title: Reinhold Niebuhr

text: King invited Niebuhr to participate in the third Selma to Montgomery March in 1965, and Niebuhr responded by telegram: "Only a severe stroke prevents me from accepting ... I hope there will be a massive demonstration of all the citizens with conscience in favor of the elemental human rights of voting and freedom of assembly" (Niebuhr, March 19, 1965). Two years later, Niebuhr defended King's decision to speak out against the Vietnam War, calling him "one of the greatest religious leaders of our time". Niebuhr asserted: "Dr. King has the right and a duty, as both a religious and a civil rights leader, to express his concern in these days about such a major human problem as the Vietnam War." Of his country's intervention in Vietnam, Niebuhr admitted: "For the first time I fear I am ashamed of our beloved nation."


title: Reinhold Niebuhr

text: Throughout his life, Niebuhr cultivated a good reputation and rapport with the Jewish community. He was an early critic of Christian antisemitism, including proselytism, and a persistent critic of Nazism and rising antisemitism in Germany throughout the 1930s.


title: Reinhold Niebuhr

text: When he began as a young pastor in 1923 Detroit, he favored conversion of Jews to Christianity, scolding evangelical Christians who were either antisemitic or ignored them. He spoke out against "the un-Christlike attitude of Christians", and what he called "Jewish bigotry". Within three years, his theological views had evolved, and he spoke out against the practicality and necessity of missionizing Jews. He was the first prominent Christian theologian to argue it was inappropriate for Christians to seek to convert Jews to their faith, saying this negated “every gesture of our common biblical inheritance.” His experience in Detroit led him to the conclusion that the Jewish community was already sincerely committed to Social Justice.


title: Reinhold Niebuhr

text: In a 1926-01-10 lecture, Niebuhr said: "If I were a self-respecting Jew, I certainly would not renounce the faith of the fathers to embrace a faith which is as involved as Christianity is with racialism, Nordicism and gentile arrogance. (...) What we need is an entente cordiale between prophetic Judaism and prophetic Christianity in which both religions would offer the best they have to each other"


title: Reinhold Niebuhr

text: Niebuhr's 1933 article in "The Christian Century" was an attempt to sound the alarm within the Christian community over Hitler's "cultural annihilation of the Jews".


title: Reinhold Niebuhr

text: As a preacher, writer, leader, and adviser to political figures, Niebuhr supported Zionism and the development of Israel. His solution to antisemitism was a combination of a Jewish homeland, greater tolerance, and assimilation in other countries. Unlike other Christian Zionists, Niebuhr's support of Zionism was practical, not theological, and not rooted in fulfillment of Biblical prophesy nor anticipation of the End-of-Days. Despite being a religious leader, he cautioned against the involvement of religious claims in the conflict. Although Niebuhr qualified his support for Zionism, he has been sharply criticized by Anti-Zionist figures such as Edward Said, who derided his claims to care about the Palestinians as insincere.


title: Reinhold Niebuhr

text: Niebuhr noted that “Zionism is the expression of a national will to live that transcends the traditional orthodox religion of the Jews.” Jewish statehood was necessary because “the bigotry of majority groups toward minority groups that affront the majority by diverging from the dominant type is a perennial aspect of man’s collective life. The force of it may be mitigated, but it cannot be wholly eliminated.”


title: Reinhold Niebuhr

text: "How is the ancient and hereditary title of the Jews to Palestine to be measured against the right of the Arab’s present possession? … The participants cannot find a common ground of rational morality from which to arbitrate the issues because the moral judgments which each brings to them are formed by the historical forces which are in conflict. … The effort to bring such a conflict under the dominion of a spiritual unity may be partly successful, but it always produces a tragic by-product of the spiritual accentuation of natural conflict. The introduction of religious motives into these conflicts is usually no more than the final and most demonic pretension."


title: Reinhold Niebuhr

text: In 1952, Niebuhr published "The Irony of American History", in which he interpreted the meaning of the United States' past. Niebuhr questioned whether a humane, "ironical" interpretation of American history was credible on its own merits, or only in the context of a Christian view of history. Niebuhr's concept of irony referred to situations in which "the consequences of an act are diametrically opposed to the original intention", and "the fundamental cause of the disparity lies in the actor himself, and his original purpose." His reading of American history based on this notion, though from the Christian perspective, is so rooted in historical events that readers who do not share his religious views can be led to the same conclusion. Niebuhr's great foe was idealism. American idealism, he believed, comes in two forms: the idealism of the antiwar non-interventionists, who are embarrassed by power; and the idealism of pro-war imperialists, who disguise power as virtue. He said the non-interventionists, without mentioning Harry Emerson Fosdick by name, seek to preserve the purity of their souls, either by denouncing military actions or by demanding that every action taken be unequivocally virtuous. They exaggerate the sins committed by their own country, excuse the malevolence of its enemies and, as later polemicists have put it, inevitably blame America first. Niebuhr argued this approach was a pious way to refuse to face real problems.


title: Reinhold Niebuhr

text: Niebuhr said he wrote the short Serenity Prayer. Fred R. Shapiro, who had cast doubts on Niebuhr's claim, conceded in 2009 that, "The new evidence does not prove that Reinhold Niebuhr wrote [the prayer], but it does significantly improve the likelihood that he was the originator." The earliest known version of the prayer, from 1937, attributes the prayer to Niebuhr in this version: "Father, give us courage to change what must be altered, serenity to accept what cannot be helped, and the insight to know the one from the other." The most popular version, the authorship of which is unknown, reads:


title: Reinhold Niebuhr

text: Many political scientists, such as George F. Kennan, Hans Morgenthau, Kenneth Waltz, and Samuel P. Huntington, and political historians, such as Richard Hofstadter, Arthur M. Schlesinger Jr., and Christopher Lasch, have noted his influence on their thinking.


title: Reinhold Niebuhr

text: Niebuhr exerted a significant influence upon mainline Protestant clergy in the years immediately following World War II, much of it in concord with the neo-orthodox and the related movements. That influence began to wane and then drop toward the end of his life.


title: Reinhold Niebuhr

text: The historian Arthur M. Schlesinger Jr. in the late twentieth century described the legacy of Niebuhr as being contested between American liberals and conservatives, both of whom wanted to claim him. Martin Luther King Jr. gave credit to Niebuhr's influence. Foreign-policy conservatives point to Niebuhr's support of the containment doctrine during the Cold War as an instance of moral realism; progressives cite his later opposition to the Vietnam War.


title: Reinhold Niebuhr

text: In more recent years, Niebuhr has enjoyed something of a renaissance in contemporary thought, although usually not in liberal Protestant theological circles. Both major-party candidates in the 2008 presidential election cited Niebuhr as an influence: Senator John McCain, in his book "Hard Call", "celebrated Niebuhr as a paragon of clarity about the costs of a good war". President Barack Obama said that Niebuhr was his " philosopher" and "favorite theologian". "Slate" magazine columnist Fred Kaplan characterized Obama's 2009 Nobel Peace Prize acceptance speech as a "faithful reflection" of Niebuhr.


title: Reinhold Niebuhr

text: Kenneth Waltz's seminal work on international relations theory, "Man, the State, and War", includes many references to Niebuhr's thought. Waltz emphasizes Niebuhr's contributions to political realism, especially "the impossibility of human perfection". Andrew Bacevich's book "The Limits of Power: The End of American Exceptionalism" refers to Niebuhr 13 times. Bacevich emphasizes Niebuhr's humility and his belief that Americans were in danger of becoming enamored of US power.


title: Reinhold Niebuhr

text: Other leaders of American foreign policy in the late twentieth century and early twenty-first century have acknowledged Niebuhr's importance to them, including Jimmy Carter, Madeleine Albright, and Hillary Clinton.


title: Reinhold Niebuhr

text: Niebuhr's influence was at its peak during the first two decades of the Cold War. By the 1970s, his influence was declining because of the rise of liberation theology, antiwar sentiment, the growth of conservative evangelicalism, and postmodernism. According to historian Gene Zubovich, "It took the tragic events of September 11, 2001, to revive Niebuhr."


title: Reinhold Niebuhr

text: In spring of 2017, it was speculated (and later confirmed) that former FBI director James Comey used Niebuhr's name as a screen name for his personal Twitter account. Comey, as a religion major at the College of William & Mary, wrote his undergraduate thesis on Niebuhr and televangelist Jerry Falwell.


title: Reinhold Niebuhr

text: Niebuhr was often described as a charismatic speaker. The journalist Alden Whitman wrote of his speaking style:


title: Reinhold Niebuhr

text: He possessed a deep voice and large blue eyes. He used his arms as though he were an orchestra conductor. Occasionally one hand would strike out, with a pointed finger at the end, to accent a trenchant sentence. He talked rapidly and (because he disliked to wear spectacles for his far-sightedness) without notes; yet he was adroit at building logical climaxes and in communicating a sense of passionate involvement in what he was saying.


title: Nina Agdal

text: Nina Brohus Agdal (born 26 March 1992) is a Danish model known for her appearances in the "Sports Illustrated Swimsuit Issue" and, alongside Chrissy Teigen and Lily Aldridge, appeared on the 50th anniversary cover in 2014.


title: Nina Agdal

text: Agdal was discovered while on a street in her home town. Having no modeling experience, she entered the Elite Model Look competition. She did not win, but did then sign with Elite Models Copenhagen and continued school until she was 18. After graduation, she moved to the United States, after which her modeling career blossomed. She has modeled for Billabong, Victoria's Secret, Adore Me, Bebe Stores and Calzedonia. She has also been in fashion editorials for "Vogue" Mexico, "Elle", "Cosmopolitan" and "CR fashion" book by Carine Roitfeld. In 2012, she made her first appearance in the "Sports Illustrated Swimsuit Issue" and was subsequently named the issue's "Rookie of the Year". She also appeared on the cover of "Maxim" magazine for its March issue in 2017. In 2014, she appeared on the 50th anniversary cover of the "Sports Illustrated Swimsuit Issue" with Chrissy Teigen and Lily Aldridge, which she regards as the "highlight" of her modeling career.


title: Nina Agdal

text: Agdal appeared in a 2013 Super Bowl television commercial for Carl's Jr./Hardee's. In August 2016 she signed with IMG Models.


title: Lorraine

text: Lorraine is a cultural and historical region in Northeastern France, now located in the administrative region of Grand Est. Its name stems from the medieval kingdom of Lotharingia, which in turn was named after either Emperor Lothair I or King Lothair II. Lorraine later was ruled as the Duchy of Lorraine before the Kingdom of France annexed it in 1766.


title: Lorraine

text: From 1982 until January 2016, Lorraine was an administrative region of France. In 2016, under a reorganisation, it became part of the new region Grand Est. As a region in modern France, Lorraine consisted of the four departments Meurthe-et-Moselle, Meuse, Moselle and Vosges (from a historical point of view the Haute-Marne department is located in the region), containing 2,337 communes. Metz is the regional prefecture. The largest metropolitan area of Lorraine is Nancy, which had developed for centuries as the seat of the duchy.


title: Lorraine

text: Lorraine borders Germany, Belgium, and Luxembourg. Its inhabitants are called "Lorrains" and "Lorraines" in French and number about 2,356,000.


title: Lorraine

text: Lorraine's borders have changed often in its long history. The location of Lorraine led to it being a paramount strategic asset as the crossroads of four nations. This, along with its political alliances, marriage alliances, and the ability of rulers over the centuries to choose sides between East and West, gave it a tremendously powerful and important role in transforming all of European history. Its rulers intermarried with royal families over all of Europe, played kingmaker, and seated rulers on the thrones of the Holy Roman Empire and the Austro-Hungarian Empire, and others.


title: Lorraine

text: In 840, Charlemagne's son Louis the Pious died. The Carolingian Empire was divided among Louis' three sons by the Treaty of Verdun of 843. The middle realm, known as Middle Francia, went to Lothair I, reaching from Frisia in Northern Germany through the Low Countries, Eastern France, Burgundy, Provence, Northern Italy, and down to Rome. On the death of Lothair I, Middle Francia was divided in three by the Treaty of Prüm in 855, with the northern third called Lotharingia and going to Lothair II. Due to Lotharingia being sandwiched between East and West Francia, the rulers identified as a duchy from 870 onward, enabling the duchy to ally and align itself nominally with either eastern or western Carolingian kingdoms in order to survive and maintain its independence. Thus, it was a duchy in name but operated as an independent kingdom.


title: Lorraine

text: In 870, Lorraine allied with East Francia while remaining an autonomous duchy. In 962, when Otto I, Holy Roman Emperor, restored the Empire ("restauratio imperii"), Lorraine was designated as the autonomous Duchy of Lorraine within the Holy Roman Empire. It maintained this status until 1766, after which it was annexed under succession law by the Kingdom of France, via derivative aristocratic house alliances.


title: Lorraine

text: The succession within these houses, in tandem with other historical events, would have later restored Lorraine's status as its own duchy, but a vacuum in leadership occurred. Its duke Francois Stephen de Lorraine took the throne of the Holy Roman Empire as Francis I, and his brother Prince Charles Alexander of Lorraine became governor of the Austrian Netherlands. For political reasons, he decided to hide those heirs who were not born by his first wife, Archduchess Maria Anna of Austria, who was deceased when he took office.


title: Lorraine

text: The vacuum in leadership, the French Revolution, and the political results and changes issuing from the many nationalistic wars that followed in the next 130 years, ultimately resulted in Lorraine becoming a permanent part of the modern Republic of France. Because of wars, it came under control of Germany several times as the border between the nations shifted. While Lorrainian separatists do exist in the 21st century, their political power and influence is negligible. Lorraine separatism today consists more of preserving its cultural identity rather than seeking genuine political independence.


title: Lorraine

text: With enlightened leadership and at a crossroads between French and German cultures, Lotharingia experienced tremendous economic, artistic, and cultural prosperity during the 12th and 13th centuries under the Hohenstaufen emperors. Along with the rest of Europe, this prosperity was terminated in Lorraine in the 14th century by a series of harsh winters, bad harvests, and the Black Death. During the Renaissance, a flourishing prosperity returned to Lotharingia until the Thirty Years' War.


title: Lorraine

text: France inherited Lorraine in 1766. Due to the region's location, the population has been mixed. The north is largely German, speaking Lorraine Franconian and other German dialects. Strong centralized nationalism had only begun to replace the feudalist system which had formed the multilingual borders, and insurrection against the French occupation influenced much of the area's early identity. In 1871, the German Empire regained a part of Lorraine (Bezirk Lothringen, corresponding to the current department of Moselle). The department formed part of the new German Empire's Imperial Territory of Alsace–Lorraine. In the French Third Republic, the revanchist movement developed to recover this territory.


title: Lorraine

text: The Imperial German administration strongly discouraged the French language and culture in favor of High German, which became the administrative language (Geschäftssprache.) It required the use of German in schools in areas which it considered or designated as German-speaking, an often arbitrary categorisation. French was allowed to remain in use only in primary and secondary schools in municipalities definitely considered Francophone, such as Château-Salins and the surrounding arrondissement, as well and in their local administration.


title: Lorraine

text: But after 1877, higher education, including state-run colleges, universities and teacher seminaries, was conducted exclusively in German. The predominance of German and the partial usage of French, though restricted, were both guaranteed by the 1911 constitution of Alsace-Lorraine. While many toponyms of German etymology in Lorraine were adapted to the High German standard (i.e. Germanised) a number of genuine Francophone toponyms remained untouched. During the Nazi occupation between 1940 and 1944, however, its government imposed arbitrary German translations to replace all French names. For instance, Château-Salins was called Salzburg in Lothringen.


title: Lorraine

text: During the Battle of the Frontiers at the beginning of World War I, the French First Army invaded Lorraine and briefly occupied Mulhouse. However, the German Sixth Army under Crown Prince Rupprecht of Bavaria counterattacked and forced the French forces into retreat at the Battles of Sarrebourg and Morhange. Lorraine remained under martial law, close to the Western Front in northeastern France, and suffering from refugee crises for the rest of the war. The population effectively revolted against German rule by participating in the German Revolution of 1918–1919, and welcomed French troops into the region several days later.


title: Lorraine

text: In the 1919 Treaty of Versailles, the Weimar Republic suffered severe territorial losses following World War I, including the portion of Lorraine territory that had been part of its state of Alsace-Lorraine. With the exception of its de facto annexation by Nazi Germany as part of the Gau Westmark during World War II, that area has since remained a part of France. During that war, the cross of Lorraine was a symbol of Free France.


title: Lorraine

text: The administrative region of Lorraine is larger than the 18th century duchy of Lorraine, which gradually came under French sovereignty between 1737 and 1766. The modern region includes provinces and areas that were historically separate from the duchy of Lorraine proper. These are:


title: Lorraine

text: Some historians consider the traditional province of Lorraine as limited to the duchy of Lorraine proper, while others consider that it includes Barrois and the Three Bishoprics. The duchy of Lorraine was originally the duchy of "upper" Lorraine, and did not include the entire area since called "Lorraine".


title: Lorraine

text: The case of Barrois is the most complicated: the western part of Barrois (west of the Meuse), known as "Barrois mouvant", was detached from the rest of Barrois in the early 14th century and taken over by French sovereignty. The largest part of Barrois (east of the Meuse River) was the Duchy of Bar, part of the Holy Roman Empire. In the 15th century, it was united with the Duchy of Lorraine by the marriage of the Duke of Bar, René of Anjou, with Isabella, daughter of the Duke of Lorraine. Thus the duchies of Bar and Lorraine were united in personal union under the same duke, although formally they were officially separate until being annexed and incorporated into the Kingdom of France in 1766.


title: Lorraine

text: During the French Revolution, four departments were created from the main parts of the territories of Barrois, Three Bishoprics and the Duchy of Lorraine:


title: Lorraine

text: After 1870 some parts of "Moselle" and "Meurthe" became German. Of the remaining parts, France formed the new department named Meurthe-et-Moselle. After 1918 and the Great War, France took over control again of "Moselle".


title: Lorraine

text: When France created its administrative regions in the middle of the 20th century, it decided to gather "Meurthe et Moselle", "Meuse", "Moselle" and "Vosges" into a single region, known as Lorraine.


title: Lorraine

text: Lorraine is the only French region to have borders with three other countries: Belgium (Wallonia), Luxembourg, and Germany (Saarland, Rhineland-Palatinate). It also borders the French regions of Franche-Comté, Champagne-Ardenne, which were at times part of historical Lorraine Lotharingia, and Alsace, which, while still part of Lorraine's identity, is now a separate administrative region.


title: Lorraine

text: Most of the region forms part of the Paris Basin, with a plateau relief cut by river valleys presenting cuestas in the north–south direction. The eastern part is sharper with the Vosges. Many rivers run through Lorraine, including Moselle, Meurthe, and Meuse. Most of them are on the Rhine drainage basin.


title: Lorraine

text: Most of Lorraine has a clear French identity, with the exception of the northeastern part of the region, today known as Moselle, which historically has had an ethnic German, and German-speaking, population.


title: Lorraine

text: In 1871, Bismarck annexed about a third of today's Lorraine to the new federation of the German Empire following a decisive victory in the Franco-Prussian War. This disputed third has a culture not easily classifiable as either French or German, since both Romance and German dialects are spoken here. Like many border regions, Lorraine was a patchwork of ethnicities and dialects not mutually intelligible with either standard French or German (see linguistic boundary of Moselle).


title: Lorraine

text: Traditionally, two languages are native to Lorraine. The first is Lorrain, which is a moribund minority Romance language that is spoken in southeastern Lorraine. The second is the German dialect of Lorraine Franconian, a group of three Franconian dialects independently surviving in northern and western Lorraine. They are referred to collectively as "Plàtt" in Franconian or "francique" or "platt (lorrain)" in French (not to be confused with "Lorrain", the Romance language). Now mainly rural and isolated, these dialects gradually differ in the region, though they are mutually intelligible. Lorraine Franconian is distinct from neighbouring Alsatian, to the south, although the two are often confused. Neither of them has official status where they are spoken, but Alsatian is far more widely used.


title: Lorraine

text: Technically, Lorraine Franconian is a catch-all term for what were historically three dialects: Luxemburgish, Mosel Franconian, and Rhine Franconian. Each is identical to the same dialects spoken in the neighboring Rhineland of Germany.


title: Lorraine

text: Like most of France's regional languages (e.g. Basque, Breton, West Flemish, Catalan, Provençal, and Alsatian), Lorrain and Lorraine Franconian have largely been replaced in use by French. For more than a century, nationalistic policies of the central government required public schooling to be conducted only in French. Now, however, there are efforts being made to revive Lorraine Franconian, whose linguistic vitality is still relatively high. Recent efforts include the use of bilingual signs in Franconian areas, and Franconian-language classes for young children whose parents can no longer speak their ancestral language.


title: Lorraine

text: During World War II, the cross was adopted as the official symbol of the Free French Forces (French: "Forces Françaises Libres", or FFL) under Charles de Gaulle. Georges Thierry d'Argenlieu suggested the adoption of the Cross of Lorraine as the symbol of the Free French.


title: Lorraine

text: In his General Order No. 2 of 3 July 1940, Vice-Admiral Émile Muselier, chief of the naval and air forces of the Free French for two days, created the bow flag displaying the French colours with a red Cross of Lorraine, and a cockade also featuring the Cross of Lorraine.


title: Lorraine

text: De Gaulle is memorialised at his home village of Colombey-les-Deux-Églises by a gigantic 44.3-meter (145 feet) high Cross of Lorraine.


title: Lorraine

text: The use of the potato in Lorraine can be traced back to 1665. It was imported to Europe from South America. It is used in what developed as various traditional dishes of the region, such as the "potée lorraine". The Breux potato, which takes its name from the village of Breux in the north of the Meuse, is considered to be excellent due to the perfect conditions of the area for its cultivation.


title: Lorraine

text: Smoked bacon is also a traditional ingredient of the cuisine of Lorraine. It is used in various traditional dishes of the region, including the famous quiche Lorraine. The mirabelle plum of Lorraine is the emblematic fruit of Lorraine. It is used in pies and other desserts, as well as in alcoholic beverages.


title: Lorraine

text: Traditional cheeses of Lorraine include the following: Carré de l'Est, Brouère, Munster-géromé, Tourrée de l'Aubier.


title: Lorraine

text: Desserts from the region include: Madeleine, Macaron, Rum baba, Plombières ice-cream, various pie recipes ("brimbelles" bilberry, "mirabelle" plum, rhubarb, quark...). The Christstollen is also popular in Lorraine during the Christmas season.


title: Lorraine

text: Lorraine has a Roman Catholic heritage. Almost every village has a church, often centuries old, although many do not have a dedicated priest anymore. Church bells are traditionally rung to announce Angelus time (and often toll the hours). By tradition, they do not toll during Holy Week preceding Easter. Instead, the children of the villages play ratchets and announce, "C'est l'Angélus!" (It's the Angelus). After Easter, the children go from house to house and receive small presents for their service.


title: Lorraine

text: Sinterklaas is celebrated in Lorraine, where he is called "Saint Nicolas". Each year, more than 150,000 people gather in the streets of Nancy to celebrate Sinterklaas. A total of that number gather in other areas across the region.


title: Lorraine

text: Except for dispersed settlement in the Vosges mountains, traditional farms display linked houses, forming linear villages. They are built quite far from the road. The area between the house and the road is called "". Until the 1970s, the usoir was used to store farming tools, firewood, or manure. Today this area is generally used as a garden or for car parking.


title: Lorraine

text: At €44 billion (in 2000), Lorraine generates 3.4% of France's GDP. Despite ranking 11th in population, it ranks 8th in GDP out of the 22 regions of France, making it per capita among the top economic producing regions in the country, along with Alsace and Île-de-France (Paris). The logistics and service sectors have experienced the strongest growth in recent years. The traditional industries (textiles, mining, metallurgy) have undergone a decline due to restructuring and the move of some jobs offshore. Consequently, the region has struggled with rising unemployment, although its rate is still below the national average. In 1997 the last iron ore mine in Lorraine was closed; it had once produced more than 50 million tonnes of iron.


title: ZP Theart

text: ZP De Villiers Theart (born 27 May 1975) is a South African singer, songwriter and the former lead vocalist for the British power metal band DragonForce and American rock band Skid Row. Theart was also hired by Riot Games for the voice of Karthus in the songs "Deathfire Grasp" and "Last Whisper" by the metal band Pentakill.


title: ZP Theart

text: Theart was born on 27 May 1975 in Clanwilliam, Western Cape, South Africa, and grew up in Hazyview in the Eastern Transvaal (now the Mpumalanga province), on a banana and Lychee farm, and was raised there by his mother. His older brother lived with him as well. He has stated that according to his mother, at the age of three years, he began to hold a tablespoon up to his mouth, pretending that it was a microphone, and singing to whatever was on the radio. He has stated that in his early childhood, he listened to artists such as Gé Korsten, Carika Keuzenkamp and Rina Hugo, but his older brother began to introduce him to other music cassette tapes that he had gotten from high school, some of them being A-ha, Alphaville, Depeche Mode and then one day, Bon Jovi's "Slippery When Wet", which is a favorite of Theart's. "I loved the way he pronounced the words and the way he wrote", he said in an interview. He then began to discover other favorite bands such as Mötley Crüe, Def Leppard, Iron Maiden, Metallica, and Skid Row. He stated that his two favorites were Bon Jovi and Skid Row. During his teen years, Theart fronted and played in many bands. Not all of them are known but one was a Pretoria-based band called Santaria which was active during the late eighties and early nineties. Some of the members were the current drummer of Cold Hand Chemistry, Robert Fick, ex-Strider guitarist Pierre Goosen, and Stefan Steyn. After Theart graduated high school, he moved away to London, England, seeking global popularity. In the late 1990s, Theart fronted a garage/hard rock band called Easy Voodoo. They released a demo in 1999 but shortly after its release, Theart left the band. In the early 2000s Theart worked as a shuttle bus driver for Edexcel, between Stewart House and Blundell Street.


title: ZP Theart

text: In late 1999, Theart began to put out advertisements at Thin Ice Studios, which were eventually responded to by former Demoniac guitarists Herman Li and Sam Totman. Together, they formed a band called DragonHeart, but the name was later changed to DragonForce. The band recorded a demo in 2000 and the album "Valley of the Damned" in 2003 on Noise Records. The following year, another album Sonic Firestorm was released on the same label and a world tour followed. In 2005, Dragonforce signed to Roadrunner Records, and "Inhuman Rampage" was released in 2006, eventually going gold. In 2008, Theart's fourth and final album with the band, "Ultra Beatdown," was released, and in 2009, another world tour followed. In 2010, "Valley of the Damned" and "Sonic Firestorm" were re-released with bonus DVDs, featuring live footage, interviews, and other things. Later that year, Theart left the band due to "insurmountable differences of musical opinion". He has since stated that he does not regret his decision to leave.


title: ZP Theart

text: Theart served as the touring vocalist for Tank in 2013, becoming an official member the following year. His only studio project with the band was "Valley of Tears" in 2015, being replaced with David Readman shortly after due to his transition into Skid Row.


title: ZP Theart

text: On 13 February 2016 Theart premiered as the touring vocalist for Skid Row. The band continued to tour throughout 2016 with Theart as their frontman. Following a year of touring, on 14 January 2017, he was announced as their official lead vocalist.


title: ZP Theart

text: However, on March 23 2022, the band announced they had parted ways with the singer and named a replacement without giving many details about the separation.


title: ZP Theart

text: After leaving DragonForce, Theart founded his own band, I Am I, in which he sings lead vocals. The band has so far released one studio album, "Event Horizon", which has been released on a USB format and CD.


title: ZP Theart

text: Before DragonForce, Theart was also briefly involved with hard rock band Easy Voodoo. During the first few years since DragonForce's inception, Theart and his bandmate Sam Totman recorded a demo under the name Shadow Warriors, and Theart recorded the vocals for the 2001 two track Power Quest demo album.


title: The Edge (1997 film)

text: The Edge is a 1997 American epic survival thriller film written by David Mamet and directed by Lee Tamahori starring Anthony Hopkins and Alec Baldwin. The plot follows wealthy businessman Charles Morse (Hopkins), photographer Bob Green (Baldwin), and assistant Stephen (Harold Perrineau), who must trek through the elements and try to survive after their plane crashes down in the Alaskan wilderness; all while being hunted by a large Kodiak bear and the men's fraying friendships. Bart the Bear, a trained Kodiak bear known for appearances in several Hollywood movies, appears in the film as the bloodthirsty Kodiak, in one of his last film roles.


title: The Edge (1997 film)

text: Billionaire Charles Morse, photographer Robert "Bob" Green, and Bob's assistant Stephen arrive at a remote Alaskan resort with Charles's wife Mickey, a model, and a team of photographers. Styles, the proprietor of the lodge, warns everyone about leaving uncovered food out, as it will attract bears. During a surprise birthday party, Mickey gives Charles a watch, while Bob gifts him a pocket knife.


title: The Edge (1997 film)

text: At a photo shoot, Charles observes Bob and Mickey flirting from a distance. Short on time and missing a model, Bob decides to seek out Jack Hawk, a local hunter. Charles, Bob and Stephen fly to Jack Hawk’s home, only to find a note on his door that indicates he is miles away hunting. They fly to where the man is supposed to be, but the plane strikes a flock of birds and nose-dives into a lake, killing the pilot. Charles, Bob and Stephen barely reach the shore of the lake. Lost in the crash is a book that Charles was recently given on surviving in the wild.


title: The Edge (1997 film)

text: The three men gather wood for a fire and spend the night by the lake. The next morning, Charles uses a compass leaf to determine the direction of south. They start a hike that way, but encounter an enormous male Kodiak bear; it gives chase. Bob saves Charles as they flee over a log bridge, leaving Charles in doubt over his earlier suspicions that Bob was planning to kill him for Mickey. The group continues on and they find their way back at the lake. Distraught, Stephen distracts himself by carving a spear to fish with. He accidentally stabs his own leg and Charles tends to the wound. That night, the bear, having caught the scent of Stephen’s blood, attacks their camp, devouring Stephen and chasing Charles and Bob away.


title: The Edge (1997 film)

text: Charles and Bob adapt to their harsh surroundings; while watching a squirrel fall for a trap they have constructed, they hear a rescue helicopter fly above. They run after it, yet fail to flag it down, and tensions rise when Bob expresses his disgust with Charles and his wealth in an argument. Charles rebuffs Bob, who settles down. They both resolve to walk their way back to civilization and abandon the remote hope of being found.


title: The Edge (1997 film)

text: After hiking for some time, Charles and Bob reach a creek. Charles tries to catch a fish, but is ambushed by the bear and falls back to the campsite Bob is putting together. The bear stalks them throughout the night. Charles realizes that as long as this persists, they will be unable to forage for essentials, and decides that they have to kill the bear in order to survive. The following day, the pair lure the bear into a trap and engage it in a direct battle with spears. The bear wounds Bob but Charles stabs it and the bear advances on him. It rears onto its hind legs and collapses on Charles’s spear, impaling itself. Charles and Bob feast and celebrate afterwards.


title: The Edge (1997 film)

text: Sometime later, brought together by their new comradeship, Charles and Bob come across an empty cabin along a river. Charles notices a deadfall trap outside. Inside are supplies, including a canoe, rifle, and ammunition. As Bob checks if the canoe is usable, Charles finds a receipt from the box he kept his knife in to use as tinder. The receipt contains information confirming his suspicions about Mickey’s infidelities with Bob. Charles subtly confronts Bob, who reveals that he plans to kill Charles for Mickey. He orders Charles to go outside, but before he is able to shoot him with the rifle, Bob falls into the deadfall and is badly injured. Charles refuses to kill Bob and removes him from the pit to tend to his wounds. They go downriver in the canoe together.


title: The Edge (1997 film)

text: Charles stops and makes a fire to keep Bob warm. Bob apologizes for betraying Charles and says Mickey was unaware that he intended to murder him. A helicopter appears in the distance and Charles successfully attracts its attention, but Bob succumbs to his wounds just as the helicopter approaches. Brought back to the lodge, Charles reveals to his wife that he is aware of her betrayal by handing her Bob's wristwatch. When questioned by the gathered press on how his companions died, Charles emotionally states, “They died saving my life.”


title: The Edge (1997 film)

text: "The Edge" began principal photography on August 19, 1996. Footage was taken primarily in Alberta. Among the Alberta locations were Banff National Park, Canmore, Edmonton, Thunderstone Quarries, Fortress Mountain Resort and Allarcom Studios. Additional scenes were shot in Yoho National Park and Golden both in British Columbia. Filming ended on November 22, 1996.


title: The Edge (1997 film)

text: The shooting of the film is discussed by Art Linson in his 2002 book "What Just Happened?", later made into a film starring Robert De Niro. Initially called "Bookworm", the script was turned down by Harrison Ford and Dustin Hoffman before Alec Baldwin settled on the role of Green. De Niro showed some interest in the role of Morse but ultimately declined. Baldwin's unwillingness to shave a beard that he had grown for the role is reenacted by Bruce Willis in Barry Levinson's adaptation of Linson's book.


title: The Edge (1997 film)

text: Like many other actors who had worked with Bart the Bear, Baldwin was extremely impressed with how well-trained and docile the bear was. In interviews, he revealed that during filming he was concerned that the film simply would not work because of how docile Bart was. After the film was completed, Baldwin commented that Bart "should send the film editor a fruit basket every day for making him look so scary." As for Hopkins, who had worked with Bart in "Legends of the Fall", he "was absolutely brilliant with Bart," according to trainer Lynn Seus, who went on to say that Hopkins "acknowledged and respected (Bart) like a fellow actor. He would spend hours just looking at Bart and admiring him. He did so many of his own scenes with Bart."


title: The Edge (1997 film)

text: Three months before the film was to be released, the studio felt "Bookworm" needed a more commercial title. Dozens of others were considered, according to Linson, until the film was renamed "The Edge".


title: The Edge (1997 film)

text: This movie was shot in Alberta, Canada, in freezing conditions. Elle Macpherson was required to perform one long scene in a Native American get-up of beads, feathers and suede loincloth. "You rehearse with a coat on and then you have to take the coat off," she said. "It feels the coldest under your arms. You don't want to ever uncover your arms again."


title: The Edge (1997 film)

text: The film's musical score was composed by Jerry Goldsmith, who worked closely with director Lee Tamahori to develop a score more diverse than other works by Goldsmith in the 1990s. Initially, the score was released on CD in 1997, upon the film's release, by RCA Records. Over time, the first release went out of print, leading to La-La Land Records issuing a limited 3500-unit pressing of the complete score, which was also out of print by July 2013. The new release contains 25 minutes of unreleased music and fixes a problem found on the RCA release affecting the track "Rescued," which contained rustling noises during some quieter parts.


title: The Edge (1997 film)

text: "The Edge" had its premiere at the Toronto International Film Festival in Canada on September 6, 1997. It was released in the U.S. on September 26, 1997 in 2,351 theaters, and grossed $7.7 million during its opening weekend. It went on to gross $27.8 million in the U.S. and $15.4 million overseas, for a worldwide total of $43.3 million in its theatrical run.


title: The Edge (1997 film)

text: Upon release, "The Edge" received mixed to positive reviews from critics. Based on 50 reviews collected by Rotten Tomatoes, the film received a 64% approval rating, with an average score of 6.38/10. The consensus reads, ""The Edge" is an entertaining hybrid of brainy Mamet dialogue with brawny outdoors action—albeit one that sadly lacks as much bite as its furry antagonist." Roger Ebert of the "Chicago Sun-Times" gave the film 3 out of 4 stars, writing that the filmmakers did well by not going berserk with the action sequences as other films do. He did criticize the ending, saying that:


title: The Edge (1997 film)

text: Following its initial release on VHS, "The Edge" was released on a non-anamorphic widescreen NTSC DVD in the US, with no extras, save the original theatrical trailer. Meanwhile, PAL DVDs released in Europe, Australia, etc. feature an anamorphic transfer, the trailer, a six-minute featurette, seven short cast and crew interviews and five text biographies.


title: The Edge (1997 film)

text: As of 2017, the film has also been released on Blu-ray in the US and Germany, with the same extras as each country's DVD.


title: Lazy Susan

text: A Lazy Susan is a turntable (rotating tray) placed on a table or countertop to aid in distributing food. Lazy Susans may be made from a variety of materials but are usually glass, wood, or plastic. They are circular and placed in the centre of a table to share dishes easily among diners. Although they are common in Chinese restaurants, the Lazy Susan is a Western invention. Owing to the nature of Chinese cuisine, especially dim sum, they are common at formal Chinese restaurants both in mainland China and abroad. In Chinese, they are known as (t. 餐桌轉盤) (p "cānzhuō zhuànpán") or "dinner-table turntables".


title: Lazy Susan

text: It is likely that the explanation of the term Lazy Susan has been lost to history. Folk etymologies claim it as an American invention. According to lore, Thomas Jefferson invented the device, which was known as a "dumbwaiter", for his daughter Susan. Regardless of the origins of the name, by 1917 it was advertised in "Vanity Fair" as "Ovington's $8.50 mahogany 'Revolving Server or Lazy Susan'", but the term's use predates both the advertisement and, probably, the country.


title: Lazy Susan

text: Part of the mystery arises from the variety of devices that were grouped under the term "dumb waiter" (today written dumbwaiter). An early 18th-century British article in "The Gentleman's Magazine" describes how silent machines had replaced garrulous servants at some tables and, by the 1750s, Christopher Smart was praising the "foreign" but discreet devices in verse. It is, however, almost certain that the devices under discussion were wheeled serving trays similar to those introduced by Thomas Jefferson to the United States from France, where they were known as "étagères". At some point during or before the third quarter of the 18th century, the name dumb waiter also began to be applied to rotating trays. (Jefferson never had a Lazy Susan at Monticello, but he did construct a box-shaped rotating book stand and, as part of serving "in the French style", employed a revolving dining-room door whose reverse side supported a number of shelves.). By the 1840s, Americans were applying the term to small lifts carrying food between floors as well. The success of George W. Cannon's 1887 mechanical dumbwaiter popularised this usage, replacing the previous meanings of "dumbwaiter".


title: Lazy Susan

text: The Lazy Susan was initially uncommon enough in the United States for the utopianist Oneida Community to be credited with its invention. They employed the devices as part of their practice of communal living, making food easily and equally available to residents and visitors at meals. An American patent was issued in 1891 to Elizabeth Howell for "certain new and useful Improvements in Self-Waiting Tables". Howell's device ran more smoothly and did not permit bread crumbs to fall into the space between the Lazy Susan and the table.


title: Lazy Susan

text: Despite various folk etymologies linking the name to Jefferson and Edison's daughters, the earliest use of these "serviettes" or "butler's assistants" being called a "Lazy Susan" dates to the 1903 "Boston Journal":


title: Lazy Susan

text: John B. Laurie, as the resuscitator of "Lazy Susan", seems destined to leap into fortune as an individual worker. "Lazy Susan" is a step toward solving the ever-vexing servant problem. She can be seen, but not heard, nor can she hear, she simply minds her business and carries out your orders in a jiffy.


title: Lazy Susan

text: Laurie was a Scottish carpenter who made his "Lazy Susan" to the personal specifications of a Hingham-area woman. Unfortunately he presented this gift to her too late, which caused her to unleash an abusive tirade upon Laurie. When she finally asked him for the price, he "told her it wasn't for sale, though of course it is". The name was repeated in a 1911 "Idaho Statesman" article which describes it as "a cousin to the 'curate's assistant', as the English muffin stand is called" and again in the 1912 "Christian Science Monitor", which calls the "silver" lazy Susan "the characteristic feature of the self-serving dinner table". By the next year, the "Lima Daily News" described an Ohioan "inaugurat[ing] ... the 'Lazy Susan' method of serving". Henry Ford used an enormous one on his camping trips in the 1920s to avoid bringing a full contingent of servants along with his guests. In 1933, the term was added to the Webster's Dictionary.


title: Lazy Susan

text: There is a table arrangement used much in Germany, which has now found its way to America, though it is still by no means common. The German "frau" calls it "Lazy Susan", but it is entirely different from our product used for salt and pepper shakers. Its only point of similarity is the swivel upon which it turns. The one which joys my heart is of mahogany, and it turns automatically at the slightest touch. It contains seven china dishes, six of which are trapezoids, the center one being octagonal. The trapezoids fit about the center octagon, forming a perfect whole.


title: Lazy Susan

text: By 1918, "Century Magazine" was already describing the Lazy Susan as out of fashion, but beginning in the 1950s its popularity soared once again after the redesign and reintroduction of the Lazy Susan by George Hall, an engineer, soy sauce manufacturer, and partner in popular San Francisco-area Chinese restaurants (Johnny Kan's and Ming's of Palo Alto), and the rotating tray became ubiquitous in Chinese restaurants and was used in homes around the globe. The decline in America's domestic service sector after World War I and its collapse following World War II, combined with the post-war Baby Boom, led to a great demand for them in US households across the country in the 1950s and 1960s. This popularity has had the effect, however, of making them seem kitsch in subsequent decades.


title: Lazy Susan

text: The term is infrequently used for the much older turntables employed in pottery wheels and related tasks like sculpture, modeling, repair work, etc.


title: Chebyshev polynomials

text: The Chebyshev polynomials are two sequences of polynomials related to the cosine and sine functions, notated as formula_1 and formula_2. They can be defined in several equivalent ways, one of which starts with trigonometric functions:


title: Chebyshev polynomials

text: That these expressions define polynomials in formula_7 may not be obvious at first sight, but follows by rewriting formula_8 and formula_9 using de Moivre's formula or by using the angle sum formulas for formula_10 and formula_11 repeatedly. For example, the double angle formulas, which follow directly from the angle sum formulas, may be used to obtain formula_12 and formula_13, which are respectively a polynomial in formula_7 and a polynomial in formula_7 multiplied by formula_16. Hence formula_17 and formula_18.


title: Chebyshev polynomials

text: An important and convenient property of the is that they are "orthogonal" with respect to the inner product:


title: Chebyshev polynomials

text: The Chebyshev polynomials are polynomials with the largest possible leading coefficient whose absolute value on the interval is bounded by 1. They are also the "extremal" polynomials for many other properties.


title: Chebyshev polynomials

text: Chebyshev polynomials are important in approximation theory because the roots of , which are also called "Chebyshev nodes", are used as matching points for optimizing polynomial interpolation. The resulting interpolation polynomial minimizes the problem of Runge's phenomenon and provides an approximation that is close to the best polynomial approximation to a continuous function under the maximum norm, also called the "minimax" criterion. This approximation leads directly to the method of Clenshaw–Curtis quadrature.


title: Chebyshev polynomials

text: These polynomials were named after Pafnuty Chebyshev. The letter is used because of the alternative transliterations of the name "Chebyshev" as , (French) or (German).


title: Chebyshev polynomials

text: There are several other generating functions for the Chebyshev polynomials; the exponential generating function is


title: Chebyshev polynomials

text: As described in the introduction, the Chebyshev polynomials of the first kind can be defined as the unique polynomials satisfying


title: Chebyshev polynomials

text: for which as a technical point is a variant (equivalent transpose) of Schröder's equation. That is, is functionally conjugate to , codified in the nesting property below.


title: Chebyshev polynomials

text: That is an th-degree polynomial in can be seen by observing that is the real part of one side of de Moivre's formula. The real part of the other side is a polynomial in and , in which all powers of are even and thus replaceable through the identity .


title: Chebyshev polynomials

text: By the same reasoning, is the imaginary part of the polynomial, in which all powers of are odd and thus, if one factor of is factored out, the remaining factors can be replaced to create a st-degree polynomial in .


title: Chebyshev polynomials

text: The identity is quite useful in conjunction with the recursive generating formula, inasmuch as it enables one to calculate the cosine of any integer multiple of an angle solely in terms of the cosine of the base angle.


title: Chebyshev polynomials

text: The first two Chebyshev polynomials of the first kind are computed directly from the definition to be


title: Chebyshev polynomials

text: Conversely, an arbitrary integer power of trigonometric functions may be expressed as a linear combination of trigonometric functions using Chebyshev polynomials


title: Chebyshev polynomials

text: where the prime at the summation symbol indicates that the contribution of needs to be halved if it appears, and formula_38.


title: Chebyshev polynomials

text: An immediate corollary is the expression of complex exponentiation in terms of Chebyshev polynomials: given ,


title: Chebyshev polynomials

text: If formula_40 is a family of monic polynomials with coefficients in a field of characteristic formula_41 such that formula_42 and formula_43 for all


title: Chebyshev polynomials

text: formula_44 and formula_45, then, up to a simple change of variables, either formula_46 for all formula_45 or


title: Chebyshev polynomials

text: in a ring . Thus, they can be generated by the standard technique for Pell equations of taking powers of a fundamental solution:


title: Chebyshev polynomials

text: The Chebyshev polynomials of the first and second kinds correspond to a complementary pair of Lucas sequences and with parameters and :


title: Chebyshev polynomials

text: The second of these may be rearranged using the recurrence definition for the Chebyshev polynomials of the second kind to give


title: Chebyshev polynomials

text: while replacing formula_2 and formula_57 using the derivative formula for formula_1 gives the recurrence relationship for the derivative of formula_3:


title: Chebyshev polynomials

text: Different approaches to defining Chebyshev polynomials lead to different explicit expressions such as:


title: Chebyshev polynomials

text: where the prime at the summation symbol indicates that the contribution of needs to be halved if it appears.


title: Chebyshev polynomials

text: That is, Chebyshev polynomials of even order have even symmetry and therefore contain only even powers of . Chebyshev polynomials of odd order have odd symmetry and therefore contain only odd powers of .


title: Chebyshev polynomials

text: A Chebyshev polynomial of either kind with degree has different simple roots, called Chebyshev roots, in the interval . The roots of the Chebyshev polynomial of the first kind are sometimes called Chebyshev nodes because they are used as "nodes" in polynomial interpolation. Using the trigonometric definition and the fact that


title: Chebyshev polynomials

text: One unique property of the Chebyshev polynomials of the first kind is that on the interval all of the extrema have values that are either −1 or 1. Thus these polynomials have only two finite critical values, the defining property of Shabat polynomials. Both the first and second kinds of Chebyshev polynomial have extrema at the endpoints, given by:


title: Chebyshev polynomials

text: The extrema of formula_1 on the interval formula_76 where formula_77 are located at formula_78 values of formula_79. They are formula_80, or formula_81 where formula_82, formula_83, formula_84 and formula_85, i.e., formula_86 and formula_87 are relatively prime numbers.


title: Chebyshev polynomials

text: This result has been generalized to solutions of formula_113, and to formula_114 and formula_115 for Chebyshev polynomials of the third and fourth kinds, respectively.


title: Chebyshev polynomials

text: The derivatives of the polynomials can be less than straightforward. By differentiating the polynomials in their trigonometric forms, it can be shown that:


title: Chebyshev polynomials

text: The last two formulas can be numerically troublesome due to the division by zero ( indeterminate form, specifically) at and . It can be shown that:


title: Chebyshev polynomials

text: which, if evaluated as shown above, poses a problem because it is indeterminate at . Since the function is a polynomial, (all of) the derivatives must exist for all real numbers, so the taking to limit on the expression above should yield the desired values – taking the limit as :


title: Chebyshev polynomials

text: Since the limit as a whole must exist, the limit of the numerator and denominator must independently exist, and


title: Chebyshev polynomials

text: The denominator (still) limits to zero, which implies that the numerator must be limiting to zero, i.e. which will be useful later on. Since the numerator and denominator are both limiting to zero, L'Hôpital's rule applies:


title: Chebyshev polynomials

text: where the prime at the summation symbols means that the term contributed by is to be halved, if it appears.


title: Chebyshev polynomials

text: and the recurrence relation for the first kind polynomials involving derivatives establishes that for


title: Chebyshev polynomials

text: The last formula can be further manipulated to express the integral of as a function of Chebyshev polynomials of the first kind only:


title: Chebyshev polynomials

text: For this results in the already known recurrence formula, just arranged differently, and with it forms the recurrence relation for all even or all odd indexed Chebyshev polynomials (depending on the parity of the lowest ) which implies the evenness or oddness of these polynomials. Three more useful formulas for evaluating Chebyshev polynomials can be concluded from this product expansion:


title: Chebyshev polynomials

text: which establishes the evenness or oddness of the even or odd indexed Chebyshev polynomials of the second kind depending on whether starts with 2 or 3.


title: Chebyshev polynomials

text: For the order of composition may be reversed, making the family of polynomial functions a commutative semigroup under composition.


title: Chebyshev polynomials

text: Since is divisible by if is odd, it follows that is divisible by if is odd. Furthermore, is divisible by , and in the case that is even, divisible by .


title: Chebyshev polynomials

text: Both and form a sequence of orthogonal polynomials. The polynomials of the first kind are orthogonal with respect to the weight


title: Chebyshev polynomials

text: These orthogonality properties follow from the fact that the Chebyshev polynomials solve the Chebyshev differential equations


title: Chebyshev polynomials

text: which are Sturm–Liouville differential equations. It is a general feature of such differential equations that there is a distinguished orthonormal set of solutions. (Another way to define the Chebyshev polynomials is as the solutions to those equations.)


title: Chebyshev polynomials

text: For the polynomials of the second kind and any integer with the same Chebyshev nodes , there are similar sums:


title: Chebyshev polynomials

text: From the intermediate value theorem, has at least roots. However, this is impossible, as is a polynomial of degree , so the fundamental theorem of algebra implies it has at most roots.


title: Chebyshev polynomials

text: By the equioscillation theorem, among all the polynomials of degree , the polynomial minimizes on if and only if there are points such that .


title: Chebyshev polynomials

text: Of course, the null polynomial on the interval can be approximated by itself and minimizes the -norm.


title: Chebyshev polynomials

text: Above, however, reaches its maximum only times because we are searching for the best polynomial of degree (therefore the theorem evoked previously cannot be used).


title: Chebyshev polynomials

text: The Chebyshev polynomials are a special case of the ultraspherical or Gegenbauer polynomials formula_151, which themselves are a special case of the Jacobi polynomials formula_152:


title: Chebyshev polynomials

text: The curves given by , or equivalently, by the parametric equations , , are a special case of Lissajous curves with frequency ratio equal to .


title: Chebyshev polynomials

text: In the appropriate Sobolev space, the set of Chebyshev polynomials form an orthonormal basis, so that a function in the same space can, on , be expressed via the expansion:


title: Chebyshev polynomials

text: Furthermore, as mentioned previously, the Chebyshev polynomials form an orthogonal basis which (among other things) implies that the coefficients can be determined easily through the application of an inner product. This sum is called a Chebyshev series or a Chebyshev expansion.


title: Chebyshev polynomials

text: Since a Chebyshev series is related to a Fourier cosine series through a change of variables, all of the theorems, identities, etc. that apply to Fourier series have a Chebyshev counterpart. These attributes include:


title: Chebyshev polynomials

text: The abundance of the theorems and identities inherited from Fourier series make the Chebyshev polynomials important tools in numeric analysis; for example they are the most popular general purpose basis functions used in the spectral method, often in favor of trigonometric series due to generally faster convergence for continuous functions (Gibbs' phenomenon is still a problem).


title: Chebyshev polynomials

text: One can find the coefficients either through the application of an inner product or by the discrete orthogonality condition. For the inner product,


title: Chebyshev polynomials

text: Alternatively, when the inner product of the function being approximated cannot be evaluated, the discrete orthogonality condition gives an often useful result for "approximate" coefficients,


title: Chebyshev polynomials

text: For any , these approximate coefficients provide an exact approximation to the function at with a controlled error between those points. The exact coefficients are obtained with , thus representing the function exactly at all points in . The rate of convergence depends on the function and its smoothness.


title: Chebyshev polynomials

text: This allows us to compute the approximate coefficients very efficiently through the discrete cosine transform


title: Chebyshev polynomials

text: are very useful in the approximation of various functions and in the solution of differential equations (see spectral method). Two common methods for determining the coefficients are through the use of the inner product as in Galerkin's method and through the use of collocation which is related to interpolation.


title: Chebyshev polynomials

text: As an interpolant, the coefficients of the st partial sum are usually obtained on the Chebyshev–Gauss–Lobatto points (or Lobatto grid), which results in minimum error and avoids Runge's phenomenon associated with a uniform grid. This collection of points corresponds to the extrema of the highest order polynomial in the sum, plus the endpoints and is given by:


title: Chebyshev polynomials

text: An arbitrary polynomial of degree can be written in terms of the Chebyshev polynomials of the first kind. Such a polynomial is of the form


title: Chebyshev polynomials

text: Polynomials denoted formula_176 and formula_177 closely related to Chebyshev polynomials are sometimes used. They are defined by


title: Chebyshev polynomials

text: A. F. Horadam called the polynomials formula_176 Vieta–Lucas polynomials and denoted them formula_181. He called the polynomials formula_177 Vieta–Fibonacci polynomials and denoted them formula_183. Lists of both sets of polynomials are given in Viète's "Opera Mathematica", Chapter IX, Theorems VI and VII. The Vieta–Lucas and Vieta–Fibonacci polynomials of real argument are, up to a power of formula_184 and a shift of index in the case of the latter, equal to Lucas and Fibonacci polynomials and of imaginary argument.


title: Chebyshev polynomials

text: Shifted Chebyshev polynomials of the first and second kinds are related to the Chebyshev polynomials by


title: Chebyshev polynomials

text: When the argument of the Chebyshev polynomial satisfies the argument of the shifted Chebyshev polynomial satisfies . Similarly, one can define shifted polynomials for generic intervals .


title: Chebyshev polynomials

text: Around 1990 the terms "third-kind" and "fourth-kind" came into use in connection with Chebyshev polynomials, although the polynomials denoted by these terms had an earlier development under the name airfoil polynomials. According to J. C. Mason and G. H. Elliott, the terminology "third-kind" and "fourth-kind" is due to Walter Gautschi, "in consultation with colleagues in the field of orthogonal polynomials." The Chebyshev polynomials of the third kind are defined as


title: Chebyshev polynomials

text: where formula_188. In the airfoil literature formula_183 and formula_190 are denoted formula_191 and formula_192. The polynomial families formula_1, formula_2, formula_183, and formula_190 are orthogonal with respect to the weights


title: Chebyshev polynomials

text: All four families satisfy the recurrence formula_200 with formula_201, where formula_202, formula_5, formula_204, or formula_205, but they differ according to whether formula_206 equals formula_79, formula_208, formula_209, or formula_210.


title: Bodega (store)

text: A bodega is a small owner-operated convenience store serving hot and prepared food, often open late hours and typically with ethnic market influences. Most famously located on New York's street corners as an introduction by Puerto Ricans in New York City, they are renowned for their convivial culture and colorful character. There are an estimated 13,000 bodegas across the city.


title: Bodega (store)

text: In Spanish, "bodega" is a term for "storeroom" or "wine cellar", or "warehouse", with a similar origin to boutique or apothecary; the precise meaning varies regionally in the Spanish language, and the later New York City term evolved from Puerto Rican and Cuban usage for a small grocery. (In contemporary Cuba, the term now usually connotes a government ration store.)


title: Bodega (store)

text: In English, the first appearance of the bodega in print dates to a travelogue of Spain from 1846, describing wine cellars. In New York City, "The Sun" reported the first bodega opening in 1902, which was described as a Spanish barroom, more like a cantina. The more specific meaning of a type of New York City Puerto Rican convenience store only came about in the mid-20th century, with the first print appearance in "Time" in 1956; though the term has also been applied retrospectively to such establishments as far back as the 1920s/30s.


title: Bodega (store)

text: In a New York City context, the "bodega" is similar to, and may overlap with, delicatessen, newsstand, corner store, corner grocery store, and candy store.


title: Bodega (store)

text: Bodegas were popularized in the mid-twentieth century by Puerto Ricans. Some stores were named after places in Puerto Rico. Although they were initially documented in the 1930s (a 50th anniversary was marked on Spanish-language radio station WADO in 1986), the first bodega may have opened even earlier. Early examples were establishments serving factory workers in Greenpoint, Brooklyn, and La Marqueta in East Harlem, where stalls serving Puerto Rican staples (at first included among goods sold by local Jewish merchants) became increasingly Puerto Rican-owned in the 1920s/30s. Other Latino groups in the city have also embraced the bodega, serving a wider variety of Latin American cuisine. Centro de Estudios Puertorriqueños at CUNY Hunter College owns a collection of historical bodega photography. Despite their Hispanic origins, by the late 2010s approximately half of all bodegas were operated by Yemeni American immigrants. Yemeni business owners led a campaign of bodega closures in February 2017 in protest of the Trump travel ban.


title: Bodega (store)

text: Many bodegas keep late hours or even 24/7 service, contributing to New York City's reputation as The City That Never Sleeps.


title: Bodega (store)

text: One famous bodega, Gem Spa, was a gathering place for beat poets in New York's Greenwich Village in the 1960s. Gem Spa is also thought by some to be the birthplace of the egg cream.


title: Bodega (store)

text: In the 1998 stoner comedy Half Baked, Thurgood, played by Dave Chappelle, refers to purchasing cannabis at bodegas: "“You can get the stuff at little corner stores called bodegas. Say it with me - BO-DE-GAS. Yes, very good! These places always have incredibly old products, but the weed ain't bad.”"


title: Bodega (store)

text: In 2018, Camden, N.J. rapper released an EP titled "Macaroni Tony" featuring a track titled "Bodega" that emphasizes the central role bodegas play in urban communities. When asked about bodega's, Mir Fontane explained: "To me, the bodega always represented a hub for the community… but it also embodies the spirit of the hustle and grind. The owner of the bodega is one of the first true businessmen you meet growing up in the hood."


title: Enisa Nikaj

text: Enisa Nikaj (; born March 5, 1996), known professionally as Enisa (stylized in all caps), is an American singer, songwriter and model. She began her music career in 2015 performing cover songs and began releasing original music in 2016. She signed to Atlantic Records and Highbridge The Label in December 2019, and competed in the "American Song Contest" in March 2022.


title: Enisa Nikaj

text: Enisa was born in Brooklyn, New York to Albanian parents from Tuzi, Montenegro. Her father emigrated from the SFR Yugoslavia to the United States at the age of 25, and was later followed by her mother. Enisa is a middle child, and has an older and a younger brother, both of whom took up playing basketball while Enisa leaned towards music. She began singing at home as a young child. Enisa attended elementary school, where she participated in theater and the school choir, graduating as valedictorian. At age seven, she played the role of Dorothy in a school play of "The Wizard of Oz" in the fourth grade.


title: Enisa Nikaj

text: Enisa attended J.H.S 259 William Mckinley and Edward R. Murrow High School, graduating in 2015. Rapper Joey Badass was one of her schoolmates. She attended Brooklyn College, graduating early with a bachelor's degree in business administration in May 2018. She plays the piano, and has done internships at advertising agencies. Enisa grew up listening to Albanian music, in addition to artists such as Frank Sinatra, Nina Simone and Justin Timberlake. She has cited Adele and Amy Winehouse as her inspirations.


title: Enisa Nikaj

text: In 2015, Enisa began performing cover songs to artists such as David Guetta and Sia ("Titanium"), Hozier ("Take Me to Church"), Justin Timberlake ("Cry Me a River") and Adele ("Hello"). After graduating from high school she had wanted to get into the music industry, and filmed her first video with a photographer friend who wanted to get into videography. Her cover of Hozier's song hit 100,000 views on YouTube within three months, while a reupload posted by a Facebook page amassed one million views in three days. Enisa has stated in interviews that her lack of connections in the industry prompted her to post herself performing cover songs as a way to showcase her talent and she hoped that it would grab the attention of a music producer or a manager.


title: Enisa Nikaj

text: In 2016, she released her debut single "Burn This Bridge" on September 15, with the music video releasing on November 23. Enisa had been inspired to write the song after being discouraged by someone in the industry who she thought would help her instead tell her that "I didn't have what it takes and I wasn't good enough basically ... I just took it out on the studio. I wrote a song and I was feeling it like 'I don't need you, I could do this on my own.'" The song went on to be used in a Beats Electronics advertisement starring soccer player Alex Morgan in June 2017.


title: Enisa Nikaj

text: In 2017, she released her sophomore single "Glory Days" on May 26. It went on to be her first placement in a film soundtrack when it was featured in the opening scene of "Miss Virginia" (2019). Enisa released her third single "Freedom" on August 25, with the music video releasing on September 10. She was featured on Statik Selektah's single "Ain't a Damn Thing Change," alongside G-Eazy and Joey Badass, released on November 30.


title: Enisa Nikaj

text: Enisa released her fourth single "Reunite" and its music video on February 4, 2018. It was a tribute song to her uncle who had died years earlier. After graduating from college in May, she began pursuing her music career full-time at age 22. On October 18, she teased a collaboration track with French singer Scridge, which went on to be "Karma (Remix)". Following prolonged delays, Enisa confirmed in June 2019 that the French label had canceled its release. After the track was leaked in October 2019, it was officially released on November 15. Enisa performed a number of cover songs from 2018 through 2020, one of which was her cover of "Mockingbird" by Eminem that she released on December 9, 2018, which went on to amass 10 million views on YouTube by December 2020.


title: Enisa Nikaj

text: In 2019, she released her fifth single "Wait For Love" and its music video on July 6. Enisa was featured on Termanology and Dame Grease's single "Travel The World", alongside Bun B, released on September 19, with the music video releasing on January 29, 2020. She released her sixth single "Something Beautiful" and its music video on December 15, being a tribute to the victims of the 2019 Albania earthquake which had struck on November 26.


title: Enisa Nikaj

text: A person connected to Highbridge the Label had heard Enisa's music in 2017 while at a Philippe Chow restaurant in Manhattan, New York. A waiter had been playing "Freedom" and introduced him to Enisa's music after being asked about it. Enisa was eventually invited to the studio by rapper A Boogie wit da Hoodie and his team in January 2018. Over a year later, while she was speaking with RCA Records, Enisa had a chance encounter with and was invited to the studio again to play her unreleased music. She was later introduced to higher-ups at Atlantic Records and was eventually offered a contract in May 2019, and subsequently signed her first record deal on December 6, 2019.


title: Enisa Nikaj

text: In 2020, she released her seventh single "Love Cycle" and its music video on September 18. After it went viral and gained particular attention among Nigerian fans, she adopted the name 'Eniola' in their honor in December 2020. Enisa released her eighth single "Dumb Boy" and its music video on November 20. She recorded the song at home due to the COVID-19 pandemic which forced her to become proficient with video editing and Ableton audio software. Enisa styled her own hair and makeup, and recorded, edited and color corrected all her video releases that year. Both music videos went on to amass 12 millions views each on YouTube within a year from their respective releases.


title: Enisa Nikaj

text: In 2021, she was featured on Tanzanian singer Rayvanny's "Number One (Remix)" released on February 1, with the music video releasing on February 24. Enisa released her ninth single "Count My Blessings" and its music video on February 26. The song sampled Tunisian singer Saber Rebaï's rendition of "Sidi Mansour." Enisa released her single "Love Cycle (Remix)" featuring Nigerian singer Davido on March 26. She released her tenth solo single "Tears Hit The Ground" and its music video on July 4, which went on to serve as the lead single for her debut EP released in 2022. A live acoustic version of the song was released on October 28, 2021.


title: Enisa Nikaj

text: In 2022, Enisa released her debut EP titled "Fake Love" on February 18. The music video for "One Thing" was released on January 28 and for "Get That Money" was released on February 18. On March 3, Enisa was announced as one of the contestants to compete in the "American Song Contest", representing New York state. On October 14, she stated in a tweet that she was supposed to represent Montenegro in the Eurovision Song Contest 2023 in Liverpool, shortly after the country's broadcaster announced that it would not be participating.


title: Enisa Nikaj

text: Enisa was the cover model on the annual 2014 edition of "Prom Guide" magazine. In November 2013, she had been shortlisted as one of the top five contestants selected from nationwide submissions before gracing the cover in January 2014 and winning a $5,000 scholarship. After her foray into music in 2015, Enisa was approached through social media by record labels and managers. She chose to sign with Wilhelmina Models in January 2016 and was managed by Bobby Gutierrez. During this period, she appeared in fashion magazine editorials for "C-Heads" in February 2016, "Vulkan" in April 2016, "Slimi" in November 2016, and "Twelv" in October 2017.


title: Enisa Nikaj

text: She has described her style as being "timeless and classic with a modern edge and a hint of Brooklyn attitude," and as being "more conservative. Rather than being flashy and all that. But it's very New York City." Enisa describes the city as her biggest inspiration, "I'm influenced just by walking down the street in SoHo or on 5th Avenue. I just get influenced by so many people," and admires the style of Victoria Beckham. Enisa is known for her long hair as her signature look. When asked about it in 2021, she stated that she avoids heat treatments and receives a haircut each month, with only her mother being allowed to cut her hair.


title: Enisa Nikaj

text: She appeared in the promotional campaign for Puma's "GRL PWR" Nova sneaker in January 2019. She appeared in editorials for "Flaunt" in March 2021, and "Out Now" in June 2021.


title: Interstellar medium

text: In astronomy, the interstellar medium is the matter and radiation that exist in the space between the star systems in a galaxy. This matter includes gas in ionic, atomic, and molecular form, as well as dust and cosmic rays. It fills interstellar space and blends smoothly into the surrounding intergalactic space. The energy that occupies the same volume, in the form of electromagnetic radiation, is the interstellar radiation field.


title: Interstellar medium

text: The interstellar medium is composed of multiple phases distinguished by whether matter is ionic, atomic, or molecular, and the temperature and density of the matter. The interstellar medium is composed, primarily, of hydrogen, followed by helium with trace amounts of carbon, oxygen, and nitrogen. The thermal pressures of these phases are in rough equilibrium with one another. Magnetic fields and turbulent motions also provide pressure in the ISM, and are typically more important, dynamically, than the thermal pressure is.


title: Interstellar medium

text: In the interstellar medium, matter is primarily in molecular form, and reaches number densities of 10 molecules per cm (1 million molecules per cm). In hot, diffuse regions of the ISM, matter is primarily ionized, and the density may be as low as 10 ions per cm. Compare this with a number density of roughly 10 molecules per cm for air at sea level, and 10 molecules per cm (10 billion molecules per cm) for a laboratory high-vacuum chamber. By mass, 99% of the ISM is gas in any form, and 1% is dust. Of the gas in the ISM, by number 91% of atoms are hydrogen and 8.9% are helium, with 0.1% being atoms of elements heavier than hydrogen or helium, known as "metals" in astronomical parlance. By mass this amounts to 70% hydrogen, 28% helium, and 1.5% heavier elements. The hydrogen and helium are primarily a result of primordial nucleosynthesis, while the heavier elements in the ISM are mostly a result of enrichment (due to stellar gravity and radiation pressure) in the process of stellar evolution.


title: Interstellar medium

text: The ISM plays a crucial role in astrophysics precisely because of its intermediate role between stellar and galactic scales. Stars form within the densest regions of the ISM, which ultimately contributes to molecular clouds and replenishes the ISM with matter and energy through planetary nebulae, stellar winds, and supernovae. This interplay between stars and the ISM helps determine the rate at which a galaxy depletes its gaseous content, and therefore its lifespan of active star formation.


title: Interstellar medium

text: "Voyager 1" reached the ISM on August 25, 2012, making it the first artificial object from Earth to do so. Interstellar plasma and dust will be studied until the estimated mission end date of 2025. Its twin "Voyager 2" entered the ISM on November 5, 2018.


title: Interstellar medium

text: put forward the static two "phase" equilibrium model to explain the observed properties of the ISM. Their modeled ISM included of a cold dense phase ("T" < 300 K), consisting of clouds of neutral and molecular hydrogen, and a warm intercloud phase ("T" ~ 10 K), consisting of rarefied neutral and ionized gas. added a dynamic third phase that represented the very hot ("T" ~ 10 K) gas that had been shock heated by supernovae and constituted most of the volume of the ISM.


title: Interstellar medium

text: These phases are the temperatures where heating and cooling can reach a stable equilibrium. Their paper formed the basis for further study over the subsequent three decades. However, the relative proportions of the phases and their subdivisions are still not well understood.


title: Interstellar medium

text: This model takes into account only atomic hydrogen: A temperature higher than 3000 K breaks molecules, while that lower than 50000 K leaves atoms in their ground state. It is assumed that the influence of other atoms (He ...) is negligible. The pressure is assumed to be very low, so the durations of the free paths of atoms are longer than the ~ 1 nanosecond duration of the light pulses that constitute ordinary, temporally incoherent light.


title: Interstellar medium

text: In this collisionless gas, Einstein's theory of coherent light-matter interactions applies: all the gas-light interactions are spatially coherent.


title: Interstellar medium

text: Suppose that a monochromatic light is pulsed, then scattered by molecules with a quadrupole (Raman) resonance frequency. If the “length of light pulses is shorter than all involved time constants” (Lamb (1971)), an “impulsive stimulated Raman scattering (ISRS)” (Yan, Gamble & Nelson (1985)) applies: the light generated by incoherent Raman scattering at a shifted frequency has a phase independent of the phase of the exciting light, thus generating a new spectral line, and coherence between the incident and scattered light facilitates their interference into a single frequency, thus shifting the incident frequency.


title: Interstellar medium

text: Assume that a star radiates a continuous light spectrum up to X-rays. Lyman frequencies are absorbed in this light and pump atoms mainly to the first excited state. In this state, the hyperfine periods are longer than 1 ns, so an ISRS “may” redshift the light frequency, populating high hyperfine levels. Another ISRS “may” transfer energy from hyperfine levels to thermal electromagnetic waves, so the redshift is permanent. The temperature of a light beam is defined by its frequency and spectral radiance with Planck's formula. As entropy must increase, “may” becomes “does”.


title: Interstellar medium

text: However, where a previously absorbed line (first Lyman beta, ...) reaches the Lyman alpha frequency, the redshifting process stops, and all hydrogen lines are strongly absorbed. But this stop is not perfect if there is energy at the frequency shifted to Lyman beta frequency, which produces a slow redshift. Successive redshifts separated by Lyman absorptions generate many absorption lines, frequencies of which, deduced from absorption process, obey a law more dependable than Karlsson's formula.


title: Interstellar medium

text: The previous process excites more and more atoms because a de-excitation obeys Einstein's law of coherent interactions: Variation dI of radiance I of a light beam along a path dx is dI=BIdx, where B is Einstein amplification coefficient which depends on medium. I is the modulus of Poynting vector of field, absorption occurs for an opposed vector, which corresponds to a change of sign of B. Factor I in this formula shows that intense rays are more amplified than weak ones (competition of modes). Emission of a flare requires a sufficient radiance I provided by random zero point field. After emission of a flare, weak B increases by pumping while I remains close to zero: De-excitation by a coherent emission involves stochastic parameters of zero point field, as observed close to quasars (and in polar auroras).


title: Interstellar medium

text: The ISM is turbulent and therefore full of structure on all spatial scales. Stars are born deep inside large complexes of molecular clouds, typically a few parsecs in size. During their lives and deaths, stars interact physically with the ISM.


title: Interstellar medium

text: Stellar winds from young clusters of stars (often with giant or supergiant HII regions surrounding them) and shock waves created by supernovae inject enormous amounts of energy into their surroundings, which leads to hypersonic turbulence. The resultant structures – of varying sizes – can be observed, such as stellar wind bubbles and superbubbles of hot gas, seen by X-ray satellite telescopes or turbulent flows observed in radio telescope maps.


title: Interstellar medium

text: The Sun is currently traveling through the Local Interstellar Cloud, a denser region in the low-density Local Bubble.


title: Interstellar medium

text: In October 2020, astronomers reported a significant unexpected increase in density in the space beyond the Solar System as detected by the "Voyager 1" and "Voyager 2" space probes. According to the researchers, this implies that "the density gradient is a large-scale feature of the VLISM (very local interstellar medium) in the general direction of the heliospheric nose".


title: Interstellar medium

text: The interstellar medium begins where the interplanetary medium of the Solar System ends. The solar wind slows to subsonic velocities at the termination shock, 90–100 astronomical units from the Sun. In the region beyond the termination shock, called the heliosheath, interstellar matter interacts with the solar wind. "Voyager 1", the farthest human-made object from the Earth (after 1998), crossed the termination shock December 16, 2004 and later entered interstellar space when it crossed the heliopause on August 25, 2012, providing the first direct probe of conditions in the ISM .


title: Interstellar medium

text: The ISM is also responsible for extinction and reddening, the decreasing light intensity and shift in the dominant observable wavelengths of light from a star. These effects are caused by scattering and absorption of photons and allow the ISM to be observed with the naked eye in a dark sky. The apparent rifts that can be seen in the band of the Milky Way – a uniform disk of stars – are caused by absorption of background starlight by molecular clouds within a few thousand light years from Earth.


title: Interstellar medium

text: Far ultraviolet light is absorbed effectively by the neutral components of the ISM. For example, a typical absorption wavelength of atomic hydrogen lies at about 121.5 nanometers, the Lyman-alpha transition. Therefore, it is nearly impossible to see light emitted at that wavelength from a star farther than a few hundred light years from Earth, because most of it is absorbed during the trip to Earth by intervening neutral hydrogen.


title: Interstellar medium

text: The ISM is usually far from thermodynamic equilibrium. Collisions establish a Maxwell–Boltzmann distribution of velocities, and the 'temperature' normally used to describe interstellar gas is the 'kinetic temperature', which describes the temperature at which the particles would have the observed Maxwell–Boltzmann velocity distribution in thermodynamic equilibrium. However, the interstellar radiation field is typically much weaker than a medium in thermodynamic equilibrium; it is most often roughly that of an A star (surface temperature of ~10,000 K) highly diluted. Therefore, bound levels within an atom or molecule in the ISM are rarely populated according to the Boltzmann formula .


title: Interstellar medium

text: Depending on the temperature, density, and ionization state of a portion of the ISM, different heating and cooling mechanisms determine the temperature of the gas.


title: Interstellar medium

text: Grain heating by thermal exchange is very important in supernova remnants where densities and temperatures are very high.


title: Interstellar medium

text: Gas heating via grain-gas collisions is dominant deep in giant molecular clouds (especially at high densities). Far infrared radiation penetrates deeply due to the low optical depth. Dust grains are heated via this radiation and can transfer thermal energy during collisions with the gas. A measure of efficiency in the heating is given by the accommodation coefficient:


title: Interstellar medium

text: where "T" is the gas temperature, "T" the dust temperature, and "T" the post-collision temperature of the gas atom or molecule. This coefficient was measured by as "α" = 0.35.


title: Interstellar medium

text: Radio waves from ≈10 kHz (very low frequency) to ≈300 GHz (extremely high frequency) propagate differently in interstellar space than on the Earth's surface. There are many sources of interference and signal distortion that do not exist on Earth. A great deal of radio astronomy depends on compensating for the different propagation effects to uncover the desired signal.


title: Interstellar medium

text: In 1864, William Huggins used spectroscopy to determine that a nebula is made of gas. Huggins had a private observatory with an 8-inch telescope, with a lens by Alvin Clark; but it was equipped for spectroscopy which enabled breakthrough observations.


title: Interstellar medium

text: In 1904, one of the discoveries made using the Potsdam Great Refractor telescope was of calcium in the interstellar medium. The astronomer Johannes Frank Hartmann determined from spectrograph observations of the binary star Mintaka in Orion, that there was the element calcium in the intervening space.


title: Interstellar medium

text: Interstellar gas was further confirmed by Slipher in 1909, and then by 1912 interstellar dust was confirmed by Slipher. In this way the overall nature of the interstellar medium was confirmed in a series of discoveries and postulizations of its nature.


title: Interstellar medium

text: In September 2020, evidence was presented of solid-state water in the interstellar medium, and particularly, of water ice mixed with silicate grains in cosmic dust grains.


title: Interstellar medium

text: The nature of the interstellar medium has received the attention of astronomers and scientists over the centuries and understanding of the ISM has developed. However, they first had to acknowledge the basic concept of "interstellar" space. The term appears to have been first used in print by : "The Interstellar Skie.. hath .. so much Affinity with the Starre, that there is a Rotation of that, as well as of the Starre." Later, natural philosopher discussed "The inter-stellar part of heaven, which several of the modern Epicureans would have to be empty."


title: Interstellar medium

text: Before modern electromagnetic theory, early physicists postulated that an invisible luminiferous aether existed as a medium to carry lightwaves. It was assumed that this aether extended into interstellar space, as wrote, "this efflux occasions a thrill, or vibratory motion, in the ether which fills the interstellar spaces."


title: Interstellar medium

text: The advent of deep photographic imaging allowed Edward Barnard to produce the first images of dark nebulae silhouetted against the background star field of the galaxy, while the first actual detection of cold diffuse matter in interstellar space was made by Johannes Hartmann in 1904 through the use of absorption line spectroscopy. In his historic study of the spectrum and orbit of Delta Orionis, Hartmann observed the light coming from this star and realized that some of this light was being absorbed before it reached the Earth. Hartmann reported that absorption from the "K" line of calcium appeared "extraordinarily weak, but almost perfectly sharp" and also reported the "quite surprising result that the calcium line at 393.4 nanometres does not share in the periodic displacements of the lines caused by the orbital motion of the spectroscopic binary star". The stationary nature of the line led Hartmann to conclude that the gas responsible for the absorption was not present in the atmosphere of Delta Orionis, but was instead located within an isolated cloud of matter residing somewhere along the line-of-sight to this star. This discovery launched the study of the Interstellar Medium.


title: Interstellar medium

text: In the series of investigations, Viktor Ambartsumian introduced the now commonly accepted notion that interstellar matter occurs in the form of clouds.


title: Interstellar medium

text: Following Hartmann's identification of interstellar calcium absorption, interstellar sodium was detected by through the observation of stationary absorption from the atom's "D" lines at 589.0 and 589.6 nanometres towards Delta Orionis and Beta Scorpii.


title: Interstellar medium

text: Subsequent observations of the "H" and "K" lines of calcium by revealed double and asymmetric profiles in the spectra of Epsilon and Zeta Orionis. These were the first steps in the study of the very complex interstellar sightline towards Orion. Asymmetric absorption line profiles are the result of the superposition of multiple absorption lines, each corresponding to the same atomic transition (for example the "K" line of calcium), but occurring in interstellar clouds with different radial velocities. Because each cloud has a different velocity (either towards or away from the observer/Earth) the absorption lines occurring within each cloud are either blue-shifted or red-shifted (respectively) from the lines' rest wavelength, through the Doppler Effect. These observations confirming that matter is not distributed homogeneously were the first evidence of multiple discrete clouds within the ISM.


title: Interstellar medium

text: The growing evidence for interstellar material led to comment that "While the interstellar absorbing medium may be simply the ether, yet the character of its selective absorption, as indicated by Kapteyn, is characteristic of a gas, and free gaseous molecules are certainly there, since they are probably constantly being expelled by the Sun and stars."


title: Interstellar medium

text: The same year Victor Hess's discovery of cosmic rays, highly energetic charged particles that rain onto the Earth from space, led others to speculate whether they also pervaded interstellar space. The following year the Norwegian explorer and physicist Kristian Birkeland wrote: "It seems to be a natural consequence of our points of view to assume that the whole of space is filled with electrons and flying electric ions of all kinds. We have assumed that each stellar system in evolutions throws off electric corpuscles into space. It does not seem unreasonable therefore to think that the greater part of the material masses in the universe is found, not in the solar systems or nebulae, but in 'empty' space" .


title: Interstellar medium

text: In September 2012, NASA scientists reported that polycyclic aromatic hydrocarbons (PAHs), subjected to "interstellar medium (ISM)" conditions, are transformed, through hydrogenation, oxygenation and hydroxylation, to more complex organics – "a step along the path toward amino acids and nucleotides, the raw materials of proteins and DNA, respectively". Further, as a result of these transformations, the PAHs lose their spectroscopic signature which could be one of the reasons "for the lack of PAH detection in interstellar ice grains, particularly the outer regions of cold, dense clouds or the upper molecular layers of protoplanetary disks."


title: Interstellar medium

text: In February 2014, NASA announced a greatly upgraded database for tracking polycyclic aromatic hydrocarbons (PAHs) in the universe. According to scientists, more than 20% of the carbon in the universe may be associated with PAHs, possible starting materials for the formation of life. PAHs seem to have been formed shortly after the Big Bang, are widespread throughout the universe, and are associated with new stars and exoplanets.


title: Interstellar medium

text: In April 2019, scientists, working with the Hubble Space Telescope, reported the confirmed detection of the large and complex ionized molecules of buckminsterfullerene (C) (also known as "buckyballs") in the interstellar medium spaces between the stars.


title: Henrietta Maria

text: Henrietta Maria (; 25 November 1609 – 10 September 1669) was Queen of England, Scotland, and Ireland from her marriage to King Charles I on 13 June 1625 until Charles was executed on 30 January 1649. She was mother of his sons Charles II and James II and VII. Contemporaneously, by a decree of her husband, she was known in England as Queen Mary, but she did not like this name and signed her letters "Henriette R" or "Henriette Marie R" (the "R" standing for "regina", Latin for "queen".)


title: Henrietta Maria

text: Henrietta Maria's Roman Catholicism made her unpopular in England, and also prohibited her from being crowned in a Church of England service; therefore, she never had a coronation. She immersed herself in national affairs as civil war loomed, and in 1644, following the birth of her youngest daughter, Henrietta, during the height of the First English Civil War, was compelled to seek refuge in France. The execution of Charles I in 1649 left her impoverished. She settled in Paris and returned to England after the Restoration of Charles II to the throne. In 1665, she moved back to Paris, where she died four years later.


title: Henrietta Maria

text: The North American Province of Maryland, a major haven for Roman Catholic settlers, was named in honour of Queen Henrietta Maria. The name was carried over into the current U.S. state of Maryland.


title: Henrietta Maria

text: Henrietta Maria was the youngest daughter of Henry IV of France (Henry III of Navarre) and his second wife, Marie de' Medici, and was named after her parents. She was born at the Palais du Louvre on 25 November 1609, but some historians give her a birthdate of 26 November. In England, where the Julian calendar was still in use, her date of birth is often recorded as 16 November. Henrietta Maria was brought up as a Roman Catholic. As a daughter of the Bourbon king of France, she was a "Fille de France" and a member of the House of Bourbon. She was the youngest sister of the future Louis XIII of France. Her father was assassinated on 14 May 1610, when she was less than a year old. As a child, she was raised under the supervision of the royal governess Françoise de Montglat.