52 research outputs found
Scaling of the Critical Function for the Standard Map: Some Numerical Results
The behavior of the critical function for the breakdown of the homotopically
non-trivial invariant (KAM) curves for the standard map, as the rotation number
tends to a rational number, is investigated using a version of Greene's residue
criterion. The results are compared to the analogous ones for the radius of
convergence of the Lindstedt series, in which case rigorous theorems have been
proved. The conjectured interpolation of the critical function in terms of the
Bryuno function is discussed.Comment: 26 pages, 3 figures, 13 table
The Near-Infrared Spectrograph (NIRSpec) on the James Webb Space Telescope: I. Overview of the instrument and its capabilities
We provide an overview of the design and capabilities of the near-infrared
spectrograph (NIRSpec) onboard the James Webb Space Telescope. NIRSpec is
designed to be capable of carrying out low-resolution () prism
spectroscopy over the wavelength range m and higher resolution
( or ) grating spectroscopy over
m, both in single-object mode employing any one of five fixed
slits, or a 3.13.2 arcsec integral field unit, or in multiobject
mode employing a novel programmable micro-shutter device covering a
3.63.4~arcmin field of view. The all-reflective optical chain of
NIRSpec and the performance of its different components are described, and some
of the trade-offs made in designing the instrument are touched upon. The
faint-end spectrophotometric sensitivity expected of NIRSpec, as well as its
dependency on the energetic particle environment that its two detector arrays
are likely to be subjected to in orbit are also discussed
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The Near-Infrared Spectrograph (NIRSpec) on the James Webb Space Telescope: I. Overview of the instrument and its capabilities
We provide an overview of the design and capabilities of the near-infrared
spectrograph (NIRSpec) onboard the James Webb Space Telescope. NIRSpec is
designed to be capable of carrying out low-resolution () prism
spectroscopy over the wavelength range m and higher resolution
( or ) grating spectroscopy over
m, both in single-object mode employing any one of five fixed
slits, or a 3.13.2 arcsec integral field unit, or in multiobject
mode employing a novel programmable micro-shutter device covering a
3.63.4~arcmin field of view. The all-reflective optical chain of
NIRSpec and the performance of its different components are described, and some
of the trade-offs made in designing the instrument are touched upon. The
faint-end spectrophotometric sensitivity expected of NIRSpec, as well as its
dependency on the energetic particle environment that its two detector arrays
are likely to be subjected to in orbit are also discussed
The James Webb Space Telescope Mission
Twenty-six years ago a small committee report, building on earlier studies,
expounded a compelling and poetic vision for the future of astronomy, calling
for an infrared-optimized space telescope with an aperture of at least .
With the support of their governments in the US, Europe, and Canada, 20,000
people realized that vision as the James Webb Space Telescope. A
generation of astronomers will celebrate their accomplishments for the life of
the mission, potentially as long as 20 years, and beyond. This report and the
scientific discoveries that follow are extended thank-you notes to the 20,000
team members. The telescope is working perfectly, with much better image
quality than expected. In this and accompanying papers, we give a brief
history, describe the observatory, outline its objectives and current observing
program, and discuss the inventions and people who made it possible. We cite
detailed reports on the design and the measured performance on orbit.Comment: Accepted by PASP for the special issue on The James Webb Space
Telescope Overview, 29 pages, 4 figure
Computing (Un)stable Manifolds with Validated Error Bounds: Non-resonant and Resonant Spectra
How gold is the golden ratio?
We discuss the well-known importance of the golden ratio in Science and Art with few examples: its theoretical value is often taken as a good model in many applications. How good is this model in practice? We agree with many authors that more precision is needed giving, when possible, a measure of the best possible approximation. We deal with several definitions and representations, also comparing this irrational number and its rational approximations to other similar constants
Numeri in un foglio di carta
Dato un normale foglio di carta per fotocopie, di formato A4, con semplici piegature è possibile verificare alcune proprietà aritmetiche sul rapporto (radice di 2) tra le misure dei suoi lati.
Si dimostra quindi che dal foglio A4, con solo tre pieghe, si può costruire un rettangolo "aureo", il cui rapporto tra i lati sia f = (Sqrt{5}+1)/2. Si verifica anche come lo sviluppo in frazioni continue di radice di 2 e f siano legati alla proprietà comune ai due rettangoli: dopo aver tagliato un quadrato costruito sul lato più corto per due volte, si ottiene un rettangolo simile a quello di partenza.From a regular A4 sheet of paper, with simple folds, it is possible to verify some arithmetical properties on the ratio of its sides (square root of 2).
A proof is given that, starting with an A4 sheet and with just 3 folds, it is possible to construct a "golden rectangle" in wich the ratio of the sides is the golden section
f = (Sqrt{5}+1)/2.
Also, it is shown that the continued fraction representation of square root of 2 and f share a common property: cutting a maximal square twice on the smaller side gives a similar rectangle
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