6,924 research outputs found
Semiflow selection and Markov selection theorems
The deterministic analog of the Markov property of a time-homogeneous Markov
process is the semigroup property of solutions of an autonomous differential
equation. The semigroup property arises naturally when the solutions of a
differential equation are unique, and leads to a semiflow. We prove an abstract
result on measurable selection of a semiflow for the situations without
uniqueness. We outline applications to ODEs, PDEs, differential inclusions,
etc. Our proof of the semiflow selection theorem is motivated by N. V. Krylov's
Markov selection theorem. To accentuate this connection, we include a new
version of the Markov selection theorem related to more recent papers of
Flandoli & Romito and Goldys et al.Comment: In this revised version we have added a new abstract result in Sec.
2. It is used to correct the Navier-Stokes example in application
Short Cycles in Repeated Exponentiation Modulo a Prime
Given a prime , we consider the dynamical system generated by repeated
exponentiations modulo , that is, by the map , where
and . This map is in
particular used in a number of constructions of cryptographically secure
pseudorandom generators. We obtain nontrivial upper bounds on the number of
fixed points and short cycles in the above dynamical system
Integration of fiber coupled high-Q silicon nitride microdisks with atom chips
Micron scale silicon nitride (SiN_x) microdisk optical resonators are
demonstrated with Q = 3.6 x 10^6 and an effective mode volume of 15 (\lambda /
n)^3 at near visible wavelengths. A hydrofluoric acid wet etch provides
sensitive tuning of the microdisk resonances, and robust mounting of a fiber
taper provides efficient fiber optic coupling to the microdisks while allowing
unfettered optical access for laser cooling and trapping of atoms. Measurements
indicate that cesium adsorption on the SiN_x surfaces significantly red-detunes
the microdisk resonances. A technique for parallel integration of multiple (10)
microdisks with a single fiber taper is also demonstrated.Comment: Published vesion. Minor change
Wonderful blowups associated to group actions
A group action on a smooth variety provides it with the natural
stratification by irreducible components of the fixed point sets of arbitrary
subgroups. We show that the corresponding maximal wonderful blowup in the sense
of MacPherson-Procesi has only abelian stabilizers. The result is inspired by
the abelianization algorithm of Batyrev.Comment: 6 page
Interpretation of 35 Hz QPO in the Atoll Source 4U 1702-42 as a Low Branch of the Keplerian Oscillations Under the Influence of the Coriolis Force
The recent model of quasi-periodic oscillations in neutron star binaries
(Osherovich and Titarchuk 1999, Titarchuk and Osherovich 1999) has suggested
the existence of two branches of QPOs due to the influence of Coriolis force on
the linear Keplerian oscillator: one branch with frequencies from 400 to 1200
Hz and another branch with frequencies an order of magnitude lower. The
frequencies of the high branch nu_h hold a hybrid frequency relation with the
Keplerian frequency nu_K: nu_h^2=nu_K^2+ [Omega/pi]^2, where Omega is the
rotational frequency of the star's magnetosphere. The frequency of the low
branch is nu_L=(Omega/pi)(nu_K/nu_h) sin(delta), where delta is a small angle
between vector Omega and the vector normal to the plane of Keplerian
oscillations. The observations of the source 4U 1702-42 (Markwardt et al 1999)
have shown that the centroid of the 35 Hz QPO tracks the frequency of the
kilohertz oscillations. We interpret the 35 Hz oscillations as nu_L and find
delta=3.9^o +/- 0.2^o. Our results make 4U 1702-42 the second source (after Sco
X-1) for which the theoretically derived lower branch is identified (within our
model) and delta is calculated. The inferred angle delta stays approximately
the same over the significant range of nu_K (650 - 900 Hz), as expected from
the model. Based on our model we present a classification of QPO frequencies in
the source 4U 1702-42 observed above and below nu_L.Comment: 12 pages, 2 figures, accepted for publication in ApJ Letter
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