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In mathematics, the harmonic mean is one of several kinds of average, in particular, one of the Pythagorean means. It is appropriate for situations when the average of rates is desired; the harmonic mean can be expressed as the reciprocal of the arithmetic mean of the reciprocals of the given set of observations. As a simple example, the harmonic mean of 1, 4, 4 is − 1 = 3 1 1 + 1 4 + 1 4 = 3 1.5 = 2. The harmonic mean H of the positive real numbers x 1, x 2, …, x n is defined to be H = n 1 x 1 + 1 x 2 + ⋯ + 1 x n = n ∑ i = 1 n 1 x i = − 1; the third formula in the above equation expresses the harmonic mean as the reciprocal of the arithmetic mean of the reciprocals. From the following formula: H = n ⋅ ∏ j = 1 n x j ∑ i = 1 n. it is more apparent that the harmonic mean is related to the arithmetic and geometric means. It is the reciprocal dual of the arithmetic mean for positive inputs: 1 / H = A The harmonic mean is a Schur-concave function, dominated by the minimum of its arguments, in the sense that for any positive set of arguments, min ≤ H ≤ n min.

Thus, the harmonic mean cannot be made arbitrarily large by changing some values to bigger ones. The harmonic mean is one of the three Pythagorean means. For all positive data sets containing at least one pair of nonequal values, the harmonic mean is always the least of the three means, while the arithmetic mean is always the greatest of the three and the geometric mean is always in between, it is the special case M−1 of the power mean: H = M − 1 = n x 1 − 1 + x 2 − 1 + ⋯ + x n − 1 Since the harmonic mean of a list of numbers tends toward the least ele

In materials science, the yield strength anomaly refers to unusual materials wherein the yield strength increases with temperature. For the vast majority of materials the yield strength decreases with increasing temperature. Precipitation hardening superalloys exhibit yield strength anomaly over a considerable temperature range. For these materials, the yield strength shows little variation between room temperature and several hundred degrees Celsius. A maximum yield strength is reached. For ordered intermetallics, this is the case at 50% of the absolute melting temperature. For higher temperatures, the yield strength decreases and drops to zero when reaching the melting temperature, where the solid material transforms into a liquid; the yield strength anomaly is exploited in the design of gas turbines and jet engines that operate at high temperatures, where the materials used are selected based on their paramount yield and creep resistance. Superalloys can withstand high temperature loads far beyond the capabilities of steels

The George F. Allison House is a historic house located at 418 West Duval Street in Live Oak, United States, it is locally significant as the home of George F. Allison, a pioneering Live Oak businessman during the city's formative commercial years as well as being a fine example of Colonial Revival architecture in the area. Although the actual construction date and builder of the house are not known, the house is shown on a 1903 Sanborn Insurance map; the large, two-story, Colonial Revival style house was given its present appearance when it was remodeled in 1927 after 40% of the rear was damaged by a fire on New Years Day. Since however little about the house or the surrounding lot has change. On April 20, 1995, it was added to the U. S. National Register of Historic Places

Shawn Michael Patterson is an American composer and songwriter. He has been working in the field of music for over 20 years, his most notable work to date is as the songwriter/composer for the song "Everything Is Awesome", written for the Warner Brothers feature film The Lego Movie. Shawn Patterson was born in the small rural town of Athol, Massachusetts, to blue collar working parents and Joan Patterson, his father was a gifted musician playing several instruments including: saxophone, guitar and pedal steel. However, Patterson's first draw to music came from watching comedian Steve Martin play the banjo on television during his Let’s Get Small Tour. Martin's banjo playing was so influential, Patterson begged his parents to purchase a 5-string banjo and began taking lessons studying Bluegrass and Dixieland styles of music. Although he was jamming along with his father, Patterson grew bored with the instrument after a year and began tampering with the banjo, attempting to attach a pickup to the head and run it through a guitar amplifier owned by a friend from school.

He switched to electric guitar. In June 1977, Patterson and his father attended a screening of Star Wars and this was the first time film music caught his attention and a career was born. Patterson was a huge Superman fan and at the age of four years was watching black and white reruns of The Adventures of Superman with George Reeves. With great anticipation, he awaited the release of Superman in 1978 and was forever changed as a result of John Williams’ infamous score. Patterson attended multiple screenings of the film just to try and absorb the music. On June 2, 1979, Patterson's father died after suffering a brain aneurysm leaving him, his two brothers and mother, Joan Patterson; as a result, Patterson devoted himself to music and his guitar playing. He was soon exposed to rock bands such as Van AC/DC, Queen and The Who. With the release of the Blues Brothers film in 1980, Patterson was drawn to the influences of the film's soundtrack and band: Elmore James and Dave, Booker T and the MG's. For the next four years, he began writing songs.

He played in and out of local bands until he graduated from Athol High School in 1983 and attended Berklee College of Music on scholarship at age 17. At Berklee, Patterson was exposed to great and talented musicians from around the world befriending and jamming with the most talented musicians he found. However, he experienced tremendous discomfort in his left hand most due to a broken left collarbone as a child and began experimenting with composition while at Berklee. Upon leaving Berklee at the end of summer 1983, Patterson resumed playing in and around Massachusetts, teaching guitar lessons in local music stores and privately, he began studying with local legendary jazz educator and pianist Mark Marquis, who steered him to the Fitchburg Public Library with the instructions to start exploring their jazz record collection. Patterson's musical voyage took a serious turn as he discovered a wide range of jazz styles that would forever alter his musical course: Charlie Parker, Dizzy Gillespie, Joe Pass, Miles Davis, Art Blakey, Charlie Christian, Jim Hall and Wes Montgomery were beacons of inspiration which resulted in his dedication to studying with Marquis on guitar.

Many times he would study for periods of 12 hours a day. At this time, Patterson began to experiment writing a wider range of song writing material, having been influenced by Count Basie, Duke Ellington and the Benny Goodman Sextet. In 1986, Patterson left for Los Angeles to attend the Grove School of Music exploring his options of living in LA to earn a living in music. Prior to moving, Patterson worked a wide range of odd jobs around Massachusetts to sustain himself including: furniture assembly, a convenience store, a plastic factory. While at the Grove School of Music, Patterson worked full-time during the night shift as security guard on Sunset Boulevard and would attend college in the daytime. Upon completion at Grove, he returned to Massachusetts, continued his private studies with Marquis and began playing around the state in various jazz ensembles he led. In 1988, Patterson accepted a scholarship to attend the prestigious Jazz in July program and University of Massachusetts, Amherst.

Patterson was hand selected out of many students to study and perform with the featured legendary educators and musicians, Dr. Billy Taylor and Max Roach. However, he never lost sight of his dream to compose music to picture and he wrote music for a few independent documentaries. With \$400 in his pocket and a few guitars in his backseat, Patterson drove to Los Angeles in 1990 to relocate permanently, he played some live gigs on occasion with friends he had met through Grove, but his priority was to build a small studio and begin producing his own music to get composing work. He landed a job as a production assistant at the animated television show and the Chipmunks, where in 1991, he sold his first song for one of the albums of the series; the song was a rap song, "Rock The House", of which he wrote lyrics. At this time, Patterson was renting various people's small project studios to produce his own compositions and began writing for trailer houses writing the music for large international ad campaigns such as: The Fisher King, My Girl, several others.

Still not able to earn enough money to survive, Patterson moved on to The Ren & Stimpy Show as Operations Manager. Soon, however, he moved into the audio/post production department and began working as a music editor. Here on the show, Patterson spent 8–10 hours a day cutting m

Galina Vicheva Gencheva, known professionally as Galena, is a Bulgarian singer. Galena was born May 1985 in Smyadovo, Bulgaria, she attended a music school in Shumen. Two years she moved to another music school in Dimitrovgrad. Galena was discovered by the singer Milko Kalaydzhiev, she started her career under the name Galya and recorded her first single "Можеш ли". Her debut studio album as Galena came on Payner Music. Galena has released further albums, След 12 in 2008 and Официално забранен in 2010, Аз in 2011, her first duet album Кой in 2015, she has collaborated with a great number of Bulgarian acts including Niki Nankov, Malina and Andrea. She has appeared in a number of high-profile promotional ads. In February 2008, Galena was engaged to her boyfriend Galin. On 22 June 2009 they had Stefan. In February 17, 2017 they welcomed second son Aleksandar. Planeta TV Awards2006: Miss Sexy 2007: Best Young Performer 2008: Best Young Performer 2008: Best Club Song 2009: Best Video of the Year 2010: Preferred Song on Radio Veselina 2010: Female Artist of the Year 2011: Ambassador of Bulgarian music abroad 2011: DJ Hit of the Year 2011: Album of the Year 2012: Original Performance on Club Stages 2012: Video of the Year 2013: Female Artist of the Year 2013: Duet Song of the Year 2013: Video of the Year 2014: Artist of the Year 2014: Club Song of the Year 2014: Video of the Year Nov Folk Magazine Awards2007: Best young performer 2008: Best cover version 2009: Best Video of the Year 2010: Song of the Year 2011: Album of the Year, Best stage actOthers2006: Скопски филиграни, Macedonia - second Award of the Audience 2010 and 2011: Pop act of the year by Signal.bg readers Studio albums2006: Galena 2008: След 12 2010: Официално Забранен 2011: АзDuet albums2015: КойCompilation albums2013: Златните Хитове На Галена Video albums / DVDs2008: Galena Best Video Selection 2011: Az DVD 2014: "Body Language" 2015: "Te Quiero" 2015: "Pantera" From album Galena: 2004: Само миг 2005: Дъждовно реге 2005: Екстаз 2006: Чупката From album След 12 2006: Душата ми крещи 2007: Намерих те 2007: Вземи си дъх 2007: Утешителна награда 2008: Нищо общо 2008: Сама 2008: Страст на кристали 2008: След 12 2008: 100 пъти From album Официално Забранен: 2008: Знам диагнозата 2009: Дяволът ме кара 2009: Нещастница 2009: Мой 2009: За последно 2009: Лоша ли съм 2010: На две големи 2010: Тихо ми пази From album Аз: 2010: Запали 2010: За пари 2010: Аларма 2011: С кое право 2011: Хайде, откажи ме 2011: Да ти го дам ли 2011: DJ-ят ме издаде 2011: Неудобни въпроси 2011: Създай игра 2011: След раздялата 2011: Ще се проваля 2011: Искам да останем будни 2011: Знам как 2011: Мразя да те обичам 2011: Тоя става 2011: Не пред хората Various 2004: Можеш Ли 2012: Спри Ме 2012: Много Ми Отиваш 2012: Пак Ли 2013: Истински Щастлива 2013: Дай Ми 2014: Body Language 2015: Стара Каравана 2015: Една жена 2015: Коледа 2016: Да ти олекне.

2016: Пей сърце 2016: С друг ме бъркаш 2016: #МамаУраган 2017: Мина ми 2017: Moro mou 2017: #TheBo\$\$2017: Изневериш ли ми 2017: #JustShow 2018: #GiveMeLove Official website

Hugh Foliot was a medieval Bishop of Hereford. Related somehow to his predecessor at Hereford, he served as a priest and papal judge as well as being an unsuccessful candidate as Bishop of St David's in Wales. In 1219, he was appointed Bishop of Hereford. During his time in office, he attended to ecclesiastical duties, but did serve as a royal administrator, he helped found a hospital and a priory, died in 1234 after a months-long illness. Foliot was the son of Roger Foliot and his wife Rohese. Roger held three knight's fees in Northamptonshire. Born sometime between 1150 and 1160, Hugh was related in some manner to Robert Foliot, his predecessor at Hereford, he was a canon of Hereford Cathedral before becoming Archdeacon of Shropshire by May 1186. Foliot is a frequent witness on charters as archdeacon, but little else is known of his tenure of the office. From 1212 to 1219, he served as a papal judge-delegate three times. In 1215 he was King John's candidate for the see of St David's in Wales, but was not elected.

After Foliot's failed candidacy as bishop, in February 1216 John appointed him to the benefice of Colwall in Herefordshire, the king having the ability to make the appointment because Giles de Braose, the Bishop of Hereford, who would have made the appointment, had died. From this time comes Foliot's patronage of Robert Grosseteste, the theologian and future Bishop of Lincoln. Foliot had been one of three members of the cathedral chapter from Hereford sent to King Henry III's court to secure permission for the chapter to hold an election in 1219 Foliot was elected to the see of Hereford in June 1219 and consecrated on 27 October 1219 along with William de Goldcliff, the Bishop of Llandaff, at Canterbury; the new bishop accompanied Peter des Roches, the Bishop of Winchester, on a pilgrimage in 1221. Because des Roches travelled to Spain to the shrine of St James at Compostela, it is known that Foliot accompanied him, the statement by a medieval chronicler from Dunstable that Foliot's destination was not certain, being either Rome or Compostela, should be discounted.

Foliot spent most of his tenure of office in his diocese, only attending the royal court or being assigned governmental duties. On 30 December 1223, Foliot assumed one of those duties, when he took custody of Hereford Castle after it was surrendered by Hubert de Burgh, during the redistribution of royal castles when de Burgh ousted des Roches from power, he was appointed to determine the size of the royal forest in Gloucestershire. Foliot founded a hospital in Ledbury, devoted to St Katherine, he helped found Alberbury Priory, a house of the Grandmontine order. In his cathedral, he reorganised the benefices and offices of the chapter, as well as endowing further benefices. Foliot died 7 August 1234, after an illness, he was buried in Hereford Cathedral. Foliot appointed his younger brother Thomas to offices in the diocese, first as precentor in the 1220s and around 1230 as treasurer of the cathedral chapter