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 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 a programming or specification language, abstract interpretation consists of giving several semantics linked by relations of abstraction.

Given names resonant of qualities which are perceived to be either masculine or feminine are frequently given, with males being linked with strength and firmness and females with beauty and flowers.

Given that the problem of high textbook prices is linked to the " broken " economics of the market, requiring publishers to disclose textbook prices to faculty is a solution pursued by a number of legislatures.

Given that economic geoscientists had the lowest percentage of all Earth scientists surveyed, critic and author John Cook has claimed that " climate scepticism seems strongest among geologists closely linked to the mining and fossil fuel industries " and that this is due to the influence of their funding.

Given the attitude of Aes Sedai and non-channelers in the Third Age it is not likely that all leaders of the Hall of Servants could summon the Nine Rods, but that this power was linked to the individual's ability rather than his or her station as First Amongst Servants.

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 the short distances of super special stages compared to the regular special stages and consequent near-identical times for the frontrunning cars, it is very rare for these spectator-oriented stages to decide rally results, though it is a well-known axiom that a team can't win the rally at the super special, but they can certainly lose it.

:: See Committee Note to Interim Rule 8001 ( f ) (" Given the short time limit to file the petition with the circuit clerk, subdivision ( f )( 1 ) provides that entry of a certification on the docket does not occur until an effective appeal is taken under Rule 8003 ( a ) or ( b ).

Given that their favorite prey are often mammals or birds that hesitate to fly, unsurprisingly most of their prey is killed on the ground and some prey may even pursued on foot for a short distance by the eagle.

Given a short exact sequence with maps q and r:

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 landing package of NASA's Spirit rover mission rebounded off the surface in Gusev crater numerous times before coming to a standstill-taking much more time than anticipated-Beagle's timer may have been set to a too short time ( see Section 5. 4. 8 of the Inquiry Report );

Given the older ages of these stars, and the short lifetimes of micrometer-sized dust grains around stars due to Poynting Robertson drag, collisions, and radiation pressure ( typically hundreds to thousands of years ), it is thought that this dust is from the collisions of planetesimals ( e. g. asteroids, comets ).

Given Vanier's physical state, Pearson was hesitant to advise the Queen to act along those lines, but his worry was short lived, as the following day, after hearing the Holy Sacrifice of the Mass and receiving Holy Communion in the chapel, the Governor General died.

Given that the sequences that the restriction enzymes recognize are very short, the bacterium itself will almost certainly have many of these sequences present in its own DNA.

Given a sufficiently high and well known amount of electric current and voltage, the timing of the bridgewire vaporization is both extremely short ( a few microseconds ) and extremely precise and predictable ( standard deviation of time to detonate as low as a few tens of nanoseconds ).

Given only a short time to prepare, Wei was only able to demonstrate Viola's equivalent capabilities for local rather than remote files at the 2003 Eolas v. Microsoft trial, and thus fell short of proving prior art to the court's satisfaction.

Given the wide expectation that the war was going to be a short one, the majority however supported the war effort and the call to restore the " freedom of small nations " on the European continent.

Given the availability of experienced short fiction writers at the time, Elwood's choice of inexperienced authors aroused suspicions.

Given that duels were generally fought at short distances ( was typical ) between stationary opponents, accuracy was not a major problem.

Given the short distance ( 90 miles ) between Axis airfields on Sicily and the planned drop zones over Malta, it was possible for the motorized transports to make four round-trips per day.

Given the change in direction apparent in his poetry, scholars assume only his death a short time after publication prevented him from further exploration ; the collection may in fact have been published posthumously.

Given R-modules A and B, an extension of A by B is a short exact sequence of R-modules

Given the sheer size of the SOL, it seems unlikely that the hallway extended entirely from one end of the ship to the other, given that Joel and Mike were able to run from bridge to theater in so short a time ; however, if it didn't, precisely what was at the other end of the SOL was never revealed.

Given a subspace, one may form the short exact sequence

Given the short life span of past witnesses, Jimmy places him in secret protective custody.

Given its age, this short film is available to freely download from the Internet.

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.