The list of minor planets numbered 409001 to 410000 is a collection of small celestial bodies that orbit the Sun, which have been assigned numbers by the International Astronomical Union (IAU) as they were discovered and confirmed. Each minor planet (also known as an asteroid) in this range generally has a unique numerical designation and may also have a name associated with it.
Jupiter LXIX, also known as S/2003 J 12, is a small moon of Jupiter. It is one of the many natural satellites that orbit the gas giant. This moon was discovered in 2003, and it is part of a group of Jovian moons that are irregular satellites, meaning they have atypical orbits that can be eccentric and inclined.
Jupiter LXVIII, also known as S/2020 J1, is one of the many moons of Jupiter. It was discovered in 2020 and is part of a group of irregular moons that orbit the planet at great distances and with varying inclinations. This moon is relatively small and orbits Jupiter in a prograde direction, meaning it moves in the same direction as Jupiter's rotation.
The list of minor planets numbered between 443001 and 444000 includes various celestial objects known as asteroids. Each minor planet is assigned a unique identification number and often has a provisional name or designation based on its discovery.
The list of minor planets numbered from 45001 to 46000 includes a series of asteroids that have been officially cataloged by the International Astronomical Union (IAU). Each minor planet is assigned a unique numeric designation, and many of these asteroids may also have names.
Kale, also known as Kalliste, is one of the natural satellites of the planet Saturn. It is a member of the Inuit group of moons, which are characterized by their relatively small sizes and irregular shapes. Discovered in 2000, Kale has a diameter of about 22 kilometers (14 miles).
The list of minor planets numbered from 464001 to 465000 includes various asteroids and other small celestial bodies that have been cataloged by astronomers. Each of these minor planets has its own unique designation, which typically follows the pattern of a number, sometimes followed by a provisional name if it hasn't received a permanent name yet.
The list of minor planets numbered 487001 to 488000 includes a series of celestial objects (typically asteroids) that have been assigned official numbers by the International Astronomical Union (IAU). Minor planets are small solar system bodies that are neither planets nor comets. Each body in this range is often cataloged with additional information such as its discovery date, naming origin, and other relevant observations.
The "List of minor planets: 501001–502000" refers to a collection of minor planets (also known as asteroids) that have been cataloged and assigned numerical designations by the International Astronomical Union (IAU). Each minor planet is given a unique number upon discovery, and this list includes those that have received numbers between 501001 and 502000.
The list of minor planets numbered between 515001 and 516000 comprises a collection of celestial objects that have been designated with specific numbers by the Minor Planet Center. These minor planets can include asteroids and other small bodies in the solar system. Each minor planet is cataloged with a unique number as it is discovered and confirmed.
The list of minor planets from 518001 to 519000 is a range of small celestial bodies in the Solar System that are primarily located in the asteroid belt, as well as near-Earth objects and trans-Neptunian objects. Each minor planet is assigned a number by the International Astronomical Union (IAU) once it is confirmed to be an asteroid or a similar body.
The list of minor planets from 521001 to 522000 is a collection of small celestial bodies that orbit the Sun, generally considered to be asteroids. These minor planets are cataloged by their numerical designation, which reflects their order of discovery. Each minor planet typically also has a name, often based on mythological figures, scientists, or cultural references.
The list of minor planets from 537001 to 538000 includes various numbered asteroids that have been discovered and cataloged by astronomers. Each minor planet is assigned a unique number and often has a provisional designation or name.
Multiple boundary conditions for different parts of the boundary.
Control theory by Ciro Santilli 40 Updated 2025-07-16
This basically adds one more ingredient to partial differential equations: a function that we can select.
And then the question becomes: if this function has such and such limitation, can we make the solution of the differential equation have such and such property?
It's quite fun from a mathematics point of view!
Control theory also takes into consideration possible discretization of the domain, which allows using numerical methods to solve partial differential equations, as well as digital, rather than analogue control methods.
Nabla symbol by Ciro Santilli 40 Updated 2025-07-16
Nabla is one of those: it was completely made up in modern times, and just happens to look like an inverted upper case delta to make things even more confusing!
Nabla means "harp" in Greek, which looks like the symbol.
Adolfo Amidei by Ciro Santilli 40 Updated 2025-07-16
This dude mentored Enrico Fermi in high school. Ciro Santilli added some info to Fermi's Wikipedia page at: en.wikipedia.org/w/index.php?title=Enrico_Fermi&type=revision&diff=1050919447&oldid=1049187703 from Enrico Fermi: physicist by Emilio Segrè (1970):
In 1914, Fermi, who used to often meet with his father in front of the office after work, met a colleague of his father called Adolfo Amidei, who would walk part of the way home with Alberto [Enrico's father]. Enrico had learned that Adolfo was interested in mathematics and physics and took the opportunity to ask Adolfo a question about geometry. Adolfo understood that the young Fermi was referring to projective geometry and then proceeded to give him a book on the subject written by Theodor Reye. Two months later, Fermi returned the book, having solved all the problems proposed at the end of the book, some of which Adolfo considered difficult. Upon verifying this, Adolfo felt that Fermi was "a prodigy, at least with respect to geometry", and further mentored the boy, providing him with more books on physics and mathematics. Adolfo noted that Fermi had a very good memory and thus could return the books after having read them because he could remember their content very well.
Ciro Santilli really likes guys like this. Given that he does not have the right genetics, conditions and temperance for scientific greatness in this lifetime, he dreams of one day finding his own Fermi instead.
Laplace operator by Ciro Santilli 40 Updated 2025-07-16
Can be denoted either by:
Our default symbol is going to be:

Pinned article: Introduction to the OurBigBook Project

Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
We have two killer features:
  1. topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculus
    Articles of different users are sorted by upvote within each article page. This feature is a bit like:
    • a Wikipedia where each user can have their own version of each article
    • a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
    This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
    Figure 1.
    Screenshot of the "Derivative" topic page
    . View it live at: ourbigbook.com/go/topic/derivative
  2. local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:
    This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
    Figure 2.
    You can publish local OurBigBook lightweight markup files to either https://OurBigBook.com or as a static website
    .
    Figure 3.
    Visual Studio Code extension installation
    .
    Figure 4.
    Visual Studio Code extension tree navigation
    .
    Figure 5.
    Web editor
    . You can also edit articles on the Web editor without installing anything locally.
    Video 3.
    Edit locally and publish demo
    . Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.
    Video 4.
    OurBigBook Visual Studio Code extension editing and navigation demo
    . Source.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact