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Audrey Hepburn

Audrey Kathleen Hepburn (née Ruston; 4 May 1929 – 20 January 1993) was a British actress. Recognised as a film and fashion icon, she was ranked by the American Film Institute as the third-greatest female screen legend from the Classical Hollywood cinema and was inducted into the International Best Dressed Hall of Fame List.

Born into an aristocratic family in Ixelles, Brussels, Hepburn spent parts of her childhood in Belgium, England and the Netherlands. She attended boarding school in Kent, England from 1936 to 1939. With the outbreak of World War II, she returned to the Netherlands. During the war, Hepburn studied ballet at the Arnhem Conservatory and by 1944, she performed ballet to raise money to support the Dutch resistance. Hepburn studied ballet with Sonia Gaskell in Amsterdam beginning in 1945 and with Marie Rambert in London from 1948. She began performing as a chorus girl in West End musical theatre productions and then had minor appearances in several films. Hepburn rose to stardom in the romantic comedy Roman Holiday (1953) alongside Gregory Peck, for which she was the first actress to win an Oscar, a Golden Globe Award, and a BAFTA Award for a single performance. That year, she also won a Tony Award for Best Lead Actress in a Play for her performance in Ondine.

Hepburn went on to star in a number of successful films such as Sabrina (1954), in which Humphrey Bogart and William Holden compete for her affection; Funny Face (1957), a musical in which she sang her own parts; the drama The Nun's Story (1959); the romantic comedy Breakfast at Tiffany's (1961); the thriller-romance Charade (1963), opposite Cary Grant; and the musical My Fair Lady (1964). In 1967, she starred in the thriller Wait Until Dark, receiving Academy Award, Golden Globe and BAFTA nominations. After that, Hepburn only occasionally appeared in films, one being Robin and Marian (1976) with Sean Connery. Her last recorded performances were in the 1990 documentary television series Gardens of the World with Audrey Hepburn, for which she won a Primetime Emmy Award for Outstanding Individual Achievement – Informational Programming. In 1994, Hepburn's contributions to a spoken-word recording titled Audrey Hepburn's Enchanted Tales earned her a posthumous Grammy Award for Best Spoken Word Album for Children. She stands as one of few entertainers who have won Academy, Emmy, Grammy and Tony Awards.

Hepburn won three BAFTA Awards for Best British Actress in a Leading Role. In recognition of her film career, she received BAFTA's Lifetime Achievement Award, the Golden Globe Cecil B. DeMille Award, the Screen Actors Guild Life Achievement Award and the Special Tony Award. Later in life, Hepburn devoted much of her time to UNICEF, to which she had contributed since 1954. Between 1988 and 1992, she worked in some of the poorest communities of Africa, South America and Asia. In December 1992, Hepburn received the US Presidential Medal of Freedom in recognition of her work as a UNICEF Goodwill Ambassador. A month later, she died of appendiceal cancer at her home in Tolochenaz, Vaud, Switzerland at the age of 63.

1929–1938: Family and early childhood
Audrey Kathleen Ruston (later, Hepburn-Ruston) was born on 4 May 1929 at number 48 Rue Keyenveld in Ixelles, a municipality of Brussels, Belgium. She was known to her family as Adriaantje. Hepburn's mother, Baroness Ella van Heemstra (1900–1984), was a Dutch noblewoman. Ella was the daughter of Baron Aarnoud van Heemstra—who served as the mayor of Arnhem from 1910 to 1920 and as the governor of Dutch Guiana from 1921 to 1928—and Baroness Elbrig Willemine Henriette van Asbeck (1873–1939), a granddaughter of Count Dirk van Hogendorp. At age 19, she married Jonkheer Hendrik Gustaaf Adolf Quarles van Ufford—an oil executive based in Batavia, Dutch East Indies, where the couple subsequently lived. Before divorcing in 1925, they had two sons, Jonkheer Arnoud Robert Alexander Quarles van Ufford (1920–1979) and Jonkheer Ian Edgar Bruce Quarles van Ufford (1924–2010).

Hepburn's father, Joseph Victor Anthony Ruston (1889–1980), was a British subject born in Auschitz, Bohemia, Austria-Hungary. He was the son of Victor John George Ruston—who was of British and German-Austrian background—and Anna Juliana Franziska Karolina Wels, who was of German-Austrian origin and born in Kovarce. In 1923–1924, he was an Honorary British Consul in Semarang, Dutch East Indies and, prior to his marriage to Hepburn's mother, was married to Cornelia Bisschop, a Dutch heiress. Joseph later changed his surname to the more "aristocratic" double-barrelled Hepburn-Ruston—perhaps at Ella's insistence—as he mistakenly believed himself descended from James Hepburn, 4th Earl of Bothwell.

Hepburn's parents were married in Batavia in 1926. At the time, Joseph worked for a trading company, but soon after the marriage, the couple moved to Europe, where he began working for a loan company; reportedly tin merchants MacLaine, Watson, and Company in London. After a year in London, they moved to Brussels, where he had been assigned to open a branch office. After three years spent traveling between Brussels, Arnhem, The Hague and London, the family settled in the suburban Brussels municipality of Linkebeek in 1932. Hepburn's early childhood was sheltered and privileged. Due to her father's job, the family travelled back and forth between three countries, enhancing her multinational background.

In the mid-1930s, Hepburn's parents recruited and collected donations for the British Union of Fascists (B.U.F). Ella met Adolf Hitler and wrote favourable articles about him for the B.U.F. Joseph left the family abruptly in 1935 after a "scene" in Brussels. He subsequently moved to London, where he became more deeply involved in the Fascist activity and never visited Hepburn abroad. That same year, Ella moved to her family's estate in Arnhem with her daughter; her sons, Alex and Ian, were sent to The Hague to live with relatives. Joseph wanted Hepburn to be educated in England, so in 1937, she was sent to live in Kent, where she—known as Audrey Ruston or "Little Audrey"—was educated at a small private school in Elham. Her parents officially divorced the next year. Later in her life, she often spoke of the effect on a child of being "dumped" as "children need two parents"; she professed that her father's departure was "the most traumatic event of my life". In the 1960s, Hepburn renewed contact with her father after locating him in Dublin through the Red Cross; she supported him financially until his death although he remained emotionally detached.

1939–1945: Experiences during World War II
After Britain declared war on Germany in September 1939, Hepburn's mother moved her daughter back to Arnhem in the hope that, as during the First World War, the Netherlands would remain neutral and be spared a German attack. While there, Hepburn attended the Arnhem Conservatory from 1939 to 1945. She had begun taking ballet lessons during her last years at boarding school, and continued training in Arnhem under the tutelage of Winja Marova, becoming her "star pupil". After the Germans invaded the Netherlands in 1940, Hepburn used the name Edda van Heemstra, because an "English-sounding" name was considered dangerous during the German occupation. Her family was profoundly affected by the occupation, with Hepburn later stating that "had we known that we were going to be occupied for five years, we might have all shot ourselves. We thought it might be over next week… six months… next year… that's how we got through".

In 1942, her uncle, Otto van Limburg Stirum (husband of her mother's older sister, Miesje), was executed in retaliation for an act of sabotage by the resistance movement; while he had not been involved in the act, he was targeted due to his family's prominence in Dutch society. These family events were the turning point in the attitude of Hepburn's mother, who had flirted with Nazism up to this point. Hepburn's half-brother Ian was deported to Berlin to work in a German labour camp, and her other half-brother Alex went into hiding to avoid the same fate.

After her uncle's death, Hepburn, Ella, and Miesje left Arnhem to live with her grandfather, Baron Aarnoud van Heemstra, in nearby Velp. Around that time Hepburn gave silent dance performances that reportedly raised money for the Dutch resistance effort. It was long believed that she participated in the Dutch resistance itself, but in 2016 the Airborne Museum 'Hartenstein' reported that after extensive research it had not found any evidence of such activities. A 2019 book by Robert Matzen provided evidence, based on Hepburn's personal statements, that she had supported the resistance by giving "underground concerts" to raise money, delivering the underground newspaper, and taking messages and food to downed Allied flyers hiding in the woodlands north of Velp. She also volunteered at a hospital that was the center of resistance activities in Velp, and, according to Hepburn, her family temporarily hid a British paratrooper in their home during the Battle of Arnhem. In addition to other traumatic events, she witnessed the transportation of Dutch Jews to concentration camps, later stating that "more than once I was at the station seeing trainloads of Jews being transported, seeing all these faces over the top of the wagon. I remember, very sharply, one little boy standing with his parents on the platform, very pale, very blond, wearing a coat that was much too big for him, and he stepped on the train. I was a child observing a child."

After the Allied landing on D-Day, living conditions grew worse, and Arnhem was subsequently heavily damaged during Operation Market Garden. During the 1944–45 Dutch famine, the Germans hindered or reduced the already limited food and fuel supplies to civilians in retaliation for Dutch railway strikes that were held to disrupt the occupation. Like others, Hepburn's family resorted to making flour out of tulip bulbs to bake cakes and biscuits, a source of starchy carbohydrates; Dutch doctors provided recipes for using tulip bulbs throughout the famine. Suffering from the effects of malnutrition, after the war ended Hepburn became gravely ill with jaundice, anaemia, oedema, and a respiratory infection. In October 1945, a letter from Ella asking for help was received by Micky Burn, a former lover and British Army officer with whom she had corresponded whilst he was a prisoner of war in Colditz Castle. He sent back thousands of cigarettes, which she was able to sell on the black market and thus buy the penicillin which saved Hepburn's life. The Van Heemstra family's financial situation changed significantly through the occupation, during which time many of their properties (including their principal estate in Arnhem) were damaged or destroyed.

1945–1952: Ballet studies and early acting roles
After the war ended in 1945, Hepburn moved with her mother and siblings to Amsterdam, where she began ballet training under Sonia Gaskell, a leading figure in Dutch ballet, and Russian teacher Olga Tarasova. Due to the loss of the family fortune, Ella had to support them by working as a cook and housekeeper for a wealthy family. Hepburn made her film debut playing an air stewardess in Dutch in Seven Lessons (1948), an educational travel film made by Charles van der Linden and Henry Josephson. Later that year, Hepburn moved to London after accepting a ballet scholarship with Ballet Rambert, which was then based in Notting Hill. She supported herself with part-time work as a model, and dropped "Ruston" from her surname. After she was told by Rambert that despite her talent, her height and weak constitution (the after-effect of wartime malnutrition) would make the status of prima ballerina unattainable, she decided to concentrate on acting. While Ella worked in menial jobs to support them, Hepburn appeared as a chorus girl in the West End musical theatre revues High Button Shoes (1948) at the London Hippodrome, and Cecil Landeau's Sauce Tartare (1949) and Sauce Piquante (1950) at the Cambridge Theatre. Also, in 1950, she worked as a dancer in an exceptionally "ambitious" revue, Summer Nights, at Ciro's London, a prominent nightclub.

During her theatrical work, she took elocution lessons with actor Felix Aylmer to develop her voice. After being spotted by the Ealing Studios casting director, Margaret Harper-Nelson, while performing in Sauce Piquante, Hepburn was registered as a freelance actress with the Associated British Picture Corporation (ABPC). She appeared in the BBC Television play The Silent Village, and in minor roles in the films One Wild Oat, Laughter in Paradise, Young Wives' Tale, and The Lavender Hill Mob (all 1951). She was cast in her first major supporting role in Thorold Dickinson's Secret People (1952), as a prodigious ballerina, performing all of her own dancing sequences.

Hepburn then took a small role in a bilingual film, Monte Carlo Baby (French: Nous Irons à Monte Carlo, 1952), which was filmed in Monte Carlo. Coincidentally, French novelist Colette was at the Hôtel de Paris in Monte Carlo during the filming, and decided to cast Hepburn in the title role in the Broadway play Gigi. Hepburn went into rehearsals having never spoken on stage, and required private coaching. When Gigi opened at the Fulton Theatre on 24 November 1951, she received praise for her performance, despite criticism that the stage version was inferior to the French film adaptation. Life called her a "hit", while The New York Times stated that "her quality is so winning and so right that she is the success of the evening". Hepburn also received a Theatre World Award for the role. The play ran for 219 performances, closing on 31 May 1952, before going on tour, which began 13 October 1952 in Pittsburgh and visited Cleveland, Chicago, Detroit, Washington, D. C., and Los Angeles, before closing on 16 May 1953 in San Francisco.

1953–1960: Roman Holiday and stardom
Hepburn had her first starring role in Roman Holiday (1953), playing Princess Ann, a European princess who escapes the reins of royalty and has a wild night out with an American newsman (Gregory Peck). On 18 September 1951, shortly after Secret People was finished but before its premiere, Thorold Dickinson made a screen test with the young starlet and sent it to director William Wyler, who was in Rome preparing Roman Holiday. Wyler wrote a glowing note of thanks to Dickinson, saying that "as a result of the test, a number of the producers at Paramount have expressed interest in casting her." The producers of the film had initially wanted Elizabeth Taylor for the role, but Wyler was so impressed by Hepburn's screen test that he cast her instead. Wyler later commented, "She had everything I was looking for: charm, innocence, and talent. She also was very funny. She was absolutely enchanting, and we said, 'That's the girl! Originally, the film was to have had only Gregory Peck's name above its title, with "Introducing Audrey Hepburn" beneath in smaller font. Peck suggested Wyler elevate her to equal billing so her name appears before the title, and in type as large as his: "You've got to change that because she'll be a big star, and I'll look like a big jerk."

The film was a box-office success, and Hepburn gained critical acclaim for her portrayal, unexpectedly winning an Academy Award for Best Actress, a BAFTA Award for Best British Actress in a Leading Role, and a Golden Globe Award for Best Actress – Motion Picture Drama in 1953. In his review in The New York Times, A. H. Weiler wrote: "Although she is not precisely a newcomer to films, Audrey Hepburn, the British actress who is being starred for the first time as Princess Anne, is a slender, elfin, and wistful beauty, alternately regal and childlike in her profound appreciation of newly-found, simple pleasures and love. Although she bravely smiles her acknowledgement of the end of that affair, she remains a pitifully lonely figure facing a stuffy future."

Hepburn was signed to a seven-picture contract with Paramount, with 12 months in between films to allow her time for stage work. She was featured on 7 September 1953 cover of Time magazine, and also became known for her personal style. Following her success in Roman Holiday, Hepburn starred in Billy Wilder's romantic Cinderella-story comedy Sabrina (1954), in which wealthy brothers (Humphrey Bogart and William Holden) compete for the affections of their chauffeur's innocent daughter (Hepburn). For her performance, she was nominated for the 1954 Academy Award for Best Actress, while winning the BAFTA Award for Best Actress in a Leading Role the same year. Bosley Crowther of The New York Times stated that she was "a young lady of extraordinary range of sensitive and moving expressions within such a frail and slender frame. She is even more luminous as the daughter and pet of the servants' hall than she was as a princess last year, and no more than that can be said."

Hepburn also returned to the stage in 1954, playing a water nymph who falls in love with a human in the fantasy play Ondine on Broadway. A critic for The New York Times commented that "somehow, Miss Hepburn is able to translate [its intangibles] into the language of the theatre without artfulness or precociousness. She gives a pulsing performance that is all grace and enchantment, disciplined by an instinct for the realities of the stage". Her performance won her the 1954 Tony Award for Best Performance by a Leading Actress in a Play three days after she won the Academy Award for Roman Holiday, making her one of three actresses to receive the Academy and Tony Awards for Best Actress in the same year (the other two are Shirley Booth and Ellen Burstyn). During the production, Hepburn and her co-star Mel Ferrer began a relationship, and were married on 25 September 1954 in Switzerland.

Although she appeared in no new film releases in 1955, Hepburn received the Golden Globe for World Film Favorite that year. Having become one of Hollywood's most popular box-office attractions, she starred in a series of successful films during the remainder of the decade, including her BAFTA- and Golden Globe-nominated role as Natasha Rostova in War and Peace (1956), an adaptation of the Tolstoy novel set during the Napoleonic wars, starring Henry Fonda and her husband Mel Ferrer. She exhibited her dancing abilities in her debut musical film, Funny Face (1957), wherein Fred Astaire, a fashion photographer, discovers a beatnik bookshop clerk (Hepburn) who, lured by a free trip to Paris, becomes a beautiful model. Hepburn starred in another romantic comedy, Love in the Afternoon (also 1957), alongside Gary Cooper and Maurice Chevalier.

Hepburn played Sister Luke in The Nun's Story (1959), which focuses on the character's struggle to succeed as a nun, alongside co-star Peter Finch. The role produced a third Academy Award nomination for Hepburn, and earned her a second BAFTA Award. A review in Variety reads: "Hepburn has her most demanding film role, and she gives her finest performance", while Henry Hart in Films in Review stated that her performance "will forever silence those who have thought her less an actress than a symbol of the sophisticated child/woman. Her portrayal of Sister Luke is one of the great performances of the screen." Hepburn spent a year researching and working on the role, saying, "I gave more time, energy, and thought to this role than to any of my previous screen performances".

Following The Nun's Story, Hepburn received a lukewarm reception for starring with Anthony Perkins in the romantic adventure Green Mansions (1959), in which she played Rima, a jungle girl who falls in love with a Venezuelan traveller, and The Unforgiven (1960), her only western film, in which she appeared opposite Burt Lancaster and Lillian Gish in a story of racism against a group of Native Americans.

1961–1967: Breakfast at Tiffany's and continued success
Hepburn next starred as New Yorker Holly Golightly in Blake Edwards's Breakfast at Tiffany's (1961), a film loosely based on the Truman Capote novella of the same name. Capote disapproved of many changes that were made to sanitise the story for the film adaptation, and would have preferred Marilyn Monroe to have been cast in the role, although he also stated that Hepburn "did a terrific job". The character is considered one of the best-known in American cinema, and a defining role for Hepburn. The dress she wears during the opening credits has been considered an icon of the twentieth century, and perhaps the most famous "little black dress" of all time. Hepburn stated that the role was "the jazziest of my career" yet admitted: "I'm an introvert. Playing the extroverted girl was the hardest thing I ever did." She was nominated for the Academy Award for Best Actress for her performance.

The same year, Hepburn also starred in William Wyler's drama The Children's Hour (1961), in which she and Shirley MacLaine played teachers whose lives become troubled after two pupils accuse them of being lesbians. Bosley Crowther of The New York Times was of the opinion that the film "is not too well acted", with the exception of Hepburn, who "gives the impression of being sensitive and pure" of its "muted theme". Variety magazine also complimented Hepburn's "soft sensitivity, marvelous projection and emotional understatement", adding that Hepburn and MacLaine "beautifully complement each other".

Hepburn next appeared opposite Cary Grant in the comic thriller Charade (1963), playing a young widow pursued by several men who chase after the fortune stolen by her murdered husband. The 59-year-old Grant, who had previously withdrawn from the starring male lead roles in Roman Holiday and Sabrina, was sensitive about his age difference with 34-year-old Hepburn, and was uncomfortable about the romantic interplay. To satisfy his concerns, the filmmakers agreed to alter the screenplay so that Hepburn's character was pursuing him. The film turned out to be a positive experience for him; he said, "All I want for Christmas is another picture with Audrey Hepburn." The role earned Hepburn her third, and final, competitive BAFTA Award, and another Golden Globe nomination. Critic Bosley Crowther was less kind to her performance, stating that, "Hepburn is cheerfully committed to a mood of how-nuts-can-you-be in an obviously comforting assortment of expensive Givenchy costumes."

Although filmed in the summer of 1962 before Charade, Hepburn reunited with her Sabrina co-star William Holden in Paris When It Sizzles (1964), a screwball comedy in which she played the young assistant of a Hollywood screenwriter, who aids his writer's block by acting out his fantasies of possible plots. Its production was troubled by several problems. Holden unsuccessfully tried to rekindle a romance with the now-married Hepburn, and his alcoholism was beginning to affect his work. After principal photography began, she demanded the dismissal of cinematographer Claude Renoir after seeing what she felt were unflattering dailies. Superstitious, she also insisted on dressing room 55 because that was her lucky number and required that Hubert de Givenchy, her long-time designer, be given a credit in the film for her perfume. Dubbed "marshmallow-weight hokum" by Variety upon its release in April, the film was "uniformly panned" but critics were kinder to Hepburn's performance, describing her as "a refreshingly individual creature in an era of the exaggerated curve".

Hepburn's second film released in 1964 was George Cukor's film adaptation of the stage musical My Fair Lady, which premiered in October. Soundstage wrote that "not since Gone with the Wind has a motion picture created such universal excitement as My Fair Lady", although Hepburn's casting in the role of Cockney flower girl Eliza Doolittle was a source of dispute. Julie Andrews, who had originated the role on stage, was not offered the part because producer Jack L. Warner thought Hepburn was a more "bankable" proposition. Hepburn initially asked Warner to give the role to Andrews but was eventually cast. Further friction was created when, although non-singer Hepburn had sung in Funny Face and had lengthy vocal preparation for the role in My Fair Lady, her vocals were dubbed by Marni Nixon, whose voice was considered more suitable to the role. Hepburn was initially upset and walked off the set when informed.

Critics applauded Hepburn's performance. Crowther wrote that, "The happiest thing about [My Fair Lady] is that Audrey Hepburn superbly justifies the decision of Jack Warner to get her to play the title role." Gene Ringgold of Soundstage also commented that, "Audrey Hepburn is magnificent. She is Eliza for the ages", while adding, "Everyone agreed that if Julie Andrews was not to be in the film, Audrey Hepburn was the perfect choice." The reviewer in Time magazine said her "graceful, glamorous performance" was "the best of her career". Andrews won an Academy Award for Mary Poppins at the 1964 37th Academy Awards and Hepburn earned Best Actress nominations for Golden Globe and New York Film Critics Circle awards.

Hepburn appeared in an assortment of genres including the heist comedy How to Steal a Million (1966). Hepburn played the daughter of a famous art collector, whose collection consists entirely of forgeries that are about to be exposed as fakes. Her character plays the part of a dutiful daughter trying to help her father with the help of a man played by Peter O'Toole. The film was followed by two films in 1967. The first was Two for the Road, a non-linear and innovative British dramedy that traces the course of a couple's troubled marriage. Director Stanley Donen said that Hepburn was freer and happier than he had ever seen her, and he credited that to co-star Albert Finney. The second, Wait Until Dark, is a suspense thriller in which Hepburn demonstrated her acting range by playing the part of a terrorised blind woman. Filmed on the brink of her divorce, it was a difficult film for her, as husband Mel Ferrer was its producer. She lost fifteen pounds under the stress, but she found solace in co-star Richard Crenna and director Terence Young. Hepburn earned her fifth and final competitive Academy Award nomination for Best Actress; Bosley Crowther affirmed, "Hepburn plays the poignant role, the quickness with which she changes and the skill with which she manifests terror attract sympathy and anxiety to her and give her genuine solidity in the final scenes."

1968–1993: Semi-retirement and final projects
After 1967, Hepburn chose to devote more time to her family and acted only occasionally. She attempted a comeback playing Maid Marian in the period piece Robin and Marian (1976) with Sean Connery co-starring as Robin Hood, which was moderately successful. Roger Ebert praised Hepburn's chemistry with Connery, writing, "Connery and Hepburn seem to have arrived at a tacit understanding between themselves about their characters. They glow. They really do seem in love. And they project as marvellously complex, fond, tender people; the passage of 20 years has given them grace and wisdom." Hepburn reunited with director Terence Young in the production of Bloodline (1979), sharing top-billing with Ben Gazzara, James Mason, and Romy Schneider. The film, an international intrigue amid the jet-set, was a critical and box-office failure. Hepburn's last starring role in a feature film was opposite Gazzara in the comedy They All Laughed (1981), directed by Peter Bogdanovich. The film was overshadowed by the murder of one of its stars, Dorothy Stratten, and received only a limited release. Six years later, Hepburn co-starred with Robert Wagner in a made-for-television caper film, Love Among Thieves (1987).

After finishing her last motion picture role—a cameo appearance as an angel in Steven Spielberg's Always (1989)—Hepburn completed only two more entertainment-related projects, both critically acclaimed. Gardens of the World with Audrey Hepburn was a PBS documentary series, which was filmed on location in seven countries in the spring and summer of 1990. A one-hour special preceded it in March 1991, and the series itself began its national PBS premiere on 24 January 1993, the day of her funeral services in Tolochenaz. For the "Flower Gardens" episode, Hepburn was posthumously awarded the 1993 Emmy Award for Outstanding Individual Achievement – Informational Programming. The other project was a spoken word album, Audrey Hepburn's Enchanted Tales, which features readings of classic children's stories and was recorded in 1992. It earned her a posthumous Grammy Award for Best Spoken Word Album for Children.

Humanitarian work
In the 1950s, Hepburn narrated two radio programmes for UNICEF, re-telling children's stories of war. In 1989, Hepburn was appointed a Goodwill Ambassador of UNICEF. On her appointment, she stated that she was grateful for receiving international aid after enduring the German occupation as a child, and wanted to show her gratitude to the organisation.

1988–1992
Hepburn's first field mission for UNICEF was to Ethiopia in 1988. She visited an orphanage in Mek'ele that housed 500 starving children and had UNICEF send food. Of the trip, she said, "I have a broken heart. I feel desperate. I can't stand the idea that two million people are in imminent danger of starving to death, many of them children, [and] not because there isn't tons of food sitting in the northern port of Shoa. It can't be distributed. Last spring, Red Cross and UNICEF workers were ordered out of the northern provinces because of two simultaneous civil wars... I went into rebel country and saw mothers and their children who had walked for ten days, even three weeks, looking for food, settling onto the desert floor into makeshift camps where they may die. Horrible. That image is too much for me. The 'Third World' is a term I don't like very much, because we're all one world. I want people to know that the largest part of humanity is suffering."

In August 1988, Hepburn went to Turkey on an immunisation campaign. She called Turkey "the loveliest example" of UNICEF's capabilities. Of the trip, she said, "The army gave us their trucks, the fishmongers gave their wagons for the vaccines, and once the date was set, it took ten days to vaccinate the whole country. Not bad." In October, Hepburn went to South America. Of her experiences in Venezuela and Ecuador, Hepburn told the United States Congress, "I saw tiny mountain communities, slums, and shantytowns receive water systems for the first time by some miracle – and the miracle is UNICEF. I watched boys build their own schoolhouse with bricks and cement provided by UNICEF."

Hepburn toured Central America in February 1989, and met with leaders in Honduras, El Salvador, and Guatemala. In April, she visited Sudan with Wolders as part of a mission called "Operation Lifeline". Because of civil war, food from aid agencies had been cut off. The mission was to ferry food to southern Sudan. Hepburn said, "I saw but one glaring truth: These are not natural disasters but man-made tragedies for which there is only one man-made solution – peace." In October 1989, Hepburn and Wolders went to Bangladesh. John Isaac, a UN photographer, said, "Often the kids would have flies all over them, but she would just go hug them. I had never seen that. Other people had a certain amount of hesitation, but she would just grab them. Children would just come up to hold her hand, touch her – she was like the Pied Piper."

In October 1990, Hepburn went to Vietnam, in an effort to collaborate with the government for national UNICEF-supported immunisation and clean water programmes. In September 1992, four months before she died, Hepburn went to Somalia. Calling it "apocalyptic", she said, "I walked into a nightmare. I have seen famine in Ethiopia and Bangladesh, but I have seen nothing like this – so much worse than I could possibly have imagined. I wasn't prepared for this." Though scarred by what she had seen, Hepburn still had hope stating: "As we move into the twenty-first century, there is much to reflect upon. We look around us and see that the promises of yesterday have to come to pass. People still live in abject poverty, people are still hungry, people still struggle to survive. And among these people we see the children, always the children: their enlarged bellies, their sad eyes, their wise faces that show the suffering, all the suffering they have endured in their short years."

Recognition
United States president George H. W. Bush presented Hepburn with the Presidential Medal of Freedom in recognition of her work with UNICEF, and the Academy of Motion Picture Arts and Sciences posthumously awarded her the Jean Hersholt Humanitarian Award for her contribution to humanity. In 2002, at the United Nations Special Session on Children, UNICEF honoured Hepburn's legacy of humanitarian work by unveiling a statue, "The Spirit of Audrey", at UNICEF's New York headquarters. Her service for children is also recognised through the United States Fund for UNICEF's Audrey Hepburn Society.

Multilingualism
Alongside her native English and Dutch, Hepburn also had some fluency in French (which she learned at school in Belgium), German, Italian, and Spanish. Throughout her life, Hepburn lived in many countries, including spending her childhood in Belgium, England, and the Netherlands, and her adult years in the United States, Italy, and Switzerland, and traveled extensively during her later years of life as part of her humanitarian work with UNICEF.

Marriages, relationships, and children
In 1952, Hepburn became engaged to industrialist James Hanson, whom she had known since her early days in London. She called it "love at first sight", but after having her wedding dress fitted and the date set, she decided the marriage would not work because the demands of their careers would keep them apart most of the time. She issued a public statement about her decision, saying "When I get married, I want to be married". In the early 1950s, she also dated future Hair producer Michael Butler. At a cocktail party hosted by mutual friend Gregory Peck, Hepburn met American actor Mel Ferrer, and suggested that they star together in a play. The meeting led them to collaborate in Ondine, during which they began a relationship. Eight months later, on 25 September 1954, they were married in Bürgenstock, Switzerland, while preparing to star together in the film War and Peace (1956). She and Ferrer had a son, Sean Hepburn Ferrer, born on 17 June 1960. Prior to Sean's birth, Hepburn had two other pregnancies that ended in miscarriages, the second one at six months.

Ferrer was rumoured to be too controlling, and had been referred to by others as being her "Svengali" – an idea that Hepburn laughed off. William Holden was quoted as saying, "I think Audrey allows Mel to think he influences her." After a 14-year marriage, the couple divorced in 1968.

Hepburn met her second husband, Italian psychiatrist Andrea Dotti, on a Mediterranean cruise with friends in June 1968. She believed she would have more children and possibly stop working. They married on 18 January 1969, and their son Luca Andrea Dotti was born on 8 February 1970. While pregnant with Luca in 1969, Hepburn was more careful, resting for months before delivering the baby via caesarean section. Hepburn suffered a miscarriage in 1974.

Dotti and Hepburn were unfaithful, he with younger women and she with actor Ben Gazzara during the filming of Bloodline (1979). The marriage lasted twelve years and was dissolved in 1982.

From 1980 until her death in 1993, Hepburn was in a relationship with Dutch actor Robert Wolders, the widower of actress Merle Oberon. She had met Wolders through a friend during the later years of her second marriage. In 1989, she called the nine years she had spent with him the happiest years of her life, and stated that she considered them married, just not officially.

Illness and death
Upon returning to Switzerland from Somalia in late September 1992, Hepburn developed abdominal pain. While initial medical tests in Switzerland had inconclusive results, a laparoscopy performed at the Cedars-Sinai Medical Center in Los Angeles in early November revealed a rare form of abdominal cancer belonging to a group of cancers known as pseudomyxoma peritonei. Having grown slowly over several years, the cancer had metastasised as a thin coating over her small intestine. After surgery, Hepburn began chemotherapy.

Hepburn and her family returned home to Switzerland to celebrate her last Christmas. As she was still recovering from surgery, she was unable to fly on commercial aircraft. Her long-time friend, fashion designer Hubert de Givenchy, arranged for socialite Rachel Lambert "Bunny" Mellon to send her private Gulfstream jet, filled with flowers, to take Hepburn from Los Angeles to Geneva. She spent her last days in hospice care at her home in Tolochenaz, Vaud, and was occasionally well enough to take walks in her garden, but gradually became more confined to bedrest.

On the evening of 20 January 1993, Hepburn died in her sleep at home. After her death, Gregory Peck recorded a tribute to Hepburn in which he recited the poem "Unending Love" by Rabindranath Tagore. Funeral services were held at the village church of Tolochenaz on 24 January 1993. Maurice Eindiguer, the same pastor who wed Hepburn and Mel Ferrer and baptised her son Sean in 1960, presided over her funeral, while Prince Sadruddin Aga Khan of UNICEF delivered a eulogy. Many family members and friends attended the funeral, including her sons, partner Robert Wolders, half-brother Ian Quarles van Ufford, ex-husbands Andrea Dotti and Mel Ferrer, Hubert de Givenchy, executives of UNICEF, and fellow actors Alain Delon and Roger Moore. Flower arrangements were sent to the funeral by Gregory Peck, Elizabeth Taylor, and the Dutch royal family. Later on the same day, Hepburn was interred at the Tolochenaz Cemetery.

Legacy
Hepburn's legacy has endured long after her death. The American Film Institute named Hepburn third among the Greatest Female Stars of All Time. She is one of few entertainers who have won Academy, Emmy, Grammy and Tony Awards. She won a record three BAFTA Awards for Best British Actress in a Leading Role. In her last years, she remained a visible presence in the film world. She received a tribute from the Film Society of Lincoln Center in 1991 and she was a frequent presenter at the Academy Awards. She received the BAFTA Lifetime Achievement Award in 1992. She was the recipient of numerous posthumous awards including the 1993 Jean Hersholt Humanitarian Award and competitive Grammy and Emmy Awards. In January 2009, Hepburn was named on The Times' list of the top 10 British actresses of all time. In 2010, Emma Thompson opined that Hepburn "can't sing and she can't really act"; some people agreed, others disagreed. Hepburn's son Sean later said "My mother would be the first person to say that she wasn't the best actress in the world. But she was a movie star."

She has been the subject of many biographies since her death including the 2000 dramatisation of her life titled The Audrey Hepburn Story which starred Jennifer Love Hewitt and Emmy Rossum as the older and younger Hepburn respectively. Her son and granddaughter, Sean and Emma Ferrer, helped produce a biographical documentary directed by Helena Coan, entitled Audrey (2020). The film was released to positive reception. Hepburn's image is widely used in advertising campaigns across the world. In Japan, a series of commercials used colourised and digitally enhanced clips of Hepburn in Roman Holiday to advertise Kirin black tea. In the United States, Hepburn was featured in a 2006 Gap commercial that used clips of her dancing from Funny Face, set to AC/DC's "Back in Black", with the tagline "It's Back – The Skinny Black Pant". To celebrate its "Keep it Simple" campaign, the Gap made a sizeable donation to the Audrey Hepburn Children's Fund. In 2012, Hepburn was among the British cultural icons selected by artist Sir Peter Blake to appear in a new version of his best known artwork – the Beatles' Sgt. Pepper's Lonely Hearts Club Band album cover – to celebrate the British cultural figures of his life that he most admires. In 2013, a computer-manipulated representation of Hepburn was used in a television advert for the British chocolate bar Galaxy. On 4 May 2014, Google featured a doodle on its homepage on what would have been Hepburn's 85th birthday.

Sean Ferrer founded the Audrey Hepburn Children's Fund in memory of his mother shortly after her death. The US Fund for UNICEF also founded the Audrey Hepburn Society: the Society hosted annual charity balls for fund raising until Ferrer became involved in lawsuits in the late 2010s on behalf of his mother's estate. Dotti also became patron of the Pseudomyxoma Survivor charity, dedicated to providing support to patients of the rare cancer that was fatal to Hepburn, pseudomyxoma peritonei, and Sean Ferrer became the rare disease ambassador since 2014 and for 2015 on behalf of European Organisation for Rare Diseases. A year after his mother's death in 1993, Ferrer founded the Audrey Hepburn Children's Fund (originally named Hollywood for Children Inc.), a charity funded by exhibitions of Audrey Hepburn memorabilia. He directed the charity in cooperation with his half-brother Luca Dotti, and Robert Wolders, his mother's partner, which aimed to continue the humanitarian work of Audrey Hepburn. Ferrer brought the exhibition "Timeless Audrey" on a world tour to raise money for the foundation. He served as Chairman of the Fund before resigning in 2012, turning over the position to Dotti. In 2017, Ferrer was sued by the Fund for alleged self-serving conduct. In October 2017, Ferrer responded by suing the Fund for trademark infringement, claiming that the Fund no longer had the right to use Hepburn's name or likeness. Ferrer's suit against the Fund was dismissed in March 2018 due to the complaint's failure to include Dotti as a defendant. In 2019, the court sided with Ferrer, with the judge ruling there was no merit to the charity's claims it had the independent right to use Audrey Hepburn's name and likeness, or to enter into contracts with third parties without Ferrer's consent.

Hepburn's son Sean said that he was brought up in the countryside as a normal child, not in Hollywood and without a Hollywood state of mind that makes movie stars and their families lose touch with reality. There was no screening room in the house. He said that his mother didn't take herself seriously, and used to say, "I take what I do seriously, but I don't take myself seriously".

Public image and style icon
Hepburn was known for her fashion choices and distinctive look, to the extent that journalist Mark Tungate has described her as a recognisable brand. When she first rose to stardom in Roman Holiday (1953), she was seen as an alternative feminine ideal that appealed more to women than men, compared to the more sexual and curvy Marilyn Monroe and Elizabeth Taylor. With her short hairstyle, thick eyebrows, slim body, and "gamine" looks, she presented a look that young women found easier to emulate than those of more sexual film stars. In 1954, fashion photographer Cecil Beaton declared Hepburn the "public embodiment of our new feminine ideal" in Vogue, and wrote that "Nobody ever looked like her before World War II ... Yet we recognise the rightness of this appearance in relation to our historical needs. The proof is that thousands of imitations have appeared." The magazine and its British version frequently reported on her style throughout the following decade. Alongside model Twiggy, Hepburn has been cited as one of the key public figures who made being very slim fashionable. Vogue has referred to her as "the acme of classic beauty". Her style was also emulated by American singer Ariana Grande in the earlier stages of Grande's career.

Added to the International Best Dressed List in 1961, Hepburn was associated with a minimalistic style, usually wearing clothes with simple silhouettes that emphasised her slim body, such as monochromatic colours with occasional statement accessories. In the late 1950s, Audrey Hepburn popularised plain black leggings. Hepburn was in particular associated with French fashion designer Hubert de Givenchy, who was first hired to design her on-screen wardrobe for her second Hollywood film, Sabrina (1954), when she was still unknown as a film actor and he a young couturier just starting his fashion house. Although initially disappointed that "Miss Hepburn" was not Katharine Hepburn as he had mistakenly thought, Givenchy and Hepburn formed a life-long friendship.

In addition to Sabrina, Givenchy designed her costumes for Love in the Afternoon (1957), Breakfast at Tiffany's (1961), Funny Face (1957), Charade (1963), Paris When It Sizzles (1964), and How to Steal a Million (1966), as well as clothing her off screen. According to Moseley, fashion plays an unusually central role in many of Hepburn's films, stating that "the costume is not tied to the character, functioning 'silently' in the mise-en-scène, but as 'fashion' becomes an attraction in the aesthetic in its own right". She also became the face of Givenchy's first perfume, L'Interdit, in 1957. In addition to her partnership with Givenchy, Hepburn was credited with boosting the sales of Burberry trench coats when she wore one in Breakfast at Tiffany's, and was associated with Italian footwear brand Tod's.

In her private life, Hepburn preferred to wear casual and comfortable clothes, contrary to the haute couture she wore on screen and at public events. Despite being admired for her beauty, she never considered herself attractive, stating in a 1959 interview that "you can even say that I hated myself at certain periods. I was too fat, or maybe too tall, or maybe just plain too ugly... you can say my definiteness stems from underlying feelings of insecurity and inferiority. I couldn't conquer these feelings by acting indecisive. I found the only way to get the better of them was by adopting a forceful, concentrated drive." In 1989, she stated that "my look is attainable ... Women can look like Audrey Hepburn by flipping out their hair, buying the large glasses and the little sleeveless dresses."

Hepburn's influence as a style icon still continues several decades after the height of her acting career in the 1950s and 1960s. Moseley notes that especially after her death in 1993, she became increasingly admired, with magazines frequently advising readers on how to get her look, and fashion designers using her as inspiration. Throughout her career and after her death, Hepburn received numerous accolades for her stylish appearance and attractiveness. For example, she was named the "most beautiful woman of all time" and "most beautiful woman of the 20th century" in polls by Evian and QVC respectively, and in 2015, was voted "the most stylish Brit of all time" in a poll commissioned by Samsung. Her film costumes fetch large sums of money in auctions: one of the "little black dresses" designed by Givenchy for Breakfast at Tiffany's was sold by Christie's for a record sum of £467,200 in 2006.

In 1999, HarperCollins published Audrey's Style by Pamela Keogh, a 340 page tome devoted to Hepburn's personality, beliefs and style. The book included interviews with some of the people who knew her best, and also included many photographs of her, some of which had been rarely seen before.

Filmography and stage roles
Hepburn was considered by some to be one of the most beautiful women of all time. Remembered as a film and style icon, she was ranked as the third greatest screen legend in American cinema by the American Film Institute. Her debut was as a flight stewardess in the 1948 Dutch film Dutch in Seven Lessons. Hepburn then performed on the British stage as a chorus girl in the musicals High Button Shoes (1948), and Sauce Tartare (1949). Two years later she made her Broadway debut as the title character in the play Gigi. Hepburn's Hollywood debut as a runaway princess in William Wyler's Roman Holiday (1953) opposite Gregory Peck made her a star. For her performance she received the Academy Award for Best Actress, the BAFTA Award for Best British Actress, and the Golden Globe Award for Best Actress in a Motion Picture – Drama. In 1954 she played a chauffeur's daughter caught in a love triangle in Billy Wilder's romantic comedy Sabrina opposite Humphrey Bogart and William Holden. In the same year Hepburn garnered the Tony Award for Best Actress in a Play for portraying the titular water nymph in the play Ondine.

Awards and honours
Hepburn received numerous awards and honours during her career. Hepburn won, or was nominated for, awards for her work in motion pictures, television, spoken-word recording, on stage, and humanitarian work. She was five-times nominated for an Academy Award, and she was awarded the 1953 Academy Award for Best Actress for her performance in Roman Holiday and the Jean Hersholt Humanitarian Award in 1993, posthumously, for her humanitarian work. From five nominations, she won a record three BAFTA Awards for Best British Actress in a Leading Role, and received a BAFTA Special Award in 1992.

title: Audrey Hepburn


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United Nations Iraq–Kuwait Observation Mission

The United Nations Iraq–Kuwait Observation Mission (UNIKOM) was established on April 9, 1991 following the Gulf War by Security Council Resolution 689 (1991) and fully deployed by early May 1991.

The task of joint military observers was to monitor the demilitarized zone (DMZ) along the Iraq-Kuwait border and the Khawr 'Abd Allah waterway, deter border violations and report any hostile action. On February 5, 1993, under Security Council Resolution 806, the mandate was extended to include physical action to prevent violations and the force was expanded to an intended three mechanized infantry battalions plus support.

The mandate of UNIKOM was completed on October 6, 2003.

The force's headquarters were in Umm Qasr, Iraq, within the DMZ. The maximum strength of the force was 1,187 on February 28, 1995. The Security Council extended its mandate for a final time in July 2003. The mission ended on September 30, 2003. There were over 135 military observers and civilian staff at the time, mainly protecting the border checkpoints. Ultimately, a new conflict, the War in Iraq, would dissolve the "peacekeeping" mission. Swarms of military equipment would gather in Kuwait and cross into Iraq's borders during the 2003 invasion of Iraq. During the mission, there were 18 fatalities.

Contributors are Argentina, Austria, Bangladesh (including the mechanized infantry battalion), Canada, Chile, China, Denmark, Fiji, Finland, France, Germany, Ghana, Greece, Hungary, India, Indonesia, Ireland, Italy, Kenya, Malaysia, Nigeria, Norway, Pakistan, Philippines, Poland, Romania, Russian Federation (Soviet Union before December 24, 1991), Senegal, Singapore, Sweden, Switzerland, Tanzania, Thailand, Turkey, United Kingdom, United States, Uruguay and Venezuela In addition, during the setting-up phase (April–October 1991), UNIKOM included a Canadian combat engineer regiment (1 CER), a Security Battalion consisting of a multinational Bn Staff (SWE-FIN-NOR) and five infantry companies, drawn from UNFICYP and UNIFIL. Those troops were provided by Austria, Denmark, Fiji, Ghana, Nepal, and United States. There was also a maintenance/repair & recovery unit from Norway and a HQ logistic company from Sweden drawn from UNIFIL.

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


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Inversion (meteorology)

In meteorology, an inversion (or "temperature inversion") is a layer of warmer air held above colder air. Normally, air temperature gradually decreases as altitude increases, but in an inversion this relationship is reversed.

An inversion traps air pollution, such as smog, close to the ground. An inversion can also suppress convection by acting as a "cap". If this cap is broken for any of several reasons, convection of any moisture present can then erupt into violent thunderstorms. Temperature inversion can cause freezing rain in cold climates.

Normal atmospheric conditions
Usually, within the lower atmosphere (the troposphere) the air near the surface of the Earth is warmer than the air above it, largely because the atmosphere is heated from below as solar radiation warms the Earth's surface, which in turn then warms the layer of the atmosphere directly above it, e.g., by thermals (convective heat transfer). Air temperature also decreases with an increase in altitude because higher air is at lower pressure, and lower pressure results in a lower temperature, following the ideal gas law and adiabatic lapse rate.

Description
Under the right conditions, the normal vertical temperature gradient is inverted so that the air is colder near the surface of the Earth. This can occur when, for example, a warmer, less-dense air mass moves over a cooler, denser air mass. This type of inversion occurs in the vicinity of warm fronts, and also in areas of oceanic upwelling such as along the California coast in the United States. With sufficient humidity in the cooler layer, fog is typically present below the inversion cap. An inversion is also produced whenever radiation from the surface of the earth exceeds the amount of radiation received from the sun, which commonly occurs at night, or during the winter when the sun is very low in the sky. This effect is virtually confined to land regions as the ocean retains heat far longer. In the polar regions during winter, inversions are nearly always present over land.

A warmer air mass moving over a cooler one can "shut off" any convection which may be present in the cooler air mass: this is known as a capping inversion. However, if this cap is broken, either by extreme convection overcoming the cap or by the lifting effect of a front or a mountain range, the sudden release of bottled-up convective energy—like the bursting of a balloon—can result in severe thunderstorms. Such capping inversions typically precede the development of tornadoes in the Midwestern United States. In this instance, the "cooler" layer is quite warm but is still denser and usually cooler than the lower part of the inversion layer capping it.

Subsidence inversion
An inversion can develop aloft as a result of air gradually sinking over a wide area and being warmed by adiabatic compression, usually associated with subtropical high-pressure areas. A stable marine layer may then develop over the ocean as a result. As this layer moves over progressively warmer waters, however, turbulence within the marine layer can gradually lift the inversion layer to higher altitudes, and eventually even pierce it, producing thunderstorms, and under the right circumstances, tropical cyclones. The accumulated smog and dust under the inversion quickly taints the sky reddish, easily seen on sunny days.

Atmospheric consequences

Temperature inversions stop atmospheric convection (which is normally present) from happening in the affected area and can lead to high concentrations of atmospheric pollutants. Cities especially suffer from the effects of temperature inversions because they both produce more atmospheric pollutants and have higher thermal masses than rural areas, resulting in more frequent inversions with higher concentrations of pollutants. The effects are even more pronounced when a city is surrounded by hills or mountains since they form an additional barrier to air circulation. During a severe inversion, trapped air pollutants form a brownish haze that can cause respiratory problems. The Great Smog of 1952 in London, England, is one of the most serious examples of such an inversion. It was blamed for an estimated 10,000 to 12,000 deaths.

Sometimes the inversion layer is at a high enough altitude that cumulus clouds can condense but can only spread out under the inversion layer. This decreases the amount of sunlight reaching the ground and prevents new thermals from forming. As the clouds disperse, sunny weather replaces cloudiness in a cycle that can occur more than once a day.

Light
As the temperature of air increases, the index of refraction of air decreases, a side effect of hotter air being less dense. Normally this results in distant objects being shortened vertically, an effect that is easy to see at sunset when the sun is visible as an oval. In an inversion, the normal pattern is reversed, and distant objects are instead stretched out or appear to be above the horizon, leading to the phenomenon known as a Fata Morgana or mirage.

Inversions can magnify the so-called "green flash"—a phenomenon occurring at sunrise or sunset, usually visible for a few seconds, in which the sun's green light is isolated due to dispersion. The shorter wavelength is refracted most, with the blue component of sunlight "completely scattered out by Rayleigh scattering", making green the first or last light from the upper rim of the solar disc to be seen.

Radio waves
Very high frequency radio waves can be refracted by inversions, making it possible to hear FM radio or watch VHF low-band television broadcasts from long distances on foggy nights. The signal, which would normally be refracted up and away into space, is instead refracted down towards the earth by the temperature-inversion boundary layer. This phenomenon is called tropospheric ducting. Along coastlines during Autumn and Spring, due to multiple stations being simultaneously present because of reduced propagation losses, many FM radio stations are plagued by severe signal degradation disrupting reception. In higher frequencies such as microwaves, such refraction causes multipath propagation and fading.

Sound
When an inversion layer is present, if a sound or explosion occurs at ground level, the sound wave is refracted by the temperature gradient (which affects sound speed) and returns to the ground. The sound, therefore, travels much better than normal. This is noticeable in areas around airports, where the sound of aircraft taking off and landing often can be heard at greater distances around dawn than at other times of day, and inversion thunder which is significantly louder and travels further than when it is produced by lightning strikes under normal conditions.

Shock waves
The shock wave from an explosion can be reflected by an inversion layer in much the same way as it bounces off the ground in an air-burst and can cause additional damage as a result. This phenomenon killed two people in the Soviet RDS-37 nuclear test when a building collapsed.

title: Inversion (meteorology)


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Megacity

A megacity is a very large city, typically with a population of more than 10 million people. The United Nations Department of Economic and Social Affairs in its 2018 "World Urbanization Prospects" report defines megacities as urban agglomerations with over 10 million inhabitants. A University of Bonn report holds that they are "usually defined as metropolitan areas with a total population of 10 million or more people". Elsewhere in other sources, from five to eight million is considered the minimum threshold, alongside a population density of at least 2,000 per square kilometre. The terms conurbation, metropolis, and metroplex are also applied to the latter.

The total number of megacities in the world varies between different sources: The world had 33 according to the UN (in 2018), 45 according to CityPopulation.de (in 2023), and 44 according to Demographia (in 2023). About half of these urban agglomerations are in China and India. The other four countries with more than one megacity are Brazil, Japan, Pakistan, and the United States. African megacities are present in Nigeria, Egypt, South Africa, and the DRC; European megacities are present in Russia, France, the United Kingdom, and Turkey (also in Asia); megacities can be found in Latin America in the countries of Brazil, Mexico, Colombia, Peru, and Argentina. Some sources identify Tokyo's Greater Tokyo Area as the largest megacity in the world, while some others give the title to the Pearl River Delta in China.

History
The term "megacity" entered common use in the late 19th or early 20th centuries; one of the earliest documented uses of the term was by the University of Texas in 1904. Initially the United Nations used the term to describe cities of 8 million or more inhabitants, but now uses the threshold of 10 million. In the mid 1970s the term was coined by urbanist Janice Perlman referring to the phenomenon of very large urban agglomerations. In 1800, only 3% of the world's population lived in cities, a figure that rose to 47% by the end of the twentieth century. In 1950, there were 83 cities with populations exceeding one million; by 2007, this number had risen to 468. The UN forecasts that today's urban population of 3.2 billion will rise to nearly 5 billion by 2030, when three out of five, or 60%, of people will live in cities. This increase will be most dramatic on the least-urbanized continents, Asia and Africa. Surveys and projections indicate that all urban growth over the next 25 years will be in developing countries. One billion people, almost one-seventh of the world's population, now live in shanty towns. In many poor countries, overcrowded slums exhibit high rates of disease due to unsanitary conditions, malnutrition, and lack of basic health care. By 2030, over 2 billion people in the world will be living in slums. Over 90% of the urban population of Ethiopia, Malawi and Uganda, three of the world's most rural countries, already live in slums.

By 2025, Asia alone will have at least 30 megacities, including Mumbai, India (2015 population of 20.75 million people), Shanghai, China (2015 population of 35.5 million people), Delhi, India (2015 population of 21.8 million people), Tokyo, Japan (2015 population of 38.8 million people) and Seoul, South Korea (2015 population of 25.6 million people). In Africa, Lagos, Nigeria has grown from 300,000 in 1950 to an estimated 21 million today.

Growth
For almost five hundred years, Rome was the largest, wealthiest, and most politically important city in Europe. It is often stated that its population passed one million people by the end of the 1st century BC, but this is debated since it would have meant an astonishing population density equal to present day, high-rise Hong Kong; other estimates place it well below a half million.

Rome's population started declining in 402 AD when Flavius Honorius, Western Roman Emperor from 395 to 423, moved the government to Ravenna and Rome's population declined to a mere 20,000 during the Early Middle Ages, reducing the sprawling city to groups of inhabited buildings interspersed among large areas of ruins and vegetation.

Baghdad was likely the largest city in the world from shortly after its foundation in 762 AD until the 930s, with some estimates putting its population at over one million. Chinese capital cities Chang'an and Kaifeng also experienced huge population booms during prosperous empires. According to the census in the year 742 recorded in the New Book of Tang, 362,921 families with 1,960,188 persons were counted in Jingzhao Fu (京兆府), the metropolitan area including small cities in the vicinity of Chang'an. The medieval settlement surrounding Angkor, the one-time capital of the Khmer Empire which flourished between the 9th and 15th centuries, could have supported a population of up to one million people.

From around 1825 to 1918 London was the largest city in the world, with the population growing rapidly; it was the first city to reach a population of over 5 million in 1900. In 1950, New York City was the only urban area with a population of over 10 million. Geographers had identified 25 such areas as of October 2005, as compared with 19 megacities in 2004 and only nine in 1985. This increase has happened as the world's population moves towards the high (75–85%) urbanization levels of North America and Western Europe.

Since the 2000s, the largest megacity has been the Greater Tokyo Area. The population of this urban agglomeration includes areas such as Yokohama and Kawasaki, and is estimated to be between 37 and 38 million. This variation in estimates can be accounted for by different definitions of what the area encompasses. While the prefectures of Tokyo, Chiba, Kanagawa, and Saitama are commonly included in statistical information, the Japan Statistics Bureau only includes the area within 50 kilometers of the Tokyo Metropolitan Government Offices in Shinjuku, thus arriving at a smaller population estimate. A characteristic issue of megacities is the difficulty in defining their outer limits and accurately estimating the populations.

Another list defines megacities as urban agglomerations instead of metropolitan areas. As of 2021, there are 28 megacities by this definition, like Tokyo. Other sources list Nagoya and the Rhein-Ruhr as megacities.

Slums
According to the United Nations, the proportion of urban dwellers living in slums or informal settlements decreased from 47 percent to 37 percent in the developing world between 1990 and 2005. However, due to rising population, the absolute number of slum dwellers is rising. The majority of these are located in informal settlements which often lack sufficient quality housing, sanitation, drainage, water access, and officially recognized addresses. The increase in informal settlement population has been caused by massive migration, both internal and transnational, into cities, which has caused growth rates of urban populations and spatial concentrations not seen before in history. These issues raise problems in the political, social, and economic arenas. People who live in slums or informal settlements often have minimal or no access to education, healthcare, or the urban economy.

Crime
As with any large concentration of people, there is usually crime. High population densities often result in higher crime rates, as visibly seen in growing megacities such as Karachi, Delhi, Cairo, Rio de Janeiro, and Lagos.

Homelessness
Megacities often have significant numbers of homeless people. The actual legal definition of homelessness varies from country to country, or among different entities or institutions in the same country or region.

In 2002, research showed that children and families were the largest growing segment of the homeless population in the United States, and this has presented new challenges, especially in services, to agencies.

In the US, the government asked many major cities to come up with a ten-year plan to end homelessness. One of the results of this was a "Housing first" solution, rather than to have a homeless person remain in an emergency homeless shelter it was thought to be better to quickly get the person permanent housing of some sort and the necessary support services to sustain a new home. But there are many complications with this kind of program and these must be dealt with to make such an initiative work successfully in the middle to long term.

Traffic congestion

Traffic congestion is a condition on road networks that occurs as use increases, and is characterized by slower speeds, longer trip times, increased pollution, and increased vehicular queueing. The Texas Transportation Institute estimated that, in 2000, the 75 largest metropolitan areas experienced 3.6 billion vehicle-hours of delay, resulting in 5.7 billion U.S. gallons (21.6 billion liters) in wasted fuel and $67.5 billion in lost productivity, or about 0.7% of the nation's GDP. It also estimated that the annual cost of congestion for each driver was approximately $1,000 in very large cities and $200 in small cities. Traffic congestion is increasing in major cities and delays are becoming more frequent in smaller cities and rural areas.

Urban sprawl

Urban sprawl, also known as suburban sprawl, is a multifaceted concept, which includes the spreading outwards of a city and its suburbs to its outskirts to low-density, auto-dependent development on rural land, with associated design features that encourage car dependency. As a result, some critics argue that sprawl has certain disadvantages including longer transport distances to work, high car dependence, inadequate facilities (e.g. health, cultural. etc.) and higher per-person infrastructure costs. Discussions and debates about sprawl are often obfuscated by the ambiguity associated with the phrase. For example, some commentators measure sprawl only with the average number of residential units per acre in a given area. But others associate it with decentralization (spread of population without a well-defined center), discontinuity (leapfrog development), segregation of uses, etc.

Gentrification
Gentrification and urban gentrification are terms for the socio-cultural changes in an area as a result of wealthier people buying property in a less prosperous community. As living costs rise, lower-income residents are forced to move out of the community leading to an increase in average income, which in turn makes the area more desirable to other wealthier property or business owners, further pushing the living costs up. This process also tends to lead to a decrease in average family size in the area. This type of population change reduces industrial land use when it is redeveloped for commerce and housing.

Air pollution
Air pollution is the introduction into the atmosphere of chemicals, particulate matter, or biological materials that cause harm or discomfort to humans or other living organisms, or damages the natural environment. Many urban areas have significant problems with smog, a type of air pollution derived from vehicle emissions from internal combustion engines and industrial fumes that react in the atmosphere with sunlight to form secondary pollutants that also combine with the primary emissions to form photochemical smog.

Energy and material resources
The sheer size and complexity of megacities gives rise to enormous social and environmental challenges. Whether megacities can develop sustainably depends to a large extent on how they obtain, share, and manage their energy and material resources. There are correlations between electricity consumption, heating and industrial fuel use, ground transportation energy use, water consumption, waste generation, and steel production in terms of level of consumption and how efficiently they use resources.

In fiction
Megacities are a common backdrop in dystopian science fiction, with examples such as the Sprawl in William Gibson's Neuromancer, and Mega-City One, a megalopolis of between 50 and 800 million people (fluctuations due to war and disaster) across the east coast of the United States, in the Judge Dredd comic. In Demolition Man a megacity called "San Angeles" was formed from the joining of Los Angeles, Santa Barbara, San Diego and the surrounding metropolitan regions following a massive earthquake in 2010. Fictional planet-wide megacities (ecumenopoleis) include Trantor in Isaac Asimov's Foundation series of books and Coruscant (population two trillion) in the Star Wars universe.

title: Megacity


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Talk:Alan Bush

Untitled
Do we/you have copyright clearance to reproduce this article?

 * Oh dear, you've been waiting almost 4 years for an answer. Sorry to disappoint you, but you still haven't got one.  Is this some sort of record?  JackofOz 09:40, 8 April 2006 (UTC)

Index
The index ref [10]:6 in a couple of places is confusing. Can someone who understands it have a look? Mike Spathaky (talk) 10:07, 8 August 2016 (UTC)
 * superseded Brianboulton (talk) 18:25, 30 June 2017 (UTC)

Expansion
Work begins today. Let's have a worthwhile article for this significant if largely overlooked 20th century composer. Brianboulton (talk) 11:26, 21 June 2017 (UTC)
 * Done. Letting it rest for a bit. Brianboulton (talk) 18:23, 30 June 2017 (UTC)
 * Well done Brian! This is now an excellent article. Keep as well as you can! Mike Spathaky (talk) 19:54, 30 June 2017 (UTC)

Comments as requested
BB, you asked for my comments on the overhauled article, and here they are: And that's my lot. I don't see how this article could be better done, and not only has it been a pleasure to review: it has sent me off in search of Bush's music, on which you shall hear from me by email or viva voce. –  Tim riley  talk    11:18, 9 July 2017 (UTC)
 * Biography
 * Title of section. In other composer "Life-and-works" articles (e.g. Holst and Britten) we have called this section "Life and career". I see no objection to "Biography" instead, here, but some editors get strangely aerated by it, insisting that the whole article is a biography. I think they"re wrong, but it does no harm to avoid a battle.
 * Family background and early life
 * "the Principal, Sir Alexander Mackenzie" – although, as you may have spotted over the years, I tend to be quite liberal with my capitalisation, I don"t think giving "Principal" one here is in Wikipedia's usual style.
 * Royal Academy and after
 * "He met and befriended a fellow-student, Michael Head, as a result of which Bush met Head's 14-year-old sister" – two meetings. You could perhaps lose the first altogether and start "He befriended".
 * "with whom he became close" – not sure about the preposition. Does one become close with someone?
 * "In 1931, ten years after their first meeting, they would marry" … As a rule I abominate he woulds, it woulds, they woulds and so on, but I suppose it's tolerable here as you are peeking ahead of the chronology.
 * Music and politics
 * "Ian Kemp writes that "Apart from Sibelius…"" An old-fashioned pedant, e.g. me, might object that the "that" leads one to expect oratio obliqua rather than the oratio recta we get here; replacing "that" with a comma would be preferable,
 * "at the rise of Fascism and antisemitism in Germany" – if with a capital F, is Fascism strictly interchangeable with "Nazism" in Germany? The OED steers us in the direction of capitalising the word for Mussolini's shower, but lower-casing it for other right wing rabbles.
 * 1930s: emergent composer
 * "In the following years three daughters were born, after which they moved to a larger house"… – nobody is really going to suppose you mean that the daughters moved on their own, but it might still be better to say "the family moved…"
 * "this remained their home until their respective deaths in the 1990s" – I imagine the deaths are those of Alan and Nancy, rather than the whole family. I might make this something like "….Bush and Nancy lived there until their respective deaths in the 1990s."
 * "caustic comments from the Manchester Guardian's Neville Cardus" – is it just me or is there a touch of tabloidese about this construction? I should prefer to say caustic comments in The Manchester Guardian from Neville Cardus.
 * "Handel's oratorio" – you might link Handel, perhaps.
 * Second World War
 * "Queen's Hall" – another article you might want to link to.
 * Last 12 words of first para: obiter dicta from TR: proof, if proof were needed, of the capriciousness and unreliability of Glock's musical judgment. What a B.F.!
 * Post-war: struggle for recognition and performance
 * "his ODNB biographer" – I think you probably ought to give the ODNB its full title, and perhaps even add a link to the WP article on the ODNB.
 * First para: two "alikes" in quick succession. You could make the second something on the lines of "alienated both the music establishment and the public".
 * "persona non grata"– nobody reading this article is likely to need to be told what persona non grata means, but can bet your boots that some well-meaning ninny will nonetheless think you need to link it to the WP article.
 * "London's Conway Hall" – another construction that seems unnecessarily tabloidese to my eye.
 * Opera ventures
 * "St Christopher's School, Letchworth" – my partner went to school there, and I shall be at risk of a harrumph if I do not point out that its title is St Christopher School, Letchworth (no possessive apostrophe ess) and that it has a WP article you can link to.
 * Mature career
 * Title of section – you and I may be ancient enough to think of one's forties as years of immaturity but I question whether this is a suitable title for a sub-section that starts with Bush aged fifty-two. I might just make this header "1953–1975"
 * "The Guardian's Colin Mason saw in the work similarities with Richard Strauss, and considered it among Bush's best works" – two points here: first a repeat of my previous bleat about The Guardian's Neville Cardus, and secondly, you have "work" twice in the sentence. The first would read equally well if you changed it to "piece"
 * Final years
 * "Sir Edward Downes" – not yet Sir in 1986.
 * To 1945
 * "In contrast to these large-scale works" – Fowler would have us say in contrast with, rather than to.
 * Postwar and beyond
 * "Payne described the Three Concert Studies" – As this is the great and good Anthony Payne who gave us Elgar's Third Symphony he deserves his Christian name and a blue link in the text rather than just in the citation.
 * Many thanks for these comments – all done save one; I will let the ninnies prattle over persona non grata. As to Glock, well, I've softened what he actually said, which was: "The programme did not tell us that we should be faced with a relentless surge of sixth-rate music described as a pianoforte concerto by Khatachurian, or that Shostakovitch's fifth symphony is so long that there seems no reason why it should not be much longer". Sarky bastard or what, eh? Brianboulton (talk) 07:26, 10 July 2017 (UTC)

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External links modified
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 * Added archive https://web.archive.org/web/20160412140116/http://www.alanbushtrust.org.uk/music/operas/jhill.asp?room=Music to http://www.alanbushtrust.org.uk/music/operas/jhill.asp?room=Music

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WP:ERRORS
There's a request at WP:ERRORS to make a change in the TFA blurb. I'm asking here to see if there's support for making the same change in the article lead. Currently: "Bush ... enjoyed considerable success as a student at the Royal Academy of Music (RAM) ... [eight sentences later] ... He taught composition at the RAM for more than 50 years ...". Suggested: "Bush ... enjoyed considerable success as a student at the Royal Academy of Music [or Royal Academy of Music (RAM)] ... He taught composition at the Academy [or Royal Academy] for more than 50 years ...". (The RAM acronym is defined again at the first occurrence below the lead.) - Dank (push to talk) 01:49, 21 December 2018 (UTC)
 * I am the contributor who made the suggestion at ERRORS, but I see no reason why change there requires change here, and think that use of the initialism on the second occurrence here is totally justified. I have removed the redundant second explanation of the acronym in the section "Family background and early life". Kevin McE (talk) 11:50, 21 December 2018 (UTC)

title: Talk:Alan Bush


text:
Gabriel Lamé

Gabriel Lamé (22 July 1795 – 1 May 1870) was a French mathematician who contributed to the theory of partial differential equations by the use of curvilinear coordinates, and the mathematical theory of elasticity (for which linear elasticity and finite strain theory elaborate the mathematical abstractions).

Biography
Lamé was born in Tours, in today's département of Indre-et-Loire.

He became well known for his general theory of curvilinear coordinates and his notation and study of classes of ellipse-like curves, now known as Lamé curves or superellipses, and defined by the equation:

 * $$ \left|\,{x\over a}\,\right|^n + \left|\,{y\over b}\,\right|^n =1 $$

where n is any positive real number.

He is also known for his running time analysis of the Euclidean algorithm, marking the beginning of computational complexity theory. In 1844, using Fibonacci numbers, he proved that when finding the greatest common divisor of integers a and b, the algorithm runs in no more than 5k steps, where k is the number of (decimal) digits of b. He also proved a special case of Fermat's Last Theorem. He actually thought that he found a complete proof for the theorem, but his proof was flawed. The Lamé functions are part of the theory of ellipsoidal harmonics.

He worked on a wide variety of different topics. Often problems in the engineering tasks he undertook led him to study mathematical questions. For example, his work on the stability of vaults and on the design of suspension bridges led him to work on elasticity theory. In fact this was not a passing interest, for Lamé made substantial contributions to this topic. Another example is his work on the conduction of heat which led him to his theory of curvilinear coordinates.

Curvilinear coordinates proved a very powerful tool in Lamé's hands. He used them to transform Laplace's equation into ellipsoidal coordinates and so separate the variables and solve the resulting equation.

His most significant contribution to engineering was to accurately define the stresses and capabilities of a press fit joint, such as that seen in a dowel pin in a housing.

In 1854, he was elected a foreign member of the Royal Swedish Academy of Sciences.

Lamé died in Paris in 1870. His name is one of the 72 names inscribed on the Eiffel Tower.

Books

 * 1818: Examen des différentes méthodes employées pour résoudre les problèmes de géométrie ( Vve Courcier)
 * 1840: Cours de physique de l'Ecole Polytechnique. Tome premier, Propriétés générales des corps—Théorie physique de la chaleur (Bachelier)
 * 1840: Cours de physique de l'Ecole Polytechnique. Tome deuxième, Acoustique—Théorie physique de la lumière (Bachelier)
 * 1840: Cours de physique de l'Ecole Polytechnique. Tome troisième, Electricité-Magnétisme-Courants électriques-Radiations (Bachelier)
 * 1852: Leçons sur la théorie mathématique de l'élasticité des corps solides (Bachelier)
 * 1857: Leçons sur les fonctions inverses des transcendantes et les surfaces isothermes (Mallet-Bachelier)
 * 1859: Leçons sur les coordonnées curvilignes et leurs diverses applications (Mallet-Bachelier)
 * 1861: Leçons sur la théorie analytique de la chaleur (Mallet-Bachelier)

title: Gabriel Lamé


text:
Julius Plücker

Julius Plücker (16 June 1801 – 22 May 1868) was a German mathematician and physicist. He made fundamental contributions to the field of analytical geometry and was a pioneer in the investigations of cathode rays that led eventually to the discovery of the electron. He also vastly extended the study of Lamé curves.

Early years
Plücker was born at Elberfeld (now part of Wuppertal). After being educated at Düsseldorf and at the universities of Bonn, Heidelberg and Berlin he went to Paris in 1823, where he came under the influence of the great school of French geometers, whose founder, Gaspard Monge, had only recently died.

In 1825 he returned to Bonn, and in 1828 was made professor of mathematics.

In the same year he published the first volume of his Analytisch-geometrische Entwicklungen, which introduced the method of "abridged notation".

In 1831 he published the second volume, in which he clearly established on a firm and independent basis projective duality.

Career
In 1836, Plücker was made professor of physics at University of Bonn. In 1858, after a year of working with vacuum tubes of his Bonn colleague Heinrich Geißler, he published his first classical researches on the action of the magnet on the electric discharge in rarefied gases. He found that the discharge caused a fluorescent glow to form on the glass walls of the vacuum tube, and that the glow could be made to shift by applying an electromagnet to the tube, thus creating a magnetic field. It was later shown that the glow was produced by cathode rays.

Plücker, first by himself and afterwards in conjunction with Johann Hittorf, made many important discoveries in the spectroscopy of gases. He was the first to use the vacuum tube with the capillary part now called a Geissler tube, by means of which the luminous intensity of feeble electric discharges was raised sufficiently to allow of spectroscopic investigation. He anticipated Robert Wilhelm Bunsen and Gustav Kirchhoff in announcing that the lines of the spectrum were characteristic of the chemical substance which emitted them, and in indicating the value of this discovery in chemical analysis. According to Hittorf, he was the first who saw the three lines of the hydrogen spectrum, which a few months after his death, were recognized in the spectrum of the solar protuberances.

In 1865, Plücker returned to the field of geometry and invented what was known as line geometry in the nineteenth century. In projective geometry, Plücker coordinates refer to a set of homogeneous co-ordinates introduced initially to embed the space of lines in projective space $$\mathbf{P}^3$$ as a quadric in $$\mathbf{P}^5$$. The construction uses 2×2 minor determinants, or equivalently the second exterior power of the underlying vector space of dimension 4. It is now part of the theory of Grassmannians $$\mathbf{Gr}(k, V)$$ ($$ k $$-dimensional subspaces of an $$n$$-dimensional vector space $$ V$$), to which the generalization of these co-ordinates to $$k \times k $$ minors of the $$ n \times k $$ matrix of homogeneous coordinates, also known as Plücker coordinates, apply. The embedding of the Grassmannian $$\mathbf{Gr}(k, V)$$ into the projectivization $$ \mathbf{P}(\Lambda^k(V))$$ of the $$k$$th exterior power of $$V$$ is known as the Plücker embedding.

Awards
Plücker was the recipient of the Copley Medal from the Royal Society in 1866.

title: Julius Plücker


text:
Sawtooth wave

The sawtooth wave (or saw wave) is a kind of non-sinusoidal waveform. It is so named based on its resemblance to the teeth of a plain-toothed saw with a zero rake angle. A single sawtooth, or an intermittently triggered sawtooth, is called a ramp waveform.

The convention is that a sawtooth wave ramps upward and then sharply drops. In a reverse (or inverse) sawtooth wave, the wave ramps downward and then sharply rises. It can also be considered the extreme case of an asymmetric triangle wave.

The equivalent piecewise linear functions $$x(t) = t - \lfloor t \rfloor$$ $$x(t) = t \bmod 1$$ based on the floor function of time t is an example of a sawtooth wave with period 1.

A more general form, in the range −1 to 1, and with period p, is $$2\left({\frac t p} - \left\lfloor {\frac 1 2} + {\frac t p} \right\rfloor\right)$$

This sawtooth function has the same phase as the sine function.

While a square wave is constructed from only odd harmonics, a sawtooth wave's sound is harsh and clear and its spectrum contains both even and odd harmonics of the fundamental frequency. Because it contains all the integer harmonics, it is one of the best waveforms to use for subtractive synthesis of musical sounds, particularly bowed string instruments like violins and cellos, since the slip-stick behavior of the bow drives the strings with a sawtooth-like motion.

A sawtooth can be constructed using additive synthesis. For period p and amplitude a, the following infinite Fourier series converge to a sawtooth and a reverse (inverse) sawtooth wave:

$$ f = \frac{1}{p}$$ $$x_\text{sawtooth}(t) = a\left(\frac{1}{2} - \frac{1}{\pi}\sum_{k=1}^{\infty} {(-1)}^{k} \frac{\sin(2\pi kft)}{k}\right)$$ $$x_\text{reverse sawtooth}(t) = \frac{2a}{\pi}\sum_{k=1}^{\infty} {(-1)}^{k} \frac{\sin(2\pi kft)}{k}$$

In digital synthesis, these series are only summed over k such that the highest harmonic, Nmax, is less than the Nyquist frequency (half the sampling frequency). This summation can generally be more efficiently calculated with a fast Fourier transform. If the waveform is digitally created directly in the time domain using a non-bandlimited form, such as y = x − floor(x), infinite harmonics are sampled and the resulting tone contains aliasing distortion.

An audio demonstration of a sawtooth played at 440 Hz (A4) and 880 Hz (A5) and 1,760 Hz (A6) is available below. Both bandlimited (non-aliased) and aliased tones are presented.

Applications

 * Sawtooth waves are known for their use in music. The sawtooth and square waves are among the most common waveforms used to create sounds with subtractive analog and virtual analog music synthesizers.
 * Sawtooth waves are used in switched-mode power supplies. In the regulator chip the feedback signal from the output is continuously compared to a high-frequency sawtooth to generate a new duty cycle PWM signal on the output of the comparator.
 * In the field of computer science, particularly in automation and robotics, $$\mathrm{sawtooth}(\theta)=2\arctan(\tan(\frac{\theta}{2}))$$ allows to calculate sums and differences of angles while avoiding discontinuities at 360° and 0°.
 * The sawtooth wave is the form of the vertical and horizontal deflection signals used to generate a raster on CRT-based television or monitor screens. Oscilloscopes also use a sawtooth wave for their horizontal deflection, though they typically use electrostatic deflection.
 * On the wave's "ramp", the magnetic field produced by the deflection yoke drags the electron beam across the face of the CRT, creating a scan line.
 * On the wave's "cliff", the magnetic field suddenly collapses, causing the electron beam to return to its resting position as quickly as possible.
 * The current applied to the deflection yoke is adjusted by various means (transformers, capacitors, center-tapped windings) so that the half-way voltage on the sawtooth's cliff is at the zero mark, meaning that a negative current will cause deflection in one direction, and a positive current deflection in the other; thus, a center-mounted deflection yoke can use the whole screen area to depict a trace. The horizontal frequency is 15.734 kHz on NTSC, 15.625 kHz for PAL and SECAM.
 * The vertical deflection system operates the same way as the horizontal, though at a much lower frequency (59.94 Hz on NTSC, 50 Hz for PAL and SECAM).
 * The ramp portion of the wave must appear as a straight line. If otherwise, it indicates that the current isn't increasing linearly, and therefore that the magnetic field produced by the deflection yoke is not linear. As a result, the electron beam will accelerate during the non-linear portions. This would result in a television image "squished" in the direction of the non-linearity. Extreme cases will show marked brightness increases, since the electron beam spends more time on that side of the picture.
 * The first television receivers had controls allowing users to adjust the picture's vertical or horizontal linearity. Such controls were not present on later sets as the stability of electronic components had improved.

title: Sawtooth wave


text:
Talk:Megacity

A Commons file used on this page or its Wikidata item has been nominated for deletion
The following Wikimedia Commons file used on this page or its Wikidata item has been nominated for deletion: Participate in the deletion discussion at the. —Community Tech bot (talk) 22:59, 3 April 2021 (UTC)
 * SCBD, Jakarta.jpg

Table color
Why are some of the numbers in the table red? -- Beland (talk) 04:27, 28 May 2021 (UTC)
 * It means that the figures don't meet the 10-million criterion to be a megacity.Bluesatellite (talk) 04:35, 28 September 2021 (UTC)

Metropolitan Area, Not City
This states at the very beginning of the article that a megacity is defined as a "city" with a population of 10 million people or more. That is not correct. A megacity is defined as a "metropolitan area" of 10 million people or more, not a "city" of 10 million people or more. New York City, Los Angeles, London, Paris, none of these cities have a population of 10 million people. But they are megacities because their metropolitan populations are at least 10 million people. This is an internet encyclopedia so correct information must always be given. This needs to be changed in the article, which has been locked. 174.78.6.108 (talk) 18:49, 7 March 2022 (UTC)

Semi-protected edit request on 1 April 2023
Changing of a picture of Kolkata because that's quite old and replace with a better one J1234987 (talk) 18:01, 1 April 2023 (UTC)

 * Red question icon with gradient background.svg Not done: it's not clear what changes you want to be made. Please mention the specific changes in a "change X to Y" format and provide a reliable source if appropriate. The person who loves reading (talk) 18:27, 1 April 2023 (UTC)
 * Changing picture of kolkata from 'old' picture to 'New' picture
 * The picture is hereby attached I want to replace with :
 * J1234987 (talk) 04:12, 23 April 2023 (UTC)
 * Panache block1,2,3,4,5 Kolkata.jpg this is the picture, I want to change with. J1234987 (talk) 04:16, 23 April 2023 (UTC)
 * Extended-protection-unlocked.svg Not done: According to the page's protection level you should be able to edit the page yourself. If you seem to be unable to, please reopen the request with further details. The person who loves reading (talk) 04:20, 23 April 2023 (UTC)

Semi-protected edit request on 6 February 2024
In this phrase:

three out of five, or sixty percent, of people

Please replace "sixty percent" with "60%". Other spots in the same paragraph use "47%" and "90%", not "forty-seven percent" and "ninety percent". 123.51.107.94 (talk) 02:11, 6 February 2024 (UTC)
 * ✅ Thanks! NotAGenious (talk) 15:09, 6 February 2024 (UTC)

title: Talk:Megacity