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🔗 Mathematics

The Basel problem is a problem in mathematical analysis with relevance to number theory, first posed by Pietro Mengoli in 1650 and solved by Leonhard Euler in 1734, and read on 5 December 1735 in The Saint Petersburg Academy of Sciences. Since the problem had withstood the attacks of the leading mathematicians of the day, Euler's solution brought him immediate fame when he was twenty-eight. Euler generalised the problem considerably, and his ideas were taken up years later by Bernhard Riemann in his seminal 1859 paper "On the Number of Primes Less Than a Given Magnitude", in which he defined his zeta function and proved its basic properties. The problem is named after Basel, hometown of Euler as well as of the Bernoulli family who unsuccessfully attacked the problem.

The Basel problem asks for the precise summation of the reciprocals of the squares of the natural numbers, i.e. the precise sum of the infinite series:

${\displaystyle \sum _{n=1}^{\infty }{\frac {1}{n^{2}}}={\frac {1}{1^{2}}}+{\frac {1}{2^{2}}}+{\frac {1}{3^{2}}}+\cdots .}$

The sum of the series is approximately equal to 1.644934. The Basel problem asks for the exact sum of this series (in closed form), as well as a proof that this sum is correct. Euler found the exact sum to be π²/6 and announced this discovery in 1735. His arguments were based on manipulations that were not justified at the time, although he was later proven correct, and it was not until 1741 that he was able to produce a truly rigorous proof.

🔗 United States 🔗 Biography 🔗 Mexico 🔗 Biography/science and academia 🔗 India 🔗 Plants 🔗 United States/Texas 🔗 Science Policy

Norman Ernest Borlaug (; March 25, 1914 – September 12, 2009) was an American agronomist who led initiatives worldwide that contributed to the extensive increases in agricultural production termed the Green Revolution. Borlaug was awarded multiple honors for his work, including the Nobel Peace Prize, the Presidential Medal of Freedom and the Congressional Gold Medal.

Borlaug received his B.S. in forestry in 1937 and Ph.D. in plant pathology and genetics from the University of Minnesota in 1942. He took up an agricultural research position in Mexico, where he developed semi-dwarf, high-yield, disease-resistant wheat varieties. During the mid-20th century, Borlaug led the introduction of these high-yielding varieties combined with modern agricultural production techniques to Mexico, Pakistan, and India. As a result, Mexico became a net exporter of wheat by 1963. Between 1965 and 1970, wheat yields nearly doubled in Pakistan and India, greatly improving the food security in those nations.

Borlaug was often called "the father of the Green Revolution", and is credited with saving over a billion people worldwide from starvation. According to Jan Douglas, executive assistant to the president of the World Food Prize Foundation, the source of this number is Gregg Easterbrook's 1997 article "Forgotten Benefactor of Humanity." The article states that the "form of agriculture that Borlaug preaches may have prevented a billion deaths." He was awarded the Nobel Peace Prize in 1970 in recognition of his contributions to world peace through increasing food supply.

Later in his life, he helped apply these methods of increasing food production in Asia and Africa.

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🔗 Military history 🔗 Military history/Military science, technology, and theory 🔗 Military history/Weaponry 🔗 Military history/French military history 🔗 Military history/Cold War 🔗 Rocketry 🔗 Military history/European military history

The S3 was a French land-based Intermediate Range Ballistic Missile, equipped with a single 1.2-megatonne thermonuclear warhead. In France it is called an SSBS, for Sol-Sol Balistique Stratégique, or Ground-Ground Strategic Ballistic Missile.

🔗 Aviation 🔗 Telecommunications 🔗 Guild of Copy Editors

In the U.S., Federal Communications Commission (FCC) regulations prohibit the use of mobile phones aboard aircraft in flight. Contrary to popular misconception, the Federal Aviation Administration (FAA) does not actually prohibit the use of personal electronic devices (including cell phones) on aircraft. Paragraph (b)(5) of 14 CFR 91.21 leaves it up to the airlines to determine if devices can be used in flight, allowing use of "Any other portable electronic device that the operator of the aircraft has determined will not cause interference with the navigation or communication system of the aircraft on which it is to be used."

In Europe, regulations and technology have allowed the limited introduction of the use of passenger mobile phones on some commercial flights, and elsewhere in the world many airlines are moving towards allowing mobile phone use in flight. Many airlines still do not allow the use of mobile phones on aircraft. Those that do often ban the use of mobile phones during take-off and landing.

Many passengers are pressing airlines and their governments to allow and deregulate mobile phone use, while some airlines, under the pressure of competition, are also pushing for deregulation or seeking new technology which could solve the present problems. On the other hand, official aviation agencies and safety boards are resisting any relaxation of the present safety rules unless and until it can be conclusively shown that it would be safe to do so. There are both technical and social factors which make the issues more complex than a simple discussion of safety versus hazard.

🔗 Physics

In materials science, disappearing polymorphs (or perverse polymorphism) describes a phenomenon in which a seemingly stable crystal structure is suddenly unable to be produced, instead transforming into a polymorph, or differing crystal structure with the same chemical composition, during nucleation. Sometimes the resulting transformation is extremely hard or impractical to reverse, because the new polymorph may be more stable. It is hypothesized that contact with a single microscopic seed crystal of the new polymorph can be enough to start a chain reaction causing the transformation of a much larger mass of material. Widespread contamination with such microscopic seed crystals may lead to the impression that the original polymorph has "disappeared."

This is of concern to both the pharmaceutical and computer hardware industry, where disappearing polymorphs can ruin the effectiveness of their products, and make it impossible to manufacture the original product if there is any contamination. There have been cases of laboratories growing crystals of a particular structure and when they try to recreate this, the original crystal structure isn't created but a new crystal structure is. The drug paroxetine was subject to a lawsuit that hinged on such a pair of polymorphs, and multiple life-saving drugs, such as ritonavir, have been recalled due to unexpected polymorphism. Although it may seem like a so-called disappearing polymorph has disappeared for good, it is believed that it is always possible in principle to reconstruct the original polymorph, though doing so may be impractically difficult. Disappearing polymorphs are generally metastable forms, that are replaced by a more stable form.

It is hypothesized that "unintentional seeding" may also be responsible for the phenomenon in which it often becomes easier to crystallize synthetic compounds over time.

🔗 Philosophy 🔗 Philosophy/Philosophical literature 🔗 Books 🔗 Classical Greece and Rome 🔗 Greece 🔗 Philosophy/Ancient philosophy 🔗 Archaeology

The Derveni papyrus is an Ancient Greek papyrus roll that was discovered in 1962 at the archaeological site of Derveni, near Thessaloniki, in Central Macedonia. A philosophical treatise, the text is an allegorical commentary on an Orphic poem, a theogony concerning the birth of the gods, produced in the circle of the philosopher Anaxagoras. The roll dates to around 340 BC, during the reign of Philip II of Macedon, making it Europe's oldest surviving manuscript. The poem itself was originally composed near the end of the 5th century BC, and "in the fields of Greek religion, the sophistic movement, early philosophy, and the origins of literary criticism it is unquestionably the most important textual discovery of the 20th century." While interim editions and translations were published over the subsequent years, the manuscript in its entirety was first published in 2006.

🔗 Apple Inc. 🔗 Computing 🔗 Computing/Software 🔗 Computing/Free and open-source software 🔗 Linux 🔗 Perl

Vim (; a contraction of Vi IMproved) is a clone, with additions, of Bill Joy's vi text editor program for Unix. Vim's author, Bram Moolenaar, based it upon the source code for a port of the Stevie editor to the Amiga and released a version to the public in 1991. Vim is designed for use both from a command-line interface and as a standalone application in a graphical user interface. Vim is free and open-source software and is released under a license that includes some charityware clauses, encouraging users who enjoy the software to consider donating to children in Uganda. The license is compatible with the GNU General Public License through a special clause allowing distribution of modified copies "under the GNU GPL version 2 or any later version".

Since its release for the Amiga, cross-platform development has made it available on many other systems. In 2006, it was voted the most popular editor amongst Linux Journal readers; in 2015 the Stack Overflow developer survey found it to be the third most popular text editor, and the fifth most popular development environment in 2019.

🔗 California 🔗 Companies 🔗 California/San Francisco Bay Area 🔗 Apple Inc. 🔗 Computing 🔗 Computing/Software 🔗 Media 🔗 Music theory

Napster was a peer-to-peer (P2P) file sharing application primarily associated with digital audio file distribution. Founded by Shawn Fanning and Sean Parker, the platform originally launched on June 1, 1999. Audio shared on the service was typically encoded in the MP3 format. As the software became popular, the company encountered legal difficulties over copyright infringement. Napster ceased operations in 2001 after losing multiple lawsuits and filed for bankruptcy in June 2002.

The P2P model employed by Napster involved a centralized database that indexed a complete list of all songs being shared from connected clients. While effective, the service could not function without the central database, which was hosted by Napster and eventually forced to shutdown. Following Napster's demise, alternative decentralized methods of P2P file-sharing emerged, including Gnutella, Freenet, FastTrack, and BitTorrent.

Napster's assets were eventually acquired by Roxio, and it re-emerged as an online music store commonly known as Napster 2.0. Best Buy later purchased the service and merged it with its Rhapsody streaming service on December 1, 2011. In 2016, the original branding was restored when Rhapsody was renamed Napster.