15,946 research outputs found
Extrema of graph eigenvalues
In 1993 Hong asked what are the best bounds on the 'th largest eigenvalue
of a graph of order . This challenging question has
never been tackled for any . In the present paper tight bounds are
obtained for all and even tighter bounds are obtained for the 'th
largest singular value
Some of these bounds are based on Taylor's strongly regular graphs, and other
on a method of Kharaghani for constructing Hadamard matrices. The same kind of
constructions are applied to other open problems, like Nordhaus-Gaddum problems
of the kind: How large can be
These constructions are successful also in another open question: How large
can the Ky Fan norm be
Ky Fan norms of graphs generalize the concept of graph energy, so this question
generalizes the problem for maximum energy graphs.
In the final section, several results and problems are restated for
-matrices, which seem to provide a more natural ground for such
research than graphs.
Many of the results in the paper are paired with open questions and problems
for further study.Comment: 32 page
Development of an annoyance model based upon elementary auditory sensations for steady-state aircraft interior noise containing tonal components
The purpose of this investigation was to develop a noise annoyance model, superior to those already in use, for evaluating passenger response to sounds containing tonal components which may be heard within current and future commercial aircraft. The sound spectra investigated ranged from those being experienced by passengers on board turbofan powered aircraft now in service to those cabin noise spectra passengers may experience within advanced propeller-driven aircraft of the future. A total of 240 sounds were tested in this experiment. Sixty-six of these 240 sounds were steady state, while the other 174 varied temporally due to tonal beating. Here, the entire experiment is described, but the analysis is limited to those responses elicited by the 66 steady-state sounds
Smart monitoring of aeronautical composites plates based on electromechanical impedance measurements and artificial neural networks
This paper presents a structural health monitoring (SHM) method for in situ damage detection and localization in carbon fiber reinforced plates (CFRPs). The detection is achieved using the electromechanical impedance (EMI) technique employing piezoelectric transducers as high-frequency modal sensors. Numerical simulations based on the finite element method are carried out so as to simulate more than a hundred damage scenarios. Damage metrics are then used to quantify and detect changes between the electromechanical impedance spectrum of a pristine and damaged structure. The localization process relies on artificial neural networks (ANNs) whose inputs are derived from a principal component analysis of the damage metrics. It is shown that the resulting ANN can be used as a tool to predict the in-plane position of a single damage in a laminated composite plate
The Cosmic Microwave Background and Helical Magnetic Fields: the tensor mode
We study the effect of a possible helicity component of a primordial magnetic
field on the tensor part of the cosmic microwave background temperature
anisotropies and polarization. We give analytical approximations for the tensor
contributions induced by helicity, discussing their amplitude and spectral
index in dependence of the power spectrum of the primordial magnetic field. We
find that an helical magnetic field creates a parity odd component of gravity
waves inducing parity odd polarization signals. However, only if the magnetic
field is close to scale invariant and if its helical part is close to maximal,
the effect is sufficiently large to be observable. We also discuss the
implications of causality on the magnetic field spectrum.Comment: We have corrected a normalisation error which was pointed out to us
by Antony Lewis. It enhances our limits on the magnetic fields by
(2\pi)^{3/4} ~
Photon orbital angular momentum and torque metrics for single telescopes and interferometers
Context. Photon orbital angular momentum (POAM) is normally invoked in a
quantum mechanical context. It can, however, also be adapted to the classical
regime, which includes observational astronomy.
Aims. I explain why POAM quantities are excellent metrics for describing the
end-to-end behavior of astronomical systems. To demonstrate their utility, I
calculate POAM probabilities and torques from holography measurements of EVLA
antenna surfaces.
Methods. With previously defined concepts and calculi, I present generic
expressions for POAM spectra, total POAM, torque spectra, and total torque in
the image plane. I extend these functional forms to describe the specific POAM
behavior of single telescopes and interferometers.
Results. POAM probabilities of spatially uncorrelated astronomical sources
are symmetric in quantum number. Such objects have zero intrinsic total POAM on
the celestial sphere, which means that the total POAM in the image plane is
identical to the total torque induced by aberrations within propagation media &
instrumentation. The total torque can be divided into source- independent and
dependent components, and the latter can be written in terms of three
illustrative forms. For interferometers, complications arise from discrete
sampling of synthesized apertures, but they can be overcome. POAM also
manifests itself in the apodization of each telescope in an array. Holography
of EVLA antennas observing a point source indicate that ~ 10% of photons in the
n = 0 state are torqued to n != 0 states.
Conclusions. POAM quantities represent excellent metrics for characterizing
instruments because they are used to simultaneously describe amplitude and
phase aberrations. In contrast, Zernike polynomials are just solutions of a
differential equation that happen to ~ correspond to specific types of
aberrations and are typically employed to fit only phases
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