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Talk:Eisenstein's criterion

Problem with how much to shift if polynomial is monic
The example with the polynomial h(x) = x^2 + x + 2 is given and a shift is needed in order to apply Eisenstein. How much should the shift be ? is 3 enough each time or does it depend on the polynomial. (I tried other shifts for the same polynomial and the test failed for them, However it worked for 3(given in the example on the wikipedia page) and 10 and 17 worked) Clearly they depend on the polynomial so how do you know how much to shift ? This should be added to the article Stefan.petrea (talk) 10:11, 1 February 2010 (UTC)

User:Dysprosia, by all means add examples.

Charles Matthews 09:11, 4 Dec 2003 (UTC)

 * I'll probably give you some later tonight :) Dysprosia 09:12, 4 Dec 2003 (UTC)

Someone removed my edition of the article. In maths it is not important to put on the paper those things that does not lead a solution. Therefore I think it is better to say that only the case p=5. --Matikkapoika 16:04, 12 January 2006 (UTC)

 * In maths, it is sometimes more illustrative to demonstrate what doesn't work than to only adhere to what does. This aids comprehension on the reader's part. Now, you may be familiar understanding "those things that does not lead a solution" but some other reader may not. Dysprosia 22:45, 12 January 2006 (UTC)

 * Okay then. I just thought that if you want to know what is an Eisenstein criterion you know quite a lot mathematics beforehand. At least I heard Eisenstein's criterion first time in the university. Therefore I assumed that if you know what criterion says, you know also that mathematicians fails often before they can solve problems or prove new theorems. And therefore I assumed it is enought to give only the case p=5. Because if I would publish everything I think on my own, I would easily be the most prolific mathematician in the world! (Assuming everyone else publishes only valid results.) --Matikkapoika 00:21, 13 January 2006 (UTC)

 * It's not always easy for one to understand a new concept, even though one may have a large body of previous knowledge, precisely because it may be a new concept. Being deliberately terse may be fine in the body of an encyclopedic article, but for a worked example, it is best to be explicit. Dysprosia 01:11, 13 January 2006 (UTC)

I added a restriction in the general definition. If the criterion holds, then the polynomial is irreducible in $$F[x]$$, where $$F$$ is the field of fractions of $$D$$, and when the polynomial is primitive it is also irreducible over $$D[x]$$. This addition is important, since elements of $$D$$ that are not units are considered irreducible elements of $$D[x]$$. Even in the integers, $$2(x+3)$$ is the irreducible factorization of $$2x+6$$ (up to multiplication by 1 or -1), which matches the criterion for $$p = 3$$. However, since 2 is a unit in $$\mathbb Q$$, $$2x+6$$ is irreducible in $$\mathbb Q[x]$$. Stolee 05:58, 16 February 2007 (UTC)

A different generalisation
There's a generalisation of the criterion in Z (and probably over a general integral domain too) that says given a polynomial
 * $$f(x)=a_nx^n+a_{n-1}x^{n-1}+\cdots+a_1x+a_0 ,$$

if there's a prime number p such that p divides ai for 0 ≤ i < k, and p2 doesn't divide a0 then f has an irreducible factor of degree at least k. Letting k = n gives back the usual criterion. There's no point cluttering maths articles with every generalisation of a result possible, though, so if someone thinks this is notable enough then feel free to add it to the main article. Chenxlee (talk) 19:44, 15 September 2008 (UTC)

 * That polynomial f should be monic, the way I've stated the result. Whoops. Chenxlee (talk) 19:53, 15 September 2008 (UTC)

Noteworthy
Yes, I find this very noteworthy. I do nott consider this an intuitively obvious result.There ought be some mention of it. I would add it save for the fact that I add nothing at all that I am not 100% sure of. Please add it yourself with either a proof or appropriate citations.

And dont you mean that the polynomial is irreducible for factors of degree k or less? Or for degree k or more?

Furthermore, doesnt this only matter up to k=floor(n/2) ? Polynomial factors with degree smaller than floor n/2 are accompanied by a second polynomial factor greater than floor n/2, which has degree n - k.

64.134.140.53 (talk) 02:09, 21 June 2012 (UTC)

Shifting and inverting algorithms
How does this tidbit effect the algorithms for shifting or reversing coefficients in order to "force" Eisenstein's Criterion.

64.134.140.53 (talk) 02:09, 21 June 2012 (UTC)

Problem with Generalization
The generalization given at the end of the article is wrong. Consider the domain $$D = \mathbb{Z}[\sqrt{8}]$$ and the polynomial $$f(x) = x^2 - 2 \in D[x]$$. Now take the prime ideal $$P = \langle 2, \sqrt{8} \rangle \subset D$$. We have $$2 \in P$$, but $$2 \notin P^2$$, so this generalization of Eisenstein should apply... but it doesn't, since the field of fractions of D is $$F = \mathbb{Q}[\sqrt{2}]$$, and $$f(x)$$ is clearly reducible over F. I think we need D to be a unique factorization domain to fix it. Cpryby (talk) 23:52, 6 November 2008 (UTC)

Not irreducibility over Z
2X+6 satisfies the conditions with 3, but factorizes over Z as 2(X+3). So irreducibility is only over Q.80.99.11.161 (talk) 10:42, 21 October 2010 (UTC)

Change from f(x) to Q; improving this article
My recent change to this article, which among other things changed notation of polynomials from functional notations like f(x) to simple names (in capitals) like Q (I avoided the more natural P because of possible confusion with p for prime). This change, which was intended as a first step to improving parts of this article, was reverted with the summary "it is completely standard to denote a formal polynomial by f(x), no need to change notation". While I agree that many people and books almost always denote polynomials using "(x)" (thought very few are completely systematic; often people give up on this in expressions involving sums ans/or products of several polynomials, and this article is no exception), I don't think that this convention contributes positively to the readability or any other aspect of the current article. The only place where it is functional is to facilitate the notation for substituting x + 3 for x, as in h(x + 3), but even here this does not serve clarity: it masks the fact that there is an isomorphism argument that allows conclusions for h(x + 3) to be applied to h(x) as well. Also note that in the very same section this neat notational trick fails for the cyclotomic polynomial, because it is given by an explicit expression rather than by some name f(x).

I agree that my preference for using upper case instead of functional notation to distinguish polynomials from scalar is personal, though I am comforted by the fact that the polynomial article seems to adopt the same preference. I will defend (if challenged) that it is more consistent, but I'm not on a crusade to convince everybody to use it. But I maintain that adopting this convention for the current article (if done consistently) is certainly is no deterioration. If anybody thinks the opposite convention is really called for in this article, please explain on this talk page.

So I would please go on with some improvements to this article without being reverted. Simplifying the notation is just a first step to making it easier to understand and formulate. As a small justification, let me enumerate a few points that I think need improvement.
 * The style needs to be more encyclopedic (less colloquial), and more precise
 * The "basic proof" section is unclear as an argument (where for instance does it use that the one coefficient not divisible by p is in fact the leading coefficient?) and is hard to read, exactly because the distinction between polynomials and scalars is no longer clear.
 * The "advanced explanation" section is not really an explanation (but I'm not competent to improve this part in other than superficial ways)
 * There are numerous minor improvements possible (like removing the plural from "conditions" in the lead)

So I'll now turn back to the version I left, and make some of the improvements I intended. If a consensus arises that the functional notation is really better, I'll gladly turn that back afterwards, but I'd prefer not to be reverted globally. Marc van Leeuwen (talk) 08:38, 11 March 2011 (UTC)

 * I reverted you. First, I hadn't checked to make sure that you hadn't made changes other than the notational change you described in your edit summary. In the future, when you are doing making more than one type of change please indicate that in your edit summary. Second, if I come across an article where an editor has basically just changed from one notation to another with an edit summary describing how the new notation is better (when it's not clearly better), then I will revert that, because it often turns into that editor going through 10 other similar articles and making the same notation change. There are policies in wikipedia that basically say that if a convention is being used somewhere, you shouldn't just change it, not even to make things jive with other articles. Third, it's indeed typical in more advanced places to drop the (x) notation since it's redundant, and I generally do so and simply write f, g, h. Or I may even write P, Q. Or a, b, c. If you had spent time improving this article (say even just a few edits) and then had changed the notation, I don't think I would've reverted. At the time you reverted, there was no way to tell this is the first step in a larger program. Though I must say, I really don't like the notations G and H for polynomials (sure G without the presence of H, but both is jarring to me). In summary, it's not that I am of the firm belief that this article must use f(x) and such, it's simply that what seems to be a "drive-by" edit that completely changes a notational convention in an article to another one that is of about the same standard-ness is sketchy. All the other problems with the article you describe above are serious problems and I'd be very happy if you addressed them. RobHar (talk) 15:26, 11 March 2011 (UTC)

Regarding Gaussian Rational Roots
Does anyone know how or if Eisensteins Criterion says anything about the existence of Gaussian Rational roots? 64.134.140.53 (talk) 00:21, 21 June 2012 (UTC)

The Non-Primitive Caveat
The caveat needs to be elaborated and explaned in further detail, Im not sure that I am understanding it correctly.

This is my understanding: Even if Eisenstein's Criterion is met/passed and we have confirmed the non-existence of general rational roots... then we may still possibly have strictly prime roots if and only if the polynomial is not primitive.

64.134.140.53 (talk) 00:51, 21 June 2012 (UTC)

 * The criterion is about factorization, not about roots. The passage "It will also be irreducible over the integers, unless" can be illustrated as follows. Take an Eisenstein polynomial for p=5, say, for instance Q=2X3+10X2+25X+15. It is irreducible over the rational numbers by the criterion, and since this example is primitive it is also irreducible over the integers. However if we multiply by another prime, say 3, to obtain 6X3+30X2+75X+45, this still meets the Eisenstein criterion for p=5, the polynomial is still irreducible over the rational numbers, but it is reducible over the integers because it is equal to the product 3Q, and both 3 and Q are non-invertible factors over the integers. Speaking of reducibility over the rational numbers conveniently sweeps the factor 3 under the rug as invertible and therefore irrelevant. However this rather trivial case is the only reason to talk about the rationals; the criterion and its proof are really an integer affair. Marc van Leeuwen (talk) 13:05, 30 August 2012 (UTC)

Examples
The change of variables in the examples is inconsistent. First it says to set x = y + a, and then redefines x as x + 3. The cyclotomic example says to set y = x + 1, which is the right way to do it. I think the section would make more sense if the first example was consistent with the second, and set y = x + a. Further, I think it should look like h(x) = h(y + 3) = y^2 + 7*y + 14 to be clearer and not redefine x.

After the example of how to apply a shift it says that the shift is a ring automorphism, which is not true. — Preceding unsigned comment added by 131.111.221.163 (talk) 22:45, 12 June 2013 (UTC)
 * The substitution of x by x+a is an automorphism of the polynomial ring, mapping f(x) to g(x)=f(x+a). Such a substitution may also be viewed as a change of variable (y=x+a). The fact of changing or not the name of the variable is not really important, as the name of the variable in a polynomial is only a placeholder. Hover, in practice, it is safer to change the name, to avoid confusions. I have changed y into x in the example for a coherent notation in the section. D.Lazard (talk) 08:50, 13 June 2013 (UTC)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Talk:Eisenstein's criterion


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SMK (disambiguation)

SMK can refer to:

 * Statens Museum for Kunst, the Danish National Gallery
 * SMK tank, a Soviet heavy tank prototype
 * Slagsmålsklubben, Swedish band
 * Sekolah Menengah Kejuruan, a type of high school in Indonesia
 * Super Mario Kart, the first game in Nintendo's Mario Kart series, released in 1992 for the SNES
 * Sekolah Menengah Kebangsaan, a type of government owned public schools in Malaysia
 * SMK-MKP, Strana maďarskej koalície Party of the Hungarian Coalition in Slovakia
 * SMK- Composite Bridge System in dentistry
 * Sam Kee LRT station, Punggol, LRT station abbreviation
 * Stowmarket railway station, England, National Rail code
 * Smacker video, computer filename extension
 * A variant of the SMA coax connector
 * Office of the Prime Minister (Norway), Statsministerens kontor (SMK) - a cabinet department
 * Sierra MatchKing, a match-grade bullet designed for long range applications

title: SMK (disambiguation)


text:
Crystal (character)

Crystal (Crystalia Amaquelin) is a superhero appearing in American comic books published by Marvel Comics. Crystal first appeared in Fantastic Four #45 (Dec. 1965) and was created by writer Stan Lee and artist Jack Kirby.

Within the Marvel Universe, Crystal is a member of a fictional human subspecies known as Inhumans, who (due to genetic modifications performed by the Kree) became capable of developing superhuman abilities once exposed to the Terrigen Mist. Exposure to the Terrigen Mist grants abilities to psionically control the four classical elements: earth, wind, fire, and water and, by extension, can also grant the ability to manipulate various other natural materials and phenomena such as metals and electricity. Crystal was the first character to be identified as an Inhuman, and is one of the most prominent Inhuman characters. Crystal is a princess of the Inhuman Royal Family and sister to Medusa, Queen of the Inhumans. She often appears with her giant super-powered canine companion, Lockjaw.

The character has regularly appeared as a main character in several comic book titles, including various incarnations of the Inhumans as well as the Fantastic Four and the Avengers. The character is unique in her affiliation with all three of these groups. Earlier in her history, she was romantically involved with the Human Torch from the Fantastic Four. In later stories, she becomes more associated with the X-Men family of characters due to her short-lived marriage to Quicksilver, which resulted in the conception of their daughter, Luna. Crystal has also appeared in various other Marvel media such as television series and video games, as well as merchandise such as trading cards and action figures.

Crystal has been described as one of Marvel's most notable and powerful female heroes.

She made her live action debut in the 2017 Marvel Cinematic Universe (MCU) television series Inhumans, portrayed by Isabelle Cornish.

Publication history
Crystal first appeared in Fantastic Four #45 (Dec. 1965), written by Stan Lee and illustrated by Jack Kirby, titled "Among Us Hide...The Inhumans". When asked, "Who created the Inhumans, you or Stan Lee?" in a 1968 interview for Excelsior magazine, Jack Kirby replied, "I did." Like other early Fantastic Four characters, there is debate about how much Stan Lee and Jack Kirby each contributed to the characters' creation.

Throughout her many appearances, Crystal has been depicted as brave, intelligent, and compassionate. While she is undoubtedly very kind and emotional, this is in stark contrast to her remarkable power, and she is more than capable of defending herself and others.

Fantastic Four (1965–1973)
Crystal was first introduced, along with the rest of the Inhuman Royal Family and the Inhuman race as a whole, in the pages of Fantastic Four. Upon their first meeting, she and Johnny Storm fell in love with one another, a fact that led to her continued presence among the team. From this time, she would become a mainstay of the team for the duration of Stan Lee and Jack Kirby's stint on the series. She was the first character to join the Fantastic Four, outside of its original members, when she officially joined the team as a replacement for Sue Richards, who was pregnant with Franklin Richards. She remained a member of the team, even after Sue's return. During her time with the team, she became very close to its members, particularly Ben Grimm and accompanied them on many adventures. Crystal was written out of Fantastic Four in issue #105, the first story arc after Jack Kirby's departure. At this time, the character returned to her family in Attilan due to her apparent inability to survive long-term in Earth's polluted atmosphere. Her time with the team and her status as a friend and ally would continue to be part of her identity as a character, up to the present.

Quicksilver and Luna (1973–1990)
After her return to Attilan, Crystal meets and falls in love with Quicksilver, Pietro Maximoff. During this time, Crystal is mostly featured alongside Quicksilver in a number of different series including Inhumans and Vision and the Scarlet Witch, along with guest appearances in Fantastic Four, Avengers, and other titles. In addition to her marriage to Quicksilver, this time period saw the introduction of Luna, the daughter of Crystal and Pietro and the development of close friendship between Crystal and Pietro's twin sister, Scarlet Witch (Wanda Maximoff), and her then-husband, Vision. In Steve Englehart's series, Vision and the Scarlet Witch vol. 2 (1986), Crystal has an affair with Vision and Wanda's "regular Joe" neighbor, Norm Webster. Crystal is purported to have committed this betrayal as a result of her mistreatment by Pietro. A few months later in X-Factor Annual #2 (October 1987), it is revealed that the behavior exhibited by both Crystal and Pietro was the result of mind control orchestrated by Maximus. From 1987 to 1988, Crystal again rejoins the eponymous team in Fantastic Four, which was also being written by Steve Englehart, at the time. Crystal departs the team abruptly in Fantastic Four Annual #21 after being convinced to do so by her king and brother-in-law, Black Bolt. The artwork at the end of the issue features character pages for the Fantastic Four and many supporting characters. Despite this being Crystal's last issue, her character page reads "It's great to be back with the Fantastic Four! I'll never leave again!"

Avenger (1991–1998)
Crystal has also appeared as a member of the Avengers. She was a prominent member of the main Avengers team for the term of Bob Harras' time as writer for the title, but declined in prominence shortly after he left to become Editor-in-Chief of Marvel Comics. In addition to starring in Avengers, the character also appeared in the solo books of her Avengers teammates during these years such as Captain America, Invincible Iron Man, and The Vision. While serving on the team, the character lived in Avengers Mansion with Luna and her nanny, Marilla. During this time period, the character would attempt to reconcile with Quicksilver off-and-on. Crystal was featured as an Avenger through many important storylines and events including Operation: Galactic Storm, Infinity War, Infinity Crusade, Bloodties, Onslaught, and Heroes Return. Crystal proved invaluable to the team many times during her tenure and was well-loved by her teammates. The character also featured prominently in the series Quicksilver toward the end of her tour as an active Avenger.

Return to Attilan (1998–2007)
This time period was a departure from Crystal's previous appearances because it marked the first time the character had returned to Attilan by her own choice for a significant amount of time since she first encountered the Fantastic Four. Crystal appeared in Inhumans vol. 2 (1998–1999), a limited series by Paul Jenkins and Jae Lee. The series, which was part of the Marvel Knights line, was critically acclaimed, popular with readers, and earned Jenkins an Eisner Award. From 2000 to 2005, the character mostly made guest appearances in Avengers, Fantastic Four, and other titles. Son of M (2006) and Silent War (2007), written by David Hine would bring the next major arc for Crystal. These books chronicled Quicksilver's betrayal of Crystal and the Inhumans in an attempt to use the Terrigen Mist to restore the mutants depowered during the events of House of M and the resulting conflict between Attilan and a fictional version of the United States.

Cosmic Inhumans (2008–2013)
This time period marked another new development for Crystal's character as she and her fellow Inhumans became involved in intergalactic conflicts. Secret Invasion: Inhumans (2008–2009) by Joe Pokaski marked the beginning as it was discovered that Black Bolt had been replaced by a Skrull. This revelation leads to a series of events that eventually sees the Inhumans ascend to become sovereigns of the Kree Empire and Crystal betrothed to Ronan the Accuser. Crystal was then featured through a series of books by Dan Abnett and Andy Lanning including War of Kings (2009), Realm of Kings: Inhumans (2010), and The Thanos Imperative (2010). During this time, Crystal showed her prowess not only as a warrior, but as a leader, as she and her family navigated political and military conflicts, particularly against Vulcan and the Shi'ar Imperium. From 2010 to 2013, her story continues in the pages of Fantastic Four and FF, in which she is forcibly separated from Ronan against both of their wishes. Although present in Infinity (2013) and Inhumanity (2013–2014), which, under new authorship, continue the events portrayed in Abnett and Lanning's aforementioned series, she does not play a major part in these books.

All-New, All-Different Marvel (2015–)
Despite her unexplained absence in Charles Soule's Marvel NOW! series Inhuman (2014–2015), Marvel has indicated that Crystal will be returning to the spotlight as a part of their All-New, All-Different Marvel initiative. She has been announced to appear in the upcoming Uncanny Inhumans series, and leaked information indicated the character would be featured in a starring role in All-New Inhumans, both also written by Charles Soule. The character has also appeared on the teaser image for All-New All-Different Marvel Point One, which is to be an introduction to the new series that are being launched as a part of All-New, All-Different Marvel. On August 19, 2015, it was officially announced that Crystal would be the leader of a team of Inhumans in All-New Inhumans, which will be co-written by Charles Soule and James Asmus with art by Stefano Caselli. "These stories follow a diplomatic mission/covert strike team effort led by Crystal," relates Asmus. "She's been at the center of the Inhumans, but also served as an Avenger, alongside the Fantastic Four, and even dabbled with the X-Men when she was married to Quicksilver. She's been a constant presence in the Marvel Universe, but leading this faction of NuHumans is her stepping up in a big way." The character's appearance has been significantly changed, having an updated costume and a pixie cut.

Fictional character biography
Crystal is the daughter of Inhumans Quelin and Ambur, and lived in Attilan with the other Inhumans, until the Inhuman Royal Family was forced out of the Great Refuge by Maximus. Her first encounters with the outside world were via the Fantastic Four. She encountered the Human Torch, and brought him to the Inhumans' secret New York base. She left New York with her family members to escape the Seeker, but became trapped inside Maximus' "negative zone" barrier dome around the Great Refuge. She fell in love with the Human Torch, although their romance was blocked by a literal barrier, around the Inhumans' city. The Inhumans were eventually freed from the "negative zone" barrier, and left the Great Refuge along with the Royal Family to visit the outside world. She brought Triton to rescue Mister Fantastic from the real Negative Zone and aided the Fantastic Four in battle against Blastaar.

Joining the Fantastic Four
Crystal would later leave the city for a brief career with the Fantastic Four. Soon after joining, she battled the Wizard, and helped defeat Maximus. She also fought Doctor Doom alongside the Fantastic Four. She was temporarily blinded by the Mole Man, but helped the Fantastic Four defeat him. She was abducted by Medusa and reunited with the Torch in Attilan. She revealed how she had used her powers to save Black Bolt's life, and then rejoined the Fantastic Four. She fell under the mental control of Diablo, but soon regained her free will and returned to the Great Refuge.

Marriage
It was later revealed how she had rescued a dying Quicksilver (Pietro Maximoff). She chose Quicksilver over the Torch as the man she loved. Not long after that, she married Quicksilver. She later gave birth to their daughter, Luna, and accompanied the Inhumans when Attilan was relocated to Earth's Moon. During the time when the Inhumans lived on the Moon, Crystal defied the power structure of her society and fled with many Inhumans to an isolated part of Earth. They were there to help Medusa, their queen, give birth in secret. Crystal used her powers to eliminate the pollution from a wide area around their hideout, a mistake which led to even worse consequences.

Quicksilver and Crystal have had a rocky marriage. Pietro has always had a quick temper and Crystal had once had an affair with a real estate agent named Norman Webster. She and the Human Torch still had feelings for each other during his marriage to the supposed Alicia Masters (later revealed to be a Skrull named Lyja merely pretending to be Alicia). She also developed feelings for Dane Whitman, the Black Knight, but nothing physical came from it. These reasons have caused them to separate several times, egged on by Maximus the Mad taking credit for Pietro's descent into madness. One such reconciliation attempt occurred in a small town, in a rented cabin, where Crystal had to urge Quicksilver to "go slow". Unfortunately, even this was affected by outside forces.

Joining the Avengers
At one point, Crystal summoned the Avengers to help battle the Brethren. Soon after, she joined the Avengers as a provisional member. Shortly after that, she became a full Avengers member. During Crystal's time with the Avengers, Magneto's Acolytes kidnapped her daughter, causing great damage to the mansion. Luna ended up in Genosha under the control of the Acolytes. The Avengers teamed up with the X-Men and managed to recover her safely.

Decimation
After the events of House of M, Crystal was reunited with her depowered husband, only for him to steal the Terrigen Mist from Attilan, in an attempt to use it to restore the depowered mutants. He also kidnapped Luna and exposed her to the mists, granting her various abilities. Luna had previously been baseline human, thought of by some as an affront to her mutant heritage.

Silent War
When the Inhumans located Quicksilver, he allowed Black Bolt to beat him, in response to his betrayal. Crystal and Quicksilver's marriage was annulled and she participated in a series of battles against S.H.I.E.L.D. and the Mighty Avengers when the Inhumans declared war on United States.

Secret Invasion
Crystal and her sister Medusa are called upon by Iron Man to a meeting where he reveals Black Bolt has been replaced by a Skrull. When the Skrulls invade Attilan, Crystal uses her abilities to defeat a Skrull who possesses the powers of Colossus, Cyclops, and Wolverine, and a Skrull who is an amalgam of Captain America and Spider-Man. After an attack on Attilan by the Skrulls, the Royal Family travel into Kree space, seeking an alliance against the invading Skrulls. Ronan the Accuser welcomes this alliance, but only on the condition that Crystal becomes his bride. Medusa agrees, much to Crystal's chagrin.

In an attempt to crack the Skrull communication network, the Inhumans split up. Crystal and Medusa infiltrate Thundra's tribe as fellow tribeswomen. However, when they argue, per the tribe's laws, their squabble is moved to the arena. In their fight, Crystal gets Medusa to treat her more like an adult and allow her to speak to Thundra. She negotiates the release of a captured Skrull communications officer, enabling them to track down Black Bolt's prison.

War of Kings
Crystal's marriage to Ronan proceeds, even following Black Bolt's decision to usurp the throne of the Kree. She comes to accept the idea of the marriage, defending it to her sister-in-law Polaris as a matter of statecraft (though there are indications that Ronan wishes for more). The wedding proceedings are interrupted by the Shi'ar Imperial Guard, who attack as part of Emperor Vulcan's invasion of the Kree Imperium. Ronan is beaten nearly to death in this attack. While visiting Ronan in recuperation, Crystal inadvertently helps rally the Kree people when she shows compassion towards a ward filled with injured Kree commoners, acts which (thanks to her sister in law Polaris) were eventually broadcast over the Kree networks. This has led to her being referred to as the "people's princess" among some of the Kree people.

When Black Bolt attempted to set off an explosion that would spread the Terrigen Mists across the galaxy, reasoning that this action would render all equal, Crystal defied his orders and risked her life to take Lockjaw to confront him, disabling the Terrigen qualities of the explosion and convincing Black Bolt that the powers that would be created by his plan would cause more harm than good. Although Black Bolt acknowledged her wisdom, an attack by Vulcan meant that Black Bolt was kept too busy to accompany Crystal and Lockjaw when they were forced to flee before the bomb — now a simple explosive device — went off, apparently killing Black Bolt and Vulcan. After some time with Medusa ruling in Black Bolt's stead, he is resurrected and returns to the throne. Shortly thereafter, Black Bolt makes a decree that the Inhumans would return to Earth, leaving Ronan the Accuser in charge of the empire; Crystal is given the choice to leave with the royal family or stay by her husband. She decides to stay with family.

During the Civil War II storyline, Crystal and Medusa introduce the Inhuman Ulysses to Captain Marvel, War Machine, and Black Panther. Crystal was present when Iron Man infiltrated New Attilan to claim Ulysses. Iron Man managed to defeat Crystal. She later joined Medusa, Karnak, and the other Inhumans with them in their trip to Stark Tower to reclaim Ulysses. During the confrontation with Iron Man, Crystal was present when Ulysses' latest vision projected to everyone present showing a rampaging Hulk standing over the corpses of the superheroes.

During the Inhumans vs. X-Men storyline, Crystal and Gorgon are ambushed by Magneto.

Powers and abilities
Crystal is often described in her appearances as an elemental due to her unique ability to psionically control the four classical elements: air, earth, fire, and water. The character's proficiency in controlling these "elements" allows her to achieve a variety of effects and additional abilities. Her psionic powers are a result of exposure to the Terrigen Mists, which coupled with genetic engineering of the Inhumans by the Kree in the distant past, grant Inhumans abilities beyond the capabilities of an ordinary Inhuman that are unique to each individual.

Inhuman physiology
As a member of the fictional offshoot of humanity, Inhumans, Crystal possesses physical strength, durability, speed, endurance, and reflexes significantly greater than the maximum potential attainable by humans. Her physical prowess, coupled with combat training received from her cousin, Karnak, and the Avengers make her a formidable hand-to-hand combatant.

Air manipulation
Crystal can control oxygen atoms and oxygen-containing molecules to create atmospheric disturbances of various kinds. By intermingling air with earth she can cause a dust storm, air with water a typhoon, and air with fire a firestorm. She is able to create a wind of tornado intensity, approximately 115 miles per hour. She has demonstrated the ability to control air as far away as within a 30-mile radius. Using this ability, Crystal can summon wind currents strong enough to support her weight and others' and elevate herself to fly at high altitudes and speeds. By controlling air molecules, Crystal is able to bind them together psionically and compact them into a boundary to such a degree that matter cannot pass through. She uses this ability to various effects, including creating a field around her, allowing her to breathe while submerged in water and molten lava. She has also used this ability to deflect attacks and contain the atmosphere when the hull of a spaceship was compromised. She has demonstrated the ability to determine what may or may not pass through the barrier.

Earth manipulation
Crystal can control the various substances that make up common bedrock (earth: iron, granite, shale, limestone, etc.), creating seismic tremors of up to 6.7 on the Richter scale (greater if tectonic plate fault lines are nearby) by causing a sudden shifting of the earth. The upper limit of this power is unknown, although she has demonstrated the ability to lift the entire fictional city of Attilan for a significant amount of time. Her ability to control earth extends to many metals which are naturally occurring, including iron.

Fire manipulation
Crystal possesses the psionic ability to manipulate fire, cause it to grow in size and intensity, and take any form that she desires. She can also douse any oxidizing flame by altering the ionization potential of the outer electron shells of oxygen atoms. By accelerating oxygen molecules in the air, she is able to cause fire to spontaneously ignite.

Water manipulation
Further, Crystal can control the movement of water to a certain extent, via manipulation of inter-atomic van der Waals force controlling surface tension, divining water from the ground, and causing it to flow in designated directions. The maximum volume is unknown, although she has demonstrated the ability to create a maelstrom large and powerful enough to trap at least a dozen individuals, including Namor, and brought down what was described as "a sea from the sky," at least several thousand gallons. The character's control of water molecules extends to all of its forms, including ice. She is able to instantly freeze water to create ice blasts. She can also cause hydrogen and oxygen atoms in the air to recombine and form water molecules, summoning these atoms from a volume of atmosphere within a radius of approximately two miles. This allows her to spontaneously create water, even in a dry environment, provided oxygen and hydrogen are present.

Other elemental effects
Crystal possesses the ability to rearrange and manipulate the individual atoms of the elements that she controls to various effects. She is able to affect the elements she controls on an atomic level, giving them an electrical charge. Once the molecules are charged, she retains her control over them, allowing her to control the flow of the current, including the ability to summon lightning bolts. Her control over the elements at the atomic level also allows her to increase or decrease their molecular movement. This effectively allows her to instantly heat or cool the elements which she psionically controls. For example, she can instantly freeze water or ignite oxygen. By heating or cooling her surroundings, she is able to survive in environments of extreme heat or cold. She has demonstrated a limited capacity to manipulate the magnetic polarity of the metals she can psionically control. By combining her abilities to manipulate air, water, electricity, ice, and temperature, the character is able to effectively control the weather within a 30-mile radius. Also, because of her psionic connection to the elements around her, she has the ability to sense things an ordinary human or Inhuman would not, such as sensing how much moisture is contained within the air or other matter, being aware of movement in the air or water around herself, and being able to determine that a soil sample was not "native" to a particular area.

Critical reception
Steve Morris of ComicsAlliance asserted, "Crystal's elemental powers offer infinite possibility, but her most important trait may be her pragmatism. She's the most aware and self-conscious member of the Inhumans, with a better handle on how to interact with other species than the rest of her family. As a result, she offers a fascinating counterpoint to the bigger-name Inhumans, and drives a more empathetic perspective for readers. She's smart, composed, and understanding; of course she was the one to drive the forging of relationships with the Fantastic Four and the Avengers." Sara Century of Syfy stated, "We like Crystal a lot because she is a character who tries to choose her own happiness, only to get shunted off into politically convenient arranged marriages off-planet at the drop of a hat by the people closest to her. ...For Crystal, the real love story is learning to love herself enough to say "no" to the demands of others."

Accolades

 * In 2015, Entertainment Weekly ranked Crystal 62nd in their "Let's rank every Avenger ever" list.
 * In 2015, Gizmodo ranked Crystal 49th in their "Every Member Of The Avengers" list.
 * In 2016, ComicsAlliance ranked Crystal 5th in their "Marvel’s Royal Inhumans, Ranked From Worst To Best" list.
 * In 2016, Screen Rant ranked Crystal 3rd in their "10 Most Powerful Inhumans In The Marvel Universe" list.
 * In 2017, Screen Rant ranked Crystal 7th in their "Every Member Of The Fantastic Four, Ranked Worst To Best" list.
 * In 2018, CBR.com ranked Crystal 7th in their "20 Most Powerful Inhumans" list.
 * In 2018, Paste ranked Crystal 6th in their "20 Members of the Fantastic Four" list.
 * In 2019, Screen Rant ranked Crystal 4th in their "15 Strongest Female Marvel Characters" list.
 * In 2020, Scary Mommy included Crystal in their "These 195+ Marvel Female Characters Are Truly Heroic" list.
 * In 2021, CBR.com ranked Crystal 8th in their "20 Most Powerful Female Members Of The Avengers" list.
 * In 2021, Screen Rant ranked Crystal 1st in their "10 Best Alternate Members Of The Fantastic Four" list and ranked Crystal and Quicksilver 9th in their "10 Best Relationships in Avengers Comics" list.
 * In 2022, CBR.com ranked Crystal 2nd in their "10 Best Fantastic Four Substitute Members" list, 6th in their "10 Inhumans Who Should Join The Avengers" list, and 10th in their "10 Best Sisters In Comics" list.

Amalgam Comics
In the Amalgam Comics continuity, Dream Crystal, a combination of DC Comics' Beautiful Dreamer and Marvel's Crystal, is a member of the superhero group the Un-People in the Amalgam Comics universe.

Marvel Zombies
In the original Marvel Zombies miniseries, Crystal appeared in one panel as one of the many infected heroes. Later, she is seen as part of the Inhumans Royal Family, all of whom are infected.

Secret Wars
Crystal appears as a member of A-Force on the domain of Arcadia.

Ultimate Marvel
Crystal appeared in the Ultimate Marvel Universe within the Ultimate Fantastic Four Annual #1 story "Inhuman". In this story, she is being forced to marry Black Bolt's brother Maximus whom she does not like. She flirts with Johnny Storm during the issue, but ultimately leaves with the other Inhumans when they go to their new city. She later appears in Ultimate Fantastic Four #30 talking to Sue, who wants her to ask Black Bolt for help with a parasite that is eating Johnny and could kill everyone on Earth. Crystal replies that Black Bolt could not help, even if they were at risk. She reminds Sue that Black Bolt moved the entire city simply because the Fantastic Four breathed their air.

Television

 * Crystal appears in the episode The New Fantastic Four, "Medusa and the Inhumans". She used her elemental powers to create a storm that blocked Atillan's view. When the Fantastic Four attempted to leave Attilan, Crystal used her elemental power to create a storm so that their Fantasti-Car could not take off.
 * Crystal also appeared in the Fantastic Four animated series three-part episode "Inhumans Saga", voiced by Kathy Ireland. After her sister Medusa disappeared and was found, Crystal returned to the Great Refuge, but she was followed by Johnny Storm, who fell in love with her, until Maximus sealed the Great Refuge keeping the two apart. In the episode "The Sentry Sinister", after the negative barrier is destroyed by Black Bolt, Crystal reunites with Johnny Storm and they help Reed, Ben and Sue by confronting the Kree Sentry and escape the island with Lockjaw when the volcano erupts. In the end, Crystal went on to become Johnny's girlfriend and joining the Fantastic Four. In "Doomsday", she eventually helped the team and the Avengers when Doctor Doom stole the power of the Silver Surfer.
 * Crystal appears in the Inhumans motion comic, voiced by Kelly Sheridan.
 * Crystal appears in Hulk and the Agents of S.M.A.S.H., episode "Inhuman Nature", voiced by Mary Faber. This version has mutual feelings toward A-Bomb, though they were temporarily separated by Maximus' barrier around Attilan before Black Bolt destroys it.
 * Crystal appears in Ultimate Spider-Man. In the episode "Agent Web", she is with the Inhuman Royal Family when they confront Spider-Man and Triton outside the abandoned Inhuman city of Atorag, even asking for forgiveness, but it was only to send them back to the Triskelion.
 * Crystal appears in Guardians of the Galaxy, voiced by Vanessa Marshall. In the episode "Crystal Blue Persuasion", Crystal is among the Inhumans that were affected by a Terrigen Plague that caused crystals to grow on their bodies. Crystal appears at the end of the episode where Medusa thanks the Guardians of the Galaxy on Black Bolt's behalf. In the episode "Inhuman Touch" Star-Lord officially meets Crystal and tries to romance her to no avail. She later helps the Guardians of the Galaxy when Maximus escapes prison.
 * Crystal appears in Avengers Assemble, voiced by Stephanie Sheh. In the episode "The Inhuman Condition", she is seen as one of the Inhumans held hostage by Ultron. Crystal is later seen when the Royal Family thank the Avengers for Ultron's defeat. In the episode "Mists of Attilan", Crystal greets Black Panther and Ms. Marvel when they arrive in Attilan. She has also become a fan of Ms. Marvel. While Black Bolt and Medusa argue over what to do with the key fragment in case the Shadow Council shows up, Crystal helps Black Panther and Ms. Marvel obtain it only for that Crystal to be Princess Zanda of Narobia in disguise who is after the fragment that the Shadow Council is after. The real Crystal was found in the same pit trap that Zanda trapped Black Panther and Ms. Marvel in and eventually helps the two Avengers deal with Zanda.
 * Crystal appears in the live-action Marvel Cinematic Universe (MCU) television series Inhumans, portrayed by Isabelle Cornish. Upon learning of Maximus' coup, Crystal sends Lockjaw to teleport her family away while she stays behind after Pulssus stuns Lockjaw. While under house arrest, Maximus tries to persuade Crystal to side with him. One of these attempts has Auran purposely losing her communicator in a scuffle with Crystal so that he can track the rest of the Inhuman Royal Family. She eventually manages to escape with Lockjaw after coming up with a trick to get away from Maximus. Upon arriving in Hawaii, Lockjaw is injured by a passing motorist named Dave and Crystal forces him to take Lockjaw to a medic. She meets Dave's ex-girlfriend Audrey who helps treat Lockjaw. Later, Dave takes Crystal to the beach to teach her to relax every now despite the severity of her situation. At the suggestion of Dave, Crystal uses her powers to contact her family by causing lightning to strike nearby her and is reunited with Black Bolt and Medusa. However, Audrey contacts the police and reports Lockjaw's existence. Using Lockjaw's powers, Crystal and her family escape while Dave and Louise, a human ally Medusa meets, pretend that Audrey was jealous. The family returns to Attilan where Crystal confides in Medusa that she loved being on Earth and wished to have a normal life among the humans. She is soon tasked with helping the city of Attilan evacuate, and later leaves with her family using Lockjaw. She is last seen with the evacuated Inhumans as they search for a new home on Earth.
 * Crystal appears in Marvel Future Avengers, voiced by Yuka Iguchi in Japanese and Stephanie Sheh in English.

Video games

 * Crystal appears a playable character in Avengers in Galactic Storm.
 * Crystal appears as a non-player character in Marvel: Ultimate Alliance, voiced by Kim Mai Guest. She tells the heroes that Medusa went down to Earth to search for the Ultimate Nullifier. After Medusa is discovered to be transformed into one of Doctor Doom's servants, Gorgon mentions that Crystal will accompany him and Triton to fight Doom and make him change Medusa back while the heroes head to the Skrull homeworld.
 * Crystal appears as a playable character in Marvel Avengers Alliance.
 * Crystal appears as a playable character in Lego Marvel's Avengers, voiced by Gwendoline Yeo.
 * Crystal appears as a playable character in Marvel: Future Fight.
 * Crystal appears as a playable character in Lego Marvel Super Heroes 2.
 * Crystal appears as a playable character in Marvel Powers United VR, voiced by Vanessa Marshall.
 * Crystal appears as a playable character in Marvel Ultimate Alliance 3: The Black Order, voiced again by Mary Faber.
 * Crystal appears as a playable character in Marvel Puzzle Quest.

title: Crystal (character)


text:
Pneumonoultramicroscopicsilicovolcanoconiosis

- is a 45-letter word coined in 1935 by the then-president of the National Puzzlers' League, Everett M. Smith. It has sometimes been used as a synonym for the occupational disease known as silicosis, but it should not be as most silicosis is not related to mining of volcanic dusts. It is the longest word in the English language published in a popular dictionary, Oxford Dictionaries, which defines it as "an artificial long word said to mean a lung disease caused by inhaling very fine ash and sand dust".

Clinical and toxicological research conducted on volcanic crystalline silica has found little to no evidence of its ability to cause silicosis/--like diseases and geochemical analyses have shown that there are inherent factors in the crystalline structure which may render volcanic crystalline silica much less pathogenic than some other forms of crystalline silica.

Silicosis is a form of occupational lung disease caused by inhalation of crystalline silica dust, and is marked by inflammation and scarring in the form of nodular lesions in the upper lobes of the lungs. It is a type of pneumoconiosis and is known in the United Kingdom and eastern United States as the "black lung".

Etymology
- is the longest word in the English language. The word can be analysed as follows:

 * 1) Pneumono: from ancient Greek (πνεύμων, pneúmōn) which means lungs
 * 2) ultra: from Latin, meaning beyond
 * 3) micro and scopic: from ancient Greek, meaning small looking, referring to the fineness of particulates
 * 4) silico-: from Latin, silicon
 * 5) volcano: from Latin, referring to volcano
 * 6) coni: from ancient Greek (κόνις, kónis) which means dust
 * 7) -osis: from ancient Greek, suffix to indicate a medical condition

This word was invented in the daily meeting from the National Puzzlers' League (N.P.L.) by its president Everett M. Smith. The word featured in the headline for an article published by the New York Herald Tribune on February 23, 1935, titled "Puzzlers Open 103rd Session Here by Recognizing 45-Letter Word":

"- succeeded - as the longest word in the English language recognized by the National Puzzlers' League at the opening session of the organization's 103rd semi-annual meeting held yesterday at the Hotel New Yorker. The puzzlers explained that the forty-five-letter word is the synonym of a special form of pneumoconiosis caused by ultra-microscopic particles of silica volcanic dust..."

Although it has been defined as an extension of pneumoconiosis, there is no scientific evidence for a similar disease related to volcanic silica particle exposures.

Subsequently, the word was used in Frank Scully's puzzle book Bedside Manna, after which time, members of the N.P.L. campaigned to include the word in major dictionaries.

This 45-letter word, referred to as "p45", first appeared in the 1939 supplement to the Merriam-Webster New International Dictionary, Second Edition.

Any references on the internet to - or silicosis being caused by 'sharp particles [which] lacerate lining of lungs; causing victim to leak air from their lungs while simultaneously bleeding into their lung cavity' are inaccurate. Particles of a size able to enter the lung (< 10 μm diameter) gently settle on the lung lining rather than cutting or abrading the surface.


text:
Susan Richards

Susan Richards may refer to:

 * Invisible Woman, a fictional character
 * Sue Richards (artist) (1958–2014), Canadian artist
 * Susan Richards Shreve, American novelist

title: Susan Richards


text:
Incidence (geometry)

In geometry, an incidence relation is a heterogeneous relation that captures the idea being expressed when phrases such as "a point lies on a line" or "a line is contained in a plane" are used. The most basic incidence relation is that between a point, $P$, and a line, $l$, sometimes denoted $P I l$. If $P I l$ the pair $(P, l)$ is called a flag. There are many expressions used in common language to describe incidence (for example, a line passes through a point, a point lies in a plane, etc.) but the term "incidence" is preferred because it does not have the additional connotations that these other terms have, and it can be used in a symmetric manner. Statements such as "line $l_{1}$ intersects line $l_{2}$" are also statements about incidence relations, but in this case, it is because this is a shorthand way of saying that "there exists a point $P$ that is incident with both line $l_{1}$ and line $l_{2}$". When one type of object can be thought of as a set of the other type of object (viz., a plane is a set of points) then an incidence relation may be viewed as containment.

Statements such as "any two lines in a plane meet" are called incidence propositions. This particular statement is true in a projective plane, though not true in the Euclidean plane where lines may be parallel. Historically, projective geometry was developed in order to make the propositions of incidence true without exceptions, such as those caused by the existence of parallels. From the point of view of synthetic geometry, projective geometry should be developed using such propositions as axioms. This is most significant for projective planes due to the universal validity of Desargues' theorem in higher dimensions.

In contrast, the analytic approach is to define projective space based on linear algebra and utilizing homogeneous co-ordinates. The propositions of incidence are derived from the following basic result on vector spaces: given subspaces $U$ and $W$ of a (finite-dimensional) vector space $V$, the dimension of their intersection is $dim U + dim W − dim (U + W)$. Bearing in mind that the geometric dimension of the projective space $P(V)$ associated to $V$ is $dim V − 1$ and that the geometric dimension of any subspace is positive, the basic proposition of incidence in this setting can take the form: linear subspaces $L$ and $M$ of projective space $P$ meet provided $dim L + dim M ≥ dim P$.

The following sections are limited to projective planes defined over fields, often denoted by $dim (L + M) = dim L + dim M − dim (L ∩ M)$, where $dim L + dim M > dim P$ is a field, or $dim (L ∩ M) > 0$. However these computations can be naturally extended to higher-dimensional projective spaces, and the field may be replaced by a division ring (or skewfield) provided that one pays attention to the fact that multiplication is not commutative in that case.

$PG(2, F)$
Let $F$ be the three-dimensional vector space defined over the field $P^{2}F$. The projective plane $PG(2,F)$ consists of the one-dimensional vector subspaces of $V$, called points, and the two-dimensional vector subspaces of $F$, called lines. Incidence of a point and a line is given by containment of the one-dimensional subspace in the two-dimensional subspace.

Fix a basis for $P(V) = PG(2, F)$ so that we may describe its vectors as coordinate triples (with respect to that basis). A one-dimensional vector subspace consists of a non-zero vector and all of its scalar multiples. The non-zero scalar multiples, written as coordinate triples, are the homogeneous coordinates of the given point, called point coordinates. With respect to this basis, the solution space of a single linear equation $V$ is a two-dimensional subspace of $V$, and hence a line of $V$. This line may be denoted by line coordinates ${(x, y, z) | ax + by + cz = 0}$, which are also homogeneous coordinates since non-zero scalar multiples would give the same line. Other notations are also widely used. Point coordinates may be written as column vectors, $V$T, with colons, $P(V)$, or with a subscript, $[a, b, c]$. Correspondingly, line coordinates may be written as row vectors, $(x, y, z)$, with colons, $(x : y : z)$ or with a subscript, $(x, y, z)_{P}$. Other variations are also possible.

Incidence expressed algebraically
Given a point $(a, b, c)$ and a line $[a : b : c]$, written in terms of point and line coordinates, the point is incident with the line (often written as $(a, b, c)_{L}$), if and only if,

This can be expressed in other notations as:
 * $$ax + by + cz = [a,b,c] \cdot (x,y,z) =(a,b,c)_L \cdot (x,y,z)_P =$$

 * $$ = [a:b:c] \cdot (x:y:z) = (a,b,c) \left ( \begin{matrix} x \\ y \\ z \end{matrix} \right ) = 0. $$

No matter what notation is employed, when the homogeneous coordinates of the point and line are just considered as ordered triples, their incidence is expressed as having their dot product equal 0.

The line incident with a pair of distinct points
Let $P = (x, y, z)$ and $l = [a, b, c]$ be a pair of distinct points with homogeneous coordinates $P I l$ and $ax + by + cz = 0$ respectively. These points determine a unique line $P_{1}$ with an equation of the form $P_{2}$ and must satisfy the equations:
 * $(x_{1}, y_{1}, z_{1})$ and

In matrix form this system of simultaneous linear equations can be expressed as:
 * $$\left( \begin{matrix} x & y & z \\ x_1 & y_1 & z_1 \\ x_2 & y_2 & z_2 \end{matrix} \right) \left( \begin{matrix} a \\ b \\ c \end{matrix} \right) = \left( \begin{matrix} 0 \\ 0 \\ 0 \end{matrix} \right).$$

This system has a nontrivial solution if and only if the determinant,
 * $$ \left| \begin{matrix} x & y & z \\ x_1 & y_1 & z_1 \\x_2 & y_2 & z_2 \end{matrix} \right| = 0.$$

Expansion of this determinantal equation produces a homogeneous linear equation, which must be the equation of line $(x_{2}, y_{2}, z_{2})$. Therefore, up to a common non-zero constant factor we have $l$ where:
 * $ax + by + cz = 0$, and
 * $ax_{1} + by_{1} + cz_{1} = 0$, and

In terms of the scalar triple product notation for vectors, the equation of this line may be written as:

where $ax_{2} + by_{2} + cz_{2} = 0$ is a generic point.

Collinearity
Points that are incident with the same line are said to be collinear. The set of all points incident with the same line is called a range.

If $l$, and $l = [a, b, c]$, then these points are collinear if and only if
 * $$ \left| \begin{matrix} x_1 & y_1 & z_1 \\ x_2 & y_2 & z_2 \\ x_3 & y_3 & z_3 \end{matrix} \right| = 0,$$

i.e., if and only if the determinant of the homogeneous coordinates of the points is equal to zero.

Intersection of a pair of lines
Let $a = y_{1}z_{2} - y_{2}z_{1}$ and $b = x_{2}z_{1} - x_{1}z_{2}$ be a pair of distinct lines. Then the intersection of lines $c = x_{1}y_{2} - x_{2}y_{1}$ and $P ⋅ P_{1} × P_{2} = 0$ is point a $P = (x, y, z)$ that is the simultaneous solution (up to a scalar factor) of the system of linear equations:
 * $P_{1} = (x_{1}, y_{1}, z_{1}), P_{2} = (x_{2}, y_{2}, z_{2})$ and

The solution of this system gives:
 * $P_{3} = (x_{3}, y_{3}, z_{3})$, and
 * $l_{1} = [a_{1}, b_{1}, c_{1}]$, and

Alternatively, consider another line $l_{2} = [a_{2}, b_{2}, c_{2}]$ passing through the point $l_{1}$, that is, the homogeneous coordinates of $l_{2}$ satisfy the equation:

Combining this equation with the two that define $P = (x_{0}, y_{0}, z_{0})$, we can seek a non-trivial solution of the matrix equation:
 * $$\left( \begin{matrix} a & b & c \\ a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \end{matrix} \right) \left( \begin{matrix} x \\ y \\ z \end{matrix} \right) = \left( \begin{matrix} 0 \\ 0 \\ 0 \end{matrix} \right).$$

Such a solution exists provided the determinant,
 * $$ \left| \begin{matrix} a & b & c \\ a_1 & b_1 & c_1 \\a_2 & b_2 & c_2 \end{matrix} \right| = 0.$$

The coefficients of $a_{1}x + b_{1}y + c_{1}z = 0$ and $a_{2}x + b_{2}y + c_{2}z = 0$ in this equation give the homogeneous coordinates of $x_{0} = b_{1}c_{2} - b_{2}c_{1}$.

The equation of the generic line passing through the point $y_{0} = a_{2}c_{1} - a_{1}c_{2}$ in scalar triple product notation is:

Concurrence
Lines that meet at the same point are said to be concurrent. The set of all lines in a plane incident with the same point is called a pencil of lines centered at that point. The computation of the intersection of two lines shows that the entire pencil of lines centered at a point is determined by any two of the lines that intersect at that point. It immediately follows that the algebraic condition for three lines, $z_{0} = a_{1}b_{2} - a_{2}b_{1}$ to be concurrent is that the determinant,
 * $$ \left| \begin{matrix} a_1 & b_1 & c_1 \\a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3 \end{matrix} \right| = 0.$$

title: Incidence (geometry)


text:
Talk:Colorado tick fever

Wiki Education Foundation-supported course assignment
This article was the subject of a Wiki Education Foundation-supported course assignment, between 2 September 2021 and 14 December 2021. Further details are available on the course page. Student editor(s): Schroebr2754, Tuliptooley. Peer reviewers: Ksoccer22, Paulcm1464, Eierscj6816.

Above undated message substituted from Template:Dashboard.wikiedu.org assignment by PrimeBOT (talk) 18:04, 16 January 2022 (UTC)

Tick removal
The tick removal process listed actually makes it worse. This even has an outward link to a website that says so.

?
from [] but not a copyvio. Secretlondon 09:53, Dec 4, 2003 (UTC)
 * Hi! This is a great point. I'm planning to look more into this and add additional information and sources.--Yogilover3 (talk) 20:27, 3 October 2023 (UTC)

Group II or Group III virus?
Problem: the Wiki article for the Parvoviridae family identifies that family as a Group II virus family (ssDNA viruses.)  This is also the classification made by the NIH []. But this articles identifies it as Group III. Is that an error, or is there some sort of disagreement? NaySay (talk) 20:08, 13 December 2007 (UTC)

Wiki Education assignment: Plagues and People
— Assignment last updated by MatthewBroadway (talk) 22:56, 2 October 2023 (UTC)

title: Talk:Colorado tick fever


text:
Rolls-Royce RB211

The Rolls-Royce RB211 is a British family of high-bypass turbofan engines made by Rolls-Royce. The engines are capable of generating 41,030 to 59,450 lbf of thrust. The RB211 engine was the first production three-spool engine and turned Rolls-Royce from a significant player in the aero-engine industry into a global leader.

Originally developed for the Lockheed L-1011 TriStar, it entered service in 1972 and was the exclusive engine to power the L-1011. Mismanagement of the initial development and consequent cost issues led to the effective nationalisation of Rolls-Royce Limited, to save the workforce and the engine businesses important to the UK and many other aerospace and aircraft operating companies.

In the early 1970s, the engine was reckoned by the company to be capable of at least 50 years of continuous development. The RB.211 was renamed, in 1989, to become the basis of the Rolls-Royce Trent family of engines when the RB211-524L was renamed to the Trent.

Background
In 1966, American Airlines announced a requirement for a new short-medium range airliner with a focus on low-cost per-seat operations. While it was looking for a twin-engined plane, aircraft manufacturers needed more than one customer to justify developing a new airliner. Eastern Airlines had expressed interest, but required greater range and needed to operate long routes over water. At the time, this demanded three engines to provide redundancy. Other airlines also favored three engines. Lockheed and Douglas responded with designs, the L-1011 TriStar and DC-10 respectively. Both had three engines, transcontinental range and seated around 300 passengers in a widebody layout with two aisles.

The wide-body McDonnell-Douglas DC-10 was representative of the innovative aircraft and aero-engine technologies which were then being adopted by US and European airframe manufacturers to provide airlines with aircraft of very large carrying capacity and short/medium to long range. These very large capacity aircraft were needed to address the significant increases in passenger numbers and air traffic which were then being forecast by the industry. In Europe, large capacity airliner concept studies had been carried out by both private and government organisations since the late 1950s and early 1960s. Many of the studies conducted by the aviation companies were weighted towards a 200 to 300 seat aircraft, with a high cycle performance that was based on the utilisation of the game-changing new technology of the high by-pass ratio aero-engine.

Between 1964 and 1967, Hawker Siddeley's examination of British European Airways (BEA)'s requirements produced the 160-seat HS.132 and the 185-seat HS.134; both offered the prospect of a 25–30% reduction in seat mile costs over aircraft then in service. Both of the designs would have used two new-technology Rolls-Royce RB.178 aero-engines of 30,000lbf to provide superior operating performance over the first generation three-engine jets.

According to Cownie, Gunston, Hayward and the UK Department of Trade & Industry (DTI), the roots of the advanced RB.178 go back to 1961 when Rolls-Royce officially initiated work on a high by-pass ratio aero-engine as a replacement for the Conway. The company went ahead with the project and under the leadership of Adrian Lombard built the twin-spool demonstrator. Overall development costs of the RB.178 was £2.6 million. As a comparison, the GE and P&W companies were awarded nearly $20 million by the US Department of Defense to develop and build the TF39 and STF200 technology demonstrators.

The RB.178 was built on the reliable and economic advantages inherent in the Conway and, given that engine's heritage, the new engine's performance looked certain. The RB.178 (designated the 16 series) appears to have been the engine proposed for the Vickers Superb DB.265 (VC10), with four engines powering the high capacity transatlantic airliner.

There are perhaps many reasons why the RB.178 failed. Chief among them was Boeing declining to offer the Rolls-Royce engine on the 747.

The RB.178 was cancelled in May 1966 and in June 1966 Rolls-Royce indicated it did not want to battle with P&W over the Boeing 747. In September 1966 Rolls-Royce revealed its decision to launch an Advanced Technology Engine (A.T.E) family covering thrusts ranging from 10,000lbf (RB.203) through to 60,000lbf. (RB.207). The A.T.E family introduced new technologies such as the triple-shaft architecture, an annular combustor and a structurally integrated power-plant (nacelle).

Both planes also required new engines. Engines were undergoing a period of rapid advance due to the introduction of the high bypass concept, which provided for greater thrust, improved fuel economy and less noise than the earlier low-bypass designs. Rolls-Royce had been working on an engine of the required 45,000 lbf (200 kN) thrust class for an abortive attempt to introduce an updated Hawker Siddeley Trident as the RB178. This work was later developed for the 47,500 lbf (211 kN) thrust RB207 to be used on the Airbus A300, before, with the withdrawal of the UK from the Airbus programme, it was cancelled in favour of the RB211 programme.

Rolls-Royce was also working on a series of triple-spool designs as replacements for the Conway, which promised to deliver higher efficiency. In this configuration, three groups of turbines spin three separate concentric shafts to power three sections of the compressor area running at different speeds. In addition to allowing each stage of the compressor to run at its optimal speed, the triple-spool design is more compact and rigid, although more complex to build and maintain. Several designs were being worked on at the time, including a 10,000 lbf (44 kN) thrust design known as the RB203 intended to replace the Spey. Work started on the Conway replacement engine in July 1961 and a twin-spool demonstrator engine to prove the HP compressor, combustor, and turbine system designs, had been run by 1966. Rolls-Royce chose the triple-spool system in 1965 as the simplest, lowest cost solution to the problem of obtaining lower fuel consumption and reduced noise levels at a constant power setting. Work on the RB211 as essentially a scaled-down RB207 began in 1966-7 with the first certificated engines being scheduled to be available by December 1970 at 33,260lb take-off thrust and at a price of $511,000 each.

In February 1968, American Airlines had chosen the Rolls-Royce RB211 to power its order for up to 50 McDonnell-Douglas DC-10s. On 7 March 1968, the Washington correspondent of The Times wrote of an attempt being made by Congress to block Rolls-Royce's bid to supply engines for the projected United States airbus. Representative Robert Taft Jr. of Ohio had marshalled opposition because of a report that Rolls-Royce had won approval for the engine. On 9 March 1968, The Times reported that President Lyndon Johnson had received written protests from six senators and five representatives, from Ohio and New Mexico – states that would benefit if a US manufacturer was selected. Their complaint was that 'not adequately balanced information was given during talks between representatives of airlines and the British Government concerning the American Government's position on buying foreign engines'. The US Congress was concerned that the import of foreign engines would result in a US payments deficit of $3,800 million and the loss of 18,000 to 20,000 jobs.

Finalisation of design
On 23 June 1967, Rolls-Royce offered Lockheed the RB211-06 for the L-1011. The new engine was to be rated at 33260 lbf thrust and combined features of several engines then under development: the large high-power, high-bypass design from the RB207 and the triple-spool design of the RB203. To this was added one new piece of technology, a fan stage built of a new carbon fibre material called Hyfil developed at the RAE Farnborough. The weight saving was considerable over a similar fan made of titanium, and gave the RB211 an advantage over its competitors in terms of power-to-weight ratio. Despite knowing that the timetable was challenging for an engine incorporating these new features, Rolls-Royce committed to putting the RB211 into service in 1971.

Lockheed felt that the new engine enabled the L-1011 to offer a distinct advantage over the otherwise similar DC-10 product. However, Douglas had also requested proposals from Rolls-Royce for an engine to power its DC-10, and in October 1967 the response was a 35400 lbf thrust version of the RB211 designated RB211-10. There followed a period of intense negotiation between airframe manufacturers Lockheed and Douglas, engine suppliers Rolls-Royce, General Electric and Pratt & Whitney, and the major US airlines. During this time prices were negotiated downwards and the required thrust ratings were increased. By early 1968, Rolls-Royce was offering a 40600 lbf thrust engine designated RB211-18. On 29 March 1968 Lockheed announced that it had received orders for 94 TriStars, and placed an order with Rolls-Royce for 150 sets of engines designated RB211-22.

Development and testing
The RB211's complexity required a lengthy development and testing period. By Autumn 1969 Rolls-Royce was struggling to meet the performance guarantees to which it had committed: the engine had insufficient thrust, was over weight and its fuel consumption was excessive. The situation deteriorated further when in May 1970 the new Hyfil (a carbon fibre composite) fan stage, after passing other tests, shattered when a chicken carcass was fired into it at high speed as part of the bird ingestion test. The company had been developing a titanium blade as an insurance against difficulties with Hyfil, but this meant extra cost and more weight. It also brought its own technical problems when it was discovered that only one side of the titanium billet was of the right metallurgical quality for blade fabrication.

In addition, the project suffered a setback with the death of Chief Engineer Adrian "Lom" Lombard in July 1967, a loss that was described as Rolls-Royce having been "deprived of one of the finest trouble-shooting engineers in the industry".

"'It was all too obvious that the Derby engineers, normally proud and self-confident to the point of arrogance, had slid from bad to worse when their great leader, Lombard, had been so suddenly plucked from them in 1967. His death had left a vacuum which nobody could fill ... ' – Stanley Hooker"

In September 1970, Rolls-Royce reported to the government that development costs for the RB211 had risen to £170.3 million – nearly double the original estimate. The estimated production costs now exceeded the £230,375 selling price of each engine. The project was in crisis.

Insolvency and aftermath
By January 1971 Rolls-Royce had become insolvent, and on 4 February 1971 was placed into receivership, seriously jeopardising the L-1011 TriStar programme. Because of its strategic importance, the company was nationalised by the Conservative government of Edward Heath, allowing development of the RB211 to be completed.

As Lockheed was itself in a vulnerable position, the British government required that the US government guarantee the bank loans that Lockheed needed to complete the L-1011 project. If Lockheed (which was itself weakened by the difficulties) had failed, the market for the RB211 would have evaporated. Despite some opposition, the US government provided these guarantees. In May 1971, a new company called "Rolls-Royce (1971) Ltd." acquired the assets of Rolls-Royce from the Receiver, and shortly afterwards signed a new contract with Lockheed. This revised agreement cancelled penalties for late delivery, and increased the price of each engine by £110,000.

Hugh Conway (managing director RR Gas Turbines), persuaded Stanley Hooker to come out of retirement and return to Rolls-Royce. As technical director he led a team of other retirees - including Cyril Lovesey and Arthur Rubbra - to fix the remaining problems on the RB211-22. The engine was finally certified on 14 April 1972, about a year later than originally planned, and the first TriStar entered service with Eastern Air Lines on 26 April 1972. Hooker was knighted for his role in 1974.

Speaking of a famous banker in relation to the RB211:

"'We (Rolls-Royce) added a zero to his stature; he used to think £5 million a lot of money, but after a few weeks on the RB211 he came to understand that £50 million is peanuts.' – Stanley Hooker."

The RB211's initial reliability in service was not as good as had been expected because of the focus of the development programme on meeting the engine's performance guarantees. Early deliveries were of the RB211-22C model, derated slightly from the later -22B. A programme of modifications during the first few years in service improved matters considerably, and the series has since matured into a highly reliable engine.

RB211-524 series
Although originally designed for the L-1011-1, Rolls-Royce knew that the RB211 could be developed to provide greater thrust. By redesigning the fan and the IP compressor, Hooker's team increased the engine's thrust to 50000 lbf. The new version, which first ran on 1 October 1973, was designated RB211-524, and would be able to power new variants of the L-1011, as well as the Boeing 747.

Rolls-Royce tried unsuccessfully to sell the RB211 to Boeing in the 1960s, but the new -524 offered significant performance and efficiency improvements over the Pratt & Whitney JT9D which Boeing had originally selected to power the 747. In October 1973 Boeing agreed to offer the RB211-524 on the 747-200, and British Airways became the first airline to order this combination which entered service in 1977. Flight International stated in 1980:

"'The importance placed on fuel saving by airlines is emphasised by Qantas' adoption of RB.211-524 power for its new Boeing 747s – the only aircraft on which all big three fans are available. Qantas found that British Airways' Boeing 747s fitted with RB211s burnt roughly 7% less fuel than its JT9D-equipped fleet, a saving of about $1 million a year per aircraft, at today's prices.'"

Rolls-Royce continued to develop the -524, increasing its thrust through 51500 lbf with the -524C, then 53000 lbf in the -524D which was certificated in 1981. Notable airline customers included Qantas, Cathay Pacific, Air New Zealand, Cargolux and South African Airways. When Boeing launched the heavier 747-400 more thrust was required, and Rolls responded with the -524G rated at 58000 lbf thrust and then the -524H with 60,600, both introducing a full cowl nacelle with deep-chute forced mixer as already present on the -535E4. These were the first versions to feature FADEC. This was later adopted by GE and Pratt & Whitney for their engines. The -524H was also offered as a third engine choice on the Boeing 767, and the first of these entered service with British Airways in February 1990.

These would have been the final developments of the -524, but when Rolls developed the successor Trent engine, it was found it could fit the Trent 700's improved HP system to the -524G and -524H. These variants were lighter and offered improved fuel efficiency and reduced emissions; they were designated -524G-T and -524H-T respectively. It was also possible to upgrade existing -524G/H engines to the improved -T configuration, and a number of airlines did this.

The -524 became increasingly reliable as it was developed, and the -524H achieved 180-minute ETOPS approval on the 767 in 1993. An RB211 may have a thrust specific fuel consumption around 0.6 lb/(lbf·h).

The -524L, begun in 1987 to allow further growth in the A330 and 777 market, was more extensively redesigned, the considerable differences incorporated leading to the engine eventually receiving the name Trent, under which name development has continued.

RB211-535C

In the mid 1970s, Boeing was considering designs for a new twin-engined aircraft to replace its successful 727. As the size of the proposed plane grew from 150 passengers towards 200, Rolls-Royce realised that the RB211 could be adapted by reducing the diameter of the fan and removing the first IP compressor stage to produce an engine with the necessary 37400 lbf thrust. The new version was designated RB211-535. On 31 August 1978 Eastern Airlines and British Airways announced orders for the new 757, powered by the -535. Designated RB211-535C, the engine entered service in January 1983. This was the first time that Rolls-Royce had provided a launch engine on a Boeing aircraft. Eastern Airlines president Frank Borman called the -535C "The finest airline engine in the world".

RB211-535E, RB211-535E4
In 1979 Pratt & Whitney launched its PW2000 engine, claiming 8% better fuel efficiency than the -535C for the PW2037 version. Boeing put Rolls-Royce under pressure to supply a more competitive engine for the 757, and using the more advanced -524 core as a basis, the company produced the 40100 lbf thrust RB211-535E4 which entered service in October 1984. While not as efficient as the PW2037, it was more reliable and quieter. Visible differences include a long cowl with no jet nozzle protruding beyond the bypass duct. Partial mixing of hot and cold airflows takes place in the integrated or common nozzle. It was also the first to use a wide chord fan blade which increases efficiency, reduces noise and gives added protection against foreign object damage.

Probably the most important single -535E order came in May 1988 when American Airlines ordered 50 757s powered by the -535E4 citing the engine's low noise as an important factor: this was the first time since the TriStar that Rolls-Royce had received a significant order from a US airline, and it led to the -535E4's subsequent market domination on the 757. Unusually, at the time of the announcement made by American, selection of the -535E4 was made public prior to the selection of the 757, though this was welcome news to both Rolls-Royce and Boeing.

After being certified for the 757, the E4 was offered on the Russian Tupolev Tu-204-120 airliner, entering service in 1992. This was the first time a Russian airliner had been supplied with western engines. The -535E4 was also proposed by Boeing for re-engining the B-52H Stratofortress, replacing the aircraft's eight TF33s with four of the turbofans. Further upgrading of the -535E4 took place in the late 1990s to reduce emissions, borrowing technology developed for the Trent 700.

The -535E4 is considered by many to be an extremely reliable engine, and achieved 180-minute ETOPS approval on the 757 in 1990.

Industrial RB211
When Rolls-Royce was developing the -22, it realised that it would be straightforward to develop a version of the engine for land-based power generation, and in 1974 the industrial RB211 was launched. When the -524 arrived shortly afterwards, its improvements were incorporated in the industrial RB211 which was designated RB211-24. The generator was gradually developed over the following years and is still marketed today as a range of generators producing 25.2–32 MW. Many of its installations have been in the offshore oil and gas production industries.

Marine WR-21
An advanced 25 MW class WR-21 Intercooled Recuperated (ICR) gas turbine was derived for marine propulsion.

Variants
• -22

• -22B

• -22C

• -24

• -52

• -56

• -61

• -524

• -524B

• -524C

• -524D

• -524G

• -524G-T

• -524H

• -524H-T

• -535C

• -535E

• -535E4

• WR-21

Engines on display

 * An RB211-22B is on display at the Rolls-Royce Heritage Trust Collection, Derby.
 * An RB211-535C is displayed at the South Yorkshire Aircraft Museum, Doncaster

Specifications

The -535E4 was the first engine to incorporate a hollow wide-chord unsnubbered fan to improve efficiency. It used advanced materials, including titanium in the HP compressor and carbon composites in the nacelle. Later engines incorporate some features (e.g. FADEC) from improved models of the -524.

title: Rolls-Royce RB211


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User:Dodger~enwiki

Jack of all trades, master of nuns.

title: User:Dodger~enwiki


text:
Beat (music)

In music and music theory, the beat is the basic unit of time, the pulse (regularly repeating event), of the mensural level (or beat level). The beat is often defined as the rhythm listeners would tap their toes to when listening to a piece of music, or the numbers a musician counts while performing, though in practice this may be technically incorrect (often the first multiple level). In popular use, beat can refer to a variety of related concepts, including pulse, tempo, meter, specific rhythms, and groove.

Rhythm in music is characterized by a repeating sequence of stressed and unstressed beats (often called "strong" and "weak") and divided into bars organized by time signature and tempo indications.

Beats are related to and distinguished from pulse, rhythm (grouping), and meter:

"Meter is the measurement of the number of pulses between more or less regularly recurring accents. Therefore, in order for meter to exist, some of the pulses in a series must be accented—marked for consciousness—relative to others. When pulses are thus counted within a metric context, they are referred to as beats."

Metric levels faster than the beat level are division levels, and slower levels are multiple levels. Beat has always been an important part of music. Some music genres such as funk will in general de-emphasize the beat, while other such as disco emphasize the beat to accompany dance.

Division
As beats are combined to form measures, each beat is divided into parts. The nature of this combination and division is what determines meter. Music where two beats are combined is in duple meter, music where three beats are combined is in triple meter. Music where the beat is split in two are in simple meter, music where the beat is split in three are called compound meter. Thus, simple duple (,, etc.), simple triple , compound duple , and compound triple. Divisions which require numbers, tuplets (for example, dividing a quarter note into five equal parts), are irregular divisions and subdivisions. Subdivision begins two levels below the beat level: starting with a quarter note or a dotted quarter note, subdivision begins when the note is divided into sixteenth notes.

Downbeat and upbeat

The downbeat is the first beat of the bar, i.e. number 1. The upbeat is the last beat in the previous bar which immediately precedes, and hence anticipates, the downbeat. Both terms correspond to the direction taken by the hand of a conductor.

"This idea of directionality of beats is significant when you translate its effect on music. The crusis of a measure or a phrase is a beginning; it propels sound and energy forward, so the sound needs to lift and have forward motion to create a sense of direction. The anacrusis leads to the crusis, but doesn't have the same 'explosion' of sound; it serves as a preparation for the crusis."

An anticipatory note or succession of notes occurring before the first barline of a piece is sometimes referred to as an upbeat figure, section or phrase. Alternative expressions include "pickup" and "anacrusis" (the latter ultimately from Greek ana ["up towards"] and krousis ["strike"/"impact"] through French anacrouse). In English, anákrousis translates literally as "pushing up". The term anacrusis was borrowed from the field of poetry, in which it refers to one or more unstressed extrametrical syllables at the beginning of a line.

On-beat and off-beat

In typical Western music time, counted as "1 2 3 4, 1 2 3 4...", the first beat of the bar (downbeat) is usually the strongest accent in the melody and the likeliest place for a chord change, the third is the next strongest: these are "on" beats. The second and fourth are weaker—the "off-beats". Subdivisions (like eighth notes) that fall between the pulse beats are even weaker and these, if used frequently in a rhythm, can also make it "off-beat".

The effect can be easily simulated by evenly and repeatedly counting to four. As a background against which to compare these various rhythms a bass drum strike on the downbeat and a constant eighth note subdivision on ride cymbal have been added, which would be counted as follows (bold denotes a stressed beat):
 * 1 2 3 4 1 2 3 4 —
 * 1 2 3 4 1 2 3 4 — the stress here on the "on" beat But one may syncopate that pattern and alternately stress the odd and even beats, respectively:
 * 1 2 3 4 1 2 3 4 — the stress is on the "unexpected" or syncopated beat

So "off-beat" is a musical term, commonly applied to syncopation, that emphasizes the weak even beats of a bar, as opposed to the usual on-beat. This is a fundamental technique of African polyrhythm that transferred to popular western music. According to Grove Music, the "Offbeat is [often] where the downbeat is replaced by a rest or is tied over from the preceding bar". The downbeat can never be the off-beat because it is the strongest beat in time. Certain genres tend to emphasize the off-beat, where this is a defining characteristic of rock'n'roll and ska music.

Backbeat

A back beat, or backbeat, is a syncopated accentuation on the "off" beat. In a simple rhythm these are beats 2 and 4.

"A big part of R&B's attraction had to do with the stompin' backbeats that make it so eminently danceable," according to the Encyclopedia of Percussion. An early record with an emphasised back beat throughout was "Good Rockin' Tonight" by Wynonie Harris in 1948. Although drummer Earl Palmer claimed the honor for "The Fat Man" by Fats Domino in 1949, which he played on, saying he adopted it from the final "shout" or "out" chorus common in Dixieland jazz, urban contemporary gospel was stressing the back beat much earlier with hand-clapping and tambourines. There is a hand-clapping back beat on "Roll 'Em Pete" by Pete Johnson and Big Joe Turner, recorded in 1938. A distinctive back beat can be heard on "Back Beat Boogie" by Harry James And His Orchestra, recorded in late 1939. Other early recorded examples include the final verse of "Grand Slam" by Benny Goodman in 1942 and some sections of The Glenn Miller Orchestra's "(I've Got A Gal In) Kalamazoo", while amateur direct-to-disc recordings of Charlie Christian jamming at Minton's Playhouse around the same time have a sustained snare-drum backbeat on the hottest choruses.

Outside U.S. popular music, there are early recordings of music with a distinctive backbeat, such as the 1949 recording of Mangaratiba by Luiz Gonzaga in Brazil.

Slap bass executions on the backbeat are found in styles of country western music of the 1930s, and the late 1940s early 1950s music of Hank Williams reflected a return to strong backbeat accentuation as part of the honky tonk style of country. In the mid-1940s "hillbilly" musicians the Delmore Brothers were turning out boogie tunes with a hard driving back beat, such as the No. 2 hit "Freight Train Boogie" in 1946, as well as in other boogie songs they recorded. Similarly Fred Maddox's characteristic backbeat, a slapping bass style, helped drive a rhythm that came to be known as rockabilly, one of the early forms of rock and roll. Maddox had used this style as early as 1937.

In today's popular music the snare drum is typically used to play the backbeat pattern. Early funk music often delayed one of the backbeats so as "to give a 'kick' to the [overall] beat".

Some songs, such as The Beatles' "Please Please Me" and "I Want to Hold Your Hand", The Knack's "Good Girls Don't" and Blondie's cover of The Nerves' "Hanging on the Telephone", employ a double backbeat pattern. In a double backbeat, one of the off beats is played as two eighth notes rather than one quarter note.

Cross-beat
Cross-rhythm. A rhythm in which the regular pattern of accents of the prevailing meter is contradicted by a conflicting pattern and not merely a momentary displacement that leaves the prevailing meter fundamentally unchallenged
 * —New Harvard Dictionary of Music (1986: 216).

Hyperbeat
A hyperbeat is one unit of hypermeter, generally a measure. "Hypermeter is meter, with all its inherent characteristics, at the level where measures act as beats."

Beat perception
Beat perception refers to the human ability to extract a periodic time structure from a piece of music. This ability is evident in the way people instinctively move their body in time to a musical beat, made possible by a form of sensorimotor synchronization called 'beat-based timing'. This involves identifying the beat of a piece of music and timing the frequency of movements to match it. Infants across cultures display a rhythmic motor response but it is not until between the ages of 2 years 6 months and 4 years 6 months that they are able to match their movements to the beat of an auditory stimulus.

Related concepts

 * Tatum refers to a subdivision of a beat which represents the "time division that most highly coincides with note onsets".
 * Afterbeat refers to a percussion style where a strong accent is sounded on the second, third and fourth beats of the bar, following the downbeat.
 * In reggae music, the term one drop reflects the complete de-emphasis (to the point of silence) of the first beat in the cycle.
 * James Brown's signature funk groove emphasized the downbeat – that is, with heavy emphasis "on the one" (the first beat of every measure) – to etch his distinctive sound, rather than the back beat (familiar to many R&B musicians) which places the emphasis on the second beat.

title: Beat (music)


text:
User:Rrjanbiah

>>User:Rrjanbiah/monobook.css

Believe it or not, patriotism is one of the worst dividing forces
யாதும் ஊரே, யாவரும் கேளிர். - கணியன் பூங்குன்றனார் (8000 B.C.) The world is my home, and all men and women my brothern. - Kaniyan Poonguntanar

யாதானும் நாடாமால் ஊராமால் என்னொருவன் சாந்துணையுங் கல்லாத வாறு. - திருக்குறள் 397 (8000 B.C) To the learned, every country is his country; Every home, his home. And so, how can one remain without learning to his death? - Thiruvalluvar

Interesting WikiStuff...

 * User:Kate/WhyWikiPediaWorksNot
 * Enciclopedia Libre

It rocks...

 * This is film maker Bala... - Bala on The American College

 * He who created god was a fool; he who spreads his name is a scoundrel and he who worships him is a barbarian - Periyar

 * Not many of you were wise in the way the world judges wisdom. Not many of you had great influence. Not many of you came from important families. But God chose the foolish things of the world to shame the wise, and he chose the weak things of the world to shame the strong. - St. Paul

Gallery of contributed images
Photos are taken with D70s & few with Canon PowerShot SD600

title: User:Rrjanbiah


text:
Talk:1982

USSR / Afghanistan
This entry is a complete mistake ?? or a fake ? There was an invations on Dec 1979, but this one ?? Am I right or wrong ? Regards J*rgen Lund, Copenhagen Nick: The Librarian
 * November 29 - Soviet invasion of Afghanistan: The United Nations General Assembly passes United Nations Resolution 37, stating that the Soviet Union should withdraw from Afghanistan.

Page layout years
There is a discussion on my talk page on page layout.

For most of the last three hundred years there is inconsistency and duplication between the year in topic paragraph, the "see also" box and what is on the year by topic pages. Prior to 1950 I am pretty convinced we can painlessly (except for sore fingers) delete all of the year in topic paragraphs and ensure that the material goes into a "see also" box, creating such a box where none exists. Post 1950, particularly from the "year in US television" link a lot of material has been added to this paragraph as highlights (sometimes making up most of the page content pointed at).

Personally I think we should still delete the paragraph, keep the box linking to the topic sites and move any particularly important parts of the year in topic paragraph to the main chronological list. This does involve undoing quite a bit of work which someone has done.

Therefore, unlike for prior to 1950 (where I've said no objection= I do it) for post 1950 I won't touch these pages unless a significant number of people agree with the change. (I am also unlikely to get the pre 1950 stuff done before summer unless the service speed improves dramatically). talk--BozMo 13:51, 7 May 2004 (UTC)

Dengue fever in Cuba
I removed the Dengue fever outbreak in Cuba for two reasons - firstly, I haven't found any other links substantiating the number infected in one day, secondly the WHO report on DHF in Cuba (written, you may note, by Cuban scientists) states that the outbreak was in 1981 WHO report. If the comment can't even get the year right, why should we believe that allegations that the CIA was responsible are sufficiently confirmed to be non POV? Also, it is quite possible for an infectious disease to spread from south east Asia to Cuba without the help of the CIA. Average Earthman 09:42, 26 May 2005 (UTC)

Iraq
I removed "estonia's first casualty in iraqi war in the coalition of the willing" because there was in my opinion a mistake in the year (not sure which year it happened but i'm quite positive it wasn't february 1982)

Disambig might be needed
We might need a disambig link for this page. 1982 is also the name of Randy Travis' first hit. - Thanks, Hoshie 10:43, 21 August 2006 (UTC)
 * Does the song have an article? --TM 13:01, 21 August 2006 (UTC)
 * No not yet. I have the song on my iPod and was trying to use the wiki to find an article about it and I ended up here. - Thanks, Hoshie 03:39, 22 August 2006 (UTC)
 * Disambiguation pages are really only necessary when there is actually another article to link to, otherwise it doesn't serve much purpose. (And for the song to have its own article it must meet importance guidelines, I'm not sure on the criteria for individual songs though.) --TM 15:20, 4 September 2006 (UTC)

Awards
After reading the page, I noticed the awards section seems a little awkward - in particular, there's a subsection for firlds medalists, nobel prizes and the templeton prize, and I intend to merge those three sections into a single Awards section. Since the current method is in use for the various years, I want to have comments before I actually merge the section - in my opinion, this would be a bold edit that goes against the current standard. --Sigma 7 (talk) 20:51, 2 December 2008 (UTC)

Superbowl
Should the Superbowl be included for this year? Centralized discussion at WT:YEARS — Arthur Rubin (talk) 17:10, 7 June 2012 (UTC)

External links modified
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 * Added archive https://web.archive.org/web/20160306232450/http://www.pagetable.com/?p=547 to http://www.pagetable.com/?p=547

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Eclipses
See WT:YEARS for a matter relevant to this page. Arthur Rubin (alternate) (talk) 23:06, 26 June 2019 (UTC)

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Collage
If people are in favor of a photo collage as seen from '87-2022, I would like to hear some consensus on thoughts about what images should be included in it. Thanks The ganymedian (talk) 22:33, 8 October 2022 (UTC)

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title: Talk:1982