim showed that there exists a
sequence of intervals A_n such that \sum \mu(A_n)=\infty, but \{A_n\} does not
satisfy the dynamical Borel-Cantelli lemma, i.e., for almost every x, the set
\{n : T^n(x)\in A_n\} is finite. If \sum \Leb(A_n)=\infty, we prove that
\{A_n\} satisfies the Borel-Cantelli lemma. Our results apply in particular to
some maps T whose correlations are not summable.Comment: 7 page
Rare events, escape rates and quasistationarity: some exact formulae
We present a common framework to study decay and exchanges rates in a wide
class of dynamical systems. Several applications, ranging form the metric
theory of continuons fractions and the Shannon capacity of contrained systems
to the decay rate of metastable states, are given
Statistical and Probabilistic Extensions to Ground Operations' Discrete Event Simulation Modeling
NASA's human exploration initiatives will invest in technologies, public/private partnerships, and infrastructure, paving the way for the expansion of human civilization into the solar system and beyond. As it is has been for the past half century, the Kennedy Space Center will be the embarkation point for humankind's journey into the cosmos. Functioning as a next generation space launch complex, Kennedy's launch pads, integration facilities, processing areas, launch and recovery ranges will bustle with the activities of the world's space transportation providers. In developing this complex, KSC teams work through the potential operational scenarios: conducting trade studies, planning and budgeting for expensive and limited resources, and simulating alternative operational schemes. Numerous tools, among them discrete event simulation (DES), were matured during the Constellation Program to conduct such analyses with the purpose of optimizing the launch complex for maximum efficiency, safety, and flexibility while minimizing life cycle costs. Discrete event simulation is a computer-based modeling technique for complex and dynamic systems where the state of the system changes at discrete points in time and whose inputs may include random variables. DES is used to assess timelines and throughput, and to support operability studies and contingency analyses. It is applicable to any space launch campaign and informs decision-makers of the effects of varying numbers of expensive resources and the impact of off nominal scenarios on measures of performance. In order to develop representative DES models, methods were adopted, exploited, or created to extend traditional uses of DES. The Delphi method was adopted and utilized for task duration estimation. DES software was exploited for probabilistic event variation. A roll-up process was used, which was developed to reuse models and model elements in other less - detailed models. The DES team continues to innovate and expand DES capabilities to address KSC's planning needs
Almost sure functional central limit theorems for multiparameter stochastic processes
We present almost sure central limit theorems for stochastic processes whose time parameter ranges over
the d-dimensional unit cube. Our purpose here is to generalize the classic functional central limit theorem of
Prokhorov (1956) for such processes. We prove multidimensional analogues of Glivenko-Cantelli type theorems.Ми подаємо майже певнi центральнi граничнi теореми для стохастичних процесiв з часовим параметром, що змiнюється у α-вимiрному одиничному кубi. Нашою метою є узагальнення класичної функцiональної центральної граничної теореми Прохорова (1956) для таких процесiв. Ми доводимо багатовимiрнi аналоги теореми типу Глiвенко-Кантелi
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