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Page "Generating function" ¶ 51
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Some Related Sentences

When and series
When he was made a vice president only a year after the new sales job, a leading business magazine ran his photograph with a brief biography in a series on national business leaders of the future.
When the series ended in the United Kingdom, a further seven volumes were issued exclusively in Australia, meaning that over 28 volumes, all 200 episodes were released on VHS.
When the UK Channel 4 television program " The Bermuda Triangle " ( c. 1992 ) was being produced by John Simmons of Geofilms for the Equinox series, the marine insurance market Lloyd's of London was asked if an unusually large number of ships had sunk in the Bermuda Triangle area.
When an unconscious patient enters a hospital, the hospital utilizes a series of diagnostic steps to identify the cause of unconsciousness.
When they returned to San Francisco for their final series with the Giants on September 14, the Rockies had once again built a large Wild Card lead.
For example, series of humorous tips in MikroBitti 5 / 1989 said " When programming late, coffee and kebab keep nicely warm on top of the 1541.
When Beaux arrived in Paris, the Impressionists, a group of artists who had begun their own series of independent exhibitions from the official Salon in 1874, were beginning to lose their solidarity.
When the Fujiko Fujio duo broke up in 1987, the very idea of an official ending to the series was never discussed.
When the comic switched to the Tamers series the storylines adhered to continuity more strictly ; sometimes it would expand on subject matter not covered by the original Japanese anime ( such as Mitsuo Yamaki's past ) or the English adaptations of the television shows and movies ( such as Ryo's story or the movies that remained undubbed until 2005 ).
When his wife Josefa died in 1812, he was mentally and emotionally processing the war by painting The Charge of the Mamelukes and The Third of May 1808, and preparing the series of prints later known as The Disasters of War ( Los desastres de la guerra ).
When Rohmer revived the series in the early 1930s, Smith ( who has been knighted ) is Assistant Commissioner of Scotland Yard.
When a new segment producer edits footage of Brooke out of a story in I Disease ( series 3 ), she becomes upset to the point where she demands that the producer be fired for it.
When the intermediate states at intermediate times are energy eigenstates ( collections of particles with a definite momentum ) the series is called old-fashioned perturbation theory.
When Bohemians rebelled against the Emperor, the immediate result was the series of conflicts known as the Thirty Years ' War ( 1618 – 48 ), which devastated the Empire.
When the PC was introduced in 1981, it was designated as the IBM 5150, putting it in the " 5100 " series, though its architecture was not directly descended from the IBM 5100.
When The Second City opened its doors on December 16, 1959, directed by Paul Sill, his mother Viola Spolin began training new improvisers through a series of classes and exercises which became the cornerstone of modern improv training.
When the sons of Tuireann, Brian, Iuchar and Iucharba, kill his father, Cian ( who was in the form of a pig at the time ), Lugh sets them a series of seemingly impossible quests as recompense.
When Cúchulainn lay wounded after a gruelling series of combats during the Táin Bó Cuailnge ( Cattle Raid of Cooley ), Lugh appeared and healed his wounds over a period of three days.
When she was fifteen, her father began to regularly gather in his house a circle of the most learned men in Bologna, before whom she read and maintained a series of theses on the most abstruse philosophical questions.
When the Livonian knights were crushed by Samogitians in the Battle of Saule in 1236, coinciding with a series of revolts in Estonia, the Livonian Order was inherited by the Teutonic Order, allowing the Teutonic Knights to exercise political control over large territories in the Baltic region.
When the extreme danger intrinsic to nuclear war and the possession of nuclear weapons became apparent to all sides during the Cold War, a series of disarmament and nonproliferation treaties were agreed upon between the United States, the Soviet Union, and several other states throughout the world.
When there is only one touring side, there is still often a best-of-five or best-of-seven series of limited overs matches.
When Cook learned a few years later that the videotapes of the series were to be wiped, a common practice at the time, he offered to buy the recordings from the BBC but was refused because of copyright issues.
When the Athletics first joined the American League, the two teams played each other in a spring and fall series.
When traveling the Presidential limousine is always accompanied by support cars ( normally BMW 5 series driven by members of the SDU ) and several Garda motorcycle outriders which form a protective convoy around the car.

When and converges
When it is positive, the power series converges absolutely and uniformly on compact sets inside the open disk of radius equal to the radius of convergence, and it is the Taylor series of the analytic function to which it converges.
When k is even the coefficients of all its Euler factors are non-negative, so that each of the Euler factors has coefficients bounded by a constant times the coefficients of Z ( E < sup > k </ sup >, T ) and therefore converges on the same region and has no poles in this region.
When the observer gain is high, the linear Luenberger observer converges to the system states very quickly.
When the price is in an uptrend, the SAR emerges below the price and converges upwards towards it.
where x, y and denote column vectors of length T. When x and are uncorrelated, under certain regularity conditions the second term has an expected value conditional on x of zero and converges to zero in the limit, so the estimator is unbiased and consistent.
When the theory of distributions was still not widely known nor used, property above was formulated by saying that the convolution of the function ' with a given function belonging to a proper Hilbert or Banach space converges as ε → 0 to this last one: this is exactly what Friedrichs did .< ref > See, properties PI, PII, PIII and their consequence PIII < sub > 0 </ sub >.</ ref > This also clarifies why mollifiers are related to approximate identities.

When and absolutely
When the site was excavated by Soviet archaeologists during 1941-45, they realized that they had discovered a building absolutely unique for the area: a large ( 1500 square meters ) Chinese-style, likely Han Dynasty era ( 206 BCE – 220 CE ) palace.
When the King and Queen were crowned sovereigns of England, Anne gave proof of her sincerity by absolutely refusing to receive the Protestant sacrament, declaring that she preferred to forfeit her crown rather than take part in what she considered a sacrilegious profanation.
When I hear a tone, I cannot be completely sure that there is a tone in the real world, but I am absolutely certain that I do hear.
When the Avengers arrive on the scene they immediately try to destroy him but the Cube imbues him with nearly unlimited power, making him absolutely invulnerable.
When you say ' Death to Israel ,' you mean death to occupation, death to apartheid, death to oppression, death to ... absolutely not to any human being.
When it was absolutely necessary for him to say something, he would say it in the least possible number of words, and then, only in Hebrew.
" When I first realized that there was absolutely no equal opportunity, no equality, in New Brunswick ," he recalled in the 1980s, " well, I had to come to the conclusion that something had to be done immediately.
When dealing with the complex networks of interactions presented by ecosystems, one cannot assert positively that there is absolutely no competition between or benefit to either species.
When told about the plot, de Gaulle ( who was notoriously careless of his personal safety ) refuses, absolutely, to cancel his public appearances, modify his normal routines, or even allow any kind of public inquiry into the assassin's whereabouts to be made.
When it is absolutely necessary to forward messages to recipients who don't know one another, it is good practice to list the recipient names all after " bcc :" instead of after " to :".
" zoologist, David Barash ( Co-author of the book " The Myth of Monogamy ") and his wife, Dr. Judith Eve Lipton, comment on monogamy and evolution, " When it comes to human beings, there's absolutely no question about monogamy being natural.
When campaigning for re-election, Gillan said that High Speed 2 would be " a lot more than just the blight on the properties nearby ... the implications for the area will be absolutely phenomenal ".
When he left university he: " owned two pairs of jeans, a donkey jacket, a bicycle and a pilot ’ s licence ; which shows I had my priorities absolutely right .”
When the local paper approached Coleman before they published this information he told them that " This has absolutely nothing to do with me, nothing whatsoever, and if you say otherwise you will be hearing from my solicitor.
When the field is not algebraically closed, the case where the endomorphism ring is as small as possible is of particular interest: A simple module over k-algebra is said to be absolutely simple if its endomorphism ring is isomorphic to k. This is in general stronger than being irreducible over the field k, and implies the module is irreducible even over the algebraic closure of k.
* FedEx: " When your package absolutely, positively has to get there overnight "
When investigating amaurosis fugax, an ophthalmologic consult is absolutely warranted if available.
When printing to the backside of the lens, the critical registration of the fine " slices " of interlaced images must be absolutely correct during the lithographic or screen printing process or " ghosting " and poor imagery might result.
: When I hear you talk about a lot of new names, it ’ s not always possible for me to understand when I ’ ve seen absolutely nothing by them.
When Butler retired in April, 1776, Croghan lobbied for his position, but George Morgan was chosen as Indian agent and he " had absolutely no use for Croghan.
When you mass produce blue lasers in large quantities, hardware costs will absolutely come down ,” Mr. Parsons said.
When asked by a reporter why he chose to accept the Green Bay job, Sherman responded: " There is absolutely no other college job I would have left Texas A & M for and only one professional job that I've ever had any interest in and that being the Green Bay Packers.
When she found out he dated another while they were apart ( he kept it a secret ), she was absolutely furious — believing he cheated on her.

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