title: Victoria Eugenie of Battenberg

text: Victoria Eugenie grew up in Queen Victoria's household, as the British monarch had reluctantly allowed Beatrice to marry on the condition that she remain her mother's full-time companion and personal secretary. Therefore, she spent her childhood at Windsor Castle, Balmoral, and Osborne House on the Isle of Wight. She was a bridesmaid at the wedding of her cousins, the Duke (later King George V) and Duchess of York on 6 July 1893.


title: Victoria Eugenie of Battenberg

text: When she was six, Victoria Eugenie suffered a severe concussion when she was thrown off her pony at Osborne and hit her head on the ground. Queen Victoria's physicians noticed "dangerous symptoms", such as "evident signs of brain pressure, probably a haemorrhage." Her aunt Victoria, Princess Royal, wrote, "it is so grievous that [Victoria Eugenie] cannot take notice or open her eyes."


title: Victoria Eugenie of Battenberg

text: Victoria Eugenie was close to her grandmother Queen Victoria. She reflected that "having been born and brought up in her home, Queen Victoria was like a second mother to us. She was very kind but very strict, with old fashioned ideas of how children must be brought up." When Victoria Eugenie said, "I think it is time for us to go to bed," Queen Victoria corrected her. "Young woman, a princess should say, 'I think it is time for me to retire. Queen Victoria wrote that "I love these darling children so, almost as much as their own parent" and referred to Victoria Eugenie as "the little treasure."


title: Victoria Eugenie of Battenberg

text: Her father died while on active military service after contracting fever in Africa in 1896. After the death of Queen Victoria in 1901, the Battenbergs moved to London and took up residence in Kensington Palace.


title: Victoria Eugenie of Battenberg

text: In 1905, King Alfonso XIII of Spain made an official state visit to the United Kingdom. Victoria Eugenie's uncle, King Edward VII, hosted a dinner in Buckingham Palace, in honour of the Spanish king. Alfonso was seated between Queen Alexandra and Princess Helena, King Edward's sister. He noticed Victoria Eugenie and asked who the dinner guest with almost white hair was. Everybody knew that King Alfonso was looking for a suitable bride and one of the strongest candidates was Princess Patricia of Connaught, another niece of King Edward. As Princess Patricia seemed not to be impressed by the Spanish monarch, Alfonso indulged his interest in Victoria Eugenie, and so the courtship began. When Alfonso returned to Spain he frequently sent postcards to Victoria Eugenie and spoke of her approvingly. His mother, Queen Maria Cristina, did not like her son's choice, in part because she considered the Battenbergs non-royal because of the obscure origin of Prince Henry's mother, and in part because she wanted her son to marry within her own family. Other obstacles to a marriage were religion (Alfonso was Roman Catholic, and Victoria Eugenie was Anglican); and, the potential problem of haemophilia, the disease that Victoria had transmitted to some of her descendants. Eugenie's brother Leopold was a haemophiliac, so there was a 50% probability that Victoria Eugenie would be a carrier, although the degree of risk was not yet known. Still, if Alfonso married her, their issue could be affected by the disease. Nonetheless, Alfonso was not dissuaded.


title: Victoria Eugenie of Battenberg

text: After a year of rumours about which princess Alfonso would marry, his mother finally acceded to her son's selection in January 1906 and wrote a letter to Victoria Eugenie's mother, telling her about the love Alfonso felt for her daughter and seeking unofficial contact with the king. Some days later at Windsor, King Edward congratulated his niece on her future engagement.


title: Victoria Eugenie of Battenberg

text: Princess Beatrice and her daughter arrived in Biarritz on 22 January and stayed at the Villa Mauriscot where some days later King Alfonso met them. At the Villa Mauriscot, Alfonso and his future bride conducted a chaperoned, three-day romance. Then, Alfonso took Victoria Eugenie and her mother to San Sebastián to meet Queen Maria Cristina. On 3 February, the king left San Sebastian to go to Madrid and Victoria Eugenie and her mother went to Versailles where the Princess would be instructed in the Catholic faith: As the future Queen of Spain, she agreed to convert. The official reception of Victoria Eugenie into the Catholic faith took place on 5 March 1906 at Miramar Palace in San Sebastián.


title: Victoria Eugenie of Battenberg

text: The terms of the marriage were settled by two agreements, a public treaty and a private contractual arrangement. The treaty was executed between Spain and the United Kingdom in London on 7 May 1906 by their respective plenipotentiaries, the Spanish Ambassador to the Court of St. James's, Don Luis Polo de Bernabé, and the British Foreign Secretary, Sir Edward Grey, Bt. Ratifications were exchanged on 23 May following. Among other conditions, the treaty stipulated:BE it known unto all men by these Presents that whereas His Catholic Majesty Alfonso XIII, King of Spain, has judged it proper to announce his intention of contracting a marriage with Her Royal Highness Princess Victoria Eugénie Julia Ena, niece of His Majesty Edward VII, King of the United Kingdom of Great Britain and Ireland and of the British Dominions beyond the Seas, Emperor of India, and daughter of Her Royal Highness the Princess Beatrice Mary Victoria Feodore (Princess Henry of Battenberg)…"Article I." It is concluded and agreed that the marriage between His said Majesty King Alfonso XIII and Her said Royal Highness the Princess Victoria Eugénie Julia Ena shall be solemnized in person at Madrid as soon as the same may conveniently be done. "II." His said Majesty King Alfonso XIII engages to secure to Her said Royal Highness the Princess Victoria Eugénie Julia Ena from the date of her marriage with His Majesty, and for the whole period of the marriage, an annual grant of 450,000 "pesetas". His said Majesty King Alfonso XIII also engages, if, by the will of Divine Providence, the said Princess Victoria Eugénie Julia Ena should become his widow, to secure to her, from the date of his death, an annual grant of 250,000 "pesetas", unless and until she contracts a second marriage, both these grants having already been voted by the "Cortes". The private settlements to be made on either side in regard to the said marriage will be agreed upon and expressed in a separate Contract, which shall, however, be deemed to form an integral part of the present Treaty…"III." The High Contracting Parties take note of the fact that Her Royal Highness the Princess Victoria Eugénie Julia Ena, according to the due tenor of the law of England, forfeits for ever all hereditary rights of succession to the Crown and Government of Great Britain… The treaty's reference to the forfeiture of Victoria Eugénie's British succession rights reflected neither the British government's censure of the alliance nor any made by her. Rather, it was an explicit recognition of the fact that by marrying (and becoming) a Roman Catholic, Victoria Eugénie lost any right to inherit the British crown as a consequence of Britain's Act of Settlement. This exclusion was personal and limited: those among her descendants who do not become Roman Catholic remain in the line of succession to the British Throne.


title: Victoria Eugenie of Battenberg

text: Despite this treaty, concern about the reaction to the marriage and to Victoria Eugénie's conversion among Protestants was accommodated by the British government's decision that King Edward need not grant official consent to the marriage in his Privy Council, despite the fact that his niece was a British subject. Although the Royal Marriages Act of 1772 requires that descendants of King George II obtain the British sovereign's prior permission to marry by Order in Council, an exception exists for descendants of royal daughters who marry "into foreign families". Although the naturalisation of Victoria Eugénie's father in the United Kingdom had been initiated in Parliament a week prior to his marriage to Princess Beatrice, the nuptials were completed before the naturalisation, thus the Government was able to take the position that Victoria Eugénie was not bound by the Royal Marriages Act, and therefore the British king had legal authority neither to authorise nor forbid her marriage.


title: Victoria Eugenie of Battenberg

text: The King did, however, issue a royal warrant which read: "Our Will and Pleasure is and we do hereby declare and ordain that from and after the date of this Warrant our Most Dear Niece Princess Victoria Eugénie Julia Ena, only daughter of Our Most Dear Sister Beatrice Mary Victoria Feodore (Princess Henry of Battenberg) shall be styled entitled and called "Her Royal Highness" before her name and such Titles and Appellations which to her belong in all Deeds Records Instruments or Documents whatsoever wherein she may at any time hereafter be named or described. And We do hereby authorize and empower Our said Most Dear Niece henceforth at all times to assume and use and to be called and named by the Style, Title and Appellation of "Her Royal Highness" accordingly. Given at Our Court of Saint James's, the Third day of April 1906: in the Sixth Year of Our Reign. By His Majesty's Command. M Gladstone" Notice of this warrant was gazetted in the "London Gazette" which read: "Whitehall 3 April 1906. The KING has been graciously pleased to declare and ordain that His Majesty's niece, Her Highness Princess Victoria Eugenie Julia Ena, daughter of Her Royal Highness the Princess Beatrice Mary Victoria Feodore (Princess Henry of Battenberg), shall henceforth be styled and called "Her Royal Highness"; And to command that the said Royal concession and declaration be registered in His Majesty's College of Arms."


title: Victoria Eugenie of Battenberg

text: Princess Victoria Eugenie married King Alfonso XIII at the Royal Monastery of San Jerónimo in Madrid on 31 May 1906. Present at the ceremony were her widowed mother and brothers, as well as her cousins, the Prince and Princess of Wales.


title: Victoria Eugenie of Battenberg

text: After the wedding ceremony, as the royal procession was heading back to the Royal Palace, an assassination attempt was made on the King and Queen when anarchist Mateu Morral threw a bomb from a balcony at the royal carriage. Victoria Eugenie's life was saved because, at the exact moment the bomb exploded, she turned her head in order to see St. Mary's Church, which Alfonso was showing her. She escaped injury, although her dress was spotted with the blood of a guard who was riding beside the carriage. A large statue in front of the Royal Monastery of San Jeronimo commemorates the victims of the bombing of 31 May 1906.


title: Victoria Eugenie of Battenberg

text: After the inauspicious start to her tenure as Queen of Spain, Victoria Eugenie became isolated from the Spanish people and was unpopular in her new land. Her married life improved when she gave birth to a son and heir-apparent to the kingdom, Alfonso, Prince of Asturias. However, while the baby prince was being circumcised, the doctors noted that he did not stop bleeding — the first sign that the infant heir had haemophilia. Victoria Eugenie was the obvious source of the condition, which was inherited by her eldest and youngest sons. Contrary to the response of Emperor Nicholas II of Russia, whose son and heir by another granddaughter of Queen Victoria was similarly afflicted, Alfonso is alleged never to have forgiven Victoria Eugenie nor to have come to terms with what had happened. In all, King Alfonso XIII and Queen Victoria Eugenie had seven children, five sons and two daughters. Neither of their daughters is known to have been a carrier of haemophilia.


title: Victoria Eugenie of Battenberg

text: After the births of their children, Victoria Eugenie's relationship with Alfonso deteriorated, and he had numerous affairs. It has been said that he had a dalliance with the Queen's cousin, Beatrice, Duchess of Galliera, but this is disputed. Then members of the king's circle spread rumours that Beatrice had been expelled because of her bad behaviour, which was not true. All this situation was very painful for the Queen, who could do nothing to help her cousin.


title: Victoria Eugenie of Battenberg

text: Victoria Eugenie devoted herself to work for hospitals and services for the poor, as well as to education. She was also involved in the reorganization of the Spanish Red Cross. In 1929, the city of Barcelona erected a statue of her in a nurse's uniform in honor of her Red Cross work (the statue has since been destroyed). Various Spanish landmarks have been named after Victoria Eugenie. For instance, in 1909, Madrid's stately neoclassical bridge crossing the Manzanares River was named after her as the "Puente de la Reina Victoria". In 1912, the monumental opera house and theater "Teatro Victoria Eugenia" in San Sebastián, Spain, was named after her. In 1920, she launched the Spanish Navy Cruiser Reina Victoria Eugenia which was named after her.


title: Victoria Eugenie of Battenberg

text: She was the 976th Dame of the Royal Order of Queen Maria Luisa. In 1923, the Pope conferred upon her the Golden Rose which was the first time this honor had been awarded to a British princess since 1555 when Pope Julius III conferred one upon Queen Mary I of England. She was also granted the Royal Order of Victoria and Albert by her grandmother, Queen Victoria. The Queen was also awarded the Spanish Red Cross Merit Order (First Class) and the jewelled breast star was paid for by a subscription undertaken by the Corps of Lady Nurses of the Spanish Red Cross.


title: Victoria Eugenie of Battenberg

text: The Spanish royal family went into exile on 14 April 1931 after municipal elections brought Republicans to power in most of the major cities, leading to the proclamation of the Second Spanish Republic. Alfonso XIII had hoped that his voluntary exile might avert a civil war between the Republicans and the Monarchists. The family went to live in France and later Italy. Victoria Eugenie and Alfonso later separated, and she lived partly in the UK and in Switzerland. She purchased a chateau, the Vieille Fontaine, outside Lausanne.


title: Victoria Eugenie of Battenberg

text: In 1938, the whole family gathered in Rome for the baptism at the Palazzo Malta of Alfonso and Victoria Eugenie's son Juan's eldest son, Juan Carlos, by Vatican Cardinal Secretary of State Eugenio Pacelli (who stood in for the dying Pope Pius XI and would himself become Pope Pius XII in a few months). On 15 January 1941, Alfonso, feeling his death was near, transferred his rights to the Spanish crown to his son, the Count of Barcelona. On 12 February, Alfonso suffered a first heart attack. Alfonso died on 28 February 1941. In 1942 Victoria Eugenie was obliged to leave Italy, having become "persona non grata" to the Italian government, according to Harold Tittmann, a U.S. representative at the Vatican at the time, for her "ill-disguised leanings to the Allied cause."


title: Victoria Eugenie of Battenberg

text: Victoria Eugenie returned briefly to Spain in February 1968, to stand as godmother at the baptism of her great-grandson, Infante Felipe, the son of Infante Juan Carlos and Princess Sophia of Greece and Denmark. Felipe became King of Spain after his father, King Juan Carlos I, abdicated in June 2014.


title: Victoria Eugenie of Battenberg

text: Victoria Eugenie died in Lausanne on 15 April 1969, aged 81, exactly 38 years after she had left Spain for exile. She was the last surviving child of Princess Beatrice of the United Kingdom and Prince Henry of Battenberg. The funeral was held in the church of "Sacré Coeur", she was buried in the nearby cemetery Bois-de-Vaux in Lausanne. On 25 April 1985, her remains were returned to Spain and re-interred in the Royal Vault in the Escorial, outside Madrid, next to the remains of her husband, Alfonso XIII, and not far from her sons, Infante Alfonso, Infante Jaime, and Infante Gonzalo.


title: Victoria Eugenie of Battenberg

text: After the death of Spanish dictator Francisco Franco in 1975, the monarchy was restored and Victoria Eugenie's grandson Juan Carlos I became King of Spain; her great-grandson Felipe VI is the current king. Her godchildren included the Prince of Monaco, Queen Fabiola of Belgium, and Cayetana Fitz-James Stuart, 18th Duchess of Alba.


title: Victoria Eugenie of Battenberg

text: Victoria Eugenie's Cartier tiara of diamonds set with pearls (or alternatively with emeralds) was left to her daughter, Infanta Maria Cristina, Countess of Marone. It is now worn by the Queen of Spain. In addition, her Ansorena fleur-de-lis tiara given to her by Alfonso XIII at her wedding has become the most important tiara in the Spanish Royal collection and is worn by the Queen of Spain for important state occasions.


title: Victoria Eugenie of Battenberg

text: That same year, Sotheby's also sold at auction Victoria Eugenie's diamond and pink conch shell bracelet by Cartier for the extraordinary price of $3.4 million.


title: Rhian Brewster

text: Rhian Joel Brewster (born 1 April 2000) is an English professional footballer who plays as a striker for club Sheffield United and the England national under-21 team. In 2017, he was part of the England squad which won the 2017 FIFA U-17 World Cup in India and was awarded the Golden Boot award for ending as the competition's leading goalscorer.


title: Rhian Brewster

text: Brewster was born in Chadwell Heath, Greater London, to a Barbadian father and Turkish Cypriot mother. Brewster attended school at Chadwell Primary School before joining the Chadwell Heath and Shield Academy YFC. At the age of seven, he was scouted by representatives from Chelsea, Arsenal, West Ham United and Charlton Athletic. He ultimately joined Chelsea where he developed his game under coach Michael Beale in the club's academy until the age of 14, whereafter he left to join Premier League rivals Liverpool.


title: Rhian Brewster

text: In 2015, Liverpool signed Brewster from Chelsea following a recommendation by Beale who had taken up a position with the club. Brewster's decision to make the move was motivated in part by his father's influence who believed that he had a better chance of breaking through to the first team through Liverpool's academy than Chelsea's. He initially joined the club's U18 team before being promoted to the U23 squad, where he scored on his debut against Ipswich Town. During his time with the club's academy, Brewster was placed on a special training regime which included one-on-one sessions with former Liverpool and Real Madrid winger, Steve McManaman.


title: Rhian Brewster

text: Brewster was then called up by manager Jürgen Klopp to the first-team for club friendlies in October and November 2016 during which he scored a hat-trick against Accrington Stanley. Later that season, he was named on the bench for Liverpool's Premier League game against Crystal Palace on 23 April 2017, but remained an unused substitute. The following season, during Liverpool's UEFA Youth League match against Spartak Moscow, Brewster was the victim of alleged racist comments from Spartak's captain, Leonid Mironov. An investigation into the incident was opened by UEFA after the match and Brewster later said in an interview with "The Guardian" that it had been the seventh such instance he had experienced, including once before against the same opposition. UEFA later ruled that there was insufficient evidence to take further action against Mironov.


title: Rhian Brewster

text: On 12 January 2018, during an U23 match against Manchester City, Brewster received oxygen and had to be stretchered off the field after landing awkwardly following an aerial challenge. He was later diagnosed with a high ankle sprain and related ligament damage and was ruled out for the remainder of the season. In March, he had to undergo a second operation in order to repair damage to his knee which he sustained during the same incident.


title: Rhian Brewster

text: Towards the end of the season, Brewster was the subject of intense transfer speculation which culminated in Liverpool cancelling a scheduled friendly against Borussia Mönchengladbach after the German club were alleged to have 'tapped him up'.


title: Rhian Brewster

text: In June 2018, Brewster signed a five-year professional contract with Liverpool. He was named in the match squad for the second leg of Liverpool's 2018–19 Champions League semi-final against Barcelona on 7 May 2019, but remained an unused substitute. Despite never having played in a competitive game for the club, Brewster was on the bench again in the 2019 UEFA Champions League Final against Tottenham Hotspur on 1 June 2019 so collected a winner's medal as Liverpool won 2–0.


title: Rhian Brewster

text: He made his competitive debut for the club on 25 September 2019 in an EFL Cup match against Milton Keynes Dons.


title: Rhian Brewster

text: On 7 January 2020, Brewster joined Championship club Swansea City on loan for the remainder of the season, where he reunited with former England U17 manager Steve Cooper. He made his debut for the club in the South Wales derby against Cardiff City on 12 January, which ended in a goalless draw, before scoring his first professional goal in a 2–1 win over Wigan Athletic at the Liberty Stadium six days later.


title: Rhian Brewster

text: In March 2020, the Championship season was temporarily suspended due to the outbreak of the Coronavirus disease. Following the season's restart in June, Brewster scored two goals in a 3–0 win over Middlesbrough, increasing his tally to six goals in 12 games. Brewster finished the season with 11 goals in 22 appearances.


title: Rhian Brewster

text: Brewster returned to Liverpool following his loan spell at Swansea to begin preseason training prior to the beginning of the 2020–21 Premier League campaign. He appeared as a substitute in the 2020 FA Community Shield. The game ended 1–1 and went to penalties, with Brewster hitting the crossbar on his attempt, leading to Arsenal winning the shootout and lifting the trophy.


title: Rhian Brewster

text: On 2 October 2020, Sheffield United announced the signing of Brewster from Liverpool on a five-year deal, for a reported fee of around £23.5 million. The deal includes a buy-back option at £40 million, valid until 30 June 2023.


title: Rhian Brewster

text: On 6 November 2021, Brewster scored his first league goal for Sheffield United in a 3–1 loss away against Blackburn Rovers.


title: Rhian Brewster

text: Brewster is an England youth international and has represented the nation at various youth levels but remains eligible to play for Turkey through his Turkish Cypriot mother and Barbados through his Barbadian father.


title: Rhian Brewster

text: Having previously represented England at U16 level, Brewster scored six goals in five appearances for England U17 in 2016, including a hat-trick against Croatia and a brace against Germany. He then led the nation's attack at 2017 UEFA European Under-17 Championship and featured in the final against Spain. England ultimately lost on penalties with Brewster one of the players who missed his spot-kick. He ended the tournament with a return of three goals in six appearances.


title: Rhian Brewster

text: Later that year, Brewster gained widespread press attention after scoring successive hat-tricks against the United States and Brazil in the quarter-final and semi-finals of the 2017 FIFA U-17 World Cup. He then scored England's opening goal in the final as the team overcame Spain 5–2 to claim the trophy. Brewster's return of eight goals for the tournament saw him win the Golden Boot award for the top scorer and he was also awarded the Bronze Ball for his individual performances. In December 2017, Brewster revealed in an interview with "The Guardian" that his teammate Morgan Gibbs-White was racially abused by a Spanish player during the match with the FA reporting the incident to FIFA.


title: Rhian Brewster

text: On 30 August 2019, Brewster was included in the England U21 squad for the first time and made his debut as a 79th minute substitute during the 3–2 2021 U21 Euro qualifying win against Turkey on 6 September 2019.


title: Rhian Brewster

text: On 7 September 2021, Brewster scored his first U21 goal from the penalty spot during the 2–0 2023 UEFA European Under-21 Championship qualification win over Kosovo U21s at Stadium MK.


title: Rhian Brewster

text: In June 2022, Brewster and Sheffield United teammate Oli McBurnie were charged with common assault by Nottinghamshire Police "in relation to disorder at the conclusion of a game at the City Ground on 17 May 2022". Both players "strenuously denied" the allegations. The charges against Brewster were dropped in July 2022.


title: Rhian Brewster

text: In October 2022, Brewster was subjected to racial abuse on Instagram for a second time having received similar messages in March 2021.


title: Mehmed IV

text: Mehmed IV (; ; 2 January 1642 – 6 January 1693) also known as Mehmed the Hunter () was the Sultan of the Ottoman Empire from 1648 to 1687. He came to the throne at the age of six after his father was overthrown in a coup. Mehmed went on to become the second longest reigning sultan in Ottoman history after Suleiman the Magnificent. While the initial and final years of his reign were characterized by military defeat and political instability, during his middle years he oversaw the revival of the empire's fortunes associated with the Köprülü era. Mehmed IV was known by contemporaries as a particularly pious ruler, and was referred to as gazi, or "holy warrior" for his role in the many conquests carried out during his long reign.


title: Mehmed IV

text: Under Mehmed IV's reign the empire reached the height of its territorial expansion in Europe. From a young age he developed a keen interest in hunting, for which he is known as "avcı" (translated as "the Hunter"). In 1687, Mehmed was overthrown by soldiers disenchanted by the course of the ongoing War of the Holy League. He subsequently retired to Edirne, where he resided and died of natural causes in 1693.


title: Mehmed IV

text: Born at Topkapı Palace, Constantinople, in 1642, Mehmed was the son of Sultan Ibrahim (r. 1640–48) by Turhan Sultan, a concubine of Russian origin, and the grandson of Kösem Sultan of Greek origin. Soon after his birth, his father and mother quarreled, and Ibrahim was so enraged that he tore Mehmed from his mother's arms and flung the infant into a cistern. Mehmed was rescued by the harem servants. However, this left Mehmed with a lifelong scar on his head.


title: Mehmed IV

text: Mehmed ascended to the throne in 1648 at the age of six, during a very volatile time for the Ottoman dynasty. On 21 October 1649, Mehmed along with his brothers Suleiman and Ahmed were circumcised.


title: Mehmed IV

text: Kösem Sultan, Mehmed's grandmother and regent, was suspected of supporting the rebels and plotting to poison the sultan and replace him with his younger half-brother, Suleiman. As a result, Mehmed agreed to sign his grandmother's death warrant in September 1651.


title: Mehmed IV

text: The empire faced palace intrigues as well as uprisings in Anatolia, the defeat of the Ottoman navy by the Venetians outside the Dardanelles, and food shortages leading to riots in Constantinople. It was under these circumstances that Mehmed's mother granted Köprülü Mehmed Pasha full executive powers as Grand Vizier. Köprülü took office on 14 September 1656. Mehmed IV presided over the Köprülü era, an exceptionally stable period of Ottoman history. Mehmed is known as "Avcı", "the Hunter", as this outdoor exercise took up much of his time.


title: Mehmed IV

text: Mehmed's reign is notable for a revival of Ottoman fortunes led by the Grand Vizier Köprülü Mehmed and his son Fazıl Ahmed. They regained the Aegean islands from Venice, and Crete, during the Cretan War (1645–1669). They also fought successful campaigns against Transylvania (1660) and Poland (1670–1674). When Mehmed IV accepted the vassalage of Petro Doroshenko, Ottoman rule extended into Podolia and Right-bank Ukraine. This event would lead the Ottomans into the Russo-Turkish War (1676–1681). His next vizier, Köprülü Mehmed's adopted son Merzifonlu Kara Mustafa, led campaigns against Russia, besieging Chyhyryn in 1678 with 70,000 men. He next supported the 1683 Hungarian uprising of Imre Thököly against Austrian rule, marching a vast army through Hungary and besieged Vienna. At the Battle of Vienna on the Kahlenberg Heights, the Ottomans suffered a catastrophic rout by Polish-Lithuanian forces famously led by King John III Sobieski (1674–1696), and his allies, notably the Imperial army.


title: Mehmed IV

text: In 1672 and 1673, the sultan, who embarked on two Polish-Lithuanian campaigns with serdar-ı ekrem and Grand Vizier Fazıl Ahmed Pasha, and the acquisition of the Kamaniçi Castle, returned to Edirne after the signing of the Bucaş Treaty.


title: Mehmed IV

text: The fire of 4–5 July 1660 was the worst conflagration Istanbul had experienced to that date. It started in Eminönü and spread to most of the historic peninsula, burning much of the city. Even the minarets of Suleiman I's mosque burned. Two-thirds of Istanbul was turned to ash in the conflagration, as many as forty thousand people were killed. Thousands died in the famine and plague which followed the fire. Following the fire, the dynasty expelled Jews from a wide swath of Istanbul, confiscated their synagogues and homes so that in their place the Yeni Cami (New Mosque) and the Spice Bazaar (Egyptian Market) could be built.


title: Mehmed IV

text: On 12 September 1683, the Austrians and their Polish-Lithuanian allies under King John III Sobieski won the Battle of Vienna with a devastating flank attack led by Sobieski's Polish cavalry. The Turks retreated into Hungary, however this was only the beginning of the Great Turkish War, as the armies of the Holy League began their successful campaign to push the Ottomans back to the Balkans.


title: Mehmed IV

text: In May 1675, Mehmed IV's sons Mustafa II and Ahmed III were circumcised and his daughter Hatice Sultan was married. The empire celebrated it with Famous Edirne Festival to mark the occasion. Silahdar Findikli Mehmed Aga described Mehmed as a medium-sized, stocky, white-skinned, sun-burnt face, with a sparse beard, leaning forward from the waist up because he rides a lot.


title: Mehmed IV

text: 1680 witnessed the only known stoning to death of a woman convicted for adultery in Ottoman Istanbul. The unnamed woman was stoned to death on Istanbul's Hippodrome after allegedly being caught alone with a Jewish man, violating Ottoman law which forbade sexual relations between Christian or Jewish men and Muslim women. Mehmed IV witnessed the double execution: he offered the man conversion to Islam so as to avoid being stoned to death (he was beheaded instead).


title: Mehmed IV

text: After the second Battle of Mohács (1687), the Ottoman Empire fell into deep crisis. There was a mutiny among the Ottoman troops. The commander and Grand Vizier, Sarı Süleyman Pasha, became frightened that he would be killed by his own troops and fled from his command, first to Belgrade and then to Istanbul. When the news of the defeat and the mutiny arrived in Istanbul in early September, Abaza Siyavuş Pasha was appointed as the commander and soon afterward as the Grand Vizier. However, before he could take over his command, the whole Ottoman Army had disintegrated and the Ottoman household troops (Janissaries and sipahis) started to return to their base in Istanbul under their own lower-rank officers. Sarı Suleiman Pasha was executed, and Sultan Mehmed IV appointed the commander of Istanbul Straits, Köprülü Fazıl Mustafa Pasha, as the Grand Vizier's regent in Istanbul. Fazıl Mustafa made consultations with the leaders of the army that existed and the other leading Ottoman statesmen.


title: Mehmed IV

text: After these, on 8 November 1687, it was decided to depose Sultan Mehmed IV and to enthrone his brother Suleiman II as the new Sultan. Mehmed was deposed by the combined forces of Janissaries and Sekbans commanded by Osman Pasha. Mehmed was then imprisoned in Topkapı Palace. However, he was permitted to leave the Palace from time to time, as he died in Edirne Palace in 1693. He was buried in Turhan Sultan's tomb, near his mother's mosque in Constantinople. In 1691, a couple of years before his death, a plot was discovered in which the senior clerics of the empire planned to reinstate Mehmed on the throne in response to the ill health and imminent death of his successor, Suleiman II.


title: Mehmed IV

text: Mehmed's favourite harem girl was Gülnuş Sultan, a slave girl and later his wife. She was taken prisoner at Rethymno (Turkish Resmo) on the island of Crete. Their two sons, Mustafa II and Ahmed III, became Ottoman Sultans during 1695–1703 and 1703–1730 respectively.


title: Mehmed IV

text: Mehmed IV had an Haseki Sultan and several secondary concubines. However, the lack of information about them (except for his Haseki) and the relatively low number of children has created controversy over the actual existence of some of them.


title: 30 Days of Night (film)

text: 30 Days of Night is a 2007 American horror film based on the comic book miniseries of the same name. The film was directed by David Slade and stars Josh Hartnett and Melissa George. The story focuses on an Alaskan town beset by vampires as it enters into a 30-day-long polar night.


title: 30 Days of Night (film)

text: "30 Days of Night" was originally pitched as a comic, then as a film, but it was rejected. Years later, Steve Niles showed IDW Publishing the idea and it took off. The film was produced on a budget of $30 million and grossed over $75 million at the box office during its six-week run starting on October 19, 2007. Critical reviews were mixed. The film has since developed a cult following.


title: 30 Days of Night (film)

text: A sequel, "", was released on October 5, 2010, straight to home video. A prequel miniseries, "", was released on FEARnet.com and FEARnet On Demand in 2007. Another sequel miniseries, "", placed chronologically before "Dark Days", was released in 2008.


title: 30 Days of Night (film)

text: The town of Barrow, Alaska, is preparing for its annual "30 Days of Night", a period during the winter with a month-long polar night. As the town gets ready, a stranger rows ashore from a large ship and sabotages the town's communications and transport to the outside world. Barrow's sheriff, Eben Oleson, investigates and also learns that his estranged wife, Stella, missed the last plane out of town and must stay the 30 days. That night, a band of vampires, led by Marlow, attacks and slaughters most of the townspeople, forcing Eben, Stella, Eben's younger brother Jake, and several other survivors to take shelter in a boarded-up house with a hidden attic. Marlow finds the stranger, who believes the vampires are going to turn him into one of them as a reward for his help, locked up in the station. Marlow thanks him for doing what he asked, and then snaps his neck.


title: 30 Days of Night (film)

text: Eighteen days later, when a blizzard hits, the group uses the whiteout to go to the general store for supplies, but is stranded after it ends. While the group heads for the station, Eben creates a diversion by having the vampires chase him to his grandmother's house, where he uses one of her ultraviolet lights to burn the face of Marlow's lover, Iris, so badly that Marlow is forced to kill her. As he escapes, the town snowplow operator, Beau, creates another distraction with his tractor, killing many of the vampires, before trying to blow himself up; when he fails, Marlow crushes his head. Eben arrives at the station, where he is then forced to kill Carter, who was bitten and has become a vampire.


title: 30 Days of Night (film)

text: On Day 27, Stella and Eben see the deputy, Billy, signaling them with a flashlight, and bring him back to the station, after finding out he killed his family to save them from a more painful death. The trio find the others have made for the utilidor, a power and sewage treatment station that still has power, and head over there, but are separated after Stella saves Gail Robbins, a young girl whose family was slaughtered by a vampire named Zurial, who was stalking her. Eben and Billy make it to the utilidor, but are attacked by the vampire Arvin, who bites Billy; Billy knocks Arvin into the heavy-duty shredder, and in doing so, grinds his own hand to a stump by accident, before being killed by Eben because he is starting to turn.


title: 30 Days of Night (film)

text: As the month comes to an end, with the sun due to rise, the vampires start to burn down the town to destroy evidence of their presence, including survivors. Realizing Stella is trapped and that he cannot beat the vampires in his current state, Eben turns himself into a vampire by injecting himself with Billy's infected blood. He confronts Marlow and they get into a vicious fight, before Marlow is finally killed by having a hole punched through his mouth and head, causing the remaining vampires to flee. Knowing he will die soon, Eben and Stella go off to watch the sunrise together, sharing one last kiss. As the sun comes up, Eben's body burns to ash in Stella's arms.


title: 30 Days of Night (film)

text: "30 Days of Night" author Steve Niles conceived of the story in the form of a comic, but after meeting a lack of interest in initial pitches, tried to pitch it as a film. When this did not work out, Niles shelved the idea until he showed it to IDW Publishing. IDW published the comic and Ben Templesmith provided the artwork. When Niles and his agent, Jon Levin, shopped the comic around again as a potential film adaptation, Niles found that the idea "went shockingly well", with Sam Raimi and Senator International picking up the property rights based on the original concept and Templesmith's unique mood and concepts for the vampires.


title: 30 Days of Night (film)

text: Following the publication of the "30 Days of Night" comic book miniseries in 2002, studios, including DreamWorks, MGM, and Senator International, bid in the $1 million range for rights to a potential vampire film based on the story. Raimi expressed interest in adapting the miniseries and was negotiating a production deal with his producing partner Robert Tapert to establish a label with Senator Entertainment, of which Senator International is the sales division. In July 2002, Senator International acquired the rights for "30 Days of Night" in a seven-figure deal with Raimi and Tapert attached as producers.


title: 30 Days of Night (film)

text: By October 2002, Niles was working on adapting "30 Days of Night" for the big screen, keeping the film true to the miniseries, though fleshing out the characters more significantly in the adaptation process. In February 2003, Columbia Pictures partnered with Senator International to work on "30 Days of Night", which was developing under Senator International's newly established production company, Ghost House Pictures. Mike Richardson, the Dark Horse Comics publisher who supported the adaptation project from the beginning, after having turned down an offer to initially publish the project, was attached as executive producer. The following March, Richardson revealed that Steve Niles had turned in the initial draft for the "30 Days of Night" screenplay. In March 2004, however, Columbia Pictures requested that Niles's initial screenplay to be rewritten in preparation for production. Sue Binder, the business manager of Ghost House Pictures, indicated that filming for "30 Days of Night" was still at least a year away, as Ghost House planned to produce three films before the vampire thriller. The following May, Stuart Beattie, one of the writers for "", was rewriting Niles' "30 Days of Night" draft for production. Niles was pleased with Beattie's faithfully rewritten script, which was submitted to the studio in October 2004. Adi Hasak also made uncredited contributions to the script.


title: 30 Days of Night (film)

text: In September 2005, director David Slade was announced to have signed on to "30 Days of Night", which would be distributed by Columbia Pictures mainly in North America and Mandate Pictures in international territories. In March 2006, Slade revealed that screenwriter Brian Nelson, who wrote the screenplay for Slade's previous film "Hard Candy", was writing a new draft of the "30 Days of Night" script, replacing Beattie's draft. The director said that filming would begin in summer 2006 in Alaska and New Zealand.


title: 30 Days of Night (film)

text: In June 2006, Josh Hartnett was as having been cast as the husband of the married couple who serves as the town's sheriff team. Some criticized the choice because the main character (Eben Olemaun, with the last name changed to Oleson for the motion picture adaption) was originally Inuk in the comics. Melissa George joined the "30 Days of Night" cast as a sheriff and wife of Hartnett's character. Danny Huston joined the cast as the leader of the vampires.


title: 30 Days of Night (film)

text: Filming did not begin immediately, but in a September 2006 interview, executive producer Mike Richardson said that "30 Days of Night" would be shot on 35 mm film, though discussion had occurred to shoot the film on Genesis. In an interview prior to filming, Slade explained that the illustrations by Ben Templesmith would be reflected in production design. Slade also considered Nelson's draft to be the most faithful to the graphic novel. He also stated his intention to make a "scary vampire film", of which he did not think many existed. "The rest of them, they fall into all kinds of traps. We're going to try to do our best... and one of the ways we have to do it is be more naturalistic than the graphic novel, because it's very over-the-top," said Slade. Also, concern was expressed that while the vampires needed to communicate, talking might lessen the effect. To counter this, a fictional vampire language, with click consonants, was constructed with the help of a professor of linguistics and the nearby University of Auckland. Slade explained, "we designed this really simple language that didn't sound like any particular accent that you would be aware of, that was based around really simple actions, eating, hunting, yes, no, really basic, because that's what vampires do."


title: 30 Days of Night (film)

text: By February 2007, the production phase was completed, and a rough cut of the film was prepared. In April, composer Brian Reitzell was hired to score the film.


title: 30 Days of Night (film)

text: Brian Reitzell composed the film's score. A soundtrack was released by Invada Records, with an artwork by Marc Bessant in summer 2015 on vinyl.


title: 30 Days of Night (film)

text: To coincide with the film's release, a novelization by Tim Lebbon was published by Pocket Star on September 25, 2007. It is one of six novels based on the franchise.


title: 30 Days of Night (film)

text: "30 Days of Night" was released in 2,855 cinemas in the United States and Canada on October 19, 2007. In its opening weekend, the film grossed $15,951,902, placing first in the box office. The film grossed $39,568,996 in the United States and Canada and $35,735,361 overseas for a total of $75,304,357 worldwide.


title: 30 Days of Night (film)

text: On the review aggregation site Rotten Tomatoes, the film has a 51% score based on 157 reviews, with an average rating of 5.6/10. The site's consensus states: "While "30 Days of Night" offers a few thrills, it ultimately succumbs to erratic execution." Metacritic reports a score of 53 out of 100 from 29 reviews, considered to be mixed or average reviews. Roger Ebert gave the film 2.5 stars out of a possible 4. He criticized several plot holes, such as the vampires moving with supernatural speed in some attacks, but ponderous slowness in others, but also singled out Danny Huston for being "quite convincing" as the vampire leader, and summed up the film as "well-made, well-photographed, and plausibly acted, and is better than it needs to be."


title: 30 Days of Night (film)

text: "30 Days of Night" was released February 26, 2008 on DVD, Blu-ray, and UMD for PlayStation Portable in the United States. DVD sales brought in $26,949,780 in revenue, from 1,429,600 sold DVD units. This does not include Blu-ray sales. The DVD is a single disc and includes eight featurettes, one of which is a full episode of the anime "Blood+". The UK Region 2 release is a two-disc special edition, released in April 2008. Despite being exactly the same as the theatrical release, the BBFC reclassified the film from a 15 to an 18. Though it still only has the eight featurettes on the second disc, it includes a bonus "30 Days of Night" graphic novel.


title: 30 Days of Night (film)

text: A straight-to-DVD sequel entitled "" was released on October 5, 2010. The script for the sequel was written by Steve Niles and Ben Ketai with Ketai also positioned as director. When filming began on October 20, 2009, Rhys Coiro and Mia Kirshner were named as leads, with Kirshner playing the lead vampire villain Lilith. Other cast named included Harold Perrineau, Kiele Sanchez, Diora Baird, Rhys Coiro, and Monique Ganderton. Three days after filming began, Niles revealed that Kiele Sanchez replaced Melissa George in the role of Stella Oleson. The sequel was produced on a lower budget, but being straight-to-video allowed the writers to more closely follow the comic book.


title: 2014–15 Premier League

text: The 2014–15 Premier League (known as the Barclays Premier League for sponsorship reasons) was the 23rd season of the Premier League, the top English professional league for association football clubs, since its establishment in 1992, and the 116th season of top-flight English football overall. The fixtures were announced on 18 June 2014.


title: 2014–15 Premier League

text: Manchester City came into the season as defending champions of the 2013–14 season. Leicester City, Burnley and Queens Park Rangers entered as the three promoted teams.


title: 2014–15 Premier League

text: On 3 May 2015, Chelsea won the title with three games to spare after a 1–0 home win over Crystal Palace. It was their first league title since 2010, their fourth Premier League title and their fifth English league title overall. Holders Manchester City eventually finished second, after a short drop to fourth a few weeks before the final match.


title: 2014–15 Premier League

text: Burnley were the first team to be relegated despite beating Hull City 1–0, while Queens Park Rangers suffered the same fate after a 6–0 demolition by Manchester City the next day. Hull City were the third and final team to be relegated after a draw against Manchester United on the final day of the season.


title: 2014–15 Premier League

text: Manchester City's Sergio Agüero won the Golden Boot with 26 goals, with his teammate Joe Hart clinching a record fourth Golden Glove, having kept 14 clean sheets. Eden Hazard and José Mourinho were named as Player and Manager of the Season respectively.


title: 2014–15 Premier League

text: Twenty teams competed in the league – the top seventeen teams from the previous season and the three teams promoted from the Championship. The promoted teams were Leicester City, Burnley and Queens Park Rangers, returning to the top flight after respective absences of ten years, four years and one year. They replaced Norwich City, Fulham and Cardiff City, ending their respective top-flight spells of three years, thirteen years and one year.


title: Harmonic series (mathematics)

text: In mathematics, the harmonic series is the infinite series formed by summing all positive unit fractions:


title: Harmonic series (mathematics)

text: The first formula_2 terms of the series sum to approximately formula_3, where formula_4 is the natural logarithm and formula_5 is the Euler–Mascheroni constant. Because the logarithm has arbitrarily large values, the harmonic series does not have a finite limit: it is a divergent series. Its divergence was proven in the 14th century by Nicole Oresme using a precursor to the Cauchy condensation test for the convergence of infinite series. It can also be proven to diverge by comparing the sum to an integral, according to the integral test for convergence.


title: Harmonic series (mathematics)

text: Applications of the harmonic series and its partial sums include Euler's proof that there are infinitely many prime numbers, the analysis of the coupon collector's problem on how many random trials are needed to provide a complete range of responses, the connected components of random graphs, the block-stacking problem on how far over the edge of a table a stack of blocks can be cantilevered, and the average case analysis of the quicksort algorithm.


title: Harmonic series (mathematics)

text: The name of the harmonic series derives from the concept of overtones or harmonics in music: the wavelengths of the overtones of a vibrating string are etc., of the string's fundamental wavelength. Every term of the harmonic series after the first is the harmonic mean of the neighboring terms, so the terms form a harmonic progression; the phrases "harmonic mean" and "harmonic progression" likewise derive from music.


title: Harmonic series (mathematics)

text: Beyond music, harmonic sequences have also had a certain popularity with architects. This was so particularly in the Baroque period, when architects used them to establish the proportions of floor plans, of elevations, and to establish harmonic relationships between both interior and exterior architectural details of churches and palaces.


title: Harmonic series (mathematics)

text: The divergence of the harmonic series was first proven in 1350 by Nicole Oresme. Oresme's work, and the contemporaneous work of Richard Swineshead on a different series, marked the first appearance of infinite series other than the geometric series in mathematics. However, this achievement fell into obscurity. Additional proofs were published in the 17th century by Pietro Mengoli and by Jacob Bernoulli. Bernoulli credited his brother Johann Bernoulli for finding the proof, and it was later included in Johann Bernoulli's collected works.


title: Harmonic series (mathematics)

text: The partial sums of the harmonic series were named harmonic numbers, and given their usual notation formula_6, in 1968 by Donald Knuth.


title: Harmonic series (mathematics)

text: in which the terms are all of the positive unit fractions. It is a divergent series: as more terms of the series are included in partial sums of the series, the values of these partial sums grow arbitrarily large, beyond any finite limit. Because it is a divergent series, it should be interpreted as a formal sum, an abstract mathematical expression combining the unit fractions, rather than as something that can be evaluated to a numeric value. There are many different proofs of the divergence of the harmonic series, surveyed in a 2006 paper by S. J. Kifowit and T. A. Stamps.


title: Harmonic series (mathematics)

text: One way to prove divergence is to compare the harmonic series with another divergent series, where each denominator is replaced with the next-largest power of two:


title: Harmonic series (mathematics)

text: Grouping equal terms shows that the second series diverges (because every grouping of convergent series is only convergent):


title: Harmonic series (mathematics)

text: Because each term of the harmonic series is greater than or equal to the corresponding term of the second series (and the terms are all positive), it follows (by the comparison test) that the harmonic series diverges as well. The same argument proves more strongly that, for every positive


title: Harmonic series (mathematics)

text: This is the original proof given by Nicole Oresme in around 1350. The Cauchy condensation test is a generalization of this argument.


title: Harmonic series (mathematics)

text: It is possible to prove that the harmonic series diverges by comparing its sum with an improper integral. Specifically, consider the arrangement of rectangles shown in the figure to the right. Each rectangle is 1 unit wide and formula_11 units high, so if the harmonic series converged then the total area of the rectangles would be the sum of the harmonic series. The curve formula_12 stays entirely below the upper boundary of the rectangles, so the area under the curve (in the range of formula_13 from one to infinity that is covered by rectangles) would be less than the area of the union of the rectangles. However, the area under the curve is given by a divergent improper integral,


title: Harmonic series (mathematics)

text: Replacing each rectangle by the next one in the sequence would produce a sequence of rectangles whose boundary lies below the curve rather than above it.


title: Harmonic series (mathematics)

text: This shows that the partial sums of the harmonic series differ from the integral by an amount that is bounded above and below by the unit area of the first rectangle:


title: Harmonic series (mathematics)

text: Generalizing this argument, any infinite sum of values of a monotone decreasing positive function (like the harmonic series) has partial sums that are within a bounded distance of the values of the corresponding integrals. Therefore, the sum converges if and only if the integral over the same range of the same function converges. When this equivalence is used to check the convergence of a sum by replacing it with an easier integral, it is known as the integral test for convergence.


title: Harmonic series (mathematics)

text: Adding the first formula_2 terms of the harmonic series produces a partial sum, called a harmonic number and


title: Harmonic series (mathematics)

text: These numbers grow very slowly, with logarithmic growth, as can be seen from the integral test. More precisely,


title: Harmonic series (mathematics)

text: where formula_19 is the Euler–Mascheroni constant and formula_20 which approaches 0 as formula_2 goes to infinity.


title: Harmonic series (mathematics)

text: No harmonic numbers are integers, except for One way to prove that formula_6 is not an integer is to consider the highest power of two formula_23 in the range from If formula_24 is the least common multiple of the numbers from then


title: Harmonic series (mathematics)

text: in which only one of the numerators, is odd and the rest are even, and formula_24 is itself even. Therefore, the result is a fraction with an odd numerator and an even denominator, which cannot be an integer. More strongly, any sequence of consecutive integers has a unique member divisible by a greater power of two than all the other sequence members, from which it follows by the same argument that no two harmonic numbers differ by an integer.


title: Harmonic series (mathematics)

text: Another proof that the harmonic numbers are not integers observes that the denominator of formula_6 must be divisible by


title: Harmonic series (mathematics)

text: all prime numbers greater than formula_29, and uses Bertrand's postulate to prove that this set of primes is non-empty. The same argument implies more strongly that, except for formula_30, formula_31, and formula_32, no harmonic number can have a terminating decimal representation. It has been conjectured that every prime number divides the numerators of only a finite subset of the harmonic numbers, but this remains unproven.


title: Harmonic series (mathematics)

text: Just as the gamma function provides a continuous interpolation of the factorials, the digamma function provides a continuous interpolation of the harmonic numbers, in the sense that


title: Harmonic series (mathematics)

text: Many well-known mathematical problems have solutions involving the harmonic series and its partial sums.


title: Harmonic series (mathematics)

text: The jeep problem or desert-crossing problem is included in a 9th-century problem collection by Alcuin, "Propositiones ad Acuendos Juvenes" (formulated in terms of camels rather than jeeps), but with an incorrect solution. The problem asks how far into the desert a jeep can travel and return, starting from a base with formula_2 loads of fuel, by carrying some of the fuel into the desert and leaving it in depots. The optimal solution involves placing depots spaced at distances formula_35 from the starting point and each other, where formula_36 is the range of distance that the jeep can travel with a single load of fuel. On each trip out and back from the base, the jeep places one more depot, refueling at the other depots along the way, and placing as much fuel as it can in the newly placed depot while still leaving enough for itself to return to the previous depots and the base. Therefore, the total distance reached on the formula_2th trip is formula_38


title: Harmonic series (mathematics)

text: where formula_6 is the harmonic number. The divergence of the harmonic series implies that crossings of any length are possible with enough fuel.


title: Harmonic series (mathematics)

text: For instance, for Alcuin's version of the problem, formula_40: a camel can carry 30 measures of grain and can travel one leuca while eating a single measure, where a leuca is a unit of distance roughly equal to . The problem has formula_41: there are 90 measures of grain, enough to supply three trips. For the standard formulation of the desert-crossing problem, it would be possible for the camel to travel formula_42 leucas and return, by placing a grain storage depot 5 leucas from the base on the first trip and 12.5 leucas from the base on the second trip. However, Alcuin instead asks a slightly different question, how much grain can be transported a distance of 30 leucas without a final return trip, and either strands some camels in the desert or fails to account for the amount of grain consumed by a camel on its return trips.


title: Harmonic series (mathematics)

text: In the block-stacking problem, one must place a pile of formula_2 identical rectangular blocks, one per layer, so that they hang as far as possible over the edge of a table without falling. The top block can be placed with formula_44 of its length extending beyond the next lower block. If it is placed in this way, the next block down needs to be placed with at most formula_45 of its length extending beyond the next lower block, so that the center of mass of the top two block is supported and they do not topple. The third block needs to be placed with at most formula_46 of its length extending beyond the next lower block, and so on. In this way, it is possible to place the formula_2 blocks in such a way that they extend formula_48 lengths beyond the table, where formula_6 is the harmonic number. The divergence of the harmonic series implies that there is no limit on how far beyond the table the block stack can extend. For stacks with one block per layer, no better solution is possible, but significantly more overhang can be achieved using stacks with more than one block per layer.


title: Harmonic series (mathematics)

text: In 1737, Leonhard Euler observed that, as a formal sum, the harmonic series is equal to an Euler product in which each term comes from a prime number: formula_50 where formula_51 denotes the set of prime numbers. The left equality comes from applying the distributive law to the product and recognizing the resulting terms as the prime factorizations of the terms in the harmonic series, and the right equality uses the standard formula for a geometric series. The product is divergent, just like the sum, but if it converged one could take logarithms and obtain formula_52


title: Harmonic series (mathematics)

text: Here, each logarithm is replaced by its Taylor series, and the constant formula_53 on the right is the evaluation of the convergent series of terms with exponent greater than one. It follows from these manipulations that the sum of reciprocals of primes, on the right hand of this equality, must diverge, for if it converged these steps could be reversed to show that the harmonic series also converges, which it does not. An immediate corollary is that there are infinitely many prime numbers, because a finite sum cannot diverge. Although Euler's work is not considered adequately rigorous by the standards of modern mathematics, it can be made rigorous by taking more care with limits and error bounds. Euler's conclusion that the partial sums of reciprocals of primes grow as a double logarithm of the number of terms has been confirmed by later mathematicians as one of Mertens' theorems, and can be seen as a precursor to the prime number theorem.


title: Harmonic series (mathematics)

text: Another problem in number theory closely related to the harmonic series concerns the average number of divisors of the numbers in a range from 1 to formula_2, formalized as the average order of the divisor function,


title: Harmonic series (mathematics)

text: The operation of rounding each term in the harmonic series to the next smaller integer multiple of formula_11 causes this average to differ from the harmonic numbers by a small constant, and Peter Gustav Lejeune Dirichlet showed more precisely that the average number of divisors is formula_57 (expressed in big O notation). Bounding the final error term more precisely remains an open problem, known as Dirichlet's divisor problem.


title: Harmonic series (mathematics)

text: Several common games or recreations involve repeating a random selection from a set of items until all possible choices have been selected; these include the collection of trading cards and the completion of parkrun bingo, in which the goal is to obtain all 60 possible numbers of seconds in the times from a sequence of running events. More serious applications of this problem include sampling all variations of a manufactured product for its quality control, and the connectivity of random graphs. In situations of this form, once there are formula_58 items remaining to be collected out of a total of formula_2 equally-likely items, the probability of collecting a new item in a single random choice is formula_60 and the expected number of random choices needed until a new item is collected Summing over all values of formula_58 from formula_2 shows that the total expected number of random choices needed to collect all items where formula_6 is the harmonic number.


title: Harmonic series (mathematics)

text: The quicksort algorithm for sorting a set of items can be analyzed using the harmonic numbers. The algorithm operates by choosing one item as a "pivot", comparing it to all the others, and recursively sorting the two subsets of items whose comparison places them before the pivot and after the pivot. In either its average-case complexity (with the assumption that all input permutations are equally likely) or in its expected time analysis of worst-case inputs with a random choice of pivot, all of the items are equally likely to be chosen as the pivot. For such cases, one can compute the probability that two items are ever compared with each other, throughout the recursion, as a function of the number of other items that separate them in the final sorted order. If items formula_13 and formula_65 are separated by formula_58 other items, then the algorithm will make a comparison between formula_13 and formula_65 only when, as the recursion progresses, it picks formula_13 or formula_65 as a pivot before picking any of the other formula_58 items between them. Because each of these formula_72 items is equally likely to be chosen first, this happens with probability formula_73. The total expected number of comparisons, which controls the total running time of the algorithm, can then be calculated by summing these probabilities over all pairs, giving formula_74


title: Harmonic series (mathematics)

text: The divergence of the harmonic series corresponds in this application to the fact that, in the comparison model of sorting used for quicksort, it is not possible to sort in linear time.


title: Harmonic series (mathematics)

text: is known as the alternating harmonic series. It is conditionally convergent by the alternating series test, but not absolutely convergent. Its sum is the natural logarithm of 2.


title: Harmonic series (mathematics)

text: Using alternating signs with only odd unit fractions produces a related series, the Leibniz formula for


title: Harmonic series (mathematics)

text: which for formula_79 would be the harmonic series. It can be extended by analytic continuation to a holomorphic function on all complex numbers where the extended function has a simple pole. Other important values of the zeta function include the solution to the Basel problem, Apéry's constant proved by Roger Apéry to be an irrational number, and the "critical line" of complex numbers with conjectured by the Riemann hypothesis to be the only values other than negative integers where the function can be zero.


title: Harmonic series (mathematics)

text: where the values formula_81 are independent and identically distributed random variables that take the two values formula_82 and formula_83 with equal It converges with probability 1, as can be seen by using the Kolmogorov three-series theorem or of the closely related Kolmogorov maximal inequality. The sum of the series is a random variable whose probability density function is for values between and decreases to near-zero for values greater or less Intermediate between these ranges, at the the probability density is formula_84 for a nonzero but very small value


title: Harmonic series (mathematics)

text: The depleted harmonic series where all of the terms in which the digit 9 appears anywhere in the denominator are removed can be shown to converge to the value . In fact, when all the terms containing any particular string of digits (in any base) are removed, the series converges.


title: PFC CSKA Moscow

text: Professional Football Club CSKA (, derived from the historical name 'Центральный спортивный клуб армии', English: "Central Sports Club of the Army"), commonly referred to as CSKA Moscow or "CSKA Moskva" outside of Russia, or simply as CSKA (), is a Russian professional football club. It is based in Moscow, playing its home matches at the 30,000-capacity VEB Arena. It plays in red and blue colours, with various plain and striped patterns having been used.


title: PFC CSKA Moscow

text: Founded in 1911, CSKA is one of the oldest football clubs in Russia and it had its most successful period after World War II with five titles in six seasons. It won a total of 7 Soviet Top League championships and 5 Soviet Cups, including the double in the last season in 1991. The club has also won 6 Russian Premier League titles as well as 7 Russian Cups.


title: PFC CSKA Moscow

text: CSKA Moscow became the first club in Russia to win one of the European cup competitions, the UEFA Cup, after defeating Sporting CP in the final in Lisbon in 2005.


title: PFC CSKA Moscow

text: CSKA was the official team of the Soviet Army during the communist era. Since the dissolution of the Soviet Union it has become privately owned. In 2012, the Ministry of Defence sold all of its shares (24,94%) to Bluecastle Enterprises Ltd, a conglomerate owning 100% of the club since then. On 13 December 2019, state-owned development corporation VEB.RF announced they will take control of over 75% of club shares that were used as collateral by previous owners for the VEB Arena financing. Russian businessman Roman Abramovich's Sibneft corporation was a leading sponsor of the club from 2004 to 2006.


title: PFC CSKA Moscow

text: After the 2022 Russian invasion of Ukraine, the European Club Association suspended the team, along with all Russian club and national teams, from participation in European competition. Due to the Western sanctions the Governmental Investments Bank VEB.RF has sold the club to Trinfiko Investments company.


title: PFC CSKA Moscow

text: CSKA Moscow was founded in 1911 and, like many clubs in the former Soviet Union, has seen a number of name changes. From 1928 to 1950 the association was called "CDKA Moscow" (). In 1951 its name was changed to "CDSA Moscow" (). In 1957 the sports society was renamed again into "CSK MO Moscow" (). The current name of club’s football department, "PFC CSKA Moscow" () has been used since 1994.


title: PFC CSKA Moscow

text: The history of CSKA football club began in 1911, when a football section was organized in the Amateur Society of Skiing Sports (OLLS).


title: PFC CSKA Moscow

text: After the 1917 season, part of the reserve OLLS team moved to the first. In 1921, the champion of the autumn Moscow championship (winner of Fulda Cup) was determined in the final match, in which teams OLLS and KFS took part. The KFS team won 6:0. In the 1922 season, OLLS players won the spring Moscow championship and took second place in the fall championship. In the same year, OLLS won KFS-Kolomyagi Cup, in the final of which, according to the regulations, the winners of the first and second leagues of the Moscow championship met, and Tosmen Cup, where the champions of Moscow and Petrograd met.


title: PFC CSKA Moscow

text: The club had its most successful period immediately after the end of the Second World War. At this time, one of the best players in its history and the best scorer in the history of the team, Grigory Fedotov, played for the club. The army men were runners-up in the first edition of the resumed Vysschaya Liga in 1945.


title: PFC CSKA Moscow

text: Three consecutive championship titles followed for the first time in league history, including club’s first double in 1948. This year the army team won their second USSR Cup. In the semifinals, as a result of a replay, CDKA snatched victory from Dynamo Moscow, and in the final they defeated the current cup holders, Spartak. After finishing second in 1949, in 1950, the army team became champions again, and in 1951, playing under the new name CDSA (Central House of the Soviet Army), they won a double again, winning both the championship and the cup. The history of the football department from this time is closely linked to the ice hockey department of the club, HC CSKA Moscow, because the leading players like Vsevolod Bobrov played both sports in parallel.


title: PFC CSKA Moscow

text: After successful times Olympic Games 1952 in Helsinki marked the beginning of the decline of CDSA Moscow. The club's players formed the core of the national team, which, after tough negotiations, joined FIFA shortly before the Olympic football tournament. Boris Arkadiev became the coach of both the national team and the army club. The first meeting between the Soviet Union and Yugoslavia in football is still amongst the most famous matches. On the political level, the Soviet leader Joseph Stalin and the Yugoslav leader Josip Tito split in 1948, which resulted in Yugoslavia being excluded from the Communist Information Bureau. Before the match, both Tito and Stalin sent telegrams to their national teams, which showed just how important it was for the two head of states. Yugoslavia led 5–1, but a Soviet comeback in the last 15 minutes resulted in a 5–5 draw. The match was replayed, Yugoslavia winning 3–1. The defeat to the archrivals hit Soviet football hard, especially CDSA and its players. After just three games played in the season, CDSA was forced to withdraw from the league and later disbanded. Furthermore, Boris Arkadiev was stripped of his Merited Master of Sports of the USSR title. For intelligence chief Lavrentiy Beria, the Olympic elimination was the perfect opportunity to eliminate the successful city rival. As head of the KGB, he was also honorary president of Dynamo Moscow - the main rival of CDSA.


title: PFC CSKA Moscow

text: After two seasons of oblivion and after Stalin’s death in the spring of 1953 CDSA Moscow was re-established in 1954 on the initiative of then Soviet Defense Minister Nikolai Bulganin. Shortly thereafter, the team won the Soviet Cup in 1955, defeating Dynamo Moscow in the final with the legendary goalkeeper Lev Yashin being sent off. The fans had to wait 15 years for the next trophy. In 1970 season, CSKA became Soviet champions for the sixth time, gaining the same number of points with Dynamo. The first gold match held on December 5, 1970 in Tashkent, Uzbek SSR ended without goals. The next day CSKA won the second match against Dynamo 4:3 after 1:3 deficit. By winning the championship, CSKA qualified for the first round of the European Cup. CSKA defeated Turkish club Galatasaray in the first round, but lost to Belgian champion Standard Liège in the second round and was eliminated from the tournament.


title: PFC CSKA Moscow

text: With only 19 points out of a possible 68 in the 1984 season, the club had to endure the first ever relegation to the second division, where CSKA spent two seasons. After returning to the Higher league, the club did not manage to stay in it for a long time, and in the 1987 season, a second relegation followed. Nevertheless CSKA was able to fight its way back after two seasons in the First League, immediately secured the runner-up and even won the last edition of the football championship of the Soviet Union in the 1991 season. Having also won the Soviet cup, the club thus secured the last golden double in the history of the USSR football. With the championship title from the 1991 season, CSKA Moscow qualified for the first round of the 1992–93 UEFA Champions League, where they defeated the Icelandic team Víkingur Reykjavík. In the second round the Spanish top club Barcelona with coach Johan Cruyff was defeated. The opponents in Group A were the current Champions League winners Olympique Marseille, Glasgow Rangers and Club Brugge. CSKA was unable to build on the results of the matches with Barcelona, becoming the fourth in the group with two draws and four defeats, and was eliminated from the tournament.


title: PFC CSKA Moscow

text: CSKA Moscow was one of the founding members of the newly formed Russian Top Division after the dissolution of the Soviet Union. In the first six seasons, the team occupied the places in the middle of the table. In the 1998 season, the club was runner-up and in the next season finished third. In the following two seasons, CSKA Moscow again occupied places in the middle of the table. In the 2002 season, the team trained by Valery Gazzaev took second place again, winning the Russian Cup. In 2003, the team won its first championship in the history of the Russian Premier League. After that, the head coach Valery Gassayev was sacked surprisingly and the Portuguese coach Artur Jorge was signed as his successor. Under the new coach, the team could not build on the performances from the previous season. After falling to fifth place in July 2004, Arthur Jorge was sacked after only eight months at the helm of the club. After the return of Valery Gassaev, CSKA was able to save the season and become vice-champion.


title: PFC CSKA Moscow

text: In the 2004 season, after qualifying for the UEFA Champions League, the team finished third at the group stage and therefore took part in the UEFA Cup play-off. The UEFA Cup for CSKA began with a home match against Portugal's Benfica in the round of 32, which ended in a 2-0 victory for CSKA, in the away match CSKA drew 1-1. The next rival of CSKA was the Serbian club Partizan, the away match in Belgrade ended with a score of 1-1, and the home match in Krasnodar - 2-0 in favor of the red-blue team. In the next round, the army team defeated the French side Auxerre 4-0. Despite the 2-0 away defeat, CSKA was able to continue playing in the UEFA Cup. In the semifinals, CSKA’s opponent was the Italian side Parma, after beating which (0-0, 3-0), the Muscovites reached the final.


title: PFC CSKA Moscow

text: Then, on May 18, 2005, the team became the first Russian team ever to win a European competition, the 2004-05 UEFA Cup at the José Alvalade Stadium in Lisbon, Portugal, winning Sporting 3-1. The team failed to consolidate their success, losing the UEFA Super Cup to English club Liverpool on 26 August 2005 at Stade Louis II, in Monaco. Nevertheless, this year, CSKA become the first Russian club to complete a treble after winning the second Russian championship title and the Russian Cup.


title: PFC CSKA Moscow

text: The team had qualified for the third qualifying round of the 2006–07 UEFA Champions League by winning the championship in 2005 and progressed to the group stage over MFK Ružomberok. At the group stage, CSKA finished in third place and qualified for the round of 32 in the UEFA Cup, but was eliminated there against the Israeli representative Maccabi Haifa. In the 2006 season, CSKA won domestic treble, as the team won all three national titles: the Premier League, the Russian Cup and the Russian Super Cup.


title: PFC CSKA Moscow

text: As Russian champions, CSKA qualified for the 2007–08 UEFA Champions League. At the group stage, CSKA finished fourth and last with just one draw out of five defeats and was eliminated. In the Premier League, CSKA occupied the third place, but won the Russian Super Cup.


title: PFC CSKA Moscow

text: In the first half of the 2008 season, CSKA played below expectations and even finished in seventh place at the break of the season. After the European Championship, Valery Gazzaev, who announced his retirement at the end of the season, switched the game tactics to four defenders and let the young Alan Dzagoev, who was considered one of the greatest talents in Russian football, show himself. As a result, CSKA ended its negative series and from then on showed effective football. But it was no longer enough to win the championship, and CSKA took the runner-up behind Rubin Kazan. In the 2008-09 UEFA Cup, CSKA was the only team to achieve twelve points from four group matches. Then the team advanced to the round of 16, where they were defeated by the eventual UEFA Cup winners Shakhtar Donetsk from Ukraine after a 1-0 home win and subsequent 0-2 away defeat. The team also won the Russian Cup for the fourth time.


title: PFC CSKA Moscow

text: In January 2009, the Brazilian Zico took over the position of head coach at CSKA. After the half of the 2009 season, the club was only fourth. At the end of the 2009 season, fifth place was just enough for participation in the 2010-11 UEFA Europa League. As a result, the Brazilian head coach was dismissed in September 2009. In the same month, the Spaniard Juande Ramos was signed as his successor, but only lasted 47 days before being released on October 26 and replaced by Leonid Slutsky. The club won the Russian Supercup for the fourth time and became the Russian Cup winner for the fifth time. The team had also qualified for the quarter-finals of the Champions League for the first time after defeating Sevilla FC 3–2 on aggregate. They were later eliminated from competition by the eventual winners Inter Milan, losing by 1–0 scorelines in both Milan and Moscow.


title: PFC CSKA Moscow

text: Leonid Slutsky was introduced as the new head coach in October 2009. In the 2010 Russian Premier League season, the team was runner-up. In the Russian Cup, the team was eliminated in the round of 32 against the second division Ural Ekaterinburg. In the Europa League, CSKA made it to the round of 16, where the team lost to the eventual winners Porto after two defeats (0-1 and 1-2).


title: PFC CSKA Moscow

text: Finishing as the runners-up in the previous season, the club qualified for the group stage of the 2011–12 UEFA Champions League. The opponents in Group B were Inter Milan, Trabzonspor and Lille. On 7 December 2011, CSKA qualified for the knockout phase after winning crucial 3 points by defeating Inter Milan with scoreline 1–2 in Milan and finishing as the runners-up in the group behind the Milanese. In the round of 16 the team met Spanish top club Real Madrid, to which CSKA lost 2-5 on aggregate. In the 2011–12 Russian championship, CSKA could only reach third place despite finishing second after the first phase of the season. By the 100th anniversary of the club, CSKA could not leave its fans without a trophy and won its sixth Russian Cup, beating Alania Vladikavkaz in the final 2-1 on May 22, 2011.


title: PFC CSKA Moscow

text: In the 2012–13 season, CSKA took part in the play-off round of the 2012–13 UEFA Europa League, where they were eliminated against Swedish side AIK after 1-0 in Moscow and 0-2 in Stockholm. At the end of the season, however, CSKA were crowned the champions of Russia. It was the eleventh championship title in club history. The team won the Russian Cup and thus achieving a double.


title: PFC CSKA Moscow

text: As Russian champions CSKA took part in the 2013–14 UEFA Champions League. The club was eliminated from the competition after the group stage against Bayern Munich, Manchester City and Viktoria Plzeň with only one win and five defeats resulting in the fourth place. In the domestic League, however, the club celebrated the second championship title in a row after Zoran Tošić scored the decisive goal against Lokomotiv Moscow on the last Matchday of the season for the tenth victory in the league in a row.


title: PFC CSKA Moscow

text: In the 2015–16 season, CSKA advanced to the Champions League group stage over Sparta Prague and Sporting. With PSV Eindhoven, Manchester United and Wolfsburg, CSKA completed Group B of the competition, but wasn’t able to advance to the round of 16. In the Premier League, the club started with six consecutive wins, with the first four games being won without conceding a single goal. At the end of the season, the army club finished two points ahead of the second-placed Rostov and won its sixth Russian title (and 13th overall).


title: PFC CSKA Moscow

text: As a result, CSKA took part in the group stage of the 2016–17 UEFA Champions League. Opponents in Group E were Monaco, Bayer Leverkusen and Tottenham Hotspur. On 6 October 2016, during the group stage, Finland announced that Roman Eremenko had been handed a 30-day ban from football by UEFA, with UEFA announcing on 18 November 2016, that Eremenko had been handed a two-year ban from football due to testing positive for cocaine.


title: PFC CSKA Moscow

text: Following the ban of one of the team leaders CSKA couldn't win a single game and was therefore eliminated from the tournament. After the last group game against Tottenham and after a negative run in the league, longtime head coach Leonid Slutsky left the club at his own request.


title: PFC CSKA Moscow

text: On 12 December, Viktor Goncharenko was announced as the club's new manager, signing a two-year contract.


title: PFC CSKA Moscow

text: As CSKA finished second in the 2016–17 Premier League, they started their way in the 2017–18 UEFA Champions League from the third qualifying round, defeating AEK Athens there and then Young Boys in the play-off round. In Group A, the army club met Benfica, Manchester United and Basel and finished in third place. As a result, CSKA continued to play in the Europa League and advanced to the quarter-finals, losing to Arsenal.


title: PFC CSKA Moscow

text: On 21 July 2018, Goncharenko extended his contract until the end of the 2019/20 season. During the summer of 2018 CSKA lost many of its leaders: Aleksei and Vasili Berezutski and Sergey Ignashevich finished their careers as professional players; Alexandr Golovin was bought by AS Monaco; Pontus Wernbloom became a PAOK player and Bibras Natcho went to Olympiacos. However, at the start of that season CSKA showed good results, being at the top-three in Russian champions table and beating Real Madrid in Champions League group stage in both home and away matches (1–0 in Moscow and 3–0 in Madrid).


title: PFC CSKA Moscow

text: On 13 December 2019, state-owned development corporation VEB.RF announced they will take control of over 75% of club shares that were used as collateral by previous owners for the VEB Arena financing.


title: PFC CSKA Moscow

text: On 23 March 2021, CSKA appointed their former striker Ivica Olić as their new head coach. After just nine games, culminating in a 6th place finish in the 2020–21 Russian Premier League, missing the European competitions for the first time in 20 years, Olić left CSKA by mutual consent on 15 June 2021 with Aleksei Berezutski being placed in temporary charge. On 19 July 2021, Berezutski was confirmed as CSKA's new permanent head coach.


title: PFC CSKA Moscow

text: In February 2022, CSKA were hit by sanctions from the United States Department of the Treasury as a consequence of the ongoing Russian invasion of Ukraine. CSKA is owned by Russian state-controlled VEB and was sanctioned as its asset. In addition, the European Club Association suspended the team. CSKA won season-best 6 consecutive league games (last two before the winter break and the first four after), Berezutski was selected league's coach of the month for March 2022 and the club moved up to the 3rd position in the standings within 6 points of league-leading Zenit Saint Petersburg. However, CSKA won only twice in the remaining 8 games of the league season and finished in 5th place. On 15 June 2022, Berezutski left his role as Head Coach after his contract was terminated by mutual agreement, with Vladimir Fedotov being appointed as the clubs new Head Coach the same day.


title: PFC CSKA Moscow

text: CSKA had its own stadium called "Light-Athletic Football Complex CSKA" and abbreviated as LFK CSKA. Its capacity is very small for a club of its stature; no more than 4,600 spectators.


title: PFC CSKA Moscow

text: Between 1961 and 2000, CSKA played their home games at the Grigory Fedotov Stadium. In 2007, the Grigory Fedotov Stadium was demolished in 2007, and ground was broken on the club's new stadium Arena CSKA later the same year. During construction of their new stadium, CSKA played the majority of their games at the Arena Khimki and Luzhniki Stadium. After several delays in its construction, Arena CSKA was official opened on 10 September 2016.


title: PFC CSKA Moscow

text: On 28 February 2017, CSKA Moscow announced that they had sold the naming rights to the stadium to VEB, with the stadium becoming the VEB Arena.


title: PFC CSKA Moscow

text: In 2018, CSKA decided to play its home UEFA Champions League matches at Luzhniki Stadium, instead of VEB Arena.


title: PFC CSKA Moscow

text: Had international caps for their respective countries. Players whose name is listed in bold represented their countries while playing for CSKA.


title: PFC CSKA Moscow

text: CSKA Moscow fans maintain good relations with the fans of Serbian Partizan, Greek PAOK FC, Polish Widzew Łódź and fellow Russian fans of Dynamo Moscow.


title: PFC CSKA Moscow

text: CSKA was nicknamed "Horses "because the first stadium was built on the old racecourse/hippodromo in Moscow. It was considered offensive, but later it was transformed into "The Horses", and currently this nickname is used by players and fans as the name, along with other variants such as "Army Men" () and "Red-Blues" ().


title: PFC CSKA Moscow

text: CSKA's women's football team was founded in 1990 and competed in Soviet Championship's second level. Following the dissolution of the Soviet Union that same year, it registered in the Russian Supreme Division, where it competed for two seasons before it folded.


title: PFC CSKA Moscow

text: Following the disbanding of Zorky Krasnogorsk near the end of the 2015 Top Division, FK Rossiyanka filled its vacancy for the next season and the new team was registered as CSKA in the 2016 championship. Its first game, a 1–1 draw against Chertanovo, coincided with the 93rd anniversary of the CSKA's first football match. CSKA ended the championship second-to-last, while Rossiyanka won its fifth title.


title: PFC CSKA Moscow

text: In July 2017, during the inter-season summer pause, it became a CSKA official section. Two months later the team won its first title after defeating Chertanovo 1–0 in the Russian Cup final.


title: PFC CSKA Moscow

text: In recent years CSKA Women won two Russian championships in a row, in 2019 and 2020 and made their debut in UEFA Women's Champions League.


title: PFC CSKA Moscow

text: The reserves team played on the professional level as FC CSKA-d Moscow (Russian Second League in 1992–93, Russian Third League in 1994–97, Russian Second Division in 1998–00, in 1998–00 team was called FC CSKA-2 Moscow). A separate farm club called FC CSKA-2 Moscow played in the Soviet Second League in 1986–89, Soviet Second League B in 1990–91, Russian Second League in 1992–93 and Russian Third League in 1994. That latter team was called FC Chaika-CSKA-2 Moscow for one season in 1989.


title: Miller's Crossing

text: Miller's Crossing is a 1990 American neo-noir gangster film written, directed and produced by the Coen brothers and starring Gabriel Byrne, Marcia Gay Harden, John Turturro, Jon Polito, J. E. Freeman, and Albert Finney. The plot concerns a power struggle between two rival gangs and how the protagonist, Tom Reagan (Byrne), plays both sides against each other.


title: Miller's Crossing

text: In 2005, "Time" chose "Miller's Crossing" as one of the 100 greatest films made since the inception of the periodical. "Time" critic Richard Corliss called it a "noir with a touch so light, the film seems to float on the breeze like the frisbee of a fedora sailing through the forest".


title: Miller's Crossing

text: Tom Reagan is the right-hand man for Irish mobster Leo O'Bannon, a political boss who runs an unnamed U.S. city during Prohibition. Leo sets off a mob war when he extends protection to his girlfriend's brother, a bookie named Bernie Bernbaum, who is skimming off of the match fixing scheme of Leo's rival, the Italian gangster Johnny Caspar. The situation is further complicated by the fact that behind Leo's back, the girlfriend, Verna, is also sleeping with Tom.


title: Miller's Crossing

text: Despite his own relationship with Verna, Tom presses Leo to give up her brother to Caspar. When the war heats up, with an assassination attempt on Leo, Tom tries to persuade Leo that he is foolish to protect Bernie on Verna's behalf, making the point by revealing his affair with her. Leo publicly beats up Tom and cuts ties with both him and Verna.


title: Miller's Crossing

text: Cast out and needing work, Tom turns to Caspar. As a loyalty test, Caspar commands Tom to kill Bernie, an awkward request given Tom’s relationship with Bernie’s sister. With Caspar’s henchmen in tow, Tom leads Bernie to his execution in the woods at a spot called Miller’s Crossing. Bernie grovels for his life, pleading "Look in your heart". Tom fakes the killing by firing his gun into the ground and orders Bernie to leave town. Caspar’s henchmen, who are within earshot but cannot see the two men, are fooled and neglect to check for the body before leaving with Tom.


title: Miller's Crossing

text: With Leo weakened, Caspar takes his place as city boss, controlling the police and using them to destroy Leo's operations.


title: Miller's Crossing

text: Within Caspar’s gang, there is tension between Tom and Caspar’s trusted enforcer, the brutal Eddie Dane ("the Dane"). Upon learning that his men didn't actually see Tom kill Bernie, the Dane takes Tom back to Miller's Crossing to verify that Bernie's body is there. Tom expects to find no corpse and to be executed for it, but instead the group finds a decomposing body that had been shot in the face and disfigured beyond recognition by birds. The Dane and his men assume the body is that of Bernie, but it is actually that of the Dane’s lover, a man named Mink, whom Bernie had secretly killed and placed as a decoy where his own body should have been. Tom is now vulnerable if the Dane or Caspar discovers the identity of the body, a fact that Bernie uses in attempt to blackmail Tom into killing Caspar.


title: Miller's Crossing

text: With Bernie supposedly dead, someone continues to cut into Caspar’s match fix, and Tom and the Dane each try to convince Caspar that the other is behind it. Tom uses the sudden disappearance of Mink to sow suspicion about the Dane by insinuating that Mink has gone into hiding after he and the Dane betrayed Caspar. Caspar must decide between Tom and the Dane, a dilemma he resolves by shooting the Dane in the head as Tom looks on.


title: Miller's Crossing

text: Tom then thins out his rivals by engineering a surprise meeting between Bernie and Caspar, knowing that the first one to be seen by the other is likely to be killed. Shortly after the arranged time, Tom arrives to discover that Bernie has killed Caspar. Tom tricks Bernie into surrendering his gun and declares his intent to kill him in retribution for his blackmail. Bernie again begs for mercy, saying, as he did at Miller’s Crossing, "Look in your heart" but this time Tom asks rhetorically "What heart?" and shoots him.


title: Miller's Crossing

text: With Caspar and the Dane dead, Leo resumes his post as the only boss in town. At Bernie’s burial, Verna, now back in Leo's good graces, reacts coldly to Tom and walks back to her car. Leo notifies Tom that Verna has proposed to marry him. He offers Tom his job back but Tom rejects the offer and stays behind, watching Leo as he walks away.


title: Miller's Crossing

text: While writing the screenplay, the Coen brothers tentatively titled the film "The Bighead"—their nickname for Tom Reagan. The first image they conceived was that of a black hat coming to rest in a forest clearing; then, a gust of wind lifts it into the air, sending it flying down an avenue of trees. This image closes the film's opening credit sequence.


title: Miller's Crossing

text: Because of the intricate, dense plot, the Coens suffered from writer's block with the script. They stayed with a close friend of theirs at the time, William Preston Robertson in Saint Paul, Minnesota, hoping that a change of scenery might help. After watching "Baby Boom" one night, they returned to New York City and wrote "Barton Fink" (in three weeks) before resuming the "Miller's Crossing" screenplay.


title: Miller's Crossing

text: The budget was reported by film industry magazines as around $14 million, but the Coens have said that the film cost "substantially less" than that. According to Paul Coughlin, "The casting of Byrne allows for the psychological assurance, self-confidence and icy demeanour to be physically reproduced in the sturdy and unruffled presence of the tall and lean actor. Tom is 'a man who walks behind a man, whispers in his ear', he is the brains behind Leo's operation, and he is the heartless centre of "Miller's Crossing"." Although he was a native Irishman playing a lieutenant to an Irish mobster, the Coens did not originally want Gabriel Byrne to use his own accent in the film. Byrne argued that his dialogue was structured in such a way that it was a good fit for his accent and after he tried it, the Coens agreed.


title: Miller's Crossing

text: During casting they had envisioned Trey Wilson (who played Nathan Arizona in their previous film "Raising Arizona") as gangster boss Leo O'Bannon but two days before principal photography began, Wilson died from a brain hemorrhage and Finney was cast. Roger Westcombe calls Finney's portrayal of Leo "perfectly nuanced in a brilliant performance". Finney also appears in drag in a cameo as an elderly female ladies' room attendant.


title: Miller's Crossing

text: The Coens cast family and friends in minor roles. Sam Raimi, director and friend of the Coens, appears as the snickering gunman at the siege of the Sons of Erin social club, while Frances McDormand, Joel Coen's wife, appears as the mayor's secretary. The role of The Swede was written for Peter Stormare but he could not be cast since he was playing Hamlet (a role often referred to as "the Dane"). J. E. Freeman was cast and the name of the character was changed to The Dane, while Stormare went on to be featured in "Fargo" and "The Big Lebowski".


title: Miller's Crossing

text: The city in which the story takes place is unidentified but the film was shot in New Orleans as the Coen Brothers were attracted to its look. Ethan Coen commented in an interview, "There are whole neighborhoods here of nothing but 1929 architecture. New Orleans is sort of a depressed city; it hasn't been gentrified. There's a lot of architecture that hasn't been touched, store-front windows that haven't been replaced in the last sixty years." Principal photography ran from January 27 to April 28, 1989.


title: Miller's Crossing

text: Roger Westcombe finds in the opening title sequence of a fedora being blown off its bed of fallen leaves in the forest, a subtle homage to Jean-Pierre Melville's 1963 French crime film "Le Doulos", which ends with the gangster protagonist's fate underlined wistfully by the shot of his fedora coming to rest, alone in the frame, in the soil of the forest floor.


title: Miller's Crossing

text: Writing in "The Atlantic", Christopher Orr sees in the opening scene, in which Johnny Caspar (Jon Polito) confronts Leo O'Bannon (Albert Finney) and Tom Reagan (Gabriel Byrne) "an obvious nod to the opening of "The Godfather"".


title: Miller's Crossing

text: "Miller's Crossing" quotes many gangster films and films noir. Many situations, characters and dialogue are derived from the work of Dashiell Hammett, particularly his 1931 novel "The Glass Key". There are some parallels between the two stories and many scenes and lines are lifted from this novel. The relationship between Tom and Leo in the film mirrors the relationship between Ned Beaumont and Paul Madvig, the principal characters of the Hammett novel.


title: Miller's Crossing

text: Another important Hammett source was his 1929 novel "Red Harvest", which details the story of a gang war in a corrupt Prohibition-era American city, a war initiated by the machinations of the main character. While "Miller's Crossing" follows the plot and main characters of "The Glass Key" fairly closely, the film has no direct scenes, characters, or dialogue from "Red Harvest" except for using a fixed boxing fight as a plot device.


title: Miller's Crossing

text: Orr also notes, "The ending of Miller’s Crossing makes even clearer reference to the immaculate final scene of "The Third Man": a funeral, a protagonist abandoned by his car, who watches as the last person he cares for in the world walks away down a dirt road hemmed by trees".


title: Miller's Crossing

text: "Miller's Crossing" opened in limited release in New York City on September 22, 1990, after premiering at the New York Film Festival the day before. It was a box-office failure at the time, making slightly more than $5 million, out of its $10–$14 million budget.