2,048 research outputs found
Square-free class sizes in products of groups
We obtain some structural properties of a factorised group , given
that the conjugacy class sizes of certain elements in are not
divisible by , for some prime . The case when is a mutually
permutable product is especially considered
Compensation for effects of ambient temperature on rare-earth doped fiber optic thermometer
Variations in ambient temperature have a negative effect on the performance of any fiber optic sensing system. A change in ambient temperature may alter the design parameters of fiber optic cables, connectors, sources, detectors, and other fiber optic components and eventually the performance of the entire system. The thermal stability of components is especially important in a system which employs intensity modulated sensors. Several referencing schemes have been developed to account for the variable losses that occur within the system. However, none of these conventional compensating techniques can be used to stabilize the thermal drift of the light source in a system based on the spectral properties of the sensor material. The compensation for changes in ambient temperature becomes especially important in fiber optic thermometers doped with rare earths. Different approaches to solving this problem are searched and analyzed
Mechanical oscillations in lasing microspheres
We investigate the feasibility of activating coherent mechanical oscillations
in lasing microspheres by modulating the laser emission at a mechanical
eigenfrequency. To this aim, 1.5% Nd3+:Barium-Titanium-Silicate microspheres
with diameters around 50 {\mu}m were used as high quality factor (Q>10^6)
whispering gallery mode lasing cavities. We have implemented a pump-and-probe
technique in which the pump laser used to excite the Nd3+ ions is focused on a
single microsphere with a microscope objective and a probe laser excites a
specific optical mode with the evanescent field of a tapered fibre. The studied
microspheres show monomode and multi-mode lasing action, which can be modulated
in the best case up to 10 MHz. We have optically transduced thermally-activated
mechanical eigenmodes appearing in the 50-70 MHz range, the frequency of which
decreases with increasing the size of the microspheres. In a pump-and-probe
configuration we observed modulation of the probe signal up to the maximum pump
modulation frequency of our experimental setup, i.e., 20 MHz. This modulation
decreases with frequency and is unrelated to lasing emission, pump scattering
or thermal effects. We associate this effect to free-carrier-dispersion induced
by multiphoton pump light absorption. On the other hand, we conclude that, in
our current experimental conditions, it was not possible to resonantly excite
the mechanical modes. Finally, we discuss on how to overcome these limitations
by increasing the modulation frequency of the lasing emission and decreasing
the frequency of the mechanical eigenmodes displaying a strong degree of
optomechanical coupling.Comment: 17 pages, 5 figure
Group Strategyproof Pareto-Stable Marriage with Indifferences via the Generalized Assignment Game
We study the variant of the stable marriage problem in which the preferences
of the agents are allowed to include indifferences. We present a mechanism for
producing Pareto-stable matchings in stable marriage markets with indifferences
that is group strategyproof for one side of the market. Our key technique
involves modeling the stable marriage market as a generalized assignment game.
We also show that our mechanism can be implemented efficiently. These results
can be extended to the college admissions problem with indifferences
Probing the electron-phonon coupling in ozone-doped graphene by Raman spectroscopy
We have investigated the effects of ozone treatment on graphene by Raman
scattering. Sequential ozone short-exposure cycles resulted in increasing the
doping levels as inferred from the blue shift of the 2 and peak
frequencies, without introducing significant disorder. The two-phonon 2 and
2 Raman peak intensities show a significant decrease, while, on the
contrary, the one-phonon G Raman peak intensity remains constant for the whole
exposure process. The former reflects the dynamics of the photoexcited
electrons (holes) and, specifically, the increase of the electron-electron
scattering rate with doping. From the ratio of 2 to 2 intensities, which
remains constant with doping, we could extract the ratio of electron-phonon
coupling parameters. This ratio is found independent on the number of layers up
to ten layers. Moreover, the rate of decrease of 2 and 2 intensities
with doping was found to slowdown inversely proportional to the number of
graphene layers, revealing the increase of the electron-electron collision
probability
Smoothing tautologies, hidden dynamics, and sigmoid asymptotics for piecewise smooth systems
Switches in real systems take many forms, such as impacts, electronic relays,
mitosis, and the implementation of decisions or control strategies. To
understand what is lost, and what can be retained, when we model a switch as an
instantaneous event, requires a consideration of so-called hidden terms. These
are asymptotically vanishing outside the switch, but can be encoded in the form
of nonlinear switching terms. A general expression for the switch can be
developed in the form of a series of sigmoid functions. We review the key steps
in extending the Filippov's method of sliding modes to such systems. We show
how even slight nonlinear effects can hugely alter the behaviour of an
electronic control circuit, and lead to `hidden' attractors inside the
switching surface.Comment: 12 page
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