title: Tangent

text: To make the preceding reasoning rigorous, one has to explain what is meant by the difference quotient approaching a certain limiting value "k". The precise mathematical formulation was given by Cauchy in the 19th century and is based on the notion of limit. Suppose that the graph does not have a break or a sharp edge at "p" and it is neither plumb nor too wiggly near "p". Then there is a unique value of "k" such that, as "h" approaches 0, the difference quotient gets closer and closer to "k", and the distance between them becomes negligible compared with the size of "h", if "h" is small enough. This leads to the definition of the slope of the tangent line to the graph as the limit of the difference quotients for the function "f". This limit is the derivative of the function "f" at "x" = "a", denoted "f" ′("a"). Using derivatives, the equation of the tangent line can be stated as follows:


title: Tangent

text: Calculus provides rules for computing the derivatives of functions that are given by formulas, such as the power function, trigonometric functions, exponential function, logarithm, and their various combinations. Thus, equations of the tangents to graphs of all these functions, as well as many others, can be found by the methods of calculus.


title: Tangent

text: Calculus also demonstrates that there are functions and points on their graphs for which the limit determining the slope of the tangent line does not exist. For these points the function "f" is "non-differentiable". There are two possible reasons for the method of finding the tangents based on the limits and derivatives to fail: either the geometric tangent exists, but it is a vertical line, which cannot be given in the point-slope form since it does not have a slope, or the graph exhibits one of three behaviors that precludes a geometric tangent.


title: Tangent

text: The graph "y" = "x" illustrates the first possibility: here the difference quotient at "a" = 0 is equal to "h"/"h" = "h", which becomes very large as "h" approaches 0. This curve has a tangent line at the origin that is vertical.


title: Tangent

text: The graph "y" = "x" illustrates another possibility: this graph has a "cusp" at the origin. This means that, when "h" approaches 0, the difference quotient at "a" = 0 approaches plus or minus infinity depending on the sign of "x". Thus both branches of the curve are near to the half vertical line for which "y"=0, but none is near to the negative part of this line. Basically, there is no tangent at the origin in this case, but in some context one may consider this line as a tangent, and even, in algebraic geometry, as a "double tangent".


title: Tangent

text: The graph "y" = |"x"| of the absolute value function consists of two straight lines with different slopes joined at the origin. As a point "q" approaches the origin from the right, the secant line always has slope 1. As a point "q" approaches the origin from the left, the secant line always has slope −1. Therefore, there is no unique tangent to the graph at the origin. Having two different (but finite) slopes is called a "corner".


title: Tangent

text: Finally, since differentiability implies continuity, the contrapositive states "discontinuity" implies non-differentiability. Any such jump or point discontinuity will have no tangent line. This includes cases where one slope approaches positive infinity while the other approaches negative infinity, leading to an infinite jump discontinuity


title: Tangent

text: where ("x", "y") are the coordinates of any point on the tangent line, and where the derivative is evaluated at formula_9.


title: Tangent

text: When the curve is given by "y" = "f"("x"), the tangent line's equation can also be found by using polynomial division to divide formula_10 by formula_11; if the remainder is denoted by formula_12, then the equation of the tangent line is given by


title: Tangent

text: When the equation of the curve is given in the form "f"("x", "y") = 0 then the value of the slope can be found by implicit differentiation, giving


title: Tangent

text: This equation remains true if formula_16 but formula_17 (in this case the slope of the tangent is infinite). If formula_18 the tangent line is not defined and the point ("X","Y") is said to be singular.


title: Tangent

text: For algebraic curves, computations may be simplified somewhat by converting to homogeneous coordinates. Specifically, let the homogeneous equation of the curve be "g"("x", "y", "z") = 0 where "g" is a homogeneous function of degree "n". Then, if ("X", "Y", "Z") lies on the curve, Euler's theorem implies


title: Tangent

text: The equation of the tangent line in Cartesian coordinates can be found by setting "z"=1 in this equation.


title: Tangent

text: as the equation of the tangent line. The equation in this form is often simpler to use in practice since no further simplification is needed after it is applied.


title: Tangent

text: If formula_28 the tangent line is not defined. However, it may occur that the tangent line exists and may be computed from an implicit equation of the curve.


title: Tangent

text: The line perpendicular to the tangent line to a curve at the point of tangency is called the "normal line" to the curve at that point. The slopes of perpendicular lines have product −1, so if the equation of the curve is "y" = "f"("x") then slope of the normal line is


title: Tangent

text: Similarly, if the equation of the curve has the form "f"("x", "y") = 0 then the equation of the normal line is given by


title: Tangent

text: The angle between two curves at a point where they intersect is defined as the angle between their tangent lines at that point. More specifically, two curves are said to be tangent at a point if they have the same tangent at a point, and orthogonal if their tangent lines are orthogonal.


title: Tangent

text: The formulas above fail when the point is a singular point. In this case there may be two or more branches of the curve that pass through the point, each branch having its own tangent line. When the point is the origin, the equations of these lines can be found for algebraic curves by factoring the equation formed by eliminating all but the lowest degree terms from the original equation. Since any point can be made the origin by a change of variables (or by translating the curve) this gives a method for finding the tangent lines at any singular point.


title: Tangent

text: When the curve is not self-crossing, the tangent at a reference point may still not be uniquely defined because the curve is not differentiable at that point although it is differentiable elsewhere. In this case the left and right derivatives are defined as the limits of the derivative as the point at which it is evaluated approaches the reference point from respectively the left (lower values) or the right (higher values). For example, the curve "y" = |"x" | is not differentiable at "x" = 0: its left and right derivatives have respective slopes −1 and 1; the tangents at that point with those slopes are called the left and right tangents.


title: Tangent

text: Sometimes the slopes of the left and right tangent lines are equal, so the tangent lines coincide. This is true, for example, for the curve "y" = "x" , for which both the left and right derivatives at "x" = 0 are infinite; both the left and right tangent lines have equation "x" = 0.


title: Tangent

text: Two circles of non-equal radius, both in the same plane, are said to be tangent to each other if they meet at only one point. Equivalently, two circles, with radii of "r" and centers at ("x", "y"), for "i" = 1, 2 are said to be tangent to each other if


title: Tangent

text: The tangent plane to a surface at a given point "p" is defined in an analogous way to the tangent line in the case of curves. It is the best approximation of the surface by a plane at "p", and can be obtained as the limiting position of the planes passing through 3 distinct points on the surface close to "p" as these points converge to "p".


title: Tangent

text: More generally, there is a "k"-dimensional tangent space at each point of a "k"-dimensional manifold in the "n"-dimensional Euclidean space.


title: Chang'e

text: Chang'e ( ; , alternatively rendered as Chang-Er or Ch‘ang-o), originally known as Heng'e, is the Chinese goddess of the Moon. She is the subject of several legends in Chinese mythology, most of which incorporate several of the following elements: Houyi the archer, a benevolent or malevolent emperor, an elixir of life, and the Moon. She was married to Houyi. In modern times, Chang'e has been the namesake of the Chinese Lunar Exploration Program.


title: Chang'e

text: There are many tales about Chang'e, including a well-known story about her that is given as the origin of the Mid-Autumn Festival. In one version, in a very distant past, Chang'e was a beautiful woman. Ten suns had risen together into the skies and scorched the Earth, thus causing hardship for the people. Houyi the archer shot down nine of them, leaving just one Sun, and was given either two or one with enough for two elixirs of immortality as a reward. He did not consume it straight away, but let Chang'e keep it with her, as he did not want to gain immortality without his beloved wife. However, while Houyi went out hunting, his apprentice Fengmeng broke into his house and tried to force Chang'e to give the elixir to him. She took them instead of giving them to Fengmeng. Then, Chang'e flew upward past the heavens, choosing the Moon as a residence, as she loved her husband and hoped to live nearby him. Houyi discovered what had transpired and felt guilty, so he displayed the fruits and cakes that Chang'e had enjoyed, and killed himself. In older versions of the story, Chang'e stole the elixir from Houyi, drank it, and flew to the Moon so that her husband could not go after her. Chang'e appears in Wu Cheng'en's late 16th-century novel "Journey to the West".


title: Chang'e

text: The recently rediscovered divination text "Guicang" contains the story of Chang'e as a story providing the meaning to Hexagram 54 of the I Ching, "Returning Maiden".


title: Chang'e

text: During the Mid-Autumn Festival, when the full Moon appears on the night of the eighth lunar month, an open-air altar is set up facing the Moon for the worship of Chang'e. New pastries are put on the altar for her to bless, and she is said to endow her worshippers with beauty. Her story is commonly used as a cautionary tale from older generations to warn young girls about the dangers of following selfish desires.


title: Chang'e

text: Chang'e was mentioned in a conversation between Houston CAPCOM and the Apollo 11 crew just before the first Moon landing in 1969: The International Astronomical Union has assigned the name Chang-Ngo to a small impact crater on the Moon. In 2007, China launched its first lunar probe, a robotic spacecraft named Chang'e 1 in the Goddess' honor. A second robotic probe, named Chang'e 2, was launched in 2010. A third Chang'e spacecraft, called Chang'e 3, landed on the Moon on December 14, 2013, making China the third country in the world to achieve such a feat after the former Soviet Union and the United States. The lander also delivered the robotic rover "Yutu" ("Jade Rabbit") to the lunar surface. On January 3rd, 2019, Chang'e 4 touched down on the far side of the Moon and deployed the "Yutu-2" rover.


title: Chang'e

text: The original plotline and inspiration of Naoko Takeuchi's "Sailor Moon" is inspired by the legend of Chang'e. The titular character is a princess of the Moon while her love interest is from Earth.


title: Chang'e

text: In the video game series "Touhou Project", Chang'e is the mysterious sworn enemy of Junko, the final boss of the 15th game "Legacy of Lunatic Kingdom".


title: Chang'e

text: Chang'e and her story is the main theme of the 2020 American-Chinese animated feature film "Over the Moon" produced by Netflix. The goddess is voiced by Phillipa Soo.


title: Chang'e

text: Chang'e and her story was reimagined in the 2022 fantasy novel The "Daughter of the Moon Goddess" by Sue Lynn Tan.


title: Chris Hedges

text: Christopher Lynn Hedges (born September 18, 1956) is an American journalist, Presbyterian minister, author, and commentator.


title: Chris Hedges

text: In his early career, Hedges worked as a freelance war correspondent in Central America for "The Christian Science Monitor", NPR, and "Dallas Morning News". Hedges reported for "The New York Times" from 1990 to 2005, and served as the "Times" Middle East Bureau Chief and Balkan Bureau Chief during the wars in the former Yugoslavia. In 2001, Hedges contributed to "The New York Times" staff entry that received the 2002 Pulitzer Prize for Explanatory Reporting for the paper's coverage of global terrorism.


title: Chris Hedges

text: Hedges produced a weekly column for "Truthdig" for 14 years until the outlet's hiatus in 2020. His books include "War Is a Force That Gives Us Meaning" (2002), a finalist for the National Book Critics Circle Award for Nonfiction; "" (2007); "Death of the Liberal Class" (2010); and "Days of Destruction, Days of Revolt" (2012), written with cartoonist Joe Sacco.


title: Chris Hedges

text: Christopher Lynn Hedges was born on September 18, 1956 in St. Johnsbury, Vermont. His father was a World War II veteran, Presbyterian minister, and anti-war activist. He was raised in rural Schoharie County, New York, southwest of Albany.


title: Chris Hedges

text: Hedges received a scholarship to attend Loomis Chaffee School, a private boarding school in Windsor, Connecticut. Hedges founded an underground newspaper at the school that was banned by the administration and resulted in his being put on probation. He participated in track and graduated in 1975.


title: Chris Hedges

text: Hedges enrolled into Colgate University and, though heterosexual, helped found an LGBT student group. Hedges received his Bachelor of Arts degree in English from Colgate in 1979. He sought a postgraduate education at Harvard University's Divinity School where he studied under James Luther Adams in addition to studying classics and Classical Greek. While attending Harvard, Hedges lived in Roxbury, a blighted inner city neighborhood in Boston, where he worked as a seminarian and ran a small church. He was also a member of the Greater Boston YMCA's boxing team, writing that the boxing gym was "the only place I felt safe."


title: Chris Hedges

text: Hedges gained an interest in pursuing journalism as a means of furthering ministry after a period of close communications with British journalist Robert Cox, who was at that time reporting on the Dirty War in Argentina. While having one year left before graduation, Hedges briefly dropped out of Harvard to study Spanish in Cochabamba, Bolivia with the support of the Catholic Maryknoll Fathers. Following Cox's recommendation, Hedges informally prepared for work as a reporter through studying a four-volume set of collected works by George Orwell. Hedges made some freelance contributions for "The Washington Post", and later covered the Falklands War from Buenos Aires for National Public Radio using equipment given to him by NPR reporter William Buzenberg. Hedges returned to the United States to complete a Master of Divinity degree at Harvard in 1983.


title: Chris Hedges

text: Hedges continued his career as a freelance journalist in Latin America. From 1983 to 1984, he covered the conflicts in El Salvador, Nicaragua and Guatemala for "The Christian Science Monitor" and NPR. He was hired as the Central America Bureau Chief for "The Dallas Morning News" in 1984 and held this position until 1988. Noam Chomsky wrote of Hedges at the time that he was one of the "few US journalists in Central America who merit the title."


title: Chris Hedges

text: Hedges took a sabbatical to study Arabic in 1988. He was appointed the Middle East Bureau Chief for "The Dallas Morning News" in 1989. In one of his first stories for the paper he tracked down Robert Manning in the settlement of Kiryat Arba in the Israeli-occupied West Bank. Manning, linked to the militant Jewish Defense League and allegedly behind several murders including the 1985 bombing death in California of Alex Odeh, was extradited to the United States in 1991 where he is serving a life sentence for a separate bombing incident.


title: Chris Hedges

text: In 1990, Hedges was hired by "The New York Times". He covered the first Gulf War for the paper, where he refused to participate in the military pool system that restricted the movement and reporting of journalists. He was arrested by the United States Army and had his press credentials revoked, but continued to defy the military restrictions to report outside the pool system. Hedges subsequently entered Kuwait with U.S. Marine Corps members who were distrustful of the Army's press control. Within "The New York Times", R.W. Apple Jr. supported Hedges' defiance of the pool system.


title: Chris Hedges

text: Hedges, along with Neal Conan, was taken prisoner in Basra after the war by the Iraqi Republican Guard during the Shiite uprising. He was freed after a week. Hedges was appointed the paper’s Middle East Bureau Chief in 1991. His reporting on the atrocities committed by Saddam Hussein in the Kurdish-held parts of northern Iraq saw the Iraqi leader offer a bounty for anyone who killed Hedges, along with other western journalists and aid workers in the region. Several aid workers and journalists, including the German reporter Lissy Schmidt, were assassinated and others were severely wounded.


title: Chris Hedges

text: In 1995, Hedges was named the Balkan Bureau Chief for "The New York Times". He was based in Sarajevo when the city was being hit by over 300 shells a day by the surrounding Bosnia Serbs. He reported on the Srebrenica massacre in July 1995 and shortly after the war uncovered what appeared to be one of the central collection points and hiding places for perhaps thousands of corpses at the large open pit Ljubija mine during the Bosnian Serbs' ethnic cleansing campaign. He and the photographer Wade Goddard were the first reporters to travel with armed units of the Kosovo Liberation Army (KLA) in Kosovo. Hedges investigative piece was published in "The New York Times" in June 1999 detailing how Hashim Thaçi, leader of the Kosovo Liberation Army (and later president of Kosovo), directed a campaign in which as many as half a dozen top rebel commanders were assassinated and many others were brutally purged to consolidate his power. Thaci, indicted by the special court in The Hague on 10 counts of war crimes, is in detention in The Hague awaiting trial.


title: Chris Hedges

text: Hedges was a Nieman Fellow at Harvard University during the 1998–1999 academic year, and chose to study Latin because of his prior interest in the classics from studying Classical Greek.


title: Chris Hedges

text: Hedges was based in Paris following the attacks of 9/11, covering Al Qaeda in Europe and the Middle East. He was a member of a "New York Times" investigative team that won the Pulitzer Prize for Breaking News Reporting in 2002 for their coverage of Al Qaeda. Hedges also received the Amnesty International Global Award for Human Rights Journalism in 2002. Hedges' contribution to the "Times" award was an October 2001 article describing Al Qaeda's foiled bombing plot of the Embassy of the United States, Paris.


title: Chris Hedges

text: In a collaboration between "The New York Times" and "Frontline", Hedges authored three articles covering the claims of false Iraqi defectors. Hedges worked on the behalf of Lowell Bergman of "Frontline", who could not travel to Beirut to interview the purported defectors. The trip was organized by Ahmed Chalabi, who Hedges considered to be unreliable. The first defector Hedges interviewed identified themselves as Lt. General Jamal al-Ghurairy. Hedges consulted the U.S. Embassy in Turkey to confirm their identity, and the embassy falsely did so as the real al-Ghurairy had never left Iraq.


title: Chris Hedges

text: Hedges wrote a November 8, 2001 "Times" cover story about two former Iraqi military commanders who claimed to have trained foreign mujahedeen how to hijack planes and destroy vital American infrastructure. The two defectors also asserted there was a secret compound in Salman Pak facility where a German scientist was producing biological weapons. The "Frontline" report featured statements from American officials who doubted the claims of the defectors.


title: Chris Hedges

text: Conservative outlets referenced the articles in justifying the invasion of Iraq. In the aftermath of the revelations that the Iraqi defectors were not legitimate, Hedges defended his comportment since he had done the story as a favor to Lowell Bergman, adding that "There has to be a level of trust between reporters. We cover each other's sources when it's a good story because otherwise everyone would get hold of it."


title: Chris Hedges

text: In 2003, Hedges gave a commencement speech at the graduation ceremony for Rockford College in which he criticized the ongoing American invasion of Iraq. His speech was received with boos, and his microphone was shut off three minutes after he began speaking. Hedges had to end the commencement speech short because of the various student disruptions, which included an additional microphone cut, foghorns, and chants of "God Bless America."


title: Chris Hedges

text: "The New York Times" criticized Hedges' statements and issued him a formal reprimand for "public remarks that could undermine public trust in the paper's impartiality". Hedges cited this reprimand as a motivation for resigning from the "Times" in 2005.


title: Chris Hedges

text: During the uncertainty following the loss of employment, Hedges was looking for posts to teach high school English classes. In a 2008 interview, Hedges acknowledged that he ultimately had not struggled, adding that "every year since I left the "Times", I’ve made at least twice the salary I made at the paper. So, in a way, I didn’t pay for it. And I have maintained what is most valuable to me, which is my integrity and my voice."


title: Chris Hedges

text: In 2005, Hedges became a senior fellow at Type Media Center, and a columnist at Truthdig, in addition to writing books and teaching inmates at a New Jersey correctional institution.


title: Chris Hedges

text: Hedges produced a weekly column in Truthdig for 14 years. He was fired along with all of the editorial staff in March 2020. Hedges and the staff had gone on strike earlier in the month to protest the publisher's attempt to fire the Editor-in-Chief Robert Scheer, demand an end to a series of unfair labor practices and the right to form a union. Hedges resumed work with Scheer after the launch of "Scheerpost".


title: Chris Hedges

text: In June 2014, Christopher Ketcham published an article on "The New Republic" website accusing Hedges of improper citations in several Truthdig columns, alleging the offenses constituted plagiarism. In response, some formatting and reference errors were corrected on the implicated Truthdig posts. Additional accusations of plagiarism from Ketcham were countered by an independent investigation from the Type Media Center. The "Washington Free Beacon" reported that a spokesperson for "The New York Times" said it "did not have reason to believe Hedges plagiarized in his work for the paper" and had no plans to investigate Hedges for plagiarism.


title: Chris Hedges

text: Hedges has worked for a decade teaching writing classes in prisons in New Jersey through a program offered by Princeton University and later Rutgers University. A class that Hedges taught at East Jersey State Prison in 2013 went on to collaborate in the creation of a play titled "Caged". Hedges has become a fierce critic of mass incarceration in the United States, and his experience as an educator in New Jersey prisons served as inspiration for his 2021 book "Our Class: Trauma and Transformation in an American Prison."


title: Chris Hedges

text: On October 5, 2014, Hedges was ordained a minister within the Presbyterian Church. He was installed as Associate Pastor and Minister of Social Witness and Prison Ministry at the Second Presbyterian Church Elizabeth in Elizabeth, New Jersey. He mentioned being rejected for ordination 30 years earlier, saying that "going to El Salvador as a reporter was not something the Presbyterian Church at the time recognized as a valid ministry, and a committee rejected my 'call.'"


title: Chris Hedges

text: Hedges began hosting the television show "On Contact" for the Russian-government owned network RT America in June 2016. Hedges, initially unfamiliar with the network, was approached to make a show by RT America president Mikhail "Misha" Solodovnikov, who personally guaranteed Hedges' editorial independence.


title: Chris Hedges

text: "On Contact" provided commentary on social issues, often profiling nonfiction authors and their recently published works with Hedges aiming to follow the approach of former public television shows. "On Contact" was nominated for an Emmy in 2017, RT America's first significant award nomination, but the award was won by "Steve".


title: Chris Hedges

text: On March 3, 2022, RT America ceased operations following the widespread deplatforming of Russian-sponsored media caused by the 2022 Russian invasion of Ukraine. The run of "On Contact" ended. In a March 7, 2022 "Scheerpost" column (reprinted by "Salon"), Hedges contrasted the reprimand he received from "The New York Times" for his Iraq War opposition to RT America, who made no comment on Hedges' condemnation of the Russian invasion of Ukraine. Hedges said he "might have paid with" his job for making negative comments about the war in Ukraine, "but at least for those six days", after the invasion, he remained in post.


title: Chris Hedges

text: Hedges, in collaboration with The Real News Network, began production in April 2022 for a web series called "The Chris Hedges Report".


title: Chris Hedges

text: Hedges has described himself as a socialist and an anarchist. His books "Death of the Liberal Class" and "Empire of Illusion" are strongly critical of American liberalism.


title: Chris Hedges

text: Hedges' 2007 book "American Fascists" describes the fundamentalist Christian right in the United States as a fascist movement. In March 2008, Hedges published the book "I Don't Believe in Atheists", in which he argues that new atheism presents a danger that is similar to religious extremism.


title: Chris Hedges

text: On September 20, 2014, a day before the People's Climate March, Hedges joined Bernie Sanders, Naomi Klein, Bill McKibben, and Kshama Sawant on a panel moderated by WNYC's Brian Lehrer to discuss the issue of climate change.


title: Chris Hedges

text: Hedges has argued that the impact of population growth must be addressed, saying "all measures to thwart the degradation and destruction of our ecosystem will be useless if we do not cut population growth."


title: Chris Hedges

text: Hedges appeared as a guest on an October 2011 episode of the CBC News Network's "Lang and O'Leary Exchange" to discuss his support for the Occupy Wall Street protests; co-host Kevin O'Leary criticized him, saying that he sounded "like a left-wing nutbar". Hedges said "it will be the last time" he appears on the show, and compared the CBC to Fox News. CBC's ombudsman found O'Leary's heated remarks to be a violation of the public broadcaster's journalistic standards.


title: Chris Hedges

text: On November 3, 2011, Hedges was arrested with others in New York City as part of the Occupy Wall Street demonstration, during which the activists staged a "people's hearing" on the activities of the investment bank Goldman Sachs and blocked the entrance to their corporate headquarters.


title: Chris Hedges

text: In 2012, after the Obama administration signed the National Defense Authorization Act (NDAA), Hedges sued members of the US government, asserting that Section 1021 of the law unconstitutionally allowed presidential authority for indefinite detention without "habeas corpus". He was later joined in the suit, "Hedges v. Obama", by activists including Noam Chomsky and Daniel Ellsberg. In May 2012 Judge Katherine B. Forrest of the Southern District of New York ruled that the counter-terrorism provision of the NDAA is unconstitutional. The Obama administration appealed the decision and it was overturned in July 2013 by the Second Circuit Court of Appeals. Hedges petitioned the U.S. Supreme Court to hear the case, but the Supreme Court denied certiorari in April 2014.


title: Chris Hedges

text: In the 2008 United States presidential campaign, Hedges was a speech writer for candidate Ralph Nader. Hedges supported Green Party candidate Jill Stein in the 2016 election.


title: Chris Hedges

text: On April 15, 2016, Hedges was arrested, along with 100 other protesters, during a sit-in outside the Capitol building in Washington D.C. during Democracy Spring to protest corporate political influence.


title: Chris Hedges

text: On May 27, 2020, Hedges announced that he would run as a Green Party candidate in New Jersey's 12th congressional district for the 2020 elections. After being informed the following day that running for office would conflict with FCC fairness doctrine rules because he was at that time hosting the nationally broadcast RT America television show "On Contact", Hedges decided not to pursue office in order to keep hosting the show.


title: Chris Hedges

text: In a March 2022 piece for the "Salon" website, Hedges wrote that the Russian invasion of Ukraine was "a criminal war of aggression", but argued the likelihood of conflict was aggravated by NATO's expansion after the collapse of the Soviet Union. Hedges called NATO's actions a "dangerous and sadly predictable provocation" that baited Russia to initiate a conflict. Hedges called for an immediate ceasefire and "a moratorium on arms shipments to Ukraine and the withdrawal of Russian troops from the country." He further added that the invasion was "stoked in part by NATO expansion beyond the borders of a unified Germany violating promises made to Moscow at the end of the Cold War, now looks set to become a lengthy war of attrition, one funded and backed by an increasingly bellicose United States." Hedges was critical of the $40 billion aid package for Ukraine in a May 2022 piece in "Salon", which he says demonstrates that the United States is "trapped in the death spiral of unchecked militarism" as the country "rots, morally, politically, economically, and physically" with no real plans to address the epidemic of mass shootings, decaying infrastructure, lack of universal healthcare, ever rising inequality, student debt, child poverty and the opioid epidemic.


title: Chris Hedges

text: Preemptive war, whether in Iraq or Ukraine, is a war crime. It does not matter if the war is launched on the basis of lies and fabrications, as was the case in Iraq, or because of the breaking of a series of agreements with Russia, including the promise by Washington not to extend NATO beyond the borders of a unified Germany, not to deploy thousands of NATO troops in Central and Eastern Europe, and not to meddle in the internal affairs of nations on Russia's border, as well as the refusal to implement the Minsk peace agreement. The invasion of Ukraine would, I expect, never have happened if these promises had been kept. Russia has every right to feel threatened, betrayed, and angry. But to understand is not to condone. The invasion of Ukraine, under post-Nuremberg laws, is a criminal war of aggression.


title: Chris Hedges

text: Hedges is married to the Canadian actress Eunice Wong. The couple have two children. He also has two children from a previous marriage. Hedges currently lives in Princeton, New Jersey.


title: Chris Hedges

text: Hedges has post-traumatic stress disorder from his experience reporting in war zones, and was once suicidal as a result of trauma.


title: Chris Hedges

text: In November 2014, Hedges announced that he and his family had become vegan. He compared his decision to a vow of abstinence, adding that it is necessary "to make radical changes to save ourselves from ecological meltdown." Hedges authored an introduction to a vegan cookbook in 2015, "The Anarchist Cookbook", written by Keith McHenry and Chaz Bufe. His wife, Eunice Wong, is a vegan activist and writer.


title: Translation (biology)

text: In molecular biology and genetics, translation is the process in which ribosomes in the cytoplasm or endoplasmic reticulum synthesize proteins after the process of transcription of DNA to RNA in the cell's nucleus. The entire process is called gene expression.


title: Translation (biology)

text: In translation, messenger RNA (mRNA) is decoded in a ribosome, outside the nucleus, to produce a specific amino acid chain, or polypeptide. The polypeptide later folds into an active protein and performs its functions in the cell. The ribosome facilitates decoding by inducing the binding of complementary tRNA anticodon sequences to mRNA codons. The tRNAs carry specific amino acids that are chained together into a polypeptide as the mRNA passes through and is "read" by the ribosome.


title: Translation (biology)

text: In prokaryotes (bacteria and archaea), translation occurs in the cytosol, where the large and small subunits of the ribosome bind to the mRNA. In eukaryotes, translation occurs in the cytoplasm or across the membrane of the endoplasmic reticulum in a process called co-translational translocation. In co-translational translocation, the entire ribosome/mRNA complex binds to the outer membrane of the rough endoplasmic reticulum (ER) and the new protein is synthesized and released into the ER; the newly created polypeptide can be stored inside the ER for future vesicle transport and secretion outside the cell, or immediately secreted.


title: Translation (biology)

text: Many types of transcribed RNA, such as transfer RNA, ribosomal RNA, and small nuclear RNA, do not undergo translation into proteins.


title: Translation (biology)

text: A number of antibiotics act by inhibiting translation. These include anisomycin, cycloheximide, chloramphenicol, tetracycline, streptomycin, erythromycin, and puromycin. Prokaryotic ribosomes have a different structure from that of eukaryotic ribosomes, and thus antibiotics can specifically target bacterial infections without any harm to a eukaryotic host's cells.


title: Translation (biology)

text: The basic process of protein production is addition of one amino acid at a time to the end of a protein. This operation is performed by a ribosome. A ribosome is made up of two subunits, a small subunit and a large subunit. These subunits come together before translation of mRNA into a protein to provide a location for translation to be carried out and a polypeptide to be produced. The choice of amino acid type to add is determined by an mRNA molecule. Each amino acid added is matched to a three nucleotide subsequence of the mRNA. For each such triplet possible, the corresponding amino acid is accepted. The successive amino acids added to the chain are matched to successive nucleotide triplets in the mRNA. In this way the sequence of nucleotides in the template mRNA chain determines the sequence of amino acids in the generated amino acid chain.


title: Translation (biology)

text: Addition of an amino acid occurs at the C-terminus of the peptide and thus translation is said to be amine-to-carboxyl directed.


title: Translation (biology)

text: The mRNA carries genetic information encoded as a ribonucleotide sequence from the chromosomes to the ribosomes. The ribonucleotides are "read" by translational machinery in a sequence of nucleotide triplets called codons. Each of those triplets codes for a specific amino acid.


title: Translation (biology)

text: The ribosome molecules translate this code to a specific sequence of amino acids. The ribosome is a multisubunit structure containing rRNA and proteins. It is the "factory" where amino acids are assembled into proteins.


title: Translation (biology)

text: tRNAs are small noncoding RNA chains (74–93 nucleotides) that transport amino acids to the ribosome. tRNAs have a site for amino acid attachment, and a site called an anticodon. The anticodon is an RNA triplet complementary to the mRNA triplet that codes for their cargo amino acid.


title: Translation (biology)

text: Aminoacyl tRNA synthetases (enzymes) catalyze the bonding between specific tRNAs and the amino acids that their anticodon sequences call for. The product of this reaction is an aminoacyl-tRNA. In bacteria, this aminoacyl-tRNA is carried to the ribosome by EF-Tu, where mRNA codons are matched through complementary base pairing to specific tRNA anticodons. Aminoacyl-tRNA synthetases that mispair tRNAs with the wrong amino acids can produce mischarged aminoacyl-tRNAs, which can result in inappropriate amino acids at the respective position in protein. This "mistranslation" of the genetic code naturally occurs at low levels in most organisms, but certain cellular environments cause an increase in permissive mRNA decoding, sometimes to the benefit of the cell.


title: Translation (biology)

text: The ribosome has two binding sites for tRNA. They are the aminoacyl site (abbreviated A), the peptidyl site/ exit site (abbreviated P/E). With respect to the mRNA, the three sites are oriented 5’ to 3’ E-P-A, because ribosomes move toward the 3' end of mRNA. The A-site binds the incoming tRNA with the complementary codon on the mRNA. The P/E-site holds the tRNA with the growing polypeptide chain. When an aminoacyl-tRNA initially binds to its corresponding codon on the mRNA, it is in the A site. Then, a peptide bond forms between the amino acid of the tRNA in the A site and the amino acid of the charged tRNA in the P/E site. The growing polypeptide chain is transferred to the tRNA in the A site. Translocation occurs, moving the tRNA in the P/E site, now without an amino acid; the tRNA that was in the A site, now charged with the polypeptide chain, is moved to the P/E site and the tRNA leaves and another aminoacyl-tRNA enters the A site to repeat the process.


title: Translation (biology)

text: After the new amino acid is added to the chain, and after the tRNA is released out of the ribosome and into the cytosol, the energy provided by the hydrolysis of a GTP bound to the translocase EF-G (in bacteria) and a/eEF-2 (in eukaryotes and archaea) moves the ribosome down one codon towards the 3' end. The energy required for translation of proteins is significant. For a protein containing "n" amino acids, the number of high-energy phosphate bonds required to translate it is 4"n"-1. The rate of translation varies; it is significantly higher in prokaryotic cells (up to 17–21 amino acid residues per second) than in eukaryotic cells (up to 6–9 amino acid residues per second).


title: Translation (biology)

text: Even though the ribosomes are usually considered accurate and processive machines, the translation process is subject to errors that can lead either to the synthesis of erroneous proteins or to the premature abandonment of translation, either because a tRNA couples to a wrong codon or because a tRNA is coupled to the wrong amino acid. The rate of error in synthesizing proteins has been estimated to be between 1 in 10 and 1 in 10 misincorporated amino acids, depending on the experimental conditions. The rate of premature translation abandonment, instead, has been estimated to be of the order of magnitude of 10 events per translated codon.


title: Translation (biology)

text: The correct amino acid is covalently bonded to the correct transfer RNA (tRNA) by amino acyl transferases. The amino acid is joined by its carboxyl group to the 3' OH of the tRNA by an ester bond. When the tRNA has an amino acid linked to it, the tRNA is termed "charged". Initiation involves the small subunit of the ribosome binding to the 5' end of mRNA with the help of initiation factors (IF). In bacteria and a minority of archaea, initiation of protein synthesis involves the recognition of a purine-rich initiation sequence on the mRNA called the Shine-Dalgarno sequence. The Shine-Dalgarno sequence binds to a complementary pyrimidine-rich sequence on the 3' end of the 16S rRNA part of the 30S ribosomal subunit. The binding of these complementary sequences ensures that the 30S ribosomal subunit is bound to the mRNA and is aligned such that the initiation codon is placed in the 30S portion of the P-site. Once the mRNA and 30S subunit are properly bound, an initiation factor brings the initiator tRNA-amino acid complex, f-Met-tRNA, to the 30S P site. The initiation phase is completed once a 50S subunit joins the 30 subunit, forming an active 70S ribosome. Termination of the polypeptide occurs when the A site of the ribosome is occupied by a stop codon (UAA, UAG, or UGA) on the mRNA, creating the primary structure of a protein. tRNA usually cannot recognize or bind to stop codons. Instead, the stop codon induces the binding of a release factor protein (RF1 & RF2) that prompts the disassembly of the entire ribosome/mRNA complex by the hydrolysis of the polypeptide chain from the peptidyl transferase center of the ribosome. Drugs or special sequence motifs on the mRNA can change the ribosomal structure so that near-cognate tRNAs are bound to the stop codon instead of the release factors. In such cases of 'translational readthrough', translation continues until the ribosome encounters the next stop codon.


title: Translation (biology)

text: The process of translation is highly regulated in both eukaryotic and prokaryotic organisms. Regulation of translation can impact the global rate of protein synthesis which is closely coupled to the metabolic and proliferative state of a cell. In addition, recent work has revealed that genetic differences and their subsequent expression as mRNAs can also impact translation rate in an RNA-specific manner.


title: Translation (biology)

text: Translational control is critical for the development and survival of cancer. Cancer cells must frequently regulate the translation phase of gene expression, though it is not fully understood why translation is targeted over steps like transcription. While cancer cells often have genetically altered translation factors, it is much more common for cancer cells to modify the levels of existing translation factors. Several major oncogenic signaling pathways, including the RAS–MAPK, PI3K/AKT/mTOR, MYC, and WNT–β-catenin pathways, ultimately reprogram the genome via translation. Cancer cells also control translation to adapt to cellular stress. During stress, the cell translates mRNAs that can mitigate the stress and promote survival. An example of this is the expression of AMPK in various cancers; its activation triggers a cascade that can ultimately allow the cancer to escape apoptosis (programmed cell death) triggered by nutrition deprivation. Future cancer therapies may involve disrupting the translation machinery of the cell to counter the downstream effects of cancer.


title: Translation (biology)

text: The transcription-translation process description, mentioning only the most basic ”elementary” processes, consists of:


title: Translation (biology)

text: The process of amino acid building to create protein in translation is a subject of various physic models for a long time starting from the first detailed kinetic models such as or others taking into account stochastic aspects of translation and using computer simulations. Many chemical kinetics-based models of protein synthesis have been developed and analyzed in the last four decades. Beyond chemical kinetics, various modeling formalisms such as Totally Asymmetric Simple Exclusion Process (TASEP),Probabilistic Boolean Networks (PBN), Petri Nets and max-plus algebra have been applied to model the detailed kinetics of protein synthesis or some of its stages. A basic model of protein synthesis that takes into account all eight 'elementary' processes has been developed, following the paradigm that "useful models are simple and extendable". The simplest model "M0" is represented by the reaction kinetic mechanism (Figure M0). It was generalised to include 40S, 60S and initiation factors (IF) binding (Figure M1'). It was extended further to include effect of microRNA on protein synthesis. Most of models in this hierarchy can be solved analytically. These solutions were used to extract 'kinetic signatures' of different specific mechanisms of synthesis regulation.


title: Translation (biology)

text: It is also possible to translate either by hand (for short sequences) or by computer (after first programming one appropriately, see section below); this allows biologists and chemists to draw out the chemical structure of the encoded protein on paper.


title: Translation (biology)

text: First, convert each template DNA base to its RNA complement (note that the complement of A is now U), as shown below. Note that the template strand of the DNA is the one the RNA is polymerized against; the other DNA strand would be the same as the RNA, but with thymine instead of uracil.


title: Translation (biology)

text: Then split the RNA into triplets (groups of three bases). Note that there are 3 translation "windows", or reading frames, depending on where you start reading the code.


title: Translation (biology)

text: Finally, use the table at Genetic code to translate the above into a structural formula as used in chemistry.


title: Translation (biology)

text: This will give you the primary structure of the protein. However, proteins tend to fold, depending in part on hydrophilic and hydrophobic segments along the chain. Secondary structure can often still be guessed at, but the proper tertiary structure is often very hard to determine.


title: Translation (biology)

text: Whereas other aspects such as the 3D structure, called tertiary structure, of protein can only be predicted using sophisticated algorithms, the amino acid sequence, called primary structure, can be determined solely from the nucleic acid sequence with the aid of a translation table.


title: Translation (biology)

text: This approach may not give the correct amino acid composition of the protein, in particular if unconventional amino acids such as selenocysteine are incorporated into the protein, which is coded for by a conventional stop codon in combination with a downstream hairpin (SElenoCysteine Insertion Sequence, or SECIS).


title: Translation (biology)

text: There are many computer programs capable of translating a DNA/RNA sequence into a protein sequence. Normally this is performed using the Standard Genetic Code, however, few programs can handle all the "special" cases, such as the use of the alternative initiation codons which are biologically significant. For instance, the rare alternative start codon CTG codes for Methionine when used as a start codon, and for Leucine in all other positions.


title: Translation (biology)

text: The "Starts" row indicate three start codons, UUG, CUG, and the very common AUG. It also indicates the first amino acid residue when interpreted as a start: in this case it is all methionine.


title: Translation (biology)

text: Even when working with ordinary eukaryotic sequences such as the Yeast genome, it is often desired to be able to use alternative translation tables—namely for translation of the mitochondrial genes. Currently the following translation tables are defined by the NCBI Taxonomy Group for the translation of the sequences in GenBank:


title: Howard Keel

text: Harold Clifford Keel (April 13, 1919November 7, 2004), known professionally as Howard Keel, was an American actor and singer, known for his rich bass-baritone singing voice. He starred in a number of MGM musicals in the 1950s and in the CBS television series "Dallas" from 1981 to 1991.


title: Howard Keel

text: Keel was born in Gillespie, Illinois, United States, to Navyman-turned-coalminer Homer Keel, and his wife, Grace Margaret (née Osterkamp). Keel was the younger of the couple's children, after elder son Frederick William Keel. The family was so poor that a teacher would often provide Keel with his lunch.


title: Howard Keel

text: After his father's death in 1930, Keel and his mother moved to California, where he graduated from Fallbrook High School at age 17. He worked various odd jobs until settling at Douglas Aircraft Company as a "traveling representative". He was a long haul truck driver.


title: Howard Keel

text: At age 20, Keel was overheard singing by his landlady, Mom Rider, and was encouraged to take vocal lessons. One of his music heroes was the great baritone Lawrence Tibbett. Keel later remarked that learning that his own voice was a "basso cantante" was one of the greatest disappointments of his life. Nevertheless, his first public performance took place in the summer of 1941, when he played the role of Samuel the Prophet in Handel's oratorio "Saul" (singing a duet with bass-baritone George London).


title: Howard Keel

text: In 1945, he briefly understudied for John Raitt in the Broadway hit "Carousel" before being assigned to "Oklahoma!" both written by Richard Rodgers and Oscar Hammerstein II. While performing in "Oklahoma," Keel accomplished a feat that has never been duplicated on Broadway; he once performed the leads in both shows on the same day. In 1947, "Oklahoma!" became the first American postwar musical to travel to London, England, and Keel joined the production. On April 30, 1947, at the Drury Lane Theatre, the capacity audience (which included the future Queen Elizabeth II) demanded fourteen encores.


title: Howard Keel

text: Keel made his film debut as Harold Keel at the British Lion studio in Elstree, in "The Small Voice" (1948), released in the United States as "The Hideout." He played an escaped convict holding a playwright and his wife hostage in their English country cottage. Additional Broadway credits include "Saratoga," "No Strings," and "Ambassador." He appeared at The Muny in St. Louis as Adam in "Seven Brides for Seven Brothers" (1978); Emile de Becque in "South Pacific" (1992); and as General Waverly in "White Christmas" (2000).


title: Howard Keel

text: From London's West End, Keel went to Hollywood in 1949 where he was engaged by the Metro-Goldwyn-Mayer film studio. He made his musical film debut as Frank Butler in the film version of Irving Berlin's "Annie Get Your Gun" (1950), co-starring with Betty Hutton. The film was a big hit and established Keel as a star.


title: Howard Keel

text: MGM put him opposite Esther Williams in "Pagan Love Song" (1950) which was successful, although not as profitable as most Esther William films because it went over budget. Keel had a third hit in a row with the comedy "Three Guys Named Mike" (1951), supporting Van Johnson and Jane Wyman.


title: Howard Keel

text: Even more popular was "Show Boat" (1951), where Keel played the male lead opposite Kathryn Grayson and Ava Gardner. Keel was reunited with Williams in "Texas Carnival" (1952). He had his first flop at MGM with the comedy "Callaway Went Thataway" (1952) co-starring Fred MacMurray and Dorothy McGuire. A reunion with Grayson, "Lovely to Look At" (1952), based on the stage musical "Roberta" was popular but lost money.


title: Howard Keel

text: MGM tried him in an adventure film, "Desperate Search" (1953) which was poorly received. So too was the comedy "Fast Company" (1953). More popular was a Western with Gardner and Robert Taylor, "Ride, Vaquero!" (1953).


title: Howard Keel

text: Warner Bros borrowed Keel to play Wild Bill Hickok opposite Doris Day in "Calamity Jane" (1953), another hit. Back at MGM he and Grayson made a third musical together, "Kiss Me Kate" (1953), which again was liked by the public but unprofitable. The same went for "Rose Marie" (1954) which Keel made with Ann Blyth. However "Seven Brides for Seven Brothers" (1954) with Jane Powell was a huge success and made MGM over $3 million in profit.


title: Howard Keel

text: Keel was one of many guest stars in "Deep in My Heart" (1954). He and Williams made a third film together, "Jupiter's Darling" (1955) which lost MGM over $2 million - the first Williams movie to lose money. "Kismet" (1955) with Blyth also lost over two million dollars, and Keel was released from his MGM contract.


title: Howard Keel

text: He returned to his first love, the stage. In 1957, he was in a short-lived revival of "Carousel." Keel's next film was made in Britain, the thriller "Floods of Fear" (1959). He returned to Hollywood to play Simon-Peter in a Biblical epic, "The Big Fisherman" (1960). In 1959-60 he was in a short-lived Broadway musical "Saratoga." Keel went to Europe to make a low budget war film, "Armored Command" (1961). In England, he starred in "The Day of the Triffids" (1962).


title: Howard Keel

text: As America's taste in entertainment changed, finding jobs became more difficult for Keel. The 1960s held limited prospects for career advancement and consisted primarily of nightclub work, B-Westerns and summer stock. He did "Carousel" in 1962 and 1966. He replaced Richard Kiley on Broadway in "No Strings" (1962). Keel starred in Westerns for A. C. Lyles, "Waco" (1966), "Red Tomahawk" (1966) and "Arizona Bushwhackers" (1968). He had a supporting part in a John Wayne Western, "The War Wagon" (1967).


title: Howard Keel

text: In early 1970, Keel met Judy Magamoll, who was twenty-five years his junior and knew nothing about his stardom. Years later, Keel called the relationship love at first sight, but the age difference bothered him tremendously. For Judy, however, it was not a problem, and with the aid of Robert Frost's poem "What Fifty Said", she convinced him to proceed with their relationship. He resumed his routine of nightclub, cabaret and summer stock jobs with his new wife at his side.


title: Howard Keel

text: From 1971 to 1972, Keel appeared briefly in the West End and Broadway productions of the musical "Ambassador," which flopped. In 1974, Keel became a father for the fourth time with the birth of his daughter, Leslie Grace. In January 1986, he underwent double heart bypass surgery.


title: Howard Keel

text: Keel continued to tour with his wife and daughter in tow, but by 1980 had decided to make his life change. He moved his family to Oklahoma with the intention of joining an oil company. The family had barely settled down when Keel was called back to California to appear with Jane Powell on an episode of "The Love Boat". While there, he was told that the producers of the television series "Dallas" wanted to speak with him.


title: Howard Keel

text: In 1981, after several guest appearances, Keel joined the show permanently as the dignified but hot-tempered oil baron Clayton Farlow. Starting with an appearance on the fourth season, the character had been meant as a semi-replacement patriarch for the series' Jock Ewing played by Jim Davis, who had recently died. However, Clayton was such a hit among viewers that he was made a series regular and stayed on until its end in 1991. Not only did "Dallas" revive his acting career, it breathed new life to his recording endeavors.


title: Howard Keel

text: With renewed fame, Keel commenced his first solo recording career, at age 64, as well as a successful concert career in the UK. He released an album in 1984, "With Love", which sold poorly. However, his album "And I Love You So" reached #6 in the UK Albums Chart and #37 in Australia in 1984. The follow up album, "Reminiscing – The Howard Keel Collection" peaked at #20 in the UK Albums Chart, spending twelve weeks in that listing in 1985 and 1986. The album also peaked at #83 in Australia.


title: Howard Keel

text: In 1988, the album "Just for You" reached #51 in the UK Albums Chart. In 1994, Keel and Judy moved to Palm Desert, California. The Keels were active in community charity events, and attended the annual Howard Keel Golf Classic at Mere Golf Club in Cheshire, England, which raised money for the National Society for the Prevention of Cruelty to Children (NSPCC). Keel attended the event for many years until 2004.


title: Howard Keel

text: Keel received a star on the Hollywood Walk of Fame on 8 February 1960. It is located at 6253 Hollywood Boulevard.


title: Howard Keel

text: In 2019, he was inducted into the Western Performers Hall of Fame at the National Cowboy & Western Heritage Museum in Oklahoma City, Oklahoma.


title: Howard Keel

text: In 1943, Keel met and married actress Rosemary Cooper. They were divorced in 1948, during the London run of "Oklahoma!". Keel met Helen Anderson, a member of the show's chorus, and they married in January 1949. Keel and Helen were separated in 1969 and divorced in 1970. Keel married airline flight attendant Judy Magamoll in December 1970.


title: Howard Keel

text: Keel had four children: three with second wife, Helen Anderson (two daughters, Kaija Liane and Kirstine Elizabeth; and a son, Gunnar Louis; one by his third wife of 34 years, Judy (a daughter, Leslie Grace); and ten grandchildren, including actor Bodie Olmos.


title: Howard Keel

text: Keel died at his Palm Desert home on November 7, 2004, six weeks after being diagnosed with colon cancer. He was cremated and his ashes scattered at three favourite places: Mere Golf Club, Cheshire, England; John Lennon Airport, Liverpool, England; and Tuscany, Italy.


title: Tidal locking

text: Tidal locking between a pair of co-orbiting astronomical bodies occurs when one of the objects reaches a state where there is no longer any net change in its rotation rate over the course of a complete orbit. In the case where a tidally locked body possesses synchronous rotation, the object takes just as long to rotate around its own axis as it does to revolve around its partner. For example, the same side of the Moon always faces the Earth, although there is some variability because the Moon's orbit is not perfectly circular. Usually, only the satellite is tidally locked to the larger body. However, if both the difference in mass between the two bodies and the distance between them are relatively small, each may be tidally locked to the other; this is the case for Pluto and Charon. Alternative names for the tidal locking process are gravitational locking, captured rotation, and spin–orbit locking.


title: Tidal locking

text: The effect arises between two bodies when their gravitational interaction slows a body's rotation until it becomes tidally locked. Over many millions of years, the interaction forces changes to their orbits and rotation rates as a result of energy exchange and heat dissipation. When one of the bodies reaches a state where there is no longer any net change in its rotation rate over the course of a complete orbit, it is said to be tidally locked. The object tends to stay in this state because leaving it would require adding energy back into the system. The object's orbit may migrate over time so as to undo the tidal lock, for example, if a giant planet perturbs the object.


title: Tidal locking

text: Not every case of tidal locking involves synchronous rotation. With Mercury, for example, this tidally locked planet completes three rotations for every two revolutions around the Sun, a 3:2 spin–orbit resonance. In the special case where an orbit is nearly circular and the body's rotation axis is not significantly tilted, such as the Moon, tidal locking results in the same hemisphere of the revolving object constantly facing its partner.


title: Tidal locking

text: However, in this case the exact same portion of the body does not always face the partner on all orbits. There can be some shifting due to variations in the locked body's orbital velocity and the inclination of its rotation axis.


title: Tidal locking

text: Consider a pair of co-orbiting objects, A and B. The change in rotation rate necessary to tidally lock body B to the larger body A is caused by the torque applied by A's gravity on bulges it has induced on B by tidal forces.


title: Tidal locking

text: The gravitational force from object A upon B will vary with distance, being greatest at the nearest surface to A and least at the most distant. This creates a gravitational gradient across object B that will distort its equilibrium shape slightly. The body of object B will become elongated along the axis oriented toward A, and conversely, slightly reduced in dimension in directions orthogonal to this axis. The elongated distortions are known as tidal bulges. (For the solid Earth, these bulges can reach displacements of up to around .) When B is not yet tidally locked, the bulges travel over its surface due to orbital motions, with one of the two "high" tidal bulges traveling close to the point where body A is overhead. For large astronomical bodies that are nearly spherical due to self-gravitation, the tidal distortion produces a slightly prolate spheroid, i.e. an axially symmetric ellipsoid that is elongated along its major axis. Smaller bodies also experience distortion, but this distortion is less regular.


title: Tidal locking

text: The material of B exerts resistance to this periodic reshaping caused by the tidal force. In effect, some time is required to reshape B to the gravitational equilibrium shape, by which time the forming bulges have already been carried some distance away from the A–B axis by B's rotation. Seen from a vantage point in space, the points of maximum bulge extension are displaced from the axis oriented toward A. If B's rotation period is shorter than its orbital period, the bulges are carried forward of the axis oriented toward A in the direction of rotation, whereas if B's rotation period is longer, the bulges instead lag behind.


title: Tidal locking

text: Because the bulges are now displaced from the A–B axis, A's gravitational pull on the mass in them exerts a torque on B. The torque on the A-facing bulge acts to bring B's rotation in line with its orbital period, whereas the "back" bulge, which faces away from A, acts in the opposite sense. However, the bulge on the A-facing side is closer to A than the back bulge by a distance of approximately B's diameter, and so experiences a slightly stronger gravitational force and torque. The net resulting torque from both bulges, then, is always in the direction that acts to synchronize B's rotation with its orbital period, leading eventually to tidal locking.


title: Tidal locking

text: The angular momentum of the whole A–B system is conserved in this process, so that when B slows down and loses rotational angular momentum, its "orbital" angular momentum is boosted by a similar amount (there are also some smaller effects on A's rotation). This results in a raising of B's orbit about A in tandem with its rotational slowdown. For the other case where B starts off rotating too slowly, tidal locking both speeds up its rotation, and "lowers" its orbit.


title: Tidal locking

text: The tidal locking effect is also experienced by the larger body A, but at a slower rate because B's gravitational effect is weaker due to B's smaller mass. For example, Earth's rotation is gradually being slowed by the Moon, by an amount that becomes noticeable over geological time as revealed in the fossil record. Current estimations are that this (together with the tidal influence of the Sun) has helped lengthen the Earth day from about 6 hours to the current 24 hours (over ≈ 4½ billion years). Currently, atomic clocks show that Earth's day lengthens, on average, by about 2.3 milliseconds per century. Given enough time, this would create a mutual tidal locking between Earth and the Moon. The length of the Earth's day would increase and the length of a lunar month would also increase. The Earth's sidereal day would eventually have the same length as the Moon's orbital period, about 47 times the length of the Earth's day at present. However, Earth is not expected to become tidally locked to the Moon before the Sun becomes a red giant and engulfs Earth and the Moon.


title: Tidal locking

text: For bodies of similar size the effect may be of comparable size for both, and both may become tidally locked to each other on a much shorter timescale. An example is the dwarf planet Pluto and its satellite Charon. They have already reached a state where Charon is visible from only one hemisphere of Pluto and vice versa.


title: Tidal locking

text: For orbits that do not have an eccentricity close to zero, the rotation rate tends to become locked with the orbital speed when the body is at periapsis, which is the point of strongest tidal interaction between the two objects. If the orbiting object has a companion, this third body can cause the rotation rate of the parent object to vary in an oscillatory manner. This interaction can also drive an increase in orbital eccentricity of the orbiting object around the primary – an effect known as eccentricity pumping.


title: Tidal locking

text: In some cases where the orbit is eccentric and the tidal effect is relatively weak, the smaller body may end up in a so-called "spin–orbit resonance", rather than being tidally locked. Here, the ratio of the rotation period of a body to its own orbital period is some simple fraction different from 1:1. A well known case is the rotation of Mercury, which is locked to its own orbit around the Sun in a 3:2 resonance. This results in the rotation speed roughly matching the orbital speed around perihelion.


title: Tidal locking

text: Many exoplanets (especially the close-in ones) are expected to be in spin–orbit resonances higher than 1:1. A Mercury-like terrestrial planet can, for example, become captured in a 3:2, 2:1, or 5:2 spin–orbit resonance, with the probability of each being dependent on the orbital eccentricity.


title: Tidal locking

text: All twenty known moons in the Solar System that are large enough to be round are tidally locked with their primaries, because they orbit very closely and tidal force increases rapidly (as a cubic function) with decreasing distance. On the other hand, the irregular outer satellites of the gas giants (e.g. Phoebe), which orbit much farther away than the large well-known moons, are not tidally locked.


title: Tidal locking

text: Pluto and Charon are an extreme example of a tidal lock. Charon is a relatively large moon in comparison to its primary and also has a very close orbit. This results in Pluto and Charon being mutually tidally locked. Pluto's other moons are not tidally locked; Styx, Nix, Kerberos, and Hydra all rotate chaotically due to the influence of Charon. Similarly, and Dysnomia are mutually tidally locked.


title: Tidal locking

text: The tidal locking situation for asteroid moons is largely unknown, but closely orbiting binaries are expected to be tidally locked, as well as contact binaries.


title: Tidal locking

text: Earth's Moon's rotation and orbital periods are tidally locked with each other, so no matter when the Moon is observed from Earth, the same hemisphere of the Moon is always seen. The far side of the Moon was not seen until 1959, when photographs of most of the far side were transmitted from the Soviet spacecraft "Luna 3".


title: Tidal locking

text: When the Earth is observed from the Moon, the Earth does not appear to move across the sky. It remains in the same place while showing nearly all its surface as it rotates on its axis.


title: Tidal locking

text: Despite the Moon's rotational and orbital periods being exactly locked, about 59 percent of the Moon's total surface may be seen with repeated observations from Earth, due to the phenomena of libration and parallax. Librations are primarily caused by the Moon's varying orbital speed due to the eccentricity of its orbit: this allows up to about 6° more along its perimeter to be seen from Earth. Parallax is a geometric effect: at the surface of Earth observers are offset from the line through the centers of Earth and Moon, and because of this about 1° more can be seen around the side of the Moon when it is on the local horizon.


title: Tidal locking

text: It was thought for some time that Mercury was in synchronous rotation with the Sun. This was because whenever Mercury was best placed for observation, the same side faced inward. Radar observations in 1965 demonstrated instead that Mercury has a 3:2 spin–orbit resonance, rotating three times for every two revolutions around the Sun, which results in the same positioning at those observation points. Modeling has demonstrated that Mercury was captured into the 3:2 spin–orbit state very early in its history, probably within 10–20 million years after its formation.


title: Tidal locking

text: The 583.92-day interval between successive close approaches of Venus to Earth is equal to 5.001444 Venusian solar days, making approximately the same face visible from Earth at each close approach. Whether this relationship arose by chance or is the result of some kind of tidal locking with Earth is unknown.


title: Tidal locking

text: The exoplanet Proxima Centauri b, discovered in 2016 that orbits around Proxima Centauri, is almost assuredly tidally locked, expressing either synchronized rotation or a 3:2 spin–orbit resonance like that of Mercury.


title: Tidal locking

text: One form of hypothetical tidally locked exoplanets are eyeball planets, which in turn are divided into "hot" and "cold" eyeball planets.


title: Tidal locking

text: Close binary stars throughout the universe are expected to be tidally locked with each other, and extrasolar planets that have been found to orbit their primaries extremely closely are also thought to be tidally locked to them. An unusual example, confirmed by MOST, may be Tau Boötis, a star that is probably tidally locked by its planet Tau Boötis b. If so, the tidal locking is almost certainly mutual.


title: Tidal locking

text: An estimate of the time for a body to become tidally locked can be obtained using the following formula:


title: Tidal locking

text: formula_12 and formula_13 are generally very poorly known except for the Moon, which has formula_14. For a really rough estimate it is common to take formula_15 (perhaps conservatively, giving overestimated locking times), and


title: Tidal locking

text: Even knowing the size and density of the satellite leaves many parameters that must be estimated (especially "ω", "Q", and "μ"), so that any calculated locking times obtained are expected to be inaccurate, even to factors of ten. Further, during the tidal locking phase the semi-major axis formula_20 may have been significantly different from that observed nowadays due to subsequent tidal acceleration, and the locking time is extremely sensitive to this value.


title: Tidal locking

text: Because the uncertainty is so high, the above formulas can be simplified to give a somewhat less cumbersome one. By assuming that the satellite is spherical, formula_21, and it is sensible to guess one revolution every 12 hours in the initial non-locked state (most asteroids have rotational periods between about 2 hours and about 2 days)


title: Tidal locking

text: with masses in kilograms, distances in meters, and formula_23 in newtons per meter squared; formula_23 can be roughly taken as 3 N·m for rocky objects and 4 N·m for icy ones.


title: Tidal locking

text: For the locking of a primary body to its satellite as in the case of Pluto, the satellite and primary body parameters can be swapped.


title: Tidal locking

text: One conclusion is that, "other things being equal" (such as formula_12 and formula_23), a large moon will lock faster than a smaller moon at the same orbital distance from the planet because formula_28 grows as the cube of the satellite radius formula_7. A possible example of this is in the Saturn system, where Hyperion is not tidally locked, whereas the larger Iapetus, which orbits at a greater distance, is. However, this is not clear cut because Hyperion also experiences strong driving from the nearby Titan, which forces its rotation to be chaotic.


title: Tidal locking

text: The above formulae for the timescale of locking may be off by orders of magnitude, because they ignore the frequency dependence of formula_30. More importantly, they may be inapplicable to viscous binaries (double stars, or double asteroids that are rubble), because the spin–orbit dynamics of such bodies is defined mainly by their viscosity, not rigidity.


title: Tidal locking

text: Based on comparison between the likely time needed to lock a body to its primary, and the time it has been in its present orbit (comparable with the age of the Solar System for most planetary moons), a number of moons are thought to be locked. However their rotations are not known or not known enough. These are:


title: Axel Tuanzebe

text: Axel Tuanzebe (born 14 November 1997) is an English professional footballer who plays as a defender for Premier League club Manchester United.


title: Axel Tuanzebe

text: Tuanzebe is a graduate of the Manchester United youth system and won both the Jimmy Murphy Young Player of the Year and Denzil Haroun Reserve Team Player of the Year awards. He made his competitive debut in an FA Cup game against Wigan Athletic in January 2017. He has had three spells on loan at Aston Villa and helped them to win promotion to the Premier League in 2019.


title: Axel Tuanzebe

text: Born in the Democratic Republic of the Congo, he relocated to England at a young age and has represented England at under-19, under-20 and under-21 levels.


title: Axel Tuanzebe

text: Tuanzebe was associated with the Manchester United academy from the age of eight. He was captain of the Milk Cup winning youth side in 2014. In May 2015, Tuanzebe won the Jimmy Murphy Young Player of the Year award. Academy coach Paul McGuinness noted that Tuanzebe was likely the first first-year scholar to captain the under-18 side since Gary Neville.


title: Axel Tuanzebe

text: On 31 October 2015, at the age of 17, Tuanzebe was named on the substitutes bench for a match against Crystal Palace in the Premier League, the first time he had been a member of a first-team matchday squad.


title: Axel Tuanzebe

text: On 29 January 2017, Tuanzebe made his Manchester United debut as a 68th-minute substitute, replacing Timothy Fosu-Mensah during a 4–0 FA Cup victory over Wigan Athletic at Old Trafford. Four days later, he extended his contract at Manchester United until 2020, with the option of a further year. On 7 May 2017, Tuanzebe started a senior match for the first time, in a 2–0 defeat against Arsenal in the Premier League. He won the Denzil Haroun Reserve Team Player of the Year award in May 2017.


title: Axel Tuanzebe

text: Tuanzebe made his first start of the season against Swansea City in the EFL Cup on 24 October 2017, playing a key part in the second goal of the 2–0 victory. On 5 December 2017, he made his European debut in a 2–1 victory over CSKA Moscow in the UEFA Champions League.


title: Axel Tuanzebe

text: On 25 January 2018, Tuanzebe joined Championship side Aston Villa on loan for the remainder of the season. However, due to suffering an injury and the form of preferred centre-backs James Chester and John Terry he was only able to make five appearances before returning to Manchester United. In August 2018, after going on United's pre-season tour to the United States, he joined Aston Villa on loan again for the 2018–19 season. In December 2018, he suffered another injury setback which ruled him out until March 2019. He returned from injury to help Villa reach the 2019 EFL Championship play-off Final, playing the full 90 minutes as Villa achieved promotion to the Premier League with a victory over Derby County in the final.


title: Axel Tuanzebe

text: In July 2019, Tuanzebe signed a new contract with Manchester United until June 2022, with an option for an additional year. He became the youngest player to captain United since Norman Whiteside in 1985, during an EFL Cup victory against Rochdale in September 2019.


title: Axel Tuanzebe

text: On 20 October 2020, Tuanzebe made his UEFA Champions League debut in a 2–1 away win against Paris Saint-Germain. He started his first league game of the season on 27 January 2021, in a 2–1 home defeat to eventual bottom-finishers Sheffield United.


title: Axel Tuanzebe

text: On 8 August 2021, Tuanzebe signed a new two-year contract with Manchester United, with the option of an extra year; that day, he also agreed to rejoin Aston Villa on loan for the 2021–22 season, his third loan spell with the club. On 8 January 2022, Tuanzebe was recalled from his Aston Villa loan, and loaned to Serie A team Napoli.


title: Axel Tuanzebe

text: Tuanzebe is eligible to represent England or the Democratic Republic of the Congo at international level.


title: Axel Tuanzebe

text: Tuanzebe began his international career in June 2016, when he made his first appearance for England at under-19 level, against Mexico. He was a member of the under-20 squad which won all three matches at the Four Nations tournament in October 2016. Tuanzebe was withdrawn from selection for the 2017 FIFA U-20 World Cup due to club commitments.


title: Axel Tuanzebe

text: Tuanzebe's preferred position is at centre-back, but he can also play as a right-back, and has featured as a holding midfielder. His playing style has been compared to that of teammate Eric Bailly and former Spain international Javi Martínez. Tuanzebe's performance on his first-team debut in a friendly against Wigan Athletic in July 2016 led manager José Mourinho to remark, "10 minutes is enough! The potential is there, you see it immediately."


title: Axel Tuanzebe

text: Tuanzebe was born in Bunia, in the Democratic Republic of the Congo. He relocated to England with his family at the age of four. He attended St Cuthbert's RC High School in Rochdale and captained the Year 7 football team to the final of the English National Schools Cup at Stamford Bridge in 2009. In the same year, he was awarded Sports Boy of the Year by the Mayor of Rochdale. He also represented his school in cross-country and triple-jump. He is the younger brother of ex-Clitheroe striker Dimitri Tuanzebe.


title: Axel Tuanzebe

text: In July 2018, he broke the Guinness World Record for the fastest time to individually clear a game of Hungry Hungry Hippos, while in Los Angeles on Manchester United's pre-season tour.


title: Thranduil

text: Thranduil is a fictional character in J. R. R. Tolkien's Middle-earth legendarium. He first appears as a supporting character in "The Hobbit", where he is simply known as the Elvenking, the ruler of the Elves who lived in the woodland realm of Mirkwood. The character is properly named in Tolkien's "The Lord of the Rings", and appears briefly in "The Silmarillion" and "Unfinished Tales".


title: Thranduil

text: The character has appeared in adaptations of "The Hobbit" in other media. The 2010s film adaptations of "The Hobbit" expands the character's role within the narrative, using information from Tolkien's later works about the character and original material by the filmmakers. Thranduil is portrayed by the American actor Lee Pace; he has been well received by fans and critics.


title: Thranduil

text: Thranduil is one of the Sindar or Grey Elves who speak Sindarin as opposed to Quenya, the language spoken by Noldorin Elves like Galadriel. The name "Thranduil" means "vigorous spring" in Sindarin. Following the end of the First Age and the destruction of much of Beleriand during the War of Wrath, many Sindar migrate into the east of Middle-earth. Crossing the Misty Mountains, they found populations of Silvan Elves living in the woodlands that bordered the River Anduin. The Sindar were welcomed by these people, and some were made leaders and rulers over them. In Appendix B of "The Lord of the Rings" Tolkien states that Thranduil was one of the Sindar who migrated eastward early in the Second Age and established kingdoms among the Silvan Elves. Later writings in "Unfinished Tales" make Thranduil's father Oropher the founder of the realm, which originally included the southern portions of the forest of Greenwood the Great, later known as Mirkwood.


title: Thranduil

text: Tolkien described Thranduil in "The Hobbit" as having "golden hair" with a crown made of red leaves and berries in the autumn, and wearing a similar crown of flowers in the spring.


title: Thranduil

text: Thranduil marched with his father and a large army of their people to join the Last Alliance of Elves and Men in their war against Sauron at the end of the Second Age. The Elves suffered serious losses, including Oropher, who was killed in the Battle of Dagorlad before the Black Gate of Mordor. Following the war, Thranduil, now king of his people, led the remnants of his army, only a third of what had set out, back to their woodland home in Mirkwood. Hearing word of the Disaster of the Gladden Fields shortly after their return, Thranduil set out to aid the Dúnedain; he arrived too late to save them, but was able to finish the destruction of the Orc horde and prevent the mutilation of the dead.


title: Thranduil

text: During the Third Age, Thranduil led his people to the north-east corner of the forest and there created an underground fortress and series of great halls. He was inspired in this enterprise by Thingol's halls of Menegroth in Doriath during the First Age, and like Thingol, he used the skill of the Dwarves to aid in making his stronghold.


title: Thranduil

text: Being far in the north, and on the eastern edge of an increasingly perilous Mirkwood, Thranduil's realm was somewhat isolated, but he traded with the Dwarves and Men who lived nearby in Erebor, Dale, and Esgaroth (Laketown). An attack by the dragon Smaug destroyed Erebor and Dale, and reduced Esgaroth to a shell of its former self, though there remained a healthy wine trade between the lake and the wood.


title: Thranduil

text: This situation changed with the arrival of Bilbo Baggins and a company of Dwarves, on their quest to reclaim Erebor.


title: Thranduil

text: The Dwarves were captured by Thranduil's guards and, suspicious of their intentions, he had them locked in his dungeons from which they later escaped inside barrels.


title: Thranduil

text: After the death of Smaug, Thranduil along with the people of Esgaroth demanded a share of the treasure of Erebor, beginning a confrontation with Thorin's company, who were reinforced by an army from the Iron Hills, that nearly led to war. War with the Dwarves was averted by the intervention of the wizard Gandalf upon the arrival of the allied forces of Orcs and wargs. The combined army of Elves, Dwarves, and Men was victorious in the ensuing Battle of the Five Armies, but at great cost of life.


title: Thranduil

text: During the events of the War of the Ring as depicted in the "Lord of the Rings", Thranduil does what he can to aid his allies, including holding the creature Gollum in his dungeons for interrogation by Gandalf on the history of the One Ring. Gollum later escapes with the aid of Orcs who attack Thranduil's realm, and his son Legolas is sent to Rivendell to seek the counsel of Elrond and Gandalf. Thranduil and his people withstood attacks by Sauron's forces during northern battles of the war. Having routed their foes in the north, Thranduil's forces moved south, and joined with the armies of Lorien under Celeborn and Galadriel in destroying Dol Guldur, cleansing Mirkwood of Sauron's taint of evil. In the aftermath, Thranduil, along with Celeborn, renamed Mirkwood "Eryn Lasgalen", The Wood of Greenleaves. Thranduil's realm expands after the wars, and he and his people enjoyed peace.


title: Thranduil

text: Peter Jackson cast Lee Pace for his 2012–2014 film trilogy "The Hobbit", stating that Pace had been the filmmakers' favourite for the part after his performance in the 2006 film "The Fall".


title: Thranduil

text: The New Zealand screenwriter and film producer Philippa Boyens, a co-writer of the screenplay for "The Hobbit", noted that Tolkien only revealed further detailed information about the character, including his name and backstory, in the book's sequel. Boyens suggested that there was "a lot more story" behind Thranduil, and that he was an interesting character in terms of what they had to make up or expand as part of the films' storytelling as there is not a lot of information present in the original source material.


title: Thranduil

text: The Elves of Mirkwood are a minor element in the novel, and Thranduil in particular has no quarrel with Thorin or his company of Dwarves, who are only imprisoned because they are trespassing on the Elvenking's territory and refuse to tell him why. The existing story narrative of Thranduil as an isolationist leader was identified by the writers, who worked with Pace to develop the character's backstory. In the film series, Thranduil rides a giant elk resembling a "Megaloceros"; the "elk" was a horse named Moose, made up to look like a deer. This version of the character is depicted as somewhat unhinged.


title: Thranduil

text: Pace called Thranduil the "Elvenking" instead of his actual name during interviews, following Tolkien's usage in "The Hobbit", which Pace read as a high school student. In an interview with "The Georgia Straight", Pace explained that Thranduil, unlike other villanous characters he had played like Ronan the Accuser, is morally ambiguous, as he is only at odds with the Dwarves. Pace felt that it was important for him to find enjoyment in playing characters who are larger-than-life, and that it was on him to try to figure out who his character was with what little that he knew. Pace praised the rest of the cast and crew members of "The Hobbit" film project as inspirational, noting that they were collectively telling a big story which was intended to be fully fleshed out on the green screen and which they had no idea how it would ultimately turn out.


title: Thranduil

text: Thranduil is one of the playable heroes in "" (2006) real-time strategy game, joining Elrond, Arwen, Glorfindel, and the Dwarves in destroying Dol Guldur in the final battle of the good storyline, and falling to the Goblins mustered by the Mouth of Sauron in the alternate evil storyline.


title: Thranduil

text: In 2020, Weta Workshop released a limited edition of a statue featuring "The Hobbit" film series iteration of Thranduil, depicted seated on his throne with a guard standing in attention before him. The statue recreates Pace's likeness for the character and is designed at 1:6 scale, measuring 41.33 inches in width and 39.37 inches in height.


title: Thranduil

text: In an article published by "Tor.com" as part of a bi-weekly series titled "Exploring the People of Middle-earth", Megan N. Fontenot found it surprising that in "The Fellowship of the Ring", none of the attendees at the Council of Elrond pays much attention to Legolas' status as Thranduil's heir. Fontenot found the lore behind Thranduil to be underdeveloped, as his name appeared more often in the Appendices than in the main narrative.


title: Thranduil

text: Tom Loback, writing in "Mythlore", attempts to evaluate the strength of the orc forces that attacked Thranduil in the battle under Mirkwood's dark trees (Dagor Dauroth). He estimated, on the basis of the standard words that Tolkien uses for military forces, and the need for the forces to be superior to Thranduil's, that the Witch-king used a "legion" of around 10,000 orcs for the initial reconnaissance, and an "army" of 2 or 3 legions of orcs, for the main attack.


title: Thranduil

text: Lee Pace's portrayal of the Elvenking in Jackson's film trilogy was received warmly. Dennis Perkins from "The A.V. Club" found that Pace's "eerie intensity" made him a "fine elf king". Alisha Coelho from "India Times" described Pace's Thranduil as "a cold, calculative and condescending king" who is prettier than Galadriel but has less heart than Elrond. "Business Review" praised Pace's "aggressive" Thranduil as one of the better performances of "The Battle of the Five Armies", and said that the movie gives audiences a better insight into the Elvenking's motivations as well as the reasons behind his isolationist outlook.


title: Thranduil

text: Nathan Caddell from "The Georgia Straight" observed that Pace "tried to stay as loyal as he could to the source material that he loved, using any small crumbs to try to gain more information about his role", and noted that while it is debatable as to whether Thranduil is an evil character, the "vindictive elf" is a departure from Pace's previous roles, which reflected his warm personality. In a review of the 4K Ultra HD Blu-Ray edition of "The Desolation Of Smaug", M. Enois Duarte from "High-Def Digest" wrote that the confrontation between Thorin and Thranduil was one of the more interesting aspects of the expanded material introduced by Jackson's vision of Tolkien's original narrative for "The Hobbit".


title: Thranduil

text: Conversely, Kirsten Acuna from "Business Insider" found the depiction of Thranduil's motivations in the film series contradictory; she observed that he repeatedly stresses the prioritization of his people's lives to justify his unwillingness to help other communities in "The Desolation of Smaug", and yet in the sequel is willing to risk the same over a war for the White Gems. Nevertheless, she found Thranduil to be much more likeable by the end of "The Battle of the Five Armies".


title: Thranduil

text: Tanja Välisalo, in an empirical study of the audience reception of "The Hobbit" films, found that Thranduil was mentioned by just under 5% of respondents, placing him 7th in the list of people's favourites among the films' cast of characters. They found the character sexually attractive, along with Thorin (played by the "handsome" Richard Armitage). In addition, the audience had an "allegiance" to the character; Välisalo cites as illustration comments like "Thranduil truly captured me" and "this character's make-up and character design ... were a perfect success."


title: Literotica

text: Literotica (a portmanteau of literature and erotica) is a free erotic fiction website. It allows any user to register as an author and submit stories and has over a million registered users . Amateur authors contribute stories, poems, essays, illustrated stories and audio stories in a variety of categories. there were more than 29,000 erotic stories posted. Ant.com ranks the website as the 361st most popular on the internet as of April 9, 2011. Literotica, a United States-based web site, received 44% of its web traffic from the United States.


title: Literotica

text: , it had 4.5 million visitors per month. In addition to written works, the site includes erotic audio and a store page.


title: Literotica

text: Literotica is among the first adult sites open to story creators, having replaced the usenet erotic story sections. Its few rules prohibit stories about pedophilia and bestiality (except that involving fantasy creatures such as dragons and unicorns), and it is mostly aimed at amateur writers and readers who prefer a largely image-free environment. Stories include short, one-off stories, chain-stories written in collaboration with other authors, and entire novels submitted in a "chapter-by-chapter" mode.


title: Literotica

text: The stories themselves are categorized by various themes, and there are categories for stories with pictures and stories with audio.


title: Literotica

text: Literotica's message boards account for only 6% of literotica's web traffic (Alexa.com, 2008). However, this forum has over 1,140,000 registered members, as of April 2010. Users can participate in 23 forums consisting of 16 English-speaking and seven non-English-speaking language boards. Topics include "Amateur Pictures", "Author's Hangout", "Roleplaying", "Poetry Feedback & Discussion", "Sexual Roleplaying", the unmoderated "General Board", a "How-To" forum, a place for writers to seek advice, and "BDSM" and "LGBT" sections.


title: Literotica

text: Members of the message boards, known as 'Literoticans', 'Litizens' or 'Litsters', sometimes meet in 'Litogethers', where members from particular areas plan an event, in order to socialize with others with whom they have formed online friendships.


title: Literotica

text: The site also provides a series of chat rooms. Originally this service was through DigiChat OR literotica's Java client software, but, because of continued cyber attacks, the chat platform moved to a Flash-based client. As of December 2015, it has been operating on a web-based client. Profiles are shared in the story section, and registration is required. Chat registration is free, and users can create their own public rooms. Chat rooms are moderated, and users who discuss forbidden topics are banned from the system.


title: Literotica

text: The site has published story collections under a "Best of" banner and profits from advertising sales and links to webcam, adult video-on-demand, and an online adult store.


title: Literotica

text: CHYOA is a sister site of Literotica, the users of the former of which may post their own stories. However, after a story is created, other users can add additional threads to expand a story in a different direction, similar to the way a choose-your-own-adventure book allows such changes.


title: Literotica

text: This site has 18 sections in which users may post stories. These sections include "Erotic Couplings," "Romance," "Sci-Fi/Fantasy," "Gay Male," "Fan Fiction," and "Non-English" and "Non-Erotic".


title: Literotica

text: Searches for Literotica peak at 4 am. On a list of 7 classiest porn sites by Salon, Literotica came fifth. Bustle recommends Literotica for women. Literotica has been used in scientific research.


title: Eau de toilette

text: Eau de toilette (, meaning "grooming water") is a lightly scented perfume. It is also referred to as aromatic waters and has a high alcohol content. It is usually applied directly to the skin after bathing or shaving. It is traditionally composed of alcohol and various volatile oils. Traditionally these products were named after a principal ingredient; some being geranium water, lavender water, lilac water, violet water, spirit of myrcia and 'eau de Bretfeld'. Because of this, eau de toilette was sometimes referred to as "toilet water".


title: Eau de toilette

text: In modern perfumery, eau de toilette has less concentrated fragrance than perfume ("eau de parfum") and more than cologne ("eau de Cologne").


title: Eau de toilette

text: Eau de toilette is a weaker concentration of fragrance than perfume. The concentration of aromatic ingredients is typically as follows (ascending concentration):


title: Eau de toilette

text: Perfume oils are often diluted with a solvent, though this is not always the case, and its necessity is disputed. By far the most common solvent for perfume oil dilution is ethanol or a mixture of ethanol and water. Perfume has a mixture of about 10–20% perfume oils mixed with alcohol (acting as a diffusing agent delivering the fragrant odor) and a trace of water. Colognes have about 3–5% perfume oil mixed with 80–90% alcohol with about 5 to 15 percent water in the mix. Originally, eau de cologne was a mixture of citrus oils from such fruits as lemons, oranges, tangerines, limes, and grapefruits. These were combined with such substances as lavender and neroli (orange-flower oil). Toilet water has the least amount of perfume oil mixture among the three main liquid "perfumery" categories. It has only about 2 to 8 percent of some type of perfume oil and 60–80% alcohol dispersent with water making up the difference. Toilet waters are a less concentrated form of these above types of alcohol-based perfumes. Traditionally cologne is usually made of citrus oils and fragrances, while toilet waters are not limited to this specification.


title: Eau de toilette

text: Hungarian Eau de toilette, an alcohol based perfume that is the predecessor of eau de cologne, was first produced in the fourteenth century, supposedly by a Hungarian man for Queen Elisabeth of Hungary. This toilet water was called "eau de la reine de hongrie" or Hungary Water, and contained the herb rosemary , which allowed the scent to evaporate slowly on the skin. However, some early scientists, including Johann Beckmann, doubt that it was created for the Queen of Hungary.


title: Eau de toilette

text: The King of France Louis XIV (1638–1715) used a concoction of scents called "heavenly water" to perfume his shirts; It consisted of aloewood, musk, orange flower, rose water and other spices.


title: Eau de toilette

text: Some Eau de toilette were once considered restorative skin toners with medical benefits. The journal Medical Record reported in 1905 that a toilet water spray restores energies lost in business, social, and domestic situations. During the fourteenth through sixteenth centuries a type of toilet water called "plague waters" was supposed to drive away the bubonic plague.


title: Leah

text: Leah (; ) appears in the Hebrew Bible as one of the two wives of the Biblical patriarch Jacob. Leah was Jacob's first wife, and the older sister of his second (and favored) wife Rachel. She is the mother of Jacob's first son Reuben. She has three more sons, namely Simeon, Levi and Judah, but does not bear another son until Rachel offers her a night with Jacob in exchange for some mandrake root (, "dûdâ'îm"). Leah gives birth to two more sons after this, Issachar and Zebulun, and to Jacob's only daughter, Dinah.


title: Leah

text: Leah first appears in the Book of Genesis, in Genesis 29, which describes her as the daughter of Laban and the older sister of Rachel, and is said to not compare to Rachel's physical beauty and that she has tender eyes. Earlier passages in the Book of Genesis give some background on her father's family, noting that through him, she is the niece of Rebecca, who is the wife of Isaac and the mother of Jacob and Esau, and the granddaughter of Bethuel, and rabbinic literature goes even further, with the Book of Jasher claiming Leah and Rachel were twins and recording her mother's name as Adinah and her brothers' names as Beor, Alub, and Murash. Rabbinical literature contradicts itself on whether or not Leah and Rachel were half-siblings to Zilpah and Bilhah, two sisters who would serve as mistresses to Leah's future husband, Jacob, and whose children she and Rachel would raise as their own, as one source lists them as being daughters of Laban, but not his wife Adinah, and another lists them as being the daughters of Rotheus, a man who was close to Laban but not related to him. If Zilpah and Bilhah were indeed half-sisters of Leah, this would make Leah's adoptive sons, Gad and Asher, and Rachel's adoptive sons, Dan and Naphtali, her nephews. According to Genesis 28:2, the family resided in Paddan Aram, an area believed to correspond with the historical Upper Mesopotamia.