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#integral

2 posts2 participants0 posts today
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MediaFaro News Digest

ESA's Integral gamma-ray gazer gasps its last.

After almost 23 years on the job, European Space Agency's (ESA) International Gamma-Ray Astrophysics Laboratory (Integral) is set to make its final observations.

mediafaro.org/article/20250228

The Register · ESA's Integral gamma-ray gazer gasps its lastBy Richard Speed
#ESA#Space#Integral
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Revesdespace

🛰️🔭✨ Ce 28 février, après 2 886 orbites et 22 ans dans l'espace, d'observations, le télescope gamma #Integral de l'ESA a cessé de collecter des données scientifiques.
Integral a joué un rôle essentiel dans la compréhension des sursauts gamma, des ondes gravitationnelles, etc

Public
IRAP

[End of mission for #Integral] At the time of its launch (in 2002), it was the most advanced #gamma-ray observatory and the first space observatory capable of simultaneously viewing celestial objects in the gamma, X-ray and visible domains.

Integral has transformed our understanding of the high-energy #Universe. Its observations have made it possible to identify the sources of the so-called “long” and “short” gamma-ray bursts (#GRB) : the collapse of stars into supernovae, on the one hand, and the collisions of black holes and neutron stars, on the other. Info+ : esa.int/Science_Exploration/Sp

IRAP's scientific and technical staff have contributed to the success of this mission: both in the realization of the #instruments and in the analysis of the observation data. On February 28, 2025, a long and beautiful page of our space adventure turns ...

ESA’s Integral observatory is able to detect gamma-ray bursts, the most energetic phenomena in the Universe. CREDIT : ESA/Medialab
Public
IRAP

[Fin de mission pour #Integral] Au moment de son lancement (en 2002), il était l' #observatoire de rayons #gamma le plus avancé et le premier observatoire spatial capable de voir simultanément des objets célestes dans les domaines gamma, X et visible.

Integral a transformé notre compréhension de l’ #Univers des hautes énergies. Ses observations ont notamment permis d'identifier les sources des #SursautsGamma qualifiés de "longs" et "courts" : l'effondrement d'étoiles en supernovae, d'une part, les collisions de trous noirs et d'étoiles à neutrons, d'autre part. Info+ : esa.int/Science_Exploration/Sp

Les personnels scientifiques et techniques de l'IRAP ont contribué au succès de cette mission : tant à la réalisation des #instruments qu'à l'analyse des données d'observations. Ce 28 février 2025, une longue et belle page de notre aventure spatiale se tourne ...

L'observatoire Integral de l'ESA est capable de détecter les sursauts gamma, les phénomènes les plus énergétiques de l'Univers. CRÉDIT : ESA/Medialab
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o calvaris :flag_estreleira: 🖖

Levava já um tempo a pensar em fazer uma rosca de reis na Bimby/Thermomix. A dificuldade neste caso era a farinha integral e os ovos porque a receita original não é vegan. A farinha integral não foi problema e os ovos trocámo-los por ovos de linho. O resultado foi uma maravilha. O bom é que o tempo total foi sobre as três horas mas trabalho manual foi pouco porque o fez quase tudo a máquina #roscadereis #integral #vegan #bimby #thermomix

Em primeiro plano prato com círculos de cores nos bordes e encima um cacho de rosca de reis com amêndoas encima. Justo atrás o resto da rosca.
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Pustam | पुस्तम | পুস্তম🇳🇵

An excellent general result.

If \(\Re(s)>1\),
\[\displaystyle\int_0^\infty\frac{\ln x}{x^s+1}~\mathrm dx=\frac{\pi^2}{4s^2}\left[\sec^2\left(\frac{\pi}{2s}\right)-\csc^2\left(\frac{\pi}{2s}\right)\right]\]

Special cases:
\[\displaystyle\int_0^\infty\frac{\ln x}{x^2+1}~\mathrm dx=0\]
\[\displaystyle\int_0^\infty\frac{\ln x}{x^3+1}~\mathrm dx=-\frac{2\pi^2}{27}\]
\[\displaystyle\int_0^\infty\frac{\ln x}{x^4+1}~\mathrm dx=-\frac{\pi^2}{8\sqrt2}\]
\[\displaystyle\int_0^\infty\frac{\ln x}{x^5+1}~\mathrm dx=-\frac{4\pi^2}{25}\left(\frac{2+\sqrt5}{5+\sqrt5}\right)=-\frac{(5+3\sqrt5)\pi^2}{125}\]

#Integral#Integrals#GeneralResult
Public
Long Starbird

I bought a Micro SD card, from #Integral.

Offered an "ECO" shipping option, for less packaging, I chose that.

This is what I received:

A card reader that I don't need, inside a plastic case that I don't need; Not one but TWO glossy leaflets that I don't need, both congratulating themselves on the minimal packaging; all inside a small card envelope... inside another, much larger card envelope. 🤦

I realize that the second envelope is an #Amazon decision. Even so... [drums fingers]

An SD card in a plastic case, two leaflets, and two envelopes. Final package is 10x the size and perhaps 5x the weight of the actual item purchased.
#Waste
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Emmanuel José García

I gave this integral as an answer at MathSE.

\[\int_{0}^{1}\left(\frac{5}{2} \left((x - \sqrt{x^2 - 1})^{2i} + x^4\right)-1\right)\,dx=e^\pi.\]

The integral yields \(e^{\pi}\). I don't know why the LaTeX isn't displaying properly.

Link: math.stackexchange.com/questio

Mathematics Stack ExchangeIs there a definite integral that yields $e^\pi$ or $e^{-\pi}$ in a non trivial way?The title says it all. No trivial answers like $\int_0^\pi e^tdt$ please. The idea is rather, if there are integrals like $$\int\limits_0^\infty \frac{t^{2n}}{\cosh t}dt=(-1)^{n}\left(\frac{\pi}2\r...
#math#integral#eulernumber
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Volodymyr

@vicgrinberg @elizabethtasker @schnedan

Right, I thought it was not, that's why no luck.

I realize the components are not all off-the-shelf, but not every single piece is reinvented every time. Even the platform can be re-used, like between #XMM-Newton and #INTEGRAL.

Aperture doors exist in many X-ray satellites: #XMM-Newton, #Chandra. I suppose they are somehow different?

There is a whole systems engineering work to reduce the chance of issues like this.

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