By a strange twist of their respective fates, this foursome ends up partnering together, using their unique talents to become a ragtag team of bounty hunters, although their fortunes as such are at best mixed.

By the fundamental theorem of arithmetic, every positive integer has a unique prime factorization.

By the twentieth century, the modern notion of science as a special brand of information about the world, practiced by a distinct group and pursued through a unique method, was essentially in place.

Suppose ( A < sub > 1 </ sub >, φ < sub > 1 </ sub >) is an initial morphism from X < sub > 1 </ sub > to U and ( A < sub > 2 </ sub >, φ < sub > 2 </ sub >) is an initial morphism from X < sub > 2 </ sub > to U. By the initial property, given any morphism h: X < sub > 1 </ sub > → X < sub > 2 </ sub > there exists a unique morphism g: A < sub > 1 </ sub > → A < sub > 2 </ sub > such that the following diagram commutes:

* Le Pétomane 1857-1945 a tribute to the unique act which shook and shattered the Moulin-Rouge ( 1967 ), By Jean Nohain and François Caradec-Publisher: Souvenir Press

By contrast, zero has no multiplicative inverse, but it has a unique quasi-inverse, 0 itself.

By adding a unique ink replenishment system based on a peristaltic pump mechanism, TallyGenicom produced the first impact printers to offer consistent print quality.

Thus, what the axiom schema is really saying is that, given a set A and a predicate P, we can find a subset B of A whose members are precisely the members of A that satisfy P. By the axiom of extensionality this set is unique.

By the axiom of extensionality this set is unique.

By the axiom of extensionality this set B is unique and it is called the union of A, and denoted.

By exception the three surviving lodges that formed the world's first known Grand Lodge in London ( today called the United Grand Lodge of England ) have the unique privilege to operate as time immemorial i. e. without such warrant ; only one other lodge operates without a warrant-this is the Grand Stewards ' Lodge in London, although it is not also entitled to the " time immemorial " title.

By testing various hypotheses, these researchers hope to discover the unique mechanism that causes the spontaneous pain of CRPS and that discovery may lead to new ways of blocking pain.

By combining the imagery of socialist realism, Nazism and Italian futurism, the group created a unique aesthetic style which could not pass unnoticed by the public.

" By forging her own unique identity through her artistry and her business ventures, she has been esteemed as the " Queen of Pop ".

By some arguments, while the Blue Grass Boys were the only band playing this music, it was just their unique sound ; it could not be considered a musical style until other bands began performing in similar fashion.

By the early 1990s, much of the city's unique heritage had been lost and many Chileans had given up on the city.

By the fundamental theorem of arithmetic, every positive integer greater than 1 has a unique prime factorization.

By the time he died in 1844, 77, 000 copies of his fables had been sold in Russia, and his unique brand of wisdom and humor gained popularity.

By the time of his rehabilitation in 1955, Tupolev had designed and was about to start testing his unique turboprop strategic bomber, the Tu-95.

By Mostow – Prasad rigidity, the hyperbolic structure on the complement of a hyperbolic link is unique, which means the hyperbolic volume is an invariant for these knots and links.

By comparing many hundreds of families of twins, researchers can then understand more about the complementary roles of genetic effects, shared environment, and unique environment in shaping people.

By replacing the old hierarchy with self-managed teams, more responsibility is placed upon unique and self-managed teams which create better communication and productivity.

By contrast, mosses and other bryophytes have only a single set of chromosomes and so are haploid ( i. e. each chromosome exists in a unique copy within the cell ).

By her fourth film, Deren discussed in An Anagram that she felt special attention should be given to unique possibilities of time and that the form should be ritualistic as a whole.

By issuing the Papal Bull to exterminate Hussites, Wycliffites, and other heretics in Bohemia on 1 March 1420, Martin V initiated the Hussite Wars.

By the Treaty of Utrecht that concluded the War, the Papal States lost their suzerainty over the Farnese Duchy of Parma and Piacenza in favour of Austria, and lost Comacchio as well.

By yielding the Papal claims to Parma, Clement obtained the restitution of Avignon and Benevento, and in general he succeeded in placing the relations of the spiritual and the temporal authorities on a friendlier footing.

By a series of complicated stratagems he first succeeded in rendering it impossible for the Borgias to retain their power over the Papal States.

By the end of the year Sancho VII had dropped out of the war under Papal pressure.

By decree of Pope Pius XII in 1949, the remains of Pius VI were moved to the Chapel of the Madonna below St. Peter's in the Papal Grotto.

By 1300, the Papal States, along with the rest of the Italian principalities, were effectively independent.

By Papal Bull dated 14 October 1504, Fisher was appointed the Bishop of Rochester at the personal insistence of Henry VII.

By the Lateran Treaties, Mussolini granted Pope Pius XI the crown of Vatican City as a nation to rule, made Roman Catholicism the state church of Italy, and paid the Pope compensation for the loss of the Papal States.

By 1511 the League of Cambrai had collapsed due to Papal fears of the growing power of France in Italy.

By mid-afternoon of April 29, a cease-fire, facilitated by the Papal Nuncio, was negotiated.

By June 1511, most of the Romagna was in French hands ; the Papal army, disorganized and underpaid, was in no condition to prevent Trivulzio from advancing on Ravenna.

By the twentieth century only the Bishop of Rome ( the Pope, as Sovereign Monarch of Vatican City, formerly of the Papal States, a major power on the Italian peninsula until 1870 ) and the Bishop of Urgell ( as Co-Prince of Andorra ) were still reigning, territorial " princes of the church ".

By the Papal bull Parens scientiarum ( 1231 ), the charter of the University of Paris, Pope Gregory IX authorized the masters, in the event of an outrage committed by anyone upon a scholar and not redressed within fifteen days, to suspend their lectures.

By August 1860, Keogh was appointed second lieutenant of his unit in the Battalion of St. Patrick, Papal Army under the command of General Christophe Léon Louis Juchault de Lamoricière.

By royal dispensation he was relieved of the necessity of taking the customary oaths on accepting office.

By 1994, with the show's sixth season, Swartzwelder was granted a special dispensation and allowed to no longer attend rewrite sessions with the rest of the staff, instead being allowed to send drafts of his scripts in from home so other writers could revise them as they saw fit.

By papal dispensation, he married Charlotte des Essarts, Mademoiselle de La Haye in 1611.

By Apostolic dispensation, our priests have thus far been ordained titulo missionis for the most part.