Bennett conjectured that these eleven solutions (the eight with integer exponents and the three with fractional exponents) are the only ones.
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But they involve infinitely many terms riddled with unknown exponents and coefficients.
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Abigail also suggested a cool modification to the original problem: fractional exponents!
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The ballet and its maker have always had ardent adherents and exponents.
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Exponents of the futuristic tech economy frequently adopt this fifty-year-old perspective.
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Its greatest exponents are mostly gaunt East Africans with similar-sounding names and taciturn manners.
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The most important exponents of this new doctrine, according to Sitaraman, are Warren and Sen.
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This "graffitism" is less developed than the first trend, more tentative and with fewer exponents.
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Critical exponents corresponding to other well-known universality classes lie at kinks in other exclusion plots.
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This immense number can only be practically written down in mathematical notation using exponents: 2⁷⁴,²⁰⁷,²⁸¹ − 1.
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To explain this, it helps to understand the categories into which Sunni Islam's main exponents fall.
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But the irony is that one of the key exponents of the school was Robert Bork.
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Francis, speaking on the plane, warned that the church's exponents of that view were backward-looking.
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They had trained with Le Corbusier in Paris, and they were early exponents of his ideas.
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Exponents of the "New Complexity" school, like Michael Finnissy, were directly inspired by Taylor's torrents of sound.
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Even so, students tell me they find the assignments as demanding as rational exponents and linear inequalities.
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Haldane is one of the best exponents of the new style of talking directly to the public.
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As the movement gained a name, postmodernism, Mr. Tigerman became one of its leading exponents and practitioners.
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The stretching and compressing in the different dimensions correspond to a system's positive and negative "Lyapunov exponents," respectively.
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These artists were exponents of what would later be termed, in the West, an art of institutional critique.
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I encouraged readers to consider generalizing the "doubly good" question to fractional exponents, but I got no takers.
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If you use the PEMDAS method, the order of the equation is Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction.
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Liberals have been particularly enthusiastic exponents of Powell's diversity doctrine, but the ideal of diversity is generally nonpartisan.
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Freestyle has become a popular pursuit around the world and the leading exponents compete in prestigious international championships.
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She would go on to write cookbooks that made her one of America's foremost exponents of traditional Southern cuisine.
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His American Modern Dance project is historically important, connecting his work to older and younger exponents of the tradition.
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When challenged, they take to a blackboard, leaving behind a chalky mélange of exponents, cosines and the Greek alphabet.
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Its exponents took pains to show that mainstream hip-hop videos offered only a partial representation of black life.
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Surely, I thought, a party whose leading exponents are now identified with such repugnant views can't possibly take the presidency.
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There are many exponents today of what's called flamenco nuevo, who add novel features of style, dress, music and rhythm.
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The complex refracted the continuing attempt, by Maekawa and other exponents of Corbusianism, to balance the old and the new.
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By 2016, Poland and Simmons-Duffin had calculated the two main critical exponents of the theory out to six decimal places.
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Surely there can be no finer exponents of the work of Pierre Boulez than the group he founded, the Ensemble Intercontemporain.
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Already this year, we have lost Betty Woodman and Wendell Castle — two of the greatest exponents of the American craft movement.
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The PEMDAS method adheres to the following order of operations: Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction, usually from left to right.
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Prescaling suggests that when a system first evolves from its initial, far-from-equilibrium condition, scaling exponents don't yet perfectly describe it.
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Like Mr Cocker, who cites 19th-century radicals such as William Hazlitt and William Cobbett, its exponents tend to be left-leaning.
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Caballe was considered one of the finest modern exponents of the 'bel canto repertoire', Spain's Culture Minister Jose Guirao said on Saturday.
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And flamenco dancing has so strong an element of narcissism that, even with the finest exponents, it often borders on the ridiculous.
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She's a niece of the great Madhavi Mudgal (her dance guru), one of Odissi's foremost exponents, who choreographed two of her numbers.
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He grew up believing in the superiority of the modern piano over period instruments promoted by exponents of the authentic performance movement.
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As its exponents will tell you, data wizardry is no lock against the effects of candidate quality, economic conditions, or blanket negative coverage.
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These dancers, this style's meticulous exponents, show why Mr. Alston has been Europe's finest dancemaker since the death of Frederick Ashton in 1988.
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Its exponents tend to be older and its ideas stale, seemingly fighting the same Cold War battles 30 years past their expiration date.
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Their properties are shifted only by a so-called "scaling exponent"—and scientists are discovering that these exponents are often simple numbers like ½ and -⅓.
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In fact, if we allow fractional exponents, there is a "good year" even sooner than 2046, namely the year 333 = 16(11/4)– 16.
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HOWARD JOSEPHER New York The writer is president and chief executive of Exponents, which serves people affected by drug addiction, incarceration and H.I.V.-AIDS.
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CLASSICAL MUSIC Surely there can be no finer exponents of the work of Pierre Boulez, left, than the group he founded, the Ensemble Intercontemporain.
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Daniil Trifonov's Perspectives series goes from strength to strength with this recital, and sees him paired with one of our leading exponents of song.
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This was the view of gender with which modern dance began to transform itself in the 1980s; Mr. Morris was among its earliest exponents.
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The midfield is seen as a key battleground on Saturday, with Croatia's midfielder Luka Modric regarded as one of the best exponents in the world.
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He has a free-flowing if deceptively powerful swing, and is also one of the greatest short-game exponents of his generation, if not ever.
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A meal at either one makes it obvious that Mr. Stone and Mr. von Hauske have carefully studied Copenhagen's foremost exponents of fermentation and foraging.
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It was fun to hear a piece for glass harmonica played by two fine exponents of this unusual instrument, Friedrich Heinrich Kern and Philipp Marguerre.
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"And the goal, the holy grail of all that, was these numbers," he said: Researchers wished to be able to calculate the critical exponents from scratch.
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They've since been working out a precise dictionary to translate between critical exponents and other properties of CFTs and equivalent features of the AdS-space hologram.
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Most of the time, the arguments I see from failing left-wing parties, or at least some of their exponents, are more conservative than anything else.
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Before long the fuzz tone had become a hallmark of '60s guitar rock, especially among its more psychedelic exponents, like the Jimi Hendrix Experience and Cream.
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Exponents of index investing, including Princeton University economist Burton Malkiel, author of the best-selling "A Random Walk Down Wall Street", will have none of this.
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"The statements of long-standing Republican exponents and the President elect will soothe some of the immediate pain," analysts at Julius Baer said in a note.
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But the government says there will be international election monitors — from China, Myanmar and Singapore, none of which are known as vigorous exponents of pluralist democracy.
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The win burnished Murray's reputation as one of the world's leading doubles exponents, as the Briton enjoyed his third consecutive mixed doubles triumph at Flushing Meadows.
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These critical exponents are clearly independent of either material's microscopic details, arising instead from something that both systems, and others in their "universality class," have in common.
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As Greenberg points out, the rule for dividing exponents requires us to subtract them (easy!), so we get 25 x 210(211.22-211.22)= 22 x 215 = 113,211.
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ROBERT CLARKFrankfurt The challenge to liberalism has come about not because it has failed, but because it has succeeded spectacularly, far beyond the imaginations of its exponents.
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My Favorite Page The British pianist Paul Lewis, 44, is one of today's finest exponents of Schubert, noted for his clarity of tone and simplicity of interpretation.
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Not just because they are inspiring — they are — but because they are far better ambassadors for this country and exponents of its ideals than the 45th president.
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With a rich alto and a vivacious presence onstage, this Malian singer, songwriter, guitarist and actress has become one of West Africa's most exciting young musical exponents.
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The authors exploited these symmetries to solve for the critical exponents of a famous CFT called the 2-D Ising model — essentially the theory of a flat magnet.
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The absence of the game's best exponents meant that few fans were enthusiastic about Olympic baseball, which convinced the IOC to cut it from an already teeming schedule.
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Interestingly, Bennett looked at a more general problem, which when you rephrase it a little bit is EXACTLY the question of finding "doubly good" years with fractional exponents.
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The critique actually emerges from the best traditions of journalism, which is why some of its most convincing exponents—including, most recently, Times columnist Nick Kristof—are journalists.
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Mr. Faurisson was regarded as a father figure by contemporary French exponents of Holocaust denial, the extremist fringe in a country with a long tradition of anti-Semitism.
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In another recent paper in Chaos, the Maryland team reported that their reservoir computer could successfully learn the values of these characterizing exponents from data about a system's evolution.
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Berges and his colleagues conjecture that these far-from-equilibrium particles then exhibited fractal scaling governed by universal scaling exponents as they began the thermal evolution of the universe.
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" Chase Carey, Formula One chairman and chief executive "Formula One has lost not only one of the truly great exponents of the sport but also one of its heroes.
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Trippie Redd, a Solid Foundation client, is eighteen, and is one of the leading exponents of a dark, grunge-influenced variant of hip-hop that has thrived on SoundCloud.
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"And I never felt ready," Ms. Stemme said, a bit ruefully, of passing up that chance at the part, and at studying it with one of its classic exponents.
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That two fine exponents of pressing, Hoffenheim and RB Leipzig, are performing so well this year — both are likely to qualify for next season's Champions League — proves the point.
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Yet after only a season, two out of the four main brands experimenting with the idea — Tom Ford and Thakoon — gave it up (Ralph Lauren and Burberry remain exponents).
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Its critical exponents could have landed anywhere in the allowed region on the 3-D CFT exclusion plot, but unexpectedly, the values land exactly at the kink in the plot.
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After all, many of its most infamous exponents – Diego Maradona, Sergio Busquets, Marco Matterazi – have not just won countless personal accolades, but the greatest prize in football: the World Cup.
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As Romeo and Juliet, Ms. Damrau and Mr. Grigolo will have to hold their own against a litany of famous exponents of the two most famous lovers in world literature.
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Operatic characters — an aloof pantheon of gods, monarchs, priests and countesses — are generally more outsize than approachable; their exponents have traditionally been measured on a scale of perceived regality and remoteness.
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But teaching advanced concepts to students who had not all had the chance to learn certain basic math skills, like the laws of exponents, proved more difficult than some had anticipated.
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"I think Freddie was one of the early exponents of the androgynous movement — like David Bowie," says designer Zandra Rhodes, who created some of his best-known costumes during Queen's early period.
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Mr Vucic and Ivica Dacic, the leader of the Socialists and foreign minister in the outgoing government, are both ardent exponents of maintaining friendly regional relations and of joining the European Union.
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Miami City Ballet — 30 years old and always one of America's foremost exponents of the ballets of the Russian-American choreographer George Balanchine — opens at the David H. Koch Theater this week.
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Howard JosepherNew YorkThe writer is co-founder and chief clinical officer of Exponents, an organization dedicated to improving the quality of life of people affected by drug addiction, incarceration and H.I.V./AIDS.
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As the main exponents of that doctrine, Republicans seek to distribute income from the poor to the wealthy by gutting social programs and returning the savings to high-income earners through tax cuts.
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It's certainly an unseemly side of professional sport that its exponents revert to foul or abusive language to get their point across to officials – you certainly see it in soccer on a regular basis.
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A reading of Hoche and Binding's "Permitting the Destruction of Unworthy Life" shows the similarity between what they said and what exponents of practical ethics, such as Peter Singer, say about the disabled today.
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FIFA and the Vatican have several things in common: They are both largely self-regulating, they're both wealthy, they both enjoy remarkable tax breaks, and they are both exponents of religion to the masses.
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According to its exponents, Otonamaki, which translates as "adult wrapping", was devised by a Kyoto midwife who thought replicating how children are swaddled at birth could help mothers overcome post labor shoulder and hip pain.
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People like Cyrus Teed and Father Divine were only the most zealous exponents of America's unofficial national faith: a spiritual smorgasbord of positive thinking, seasoned by the eclectic 19th-century movement known as New Thought.
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But Mr. Washington plants his music in somewhat different soil, pulling rhythms from the Caribbean and Los Angeles's fusion-driven jazz scene of the 1970s and '80s, as well as the city's more Afrocentric exponents.
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Glance at the date and you see that af Klint effectively ventured into the principles of abstraction well before its more famous exponents (Kandinsky, Mondrian, and Malevich), something the publicity material takes pains to emphasize.
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They mobilized the support of the rising organized exponents of postwar liberalism: middle-class issue activists, organized labor (especially the unions once in the CIO that in 1955 merged into the AFL-CIO), and civil rights advocates.
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It is turning out to be an especially fertile season for Miller, whose birth centennial was last year, and O'Neill, who are among the most forceful exponents ever of guilt as the reigning muse of modern drama.
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Masaaki Suzuki, one of the more intelligent exponents of Bach on period instruments, leads Juilliard students and the singers of the Yale Schola Cantorum in a free, unticketed program to commemorate the 2247th anniversary of the Reformation.
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But Mr. Ancarani's allegiances are less to traditional journalistic approaches to documentary than to the immersive, anti-interpretive ethos of Lucien Castaing-Taylor, Véréna Paravel, J.P. Sniadecki and other exponents of what is sometimes called sensory ethnography.
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Exponents of this "hardware renaissance" frequently locate themselves in old industrial towns such as Pittsburgh and Detroit, in part because there is lots of cheap space available and in part because they can draw on established manufacturing skills.
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In a way, his paintings share similarities with works from Ernst Ludwig Kirchner's Berlin-based series, such as "Street, Berlin" (1913), and exponents of the New Objectivity movement, as both depict lively yet soulless urban scenes and dwellers.
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Here, Mallarmé leapfrogs over the most radical exponents of free verse: a text of seven hundred and fourteen words is scattered across eleven double pages, in staggered lines and in type of varying sizes, often with independent sentences juxtaposed.
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"Looking for Marni" is the latest of a string of consumer-focused events by the low-wattage designer Consuelo Castiglioni and her daughter Carolina, the label's director of special projects, both of whom have long been exponents of public happenings.
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Heat iron to the critical temperature where it ceases to be magnetized, for instance, and the correlations between its atoms are defined by the same "critical exponents" that characterize water at the critical point where its liquid and vapor phases meet.
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The youthful activists at the heart of the reform effort, labeled at the time as exponents of a "New Politics," brought to their engagement with mainstream party politics an outlook that bore some clear continuities with their programmatic liberal forebears.
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The second reality, which often conflicts with the ideological priors of the exponents of the first reality, but is no less true, is that the mixed economy has promoted Baumol's Salve (yes, I am leading the charge to rename this phenomenon).
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By 1967, the duo was known as the country's leading tropicalistas, exponents of a permissive new musical idiom—Tropicalismo—that grafted British and North American rock on to the gentler song-forms of what was known as música popular brasileira (MPB).
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The lineup was certainly dazzling: stars from City Ballet and American Ballet Theater but also some of the world's greatest exponents of other forms, from modern (Matthew Rushing) to tango (Gabriel Missé) to kuchipudi (Shantala Shivalingappa) to Memphis jookin (Lil Buck).
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When his wife, the former Leah Lange, took her place behind the stove, the restaurant began evolving from a simple cafe into one of the city's foremost exponents of Creole cooking, as well as an informal gallery for black artists.
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They then built a polynomial that evaluates to zero on these completion cards, and figured out an ingeniously simple way to split the polynomial into pieces with smaller exponents, which led to a bound on the size of collections with no sets.
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Some exponents overpromise that there's a blockchain solution for every problem, but many blockchain innovations are already up and running: Oil traders have used blockchain to reduce digital trading time from 3 hours to 25 minutes by speeding up verification and fraud detection.
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And yet here is Alisson: not only a Brazilian, and a goalkeeper, but coming off the back of a season in which his performances have caused many to decide that he is among the finest exponents of his position on the planet.
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In some cases, experts have traced the exponents to the number of spatial dimensions a system occupies, as well as its symmetries—that is, all the ways it can be transformed without changing (just as a square stays the same when rotated by 90 degrees).
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And in an exhibition so devoted to introducing new audiences to the exponents of postmodern dance, it feels like MoMA owes its subjects a satisfying sequel, one that can better attest to the complex web of difficulties, setbacks, and sacrifices required of such bold work.
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Not just because retailing is a big employer that touches many industries, but also because its two greatest exponents, Jack Ma and Jeff Bezos, the founders of Alibaba and Amazon, have used it to amass a new sort of conglomerate (see our special report).
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In aggravating Zinedine Zidane to the point of violence, Marco Matterazi demonstrated exquisite furbizia; he probably didn't even mean the things he said, it was simply a verbal step-over, a type of deceit that fooled one of the greatest exponents of more conventional deceptions.
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There, devotion to the sport is an enthusiasm that unites 1.3 billion people, propels its finest exponents to a status of semi-divinity and seems to offer a shot at transformative victory to every slum kid with the physical gifts and stubbornness to master the game.
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In 2012, researchers used Rattazzi and Rychkov's trick to home in on the values of the critical exponents of the 3-D Ising model, a notoriously complex CFT that is in the same universality class as real magnets, water, liquid mixtures and many other materials at their critical points.
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It seems that as a system begins to evolve, key details, like its symmetries, are retained and become encoded in the scaling exponents dictating its fractal evolution, while other details, like the initial configuration of its particles or the interactions between them, become irrelevant to its behavior, scrambled among its particles.
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Too idiosyncratic to be identified with any of the modernist movements of his times — he was highly critical of Impressionism, for example, while remaining on cordial terms with its exponents — he is now acknowledged to have been an important modernist in his own right but remains even today hard to classify.
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The 29-year-old Briton, who will be in Brazil this summer to defend the gold he won four years ago in London, has built a championship-standard run-up and pit at his home in Woburn Sands, Bedfordshire, and has invited some of the sport's best exponents to a competition.
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But unlike other exponents of the Nashville Sound, who were drawn to material written expressly for the country market, Mr. James often recorded versions of recent pop and rhythm and blues hits, like Roy Orbison's "Only the Lonely," from 19733, and the blues singer Jimmy Reed's "Bright Lights, Big City," from 21973.
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The striking thing about twenty-first-century explorations of this terrain is that they no longer require a name or a justification; rather, a growing community of creative musicians—from elders like Anthony Braxton and Wadada Leo Smith to younger exponents like Vijay Iyer and Sylvie Courvoisier—draw on classical and jazz elements as the occasion requires.
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CHICHESTER, ENGLAND — After the end of World War I, there was a radical rethinking in the visual arts, called a "Rappel à l'ordre" (Return to Order) by the Cubist painter André Lhote, as avant-garde exponents of such movements as Cubism, Futurism and Abstraction began to re-examine classical forms as fruitful modes of expression for modern times.
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While public art and architecture assumed a reactionary classicist aesthetic, other visual arts — painting, sculpture, even performance — were animated by different currents, including the second generation of Futurists; the Valori Plastici movement and its return to order; and the exponents of Il Novecento, which was heralded by Mussolini's mistress Margherita Sarfatti and, while similar to Valori Plastici, displayed more of a nationalistic bent.
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Like the Royal Danish Ballet (which, according to this theory, should dance only ballets by August Bournonville when visiting this city), Sarasota over the past 11 years, as directed by Iain Webb and Margaret Barbieri (former Ashton dancers both), has established its credentials as the foremost exponents of Ashton works, dancing many that have seldom or never been seen elsewhere this century.
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