1,000 research outputs found
Borel-Cantelli sequences
A sequence in is called Borel-Cantelli (BC) if
for all non-increasing sequences of positive real numbers with
the set
has full Lebesgue measure. (To put it informally, BC
sequences are sequences for which a natural converse to the Borel-Cantelli
Theorem holds).
The notion of BC sequences is motivated by the Monotone Shrinking Target
Property for dynamical systems, but our approach is from a geometric rather
than dynamical perspective. A sufficient condition, a necessary condition and a
necessary and sufficient condition for a sequence to be BC are established. A
number of examples of BC and not BC sequences are presented.
The property of a sequence to be BC is a delicate diophantine property. For
example, the orbits of a pseudo-Anosoff IET (interval exchange transformation)
are BC while the orbits of a "generic" IET are not.
The notion of BC sequences is extended to more general spaces.Comment: 20 pages. Some proofs clarifie
Preserving the historic landscape of a Chinese village: the case of Wujiang, Suzhou, China, in, The HUL Guidebook: Managing heritage in dynamic and constantly changing urban environments
Optimal stability and instability for near-linear Hamiltonians
In this paper, we will prove a very general result of stability for
perturbations of linear integrable Hamiltonian systems, and we will construct
an example of instability showing that both our result and our example are
optimal. Moreover, in the same spirit as the notion of KAM stable integrable
Hamiltonians, we will introduce a notion of effectively stable integrable
Hamiltonians, conjecture a characterization of these Hamiltonians and show that
our result prove this conjecture in the linear case
Double exponential stability of quasi-periodic motion in Hamiltonian systems
We prove that generically, both in a topological and measure-theoretical
sense, an invariant Lagrangian Diophantine torus of a Hamiltonian system is
doubly exponentially stable in the sense that nearby solutions remain close to
the torus for an interval of time which is doubly exponentially large with
respect to the inverse of the distance to the torus. We also prove that for an
arbitrary small perturbation of a generic integrable Hamiltonian system, there
is a set of almost full positive Lebesgue measure of KAM tori which are doubly
exponentially stable. Our results hold true for real-analytic but more
generally for Gevrey smooth systems
Infinite ergodic theory and Non-extensive entropies
We bring into account a series of result in the infinite ergodic theory that
we believe that they are relevant to the theory of non-extensive entropie
Towards a method for rigorous development of generic requirements patterns
We present work in progress on a method for the engineering, validation and verification of generic requirements using domain engineering and formal methods. The need to develop a generic requirement set for subsequent system instantiation is complicated by the addition of the high levels of verification demanded by safety-critical domains such as avionics. Our chosen application domain is the failure detection and management function for engine control systems: here generic requirements drive a software product line of target systems. A pilot formal specification and design exercise is undertaken on a small (twosensor) system element. This exercise has a number of aims: to support the domain analysis, to gain a view of appropriate design abstractions, for a B novice to gain experience in the B method and tools, and to evaluate the usability and utility of that method.We also present a prototype method for the production and verification of a generic requirement set in our UML-based formal notation, UML-B, and tooling developed in support. The formal verification both of the structural generic requirement set, and of a particular application, is achieved via translation to the formal specification language, B, using our U2B and ProB tools
Holomorphic linearization of commuting germs of holomorphic maps
Let be germs of biholomorphisms of \C^n fixing the
origin. We investigate the shape a (formal) simultaneous linearization of the
given germs can have, and we prove that if commute and their
linear parts are almost simultaneously Jordanizable then they are
simultaneously formally linearizable. We next introduce a simultaneous
Brjuno-type condition and prove that, in case the linear terms of the germs are
diagonalizable, if the germs commutes and our Brjuno-type condition holds, then
they are holomorphically simultaneously linerizable. This answers to a
multi-dimensional version of a problem raised by Moser.Comment: 24 pages; final version with erratum (My original paper failed to
cite the work of L. Stolovitch [ArXiv:math/0506052v2]); J. Geom. Anal. 201
Second-Order Belief Hidden Markov Models
Hidden Markov Models (HMMs) are learning methods for pattern recognition. The
probabilistic HMMs have been one of the most used techniques based on the
Bayesian model. First-order probabilistic HMMs were adapted to the theory of
belief functions such that Bayesian probabilities were replaced with mass
functions. In this paper, we present a second-order Hidden Markov Model using
belief functions. Previous works in belief HMMs have been focused on the
first-order HMMs. We extend them to the second-order model
Mass Production and Size Control of Lipid–Polymer Hybrid Nanoparticles through Controlled Microvortices
Lipid–polymer hybrid (LPH) nanoparticles can deliver a wide range of therapeutic compounds in a controlled manner. LPH nanoparticle syntheses using microfluidics improve the mixing process but are restricted by a low throughput. In this study, we present a pattern-tunable microvortex platform that allows mass production and size control of LPH nanoparticles with superior reproducibility and homogeneity. We demonstrate that by varying flow rates (i.e., Reynolds number (30–150)) we can control the nanoparticle size (30–170 nm) with high productivity (~3 g/hour) and low polydispersity (~0.1). Our approach may contribute to efficient development and optimization of a wide range of multicomponent nanoparticles for medical imaging and drug delivery.National Heart, Lung, and Blood Institute (Program of Excellence in Nanotechnology (PEN) Award Contract HHSN268201000045C)National Cancer Institute (U.S.) (Grant P01 CA151884)Prostate Cancer Foundation (Award in Nanotherapeutics
PPAR γ-agonist induces regression of atherosclerotic plaques: invivo study by high resolution magnetic resonance imaging
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