Given a trigonometric series f ( x ) with S as its set of zeros, Cantor had discovered a procedure that produced another trigonometric series that had S ' as its set of zeros, where S ' is the set of limit points of S. If p ( 1 ) is the set of limit points of S, then he could construct a trigonometric series whose zeros are p ( 1 ).

Given as a series of linked short stories, the book is also interspersed with brief commentaries on contemporary British politics.

" Given the fact that it's the third film in the series, you couldn't just end with them obtaining the object.

Given formal power series

Given a formal power series

Given a series with values in a normed abelian group G and a permutation σ of the natural numbers, one builds a new series, said to be a rearrangement of the original series.

Given his jazz and salsa conga playing experience and knowledge ( working as a sideman with such bands as salsa's Frankie Dante's Orquesta Flamboyan and jazz saxophonist Archie Shepp ), Dawson also created the long running " Salsa Meets Jazz " weekly concert series at the Village Gate jazz club where jazz musicians would sit in with an established salsa band, for example Dexter Gordon jamming with the Machito band.

" Given the chance to relive his life by switching bodies with " a talentless 20 year-old wannabe rock star with all the looks and charm Rocky used to have ," the series deals with the subsequent soul-searching and reflection over such a decision.

Given two complexes M < sub >*</ sub > and N < sub >*</ sub >, a chain map between the two is a series of homomorphisms from M < sub > i </ sub > to N < sub > i </ sub > such that the entire diagram involving the boundary maps of M and N commutes.

Given that only six vessels were constructed after the Coast Guard takeover, the " LV -" series numbers are most commonly used.

Given reinforcements and more equipment, Maude directed his force in a steady series of victories.

Given the innately rich and personal world of fantasy he has left himself locked into, Morgan goes off the deep end, enacting a series of bizarre stunts in a campaign to win Leonie back, including putting a skeleton in her bed and crashing her wedding dressed as a gorilla, for which scene Reisz borrows clips from from the original King Kong film to illustrate Morgan's fantasy world.

Given a ring R and an R-module M, a composition series for M is a series of submodules

Given a limited budget, the player must design a tank that can defeat a series of ever more challenging opponent tanks.

Given the publicity Trueman had received after his performances in the 1952 Test series, there was a lot of public interest in his football and Lincoln's attendances increased considerably when he was playing.

Given an arbitrary series

Given an n-dimensional formal group law F over R and a commutative R-algebra S, we can form a group F ( S ) whose underlying set is N < sup > n </ sup > where N is the set of nilpotent elements of S. The product is given by using F to multiply elements of N < sup > n </ sup >; the point is that all the formal power series now converge because they are being applied to nilpotent elements, so there are only a finite number of nonzero terms.

Given their sales success, it was only natural that the Coupe de Ville and Sedan de Ville were moved to their own separate series in 1959, the Series 6300, being joined by a De Ville convertible in 1964.

:" Given that the structure of an econometric model consists of optimal decision rules of economic agents, and that optimal decision rules vary systematically with changes in the structure of series relevant to the decision maker, it follows that any change in policy will systematically alter the structure of econometric models.

Given a faster than light technology and weapons scaled similar to those of the Age of Sail, some of the battles described in the Honor Harrington series resemble real-life sea battles in our historical record.

Given that the coiled texture is the natural state of some African Americans ' hair, or perceived as being more " African ", this simple style is now often seen as a sign of self-acceptance and an affirmation that the beauty norms of the ( eurocentric ) dominant culture are not absolute.

Given that many of the talented young artists had been raised in housing projects and were short on social and dress skills, this Motown department was not only necessary, it created an elegant style of presentation long associated with the label.

Given that the USA maintained diplomatic relations with Taiwan Republic of China since the end of World War II and did not establish recognition of so-called ' Red ' China or People's Republic of China until the latter part of the twentieth century, the introduction of Taiwanese style racing to America corresponded to the close business and social contacts between these two nations.

Given this wide availabity of icon tools and icon sets, a problem can arise with custom icons which are mismatched in style to the other icons included on the system.

Given the inter-tribal style of powwow music it may be viewed as less traditional or valuable though the music is also used to support tribal identity and display the value of a living culture.

This corresponds in form to the style used by previous Swedish princes, including Victoria's younger brother Prince Carl Philip, Duke of Värmland, i. e. Prince + Given name + Duke of Somewhere.

Given her striking style and look, Rampling can also be seen on the cover of Vogue Magazine, Interview Magazine, Elle Magazine and CRUSHfanzine.

Given the tawaifs ' environment, their performance style of Kathak also differed from the court style, involving more of what in Kathak is termed nakhra ( mischievous playfulness ).

Given his young age ( 17 ), size, and ability to quickly adapt to the more physical style of hockey in North America, Bonk became a " can't miss " prospect.

Given the editorial style of the books, it is not surprising that they were ( and to some extent remain ) controversial within the numerical analysis community.

Given the large dialectal variety of the Arabic language, Al-Ahram is widely considered an influential source of writing style in Arabic.

' Given the nature of the most famous of texts from both groups, ZAMM, is of the latter nature style of title ( and, rather than in ) one must ask if ZAMM is not a product of the archery text, but rather, an ' unintended ' or ' inadvertent ' ( and unknown to Pirsig during writing and publication

Given the antiquity of these sculptures and a technical refinement indicative of artists fully conversant with all the aspects of Greek sculpture, it has been suggested that Greek communities were directly involved in these realizations, and that " the area might be the cradle of incipient Buddhist sculpture in Indo-Greek style ".

Given the uniqueness of the style in modern Japan, the Sumo Association employs specialist hairdressers called tokoyama to cut and prepare sumo wrestlers ' hair.

Coinciding with this concert was the release of an album that returned to Karat's more distinctive style of progressive rock, Die geschenkte Stunde ( The Given Hour ).

Given its Classical Revival style of architecture along with the fact that its color is white, the Capitol was the double for the exterior shots of The White House featured in the movie The Contender.

Order of the Stag's Blood ( DSB ): Given for use and artistry of SCA style weaponry

Given that a small bet is generally half of a big bet and that a small blind is generally half of the small bet, the minimum BB in casino style holdem is four cents.

Given the title of the album, it is also an example of their self-deprecating humor style, with the logic that silence can actually be considered some of their best work.

Given a small ball or marbles, he would invent games and play by himself for hours.

Given the similarities in the two characters ' names, professions, written works and generally dark subject matter, it is likely that Lovecraft's Alhazred provided the main inspiration for al-Hazir.

Given the absolute magnitude, for objects within our galaxy you can also calculate the apparent magnitude from any distance ( in parsecs ):

Given this, the bidding is said to start at the one-level when contracting for a total of seven tricks, at the two-level for eight tricks and so on to the seven-level to contract to take all thirteen tricks.

Given x ∈ A, the holomorphic functional calculus allows to define ƒ ( x ) ∈ A for any function ƒ holomorphic in a neighborhood of Furthermore, the spectral mapping theorem holds:

Love and Erlandson continued to pursue with the band, and released the single " Be A Man "— an outtake from the Celebrity Skin sessions — for the soundtrack of the Oliver Stone film Any Given Sunday ( 1999 ).

Given that many journeys are for relatively short distances, there is considerable scope to replace car use with walking or cycling, though in many settings this may require some infrastructure modification, particularly to attract the less experienced and confident.

Given more time to prepare for trial, Kidd likely would have been able to find the deposition Palmer gave when he was captured in Rhode Island two years earlier.

Given their speed and maneuverability, clippers frequently mounted cannon or carronades and were used for piracy, privateering, smuggling, or interdiction service.

Given Chrétien's known tendency to create new stories and characters, being the first to mention the hero Lancelot and his love affair with Queen Guinevere for example, the name might also be entirely invented.

Given that the dispute with Pizarro over Cuzco had kept intensifying, Almagro spent a great deal of time and money equipping a company of 500 men for a new exploration south of Peru.

Given a particular query, the DBMS ' query optimizer is responsible for devising the most efficient strategy for finding matching data.

Given the limited success of the Charity School, however, Wheelock intended his new College as one primarily for whites.

Given a particular query, the DBMS ' query optimizer is responsible for devising the most efficient strategy for finding matching data.

Given a subset X of a manifold M and a subset Y of a manifold N, a function f: X → Y is said to be smooth if for all p in X there is a neighborhood of p and a smooth function g: U → N such that the restrictions agree ( note that g is an extension of f ).

Given the magnitude of the disaster, reconstruction and economic recovery will remain the primary focus of the Salvadoran Government for some time to come.

Given a left neutral element and for any given then A4 ’ says there exists an such that.

Given the limited budget for schools, it is claimed that a voucher system would weaken public schools while at the same time not necessarily providing enough money for people to attend private schools.

Given also a measure on set, then, sometimes also denoted or, has as its vectors equivalence classes of measurable functions whose absolute value's-th power has finite integral, that is, functions for which one has

Given the wide disparity of concepts and methods across domains, 4GL limitations lead to recognition of the need for the 5GL.

Given these origins, there have been various suggestions over the years to rename the town ( for example, to " Invernevis ").