That brevity has also been connected to other unusual features: the fast pace of the first act, which has seemed to be " stripped for action "; the comparative flatness of the characters other than Macbeth ; the oddness of Macbeth himself compared with other Shakespearean tragic heroes.

Over 20 behavioral patterns in captive chimpanzees have been documented as ( statistically ) abnormal for frequency, severity or oddness — some of which have also been observed in the wild.

As well as the oddness of the design, the vehicle's commercial success was also stymied by unfortunate timing as it was released onto the market at the same time as the Morris Mini, which was only £ 60 more expensive.

" And in The New York Review of Books, Robert Lowell also reviewed the book, writing, " At first the brain aches and freezes at so much darkness, disorder and oddness.

It also has an Arabian Nights-style romance mixed with a large dash of psychedelia and general oddness.

Though it is odd, yet it simply reflects the oddness of life.

It is often useful to prove surjectivity or injectivity and prove oddness or evenness, if possible.

The concept of evenness or oddness is only defined for functions whose domain and range both have an additive inverse.

Almódovar does not linger in the oddness of the sexual relationship between a traditional housewife in her forties and a rebellious punk teenager, which is presented without judgment as nothing out of the ordinary.

Despite the overlordship of Ozma, many of the communities live autonomously ; Oz has great tolerance for eccentricity and oddness.

One genre, which vies in oddness with the English " Merryland " productions, was inspired by the newly translated Arabian Nights and involved the transformation of people into objects which were in propinquity with or employed in sexual relationships: such as sofas, dildos and even bidets.

" He explained unusual pseudonyms: " If a member leaves the band I can replace him by another musician and keep the name " even though this does not explain their oddness.

But, as John remarks, to themselves the family's oddness seems " right as rain.

" The book's scarcity and oddness has seen original copies priced at $ 4, 000 by book dealers.

" The book's scarcity and oddness has seen copies priced at $ 4, 000 by book dealers.

Working toward preserving the ancient interpretation of the Wunderkammer and those interested in their own oddness.

The Carmichael numbers are the Knödel numbers K < sub > 1 </ sub >.

In this sense, Carmichael numbers are similar to prime numbers ; in fact, they are called Fermat pseudoprimes.

Carmichael numbers are sometimes also called absolute Fermat pseudoprimes.

Carmichael numbers are important because they pass the Fermat primality test but are not actually prime.

Since Carmichael numbers exist, this primality test cannot be relied upon to prove the primality of a number, although it can still be used to prove a number is composite.

Still, as numbers become larger, Carmichael numbers become very rare.

For example, there are 20, 138, 200 Carmichael numbers between 1 and 10 < sup > 21 </ sup > ( approximately one in 50 billion numbers ).< ref name =" Pinch2007 "> Richard Pinch, " The Carmichael numbers up to 10 < sup > 21 </ sup >", May 2007 .</ ref > This makes tests based on Fermat's Little Theorem slightly risky compared to others such as the Solovay-Strassen primality test.

An alternative and equivalent definition of Carmichael numbers is given by Korselt's criterion.

It follows from this theorem that all Carmichael numbers are odd, since any even composite number that is square-free ( and hence has only one prime factor of two ) will have at least one odd prime factor, and thus results in an even dividing an odd, a contradiction.

From the criterion it also follows that Carmichael numbers are cyclic .< ref > Proof sketch: If is square-free but not cyclic, for two prime factors and of.

Korselt was the first who observed the basic properties of Carmichael numbers, but he could not find any examples.

The next six Carmichael numbers are:

These first seven Carmichael numbers, from 561 to 8911, were all found by the Czech mathematician Václav Šimerka in 1885 ( thus preceding not just Carmichael but also Korselt, although Šimerka did not find anything like Korselt's criterion ).

J. Chernick proved a theorem in 1939 which can be used to construct a subset of Carmichael numbers.

Whether this formula produces an infinite quantity of Carmichael numbers is an open question ( though it is implied by Dickson's conjecture ).

Linebarger also employed the literary pseudonyms " Carmichael Smith " ( for his political thriller Atomsk ), " Anthony Bearden " ( for his poetry ) and " Felix C. Forrest " ( for the novels Ria and Carola ).

Using λ instead of φ ( n ) allows more choices for d. λ can also be defined using the Carmichael function, λ ( n ).

In this version, in which Hoagy Carmichael also plays a role, the Rick Martin character lives.

Eddie Condon, Hoagy Carmichael, and Mezz Mezzrow, all of whom hyperbolically raved about his playing, also saw Beiderbecke play live or performed alongside him.

She also joined a host of distinguished comedy stars, including Ian Carmichael and Peter Sellers, in the Boulting Brothers ' satire I'm All Right Jack ( 1959 ).

" Garden Canyon was also the name of the post office and Carmichael was the postmaster.

It was also adapted for radio with Ian Carmichael as Lord Peter and Ann Bell as Harriet Vane, also part of a BBC radio series in 1973.

Others associated with Graham's ministries are also inductees: George Beverly Shea ( soloist of the Billy Graham Evangelistic Team ); Cliff Barrows ( inducted 1988-music director and choir master for all Billy Graham Evangelistic Campaigns ); Ralph Carmichael ( producer for the music in Billy Graham films such as " Mr. Texas ", " For Pete's Sake ", " The Restless Ones ", and " His Lane "); and singers Ethel Waters and Stuart Hamblen.

" Later in 1956 he had again appeared alongside Attenborough with small roles in Jay Lewis's The Baby and the Battleship and Roy Boulting's Brothers in Law, also featuring Carmichael and Terry-Thomas.

He began to compose songs, " Washboard Blues " and " Boneyard Shuffle " for Curtis Hitch, and also " Riverboat Shuffle ", recorded by Beiderbecke, which became a staple of jazz and Carmichael ’ s first recorded song.

Bix Beiderbecke ’ s early death also darkened Carmichael ’ s mood.

He also befriended influential figures such as Malcolm X, Stokely Carmichael, John Lennon and Yoko Ono.

His mother, Mabel R. Carmichael, was a stewardess for a steamship line, and his father, Adolphus, was a carpenter who also worked as a taxi driver.

Carmichael also lamented the 1967 execution of Marxist revolutionary Che Guevara, professing:

She also played, on radio, the Dowager Duchess ( Lord Peter Wimsey's mother ) in the radio adaption of Strong Poison that starred Ian Carmichael as Peter Wimsey.

The order ord < sub > n </ sub > a also divides λ ( n ), a value of the Carmichael function, which is an even stronger statement than the divisibility of φ ( n ).

Stokely Carmichael, also known as Kwame Toure, a student in the Department of Philosophy and the Howard University School of Divinity coined the term " Black Power " and worked in Lowndes County, Alabama as a voting rights activist.

She also separated from Carmichael in 1973 and continued to perform primarily in Africa, Europe and Asia, but not in the United States, where a de facto boycott was in effect.

* Sandy Carmichael, Scottish rugby player who also played for the British Lions