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The De Bruijn–Newman constant, denoted by Λ and named after Nicolaas Govert de Bruijn and Charles M. Newman, is a mathematical constant defined via the zeros of a certain function H, where λ is a real parameter and z is a complex variable. H has only real zeros if and only if λ ≥ Λ; the constant is connected with Riemann's hypothesis concerning the zeros of the Riemann zeta-function. In brief, the Riemann hypothesis is equivalent to the conjecture that Λ ≤ 0. De Bruijn showed in 1950 that H has only real zeros if λ ≥ 1/2, moreover, that if H has only real zeros for some λ, H has only real zeros if λ is replaced by any larger value. De Bruijn's upper bound of Λ ≤ 1 / 2 was not improved until 2008, when Ki, Kim and Lee proved Λ < 1 / 2, making the inequality strict. As of December 2018, the current best upper bound is Λ ≤ 0.22, achieved in the 15th Polymath project. A manuscript of the Polymath work was submitted to arXiv in late April 2019, has been accepted for publication by the journal Research In the Mathematical Sciences.

Newman proved in 1976 the existence of a constant Λ. Newman conjectured that an intriguing counterpart to the Riemann hypothesis. In January 2018 Brad Rodgers and Terence Tao published a paper on arXiv in which they claim that Λ ≥ 0, thus if Riemann hypothesis is true the value of Λ must be 0. Since H is just the Fourier transform of F H has the Wiener–Hopf representation: ξ = A π − 1 ∫ − ∞ ∞ e − 1 4 λ 2 H d x, only valid for λ positive or 0, it can be seen that in the limit λ tends to zero H = ξ for the case Lambda is negative H is defined so: H = B π − 1 ∫ − ∞ ∞ e − 1 4 λ 2 ξ d x where A and B are real constants. Weisstein, Eric W. "de Bruijn–Newman Constant". MathWorld

The Tongzhi Emperor, born Zaichun of the Aisin Gioro clan, was the 10th Emperor of the Qing dynasty, the eighth Qing emperor to rule over China proper. His reign, from 1861 to 1875, which lasted through his adolescence, was overshadowed by the rule of his mother, Empress Dowager Cixi. Although he had little influence over state affairs, the events of his reign gave rise to what historians call the "Tongzhi Restoration", an unsuccessful attempt to stabilise and modernise China; the only surviving son of the Xianfeng Emperor and Empress Dowager Cixi, the Tongzhi Emperor attempted political reform in the period of the Tongzhi Restoration. His first regnal name was Qixiang, but this name was abandoned by Cixi in favour of "Tongzhi", a contraction of the classical phrase tong gui yu zhi, which means "restoring order together". An alternative interpretation reads it as "mother and son co-emperors", which fits the state of affairs, as the empress dowager wielded real power and ruled behind the scenes.

The traditional Chinese political phrase "attending audiences behind a curtain" was coined to describe Cixi's rule through her son. The Tongzhi Emperor became emperor at the age of five upon the death of his father, the Xianfeng Emperor, his father's choice of regent, was removed in favour of a partnership between his mother Empress Dowager Cixi, Empress Dowager Ci'an, his sixth uncle Prince Gong. While there had most been hopes that the Tongzhi Emperor would become a leader like the Kangxi Emperor, those hopes would soon come to naught, as the Tongzhi Emperor grew up to become an obstinate and dissolute young man. In the fall of 1872, the teenage emperor married several concubines; the Tongzhi Emperor had wanted to take up power prompting a quarrel at court regarding the dismantling of the regency and the timing of it. However, the two empresses dowager stuck by the intended date of February 23, 1873; the day after the Tongzhi Emperor took up the reins of power, the foreign powers requested an audience with the teenage emperor.

The request precipitated a sharp disagreement between the ministers at the foreign legations, who made it clear that they would not perform the ritual kowtow to the emperor, the Zongli Yamen, regarding the protocol to be observed. The Qing government was loath to hold the audience within the confines of the Forbidden City settling on the "Pavilion of Purple Light" at one of the lakeside palaces to the west of the Forbidden City, now part of Zhongnanhai; the audience was held on 29 June 1873. After the audience, the foreign representatives made clear their annoyance at being received in a hall used by the Qing emperors to receive envoys of tributary states. In the fall of 1874, the Tongzhi Emperor got into a clash with his ministers, which included his two uncles, Prince Gong and Prince Chun over the emperor's plans to rebuild the Old Summer Palace at a time in which the empire was bankrupt, over his dissolute behavior; the emperor reacted by firing the ministers, but Empresses Dowager Ci'an and Cixi intervened, he had them reinstated.

That December, it was announced that he was ill with smallpox, the Empress Dowagers resumed the regency. He died on 12 January 1875; the Tongzhi Emperor's death left the court in a succession crisis, as, although he was childless, his empress was pregnant. The empresses dowager designated the Tongzhi Emperor's three-year-old cousin, Zaitian, as the heir to the throne. Zaitian was biologically Prince Chun's son, but was symbolically adopted as the Xianfeng Emperor's son to make him eligible to succeed the Tongzhi Emperor. Zaitian was thus enthroned as the Guangxu Emperor, with Empresses Dowager Ci'an and Cixi resuming their roles as regents; the Tongzhi Emperor's empress died a few months later. Hong Xiuquan was peculiarly affected by the social instability of the Canton region, he belonged to a family of modesty well-off peasants from Hua county north of Canton, members of the Hakka community ubiquitous in the region. Hong created his own version of Christianity with a total transformation of the Chinese nation to start his Taiping Rebellion.

In late 1851, Taiping army occupied its first walled city Yongan. When 5-year-old Tongzhi Emperor ascend the throne in 1861, the Taiping rebellion was threatening Shanghai; this move prompted several foreign missions of British and Americans to the Heavenly Capital, to warn the Taiping against interference with Western commerce. Foreign neutrality was beginning to fray as Western intelligence of the Taiping revealed both its unorthodox religious ideology and its lack of understanding of the Western world. In order to save Shanghai, Tongzhi Emperor ordered Zeng Guofan to counter-attack the rebel. Zeng's appointment was the turning point in the Taiping war. Zeng was a virtual generalissimo directing a supra-provincial campaign by armies raised and led by his various lieutenants and proteges, supported by the extrodinary mobilization of revenues including the likin tax and customs revenues, his strategy was to move from the west down the Yangzi taking successive cities, while Li Hongzhang, his principal lieutenant, advanced from the east through Jiangsu toward Nanjing.

The Heavenly Capital fell in July 1864. Hong Xiuquan was dead, on June 1, 1864; the fall of the city was followed by a great massacre. Remnant Taiping forces fled south, including Hong's son the Junior King and Hong Rengan, to continue the movement, but both were soon captured and executed; the las

Colin Harper is an Irish non-fiction author and composer. Harper was born in Belfast and graduated in Modern History 1989 from Queen's University, Belfast acquiring a postgraduate diploma in Information Management from Queen's University and a PhD in Cultural Studies from the University of Sunderland. Between 1994 and 2001 he was a professional freelance journalist. For Belfast newspaper Irish News he wrote features on famous bands on tour. In the same period he wrote features and reviewed for popular music magazines such as Q and Mojo, he contributed both theatre and music reviews to The Irish Times. Harper became a regular writer of liner notes for compilations of folk and prog-rock artists appearing on record labels including Windsong, Castle and Snapper, his long-time admiration of Bert Jansch led to his biography of Dazzling Stranger. This was launched at the Edinburgh International Book Festival, he followed up the book release by being the driving force behind the tribute album People on the Highway: A Bert Jansch Encomium.

He contributed to the Jansch documentary Dreamweaver on Channel 4 in 2000. An updated edition of Dazzling Stranger was released in 2006 including a foreword by The Smiths guitarist Johnny Marr, it was further updated with a new Afterword by Pete Paphides. Harper had a sabbatical in the public sector between 2001 and 2011, he continued to contribute to magazines for Mojo and Record Collector, until 2007. During this time he published one more book, Seaside Rock, a small monograph on pop music in North Down in the 60s, co-wrote Irish Folk and Blues: A Secret History. In support of the charity World Wide Fund for Nature Harper organised two benefit compilation albums: The Wildlife Album and Live In Hope: The Wildlife Album 2, his other annotated CD compilations include the collected works of Andy Roberts. Freedom & The Dream Penguin, a collection of his songs – fronted by guest vocalists including Judy Dyble, Alison O'Donnell, Janet Holmes, Paul Casey and Brian Houston – was released in 2008, credited to The Field Mouse Conspiracy.

An album of original instrumental compositions, Titanium Flag, was self-released in 2010. Escaping from the public sector in December 2011, Harper threw himself back into creative mode, beginning work on Bathed in Lightning: John McLaughlin, the 60s and the Emerald Beyond, his biography of guitarist John McLaughlin in the context of London's musical scenes in the 1960s; the book was published by Jawbone Press in 2015, pre-launched with a music and speech podcast event with a live audience at Belfast's RedBox Studios, involving Irish jazz personality/BBC NI broadcaster Linley Hamilton, Horslips member/RTE broadcaster Jim Lockhart and various local jazz, blues and pop musicians. Unusually, the ebook edition added nearly 100,000 words of extra content to the 215,000-word print edition, with the ebook content published as a stand-alone ebook for a nominal price at Harper's behest. Two further books followed, written in 2015; the Wheels of The World: 300 Years of Irish Uilleann Pipers is a 250,000-word history of the Irish pipes told through detailed chapters on some of its greatest player, going back to the early 1700s.

It was written in collaboration with international recording artist/piper John McSherry. The book was promoted with articles in fRoots and the Irish Times, by a number of live events at festivals and bookshops in Ireland in mid to late 2015, radio sessions on BBC NI and RTE including an edition of Arena helmed by Jim Lockhart. Eyes Wide Open: True Tales of a Wishbone Ash Warrior was published with a month of the piping book in October 2015, written by guitarist/vocalist Andy Powell in close collaboration with Harper, it was launched with an onstage Q&A at Wishbone Ash's annual AshCon event in Chesterfield in November 2015. Other creative activity in the 2012–15 period included extensive booklets for the RPM record label's celebrations of the work of 1960s–70s British folk and jazz producer Peter Eden: The Eve Folk Recordings 2-CD set and Turtle Records: Pioneering British Jazz 1970–71, a 3-CD box set with 17,000 word perfect-bound booklet, including interviews with Eden and many of his artists – Howard Riley, Barry Guy, Mike Cooper, Mike Gibbs, Norma Winstone, John Taylor and others.

Harper was involved in the reissue, including booklet essay, of another 1970 Peter Eden production, guitarist Chris Spedding's Songs Without Words, annotated a 4CD Wishbone Ash box Road Works in this period. In March 2016 Harper's instrumental album Sunset Cavaliers reviewed in Brirtish music journals, was released by Market Square Records. A homage to the musical soundworlds and time period Harper chronicles most in his writing, the album featured guest appearances from many of his recent and past collaborators – John McSherry, Chris Spedding, Andy Powell, Bert Jansch, Linley Hamilton, Duffy Power among others. Harper had been asked to write three obituaries on Power – whom he regards as one of the unsung greats of the 1960s – in February 2014, for The Guardian and Record Collector. During the first quarter of 2016, Harper focused on curating for Hux Records, as the label's 150th release, Spirits From Another Time: 1969-71 a 2-CD set of unreleased studio material by multicultural British rock band

Upper Whitewater Falls is a waterfall in North Carolina on the Whitewater River. As with most of North Carolina's waterfalls, it is in the mountainous area of the state. There is a cluster of falls in the area where the borders of Georgia and the Carolinas come together. Whitewater Falls is part of that group close to the South Carolina border; the waterfall is protected by the Nantahala National Forest. Although some claim that Whitewater Falls is the tallest East of the Mississippi, that title may belong to Crabtree Falls in Virginia, depending on how one defines "waterfall". In fact, there is debate as to whether Whitewater falls is the tallest waterfall in North Carolina, as there are some in the state which may lay claim to being taller, such as Glassmine Falls on the Blue Ridge Parkway. There is a Lower Whitewater Falls in South Carolina about 2 miles downstream from Upper Whitewater Falls. Visitors to the falls must pay a \$3/vehicle fee to view the falls. There are several viewing platforms at varying heights.

The area surrounding the falls is sufficiently treacherous that hiking off-trail in the area is discouraged by park rangers. The Foothills Trail passes through the base of the falls. Corbin Creek Falls Photos and stats Whitewater Falls Brochure made by the Nantahala National Forest Whitewater Falls on ncwaterfalls.com Corbin Creek Falls on ncwaterfalls.com

The 1990 Idaho Vandals football team represented the University of Idaho in the 1990 NCAA Division I-AA football season. The Vandals were led by second-year head coach John L. Smith, were members of the Big Sky Conference and played their home games at the Kibbie Dome, an indoor facility on campus in Moscow, Idaho; the three-time defending conference champion Vandals made the I-AA playoffs for the sixth consecutive season, under a third head coach. With future college hall of fame quarterback John Friesz in the NFL, Idaho was led by redshirt freshman Doug Nussmeier. Nussmeier's season was ended by a broken right ankle in early October, fifth-year senior Steve Nolan guided the team to seven consecutive wins, including a ninth-straight victory over rival Boise State; the season ended in the quarterfinals in December, where Idaho lost by one point at Georgia Southern, the eventual national champion. Source: Four Vandals made the all-conference team: running back Devon Pearce, wide receiver Kasey Dunn, cornerback Charlie Oliver, defensive end Jeff Robinson.

Second team selections were guard Chris Hoff, tight end Scott Dahlquist, linebacker Jimmy Jacobs, punter Joe Carrasco. Honorable mention were quarterback Steve Nolan, center Mike Rice, return specialist Roman Carter, linebacker Mark Matthews. Pearce shared the Big Sky's outstanding offensive player award with quarterback Jamie Martin of Weber State. Gem of the Mountains: 1991 University of Idaho yearbook – 1990 football season Idaho Argonaut – student newspaper – 1990 editions

Theodore Hesburgh Library is the primary building of the University of Notre Dame's library system. The present-day building opened on September 1963, as Memorial Library. In 1987 it was renamed Hesburgh Library in honor of Rev. Theodore Hesburgh, C. S. C. who served as the university's president from 1952 to 1987. The library's exterior façade that faces the university's football stadium includes a large, 134-foot by 68-foot mural called The Word of Life, or more known as Touchdown Jesus; as of 2009, the library ranked as the 61st largest collection among research universities in the United States with an estimated 3.39 million volumes. Before the establishment of a library for students, students took the initiative to establish literary societies, that served as the source of literature and discussion of scholarly topics; the first one was the St. Aloysius Literary Society, founded in 1850 and six years established the first student library, it was followed by the Philopatrians and the St Edwards Library Society.

The first circulating library at Notre Dame was created in 1873 by President Rev. Augustus Lemonnier, incorporate the existing student libraries, it was housed on the third floor of the Main Building and its first librarian was Jimmie Edwards, CSC. In 1879 the Main Building was destroyed by fire and 500 books were lost. After the Main Building was rebuilt, a new library was established with a budget of \$500 and comprised 16,000 volumes. In 1888, during the golden jubilee of Fr. Edward Sorin, a new library was opened on the third floor. By 1900 it contained 52,000 books. In 1907 the university hired a professional librarian, to catalog the collection. After the death of Edwards, Paul came to Notre Dame in 1912 and took over his positions. A new building to house the library was built in 1917, it was dedicated during the 75th anniversary of the University, with President William Taft in attendance. By 1920 its collection reached 103,000 volumes; the Dewey Decimal Classification has been used to classify the library's holdings since 1929.

Thematic collections were established in other buildings in subsequent decades. A separate engineering library opened in 1933, followed by a biology library in 1938, the Medieval Institute in 1946, the Nieuwland science library for chemistry and mathematics in 1953. In 1959 Father Theodore Hesburgh, the university's president, announced plans for construction of a new library. Ground was broken in 1961, with the Ellerbe Company of Saint Paul, Minnesota, as the project's architect. Construction took three years. Memorial Library opened on September 18, 1963; the finished structure, 210 feet tall, is built on a site that encompasses 315 square feet. The interior of 429,780 square feet has two lower floors that serve as a base for a narrower and nearly windowless 13-story tower capped with a smaller penthouse. Interior floors have few walls and are supported by bare columns to create a flexible space to arrange stacks of books; the size of the windows was minimized to avoid uneven light from the outside.

The two lower floors feature a more extensive use of glass, as well as brick and tweed granite, while the upper floors are finished in Makato stone. The library's collection reached one million volumes in 1970 and surpassed 1.5 million volumes in 1986. In 1987 the library was renamed Hesburgh Library in honor of Fr. Hesburgh, the university's retiring president, who served as Notre Dame's president for thirty-five years. In his retirement, Hesburgh maintained an office on the library's thirteenth floor, overlooking the Main Quad; as of 2009, the library housed 3.39 million volumes. The Association of Research Libraries ranked it the 61st largest collection among research universities in the United States. In 2015 the university began major renovations to the library that will modernize its interior design; the side of the library facing the stadium is covered with a mural called The Word of Life, more known as Touchdown Jesus, that measures 134 feet high and 68 feet wide. When the library opened in 1963, the mural had not yet been installed.

American artist Millard Sheets was commissioned to create a work large enough to cover the entire side of the library facing Notre Dame's football stadium. Fr. Theodore Hesburgh suggested that the theme should be scholars through the ages; the artwork was donated by Mr. and Mrs. Howard V. Phalin of Winnetka, Illinois. Installation took place in the spring of 1964; the mural is composed of 324 panels. It consists of 81 different stones from 16 countries in 171 finishes that includes 46 granites and syenites, 10 gabbros and labradorites, 4 metamorphic gneisses, 12 serpentines, 4 crystalline marbles, 5 limestones; the artwork depicts a procession of figures representing Christian saints, thinkers and writers, a topic that connected to the idea of the library. Figures were selected from different centuries and places to convey the concept of the Catholic Church's historical continuity. At the top of the procession the central figure is the resurrected Jesus Christ, conceived as the great teacher and master, the fountain of knowledge contained in the library.

The artwork, titled Word of Life, is 134 feet tall and 68 feet wide. The mural's image of Jesus, visible from Notre Dame's football stadium, has arms raised in the same fashion as a referee signifying a touchdown. From this similarity came the mural's nickname, Touchdown Jesus. A stadium expansion obscures views of the mural from the field