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Binomial coefficient

In mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem. A binomial coefficient is indexed by a pair of integers n ≥ k ≥ 0 and is written, it is the coefficient of the xk term in the polynomial expansion of the binomial power n, it is given by the formula = n! K!!. For example, the fourth power of 1 + x is 4 = x 0 + x 1 + x 2 + x 3 + x 4 = 1 + 4 x + 6 x 2 + 4 x 3 + x 4, the binomial coefficient = 4! 2! 2! = 6 is the coefficient of the x2 term. Arranging the numbers, …, in successive rows for n = 0, 1, 2, … gives a triangular array called Pascal's triangle, satisfying the recurrence relation = +; the binomial coefficients occur in many areas of mathematics, in combinatorics. The symbol is read as "n choose k" because there are ways to choose an subset of k elements from a fixed set of n elements. For example, there are = 6 ways to choose 2 elements from, and; the binomial coefficients can be generalized to for any complex number z and integer k ≥ 0, many of their properties continue to hold in this more general form.

Andreas von Ettingshausen introduced the notation in 1826, although the numbers were known centuries earlier. The earliest known detailed discussion of binomial coefficients is in a tenth-century commentary, by Halayudha, on an ancient Sanskrit text, Pingala's Chandaḥśāstra. In about 1150, the Indian mathematician Bhaskaracharya gave an exposition of binomial coefficients in his book Līlāvatī. Alternative notations include C, nCk, nCk, Cnk, Cn,k in all of which the C stands for combinations or choices. Many calculators use variants of the C notation because they can represent it on a single-line display. In this form

One (Swedish House Mafia song)

"One" is the first single by Swedish house music supergroup Swedish House Mafia. A vocal version titled "One", featuring American singer Pharrell Williams, was released in July 2010; the song appears on the group's mix album Until One, the studio album Until Now. The song debuted on BBC Radio 1 with Zane Lowe and was chosen as the hottest record in April 2010. "One" peaked at number two on the UK Dance Chart. It reached number one in the Netherlands, number seven in Ireland and in the United Kingdom on the UK Singles Chart, it charted in Sweden, Denmark and Germany. A video directed by the Swedish directors Henrik Christian Larson supported the release. "One" was produced by Axwell, Steve Angello and Sebastian Ingrosso. The lyrics in "One" are written by Pharrell Williams. According to Angello the vocals were recorded in Australia over a year, prior to the release, were intended for another song, he said, "it worked. Well, it worked after Axwell Melodyne'd the crap out of it! it's kind of old skool, chopping up one vocal and turning it into a whole dance track.".

According to an interview in Future Music magazine, the track was composed in Logic using various plug-ins. Pharrell's vocals were processed in Melodyne and the final track was mixed and mastered at Metropolis Studios London on an SSL console; the music video features a Teenage Engineering OP-1. Nick Levine of Digital Spy gave the song four out of five stars and wrote: "'One' is a booming Eurodance club banger boasting an ear-snaggingly simple synth line, trancey whooshes aplenty and cred-boosting vocals from Neptunes star Pharrell Williams it's neither original nor refined, but boy does it hit the spot." List of Dutch Top 40 number-one singles of 2010 Lyrics of this song at MetroLyrics

Glenn Reeves

Glenn Reeves was an American rockabilly singer-songwriter and radio deejay. He released eight singles in his recording career, but is best-remembered for his demo of the song "Heartbreak Hotel" which became Elvis Presley's first number one hit. Reeves was raised in Texas, he studied at the University of Houston before serving in the Korean War. After returning from the military, he received a position as a radio deejay on KCTX Radio in Childress. In 1955, Reeves recorded his debut single "I'm Johnny on the Spot" for record producer Bob Tanner's TNT Records. Reeves recorded an additional single for the label in the same year. A frequent collaborator with him was Mae Boren Axton, a high school teacher with a background in musical promotion who co-wrote all four of Reeves' TNT sides. Axton, tasked with writing a song for Elvis Presley, worked most with steel guitarist Tommy Durden, culminating with the basis for the song "Heartbreak Hotel", in October 1955; the duo asked for Reeves' help, but remarked it was "the silliest thing I've heard" after he heard the title of the track.

Nonetheless, Axton recorded an initial version with Durden before Reeves returned, agreed to record his own demo of "Heartbreak Hotel" in a style similar to Presley's. Reeves refused an offer to be co-credited with the song, when Presley recorded it, he duplicated Reeves's own phrasing, it was Presley's first record for RCA Records and the first of a string of number one hits. Reeves continued to work with Axton and Durden on compositions like "Honey Bop" for Wanda Jackson and "Rockin' Country Style", a rock and roll tune which Reeves recorded in June 1956 for Atco Records. Both "Rockin' Country Style" and an earlier single distributed by Republic Records were produced by Murray Nash in Nashville; when Atco showed no interest in renewing his recording contract and Axton advertised Reeves's services around Nashville and secured a four-record deal with Decca Records. He recorded in 1957 and 1958 with little success, focused on the music scene in Florida disc jockeying on WQIK Radio and hosting his own country music show.

In the 1970s and 1980s, Reeves became the executive producer of Jamboree USA, a long-running barn dance show, while promoting several successful country music festivals. Reeves died of cancer in 1998 at 67 years old. In 2011, Bear Family Records released Johnny on the Spot: Gonna Shake This Shack Tonight, a compilation album of Reeves's recorded works, including his demo of "Heartbreak Hotel"

Francisco Flores (wrestling)

Francisco Flores is a former Mexican professional wrestling promoter, most known for his part in creating and running the Universal Wrestling Association from the mid-1970s until the 1990s when it closed down. At one point in time the UWA's shows as the Toreo de Quatro Caminos arena were the biggest drawing shows in all of Mexico, putting the UWA in contention for being the biggest wrestling promotion in Mexico at the time; as a promoter Flores helped make such wrestlers as El Canek and El Hijo del Santo world-renowned wrestlers. Flores started his career as a wrestling promoter as a minor promoter for Empresa Mexicana de Lucha Libre, Mexico's largest and the world's oldest wrestling promotion. After working for EMLL for years he became frustrated with EMLL's conservative approach to wrestling and wanted to promote his vision for wrestling instead of EMLL's vision. In 1975 Flores, along with Ray Mendoza broke away from EMLL and formed the rival Universal Wrestling Association. In the UWA Flores focused on featuring young wrestlers who were not given a chance in EMLL, this included Ray Mendoza's sons Villano I, Villano II and Villano III.

Villano III benefitted from Flores' way of promoting as he became one of the rising young stars in the mid to late 1970s. Flores and the UWA's promotion of El Canek made him a world wide wrestling star, boking him as the "Mexican defender" against a variety of foreign wrestlers such as Hulk Hogan and André the Giant; the UWA helped give a young El Hijo del Santo his start in wrestling. The UWA flourished in the 1970s and 1980s but hit harder times in the 1990s and was forced to close down in 1995 after which Francisco Flores went into retirement. NWA All-Star Wrestling NWA Canadian Tag Team Championship - with Bobby Bass NWA Pacific Coast Heavyweight Championship NWA Hollywood Wrestling NWA Americas Tag Team Championship - with Alfonso Dantés NWA Mid-America NWA Mid-America Heavyweight Championship NWA Mid-America Tag Team Championship - with Duke Myers NWA World Six-Man Tag Team Championship - with George Gulas and Bobby Eaton Southeastern Championship Wrestling NWA Southeastern Tag Team Championship - with Duke Myers Stampede Wrestling Stampede International Tag Team Championship - with Cuban Assassin World Wrestling Council WWC World Tag Team Championship - with Fidel Sierra Wrestling Observer Newsletter awards Wrestling Observer Newsletter Hall of Fame

Sibyl of Falaise

Sibyl of Falaise was an Anglo-Norman noblewoman and kinswoman of King Henry I of England. Sibyl was called the "nepta" of King Henry; the term "niece" was used to mean that the person was an illegitimate child rather than a niece, so it is possible that she was Henry's bastard daughter. The historian Frank Barlow implies that she could have been Henry's daughter rather than his niece. Against this, Kathleen Thompson argues that Henry was not shy about recognizing his bastards, that it is more that Sibyl was the daughter of Henry's elder brother Robert Curthose. Robert was Duke of Normandy from 1086, Falaise was where Robert's legitimate son, William Clito, was being raised. Katharine Keats-Rohan argues instead that Sibyl was the younger daughter of William de Falaise and Geva de Burcy. William de Falaise was the lord of Stogursey in Somerset. Keats-Rohan says that Sibyl was just a "kinswoman" of Henry's and not a bastard of either Henry or Robert. I. J. Sanders does not believe Sibyl was William's daughter, but does not speculate further on her ancestry.

If Sibyl was a bastard, nothing is known of her mother. Thompson speculates that if Sibyl was the daughter of Robert, Sibyl's mother may have been someone employed in raising William Clito and that Sibyl was named for Robert's deceased wife, Sibyl of Conversano. Sibyl married Baldwin de Boullers, at the instigation of Henry I. Baldwin had at least two sons – Stephen and Baldwin – and two daughters – Matilda and Hillaria. Matilda married Richard fitzUrse. Only Matilda is known to be the daughter of Sibyl. Matilda was the mother of Reginald one of the murderers of Thomas Becket. Barlow, Frank. Thomas Becket. Berkeley, CA: University of California Press. ISBN 0-520-07175-1. Clanchy, M. T.. England and its Rulers: 1066–1307. Blackwell Classic Histories of England. Oxford, UK: Blackwell. ISBN 1-4051-0650-6. Given-Wilson, Chris; the Royal Bastards of Medieval England. New York: Barnes & Noble. ISBN 1-56619-962-X. Sanders, I. J.. English Baronies: A Study of Their Origin and Descent 1086–1327. Oxford, UK: Clarendon Press.

OCLC 931660. Thompson, Kathleen. "Affairs of State: The Illegitimate Children of Henry I". Journal of Medieval History. 29: 129–151. Doi:10.1016/S0304-418100015-0

204th Airlift Squadron

The 204th Airlift Squadron is a unit of the Hawaii Air National Guard 154th Wing stationed at Joint Base Pearl Harbor-Hickam, Hawaii. The 204th is equipped with the C-17 Globemaster III; the 204th Airlift Squadron is a unit of the 154th Wing. The unit is a classic associate unit with the 535th Airlift Squadron at Joint Base Pearl Harbor-Hickam, it flies the C-17 Globemaster III, the newest, most flexible cargo aircraft to enter the airlift force. The C-17 is capable of rapid strategic delivery of troops and all types of cargo to main operating bases or directly to forward bases in the deployment area; the aircraft can perform tactical airlift and airdrop missions and can transport litters and ambulatory patients during aeromedical evacuations when required. Established in 1994 to provide the Hawaii Air National Guard a theater airlift capability and to support joint exercises in Hawaii with Army and Marine Corps units; the squadron supports operational training, provides paratroop and tactical air drop capability, deliver relief supplies following natural disasters.

Since its establishment, squadron C-130 crews have made airdrops over India, shuttled military crews involved in the search for missing in action servicemen in New Zealand and Cambodia, have transported to Oahu 30 to 40 people arrested on neighbor island drugs raids. In April 1999, the 204th Airlift Squadron was awarded the Air Force's Outstanding Unit Award for the period of 14 July 1996 to 13 July 1998. While providing airlift support during the exercise Balitakan 2000, in February 2000, the 204th Airlift Squadron, HIANG, delivered books and school supplies to Virgen Delos Remedios Elementary School, Angeles City, while here supporting Balikatan 2000. After more than a decade the C-130s were the Hawaii National Guard's workhorse—the main means of moving supplies, soldiers and prisoners between the islands. In 2008, the unit was upgraded to the Air Force's latest jet cargo plane, the C-17 Globemaster III; the eight C-17s are part of a 190-member unit manned by active Air Force personnel from the 535th Airlift Squadron and the Hawaii Air Guard's 204th Airlift Squadron.

When established in 2008, it was the first active joint Air Force and Air National Guard unit outside of the mainland. In July 2018 a C-17 of the squadron collected 55 cases of human remains from Wonsan in North Korea, it is thought that these are remains of US or other UN servicemen from the Korean War. The C-17 flew to Osan Air Base in South Korea. Established as 204th Airlift Squadron and allotted to Hawaii ANG in 1994Received federal recognition and activated on 1 August 1994 154th Operations Group, 1 August 1994 – Present Hickam Air Force Base, 1 August 1994Re-designated: Joint Base Pearl Harbor-Hickam, 1 January 2010-Present C-130A Hercules, 1989-1994 C-130H2 Hercules, 1994-2006 C-17A Globemaster III, 2006–Present This article incorporates public domain material from the Air Force Historical Research Agency website