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After Hilbert's initial formulation, the later development of abstract Hilbert space and the spectral theory of a single normal operator on it did very much go in parallel with the requirements of physics ; particularly at the hands of von Neumann.
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After and Hilbert's
Some of this is based on constructing G geometrically as a Galois covering of the projective line: in algebraic terms, starting with an extension of the field Q ( t ) of rational functions in an indeterminate t. After that, one applies Hilbert's irreducibility theorem to specialise t, in such a way as to preserve the Galois group.
After some results were obtained confirming Hilbert's conjecture in special cases and for certain classes of rings ( in particular the conjecture was proved unconditionally for n =
After and initial
After an initial rejection, which he attributed to a `` general Excitement against Abolition and Emancipation '', Giffen bribed the right individuals on the jury, and got the permission without further delay.
After some initial success in his efforts to take possession, Albert was driven from Saxony, and also from his Northern march by Henry, and compelled to take refuge in south Germany.
After this initial chemotherapeutic compound proved effective, others pursued similar lines of inquiry, but it was not until in 1928 that Alexander Fleming observed antibiosis against bacteria by a fungus of the genus Penicillium.
After a protracted development cycle the initial AAM-N-2 Sparrow entered limited operational service in 1954 with specially modified Skyknights all weather carrier night fighters.
After his initial stint with small-time gangs that included the Junior Forty Thieves and the Bowery Boys, Capone joined the Brooklyn Rippers and then the powerful Five Points Gang based in Lower Manhattan.
After initial successes such as the Oslo accords of the early 1990s, Clinton attempted to address the Arab-Israeli conflict.
After the introduction of presidency the law was amended twice: on September 4, 1996 and on November 9, 1999 but on the whole the law retains its initial contents.
After acquiring an initial fleet of utility and transport aircraft, the squadron was attached to an interarmy support regiment.
After receiving their initial two cards, players have the option of getting a " hit " ( taking additional cards ) to bring their total value of cards to 21 points, or as close as possible without exceeding 21 ( called " busting ").
After receiving an initial two cards, the player has up to four standard options: " hit ," " stand ," " double down ," or " split ".
After the initial adoption of the Convention, some LDCs and environmental organizations argued that it did not go far enough.
After an initial success, his first line of cavalry, under the Imperial General of Horse, Prince Maximilian of Hanover, were pressed by the second line of Marsin's cavalry, and were forced back across the Nebel in confusion.
After its initial expansion from a singularity, the Universe cooled sufficiently to allow energy to be converted into various subatomic particles, including protons, neutrons, and electrons.
After its initial release in 1075 / 6, Gesta was complemented with supplementary Scholias until the death of Adam in the 1080s.
After these initial setbacks, the barbarians moved southwards through Haemus mountain and Decius pursued them ( likely through the Shipka Pass ) to save Philippopolis.
After the initial move, the players alternately move one piece at a time ( with the exception of castling, when two pieces are moved ).
After this initial excursion there was little interest from colonial authorities in further exploring modern-day Chile.
After initial Conservative opposition to Keynesian fiscal policy, this settlement was broadly accepted by all parties until Margaret Thatcher became Prime Minister in 1979.
After an initial release in August 1935, the Commonwealth Department of Health decided to ban future introductions until a study was conducted into the feeding habits of the toad.
After many months of negotiation, agreement was reached between Hydro Quebec and Rediffusion on February 28, 1950 for an initial 5 year period.
After an initial six-month review process, William Ruckelshaus, the Agency's first Administrator rejected an immediate suspension of DDT's registration, citing studies from the EPA's internal staff stating that DDT was not an imminent danger to human health and wildlife.
After Zwicky's initial observations, the first indication that the mass to light ratio was anything other than unity came from measurements made by Horace Babcock.
After the initial investigation, the police failed to control disclosure of information and speculation about the crime scene.
After initial resistance, the terms were eventually accepted.
After initial acquisition, Autonav keeps the subject in frame, even commandeering the spacecraft's attitude control.
After and formulation
After Labour Listens, the party went on, in 1988, to produce a new statement of aims and values — meant to supplement and supplant the formulation of Clause IV of the party's constitution ( though, crucially, this was not actually replaced until 1995 under the leadership of Tony Blair ) and was closely modelled on Anthony Crosland's social-democratic thinking — emphasising equality rather than public ownership.
After a dose of conventional oral oxycodone, peak plasma levels of the drug are attained in approximately one hour ; in contrast, after a dose of OxyContin ( an oral continuous release formulation ), peak plasma levels of oxycodone occur in about three hours.
After the technology improved, the dropout rate was greatly reduced, nevertheless Panasonic deemed ME formulation not robust enough for professional use.
After providing a mathematical formulation of locality and realism based on this, he showed specific cases where this would be inconsistent with the predictions of QM.
After the formulation of a committee, and their research reported, seven institutions: Delaware State University, Howard University, University of Maryland Eastern Shore, Morgan State University, North Carolina A & T State University, North Carolina Central University and South Carolina State College agreed to become the Mid-Eastern Athletic Conference.
After defining these two performance metrics for the quantizer, a typical Rate – Distortion formulation for a quantizer design problem can be expressed in one of two ways:
After the formulation of the Nicene Creed, its initial liturgical use was in baptism, which explains why the text uses the singular " I ... instead of " we ...." The text was gradually incorporated into the liturgies, first in the east and in Spain, and gradually into the north, from the sixth to the ninth century.
After a public backlash, Coca-Cola reintroduced the original formulation.
After the Restoration, the Lord Chancellor was made ex-officio president of the parliament ( now reflected in the Scottish Parliament by the election of a presiding officer ), his functions including the formulation of questions and putting them to the vote.
After 45-years of research and thousands of clinical trials, a patented formulation, Prime One, was created.
After he became president, collaborations between administration officials, the Rockefeller Foundation, Council staff, and Council networks led to the committee work that accompanied the formulation and implementation of Social Security.
After and later
After promoting Frost's appearance at the Inauguration, he persuaded the poet to return several months later to give a reading to a select audience of Cabinet members, members of Congress, and other Washington notables gathered in the State Department auditorium.
After the surprise was over, Linda was almost as pleased as anyone with John's good luck, though she agreed with Bobbie's decision some months later to move to Funk Furnaces.
After the death of Lincoln's mother, his older sister, Sarah, took charge of caring for him until their father remarried in 1819 ; Sarah later died in her 20s while giving birth to a stillborn son.
After the Revolution of 1917, views expressed by anthropologists in the USSR, and later the Soviet Bloc countries, were highly shaped by the requirement to conform to Marxist theories of social evolution.
After the later establishment of the People's Republic of China and its adoption of Hanyu Pinyin, the use of Zhuyin today is limited, but it's still widely used in Taiwan where the Republic of China still governs.
After the end of the Greek-Persian wars the cities on the coasts became part of the Delian League, which was, however, later dissolved.
After that, a year later, they made a couple of major improvements to the design.
After the mid-1960s, he became much less prolific, but his later work — including his final two epics, Kagemusha ( 1980 ) and Ran ( 1985 )— continued to win awards, including the Palme d ' Or for Kagemusha, though more often abroad than in Japan.
After this deed he fled to Talmai, the king of Geshur () ( see also or ), his maternal grandfather, and it was not until three years later that he was fully reinstated in his father's favour and finally returned to Jerusalem.
After a successful campaign Manuel I and Andronikos returned together to Constantinople ( 1168 ); but a year later, Andronikos refused to take the oath of allegiance to the future king Béla III of Hungary, whom Manuel desired to become his successor.
After his death, Pablo Picasso, fascinated with Jarry, acquired his pistol and wore it on his nocturnal expeditions in Paris, and later bought many of his manuscripts as well as executing a fine drawing of him.
After being expelled from Poitou by their overlord, Richard the Lion-hearted, for the murder of Patrick of Salisbury, 1st Earl of Salisbury, Amalric arrived in Palestine c. 1174, Guy possibly later.
After being defeated, Naxos is believed ( based on similar, later revolts ) to have been forced to tear down its walls, and lost its fleet and its vote in the League.
After World War II, the sport experienced a small amount of growth in the Pacific region, particularly in Nauru, Papua New Guinea and later New Zealand.
After the fall of the Conservative government to Labour in 1997, she served as Shadow Health Secretary between 1998 and 1999 and later as Shadow Home Secretary between 1999 and 2001 under William Hague.
He later wrote: " After more than forty years, we have had no third world war, and the balance of nuclear terror ... may have helped to prevent one.
After this event many Jews emigrated, in two waves ; some fled to the Muslim lands of the Ottoman Empire, but many also went to Christian Europe, first to northern Italy, then to the Netherlands, and later to England.
After retiring from the 49ers, Walsh returned as head coach at Stanford and later served as Cardinal athletic director.
After 12 years Nehemiah returns to Susa ; he later comes back to Jerusalem, and finds that there has been backsliding in his absence.
" After wearing glasses for a while, his eyes became adjusted to the lenses, and at that point he became nearsighted and really did need glasses, which would years later establish John as one of the most famous " four-eyes " in rock and roll, though Holly is widely considered to be the first.
After joining them in 1942, their son, Péter Bartók, enlisted in the United States Navy where he served in the Pacific during the remainder of the war and later settled in Florida where he became a recording and sound engineer.
After a dramatic conclusion of the 2001 World Series, less than 48 hours later, Selig held a vote on contracting two teams, reportedly the Minnesota Twins and Montreal Expos.
After his discharge from the army in August 1865, Corbett went back to work as a hatter, first in Boston, later in Connecticut, and by 1870 in New Jersey.
After three months of intense work, he predicted a position for Ceres in December 1801 — just about a year after its first sighting — and this turned out to be accurate within a half-degree when it was rediscovered by Franz Xaver von Zach on 31 December at Gotha, and one day later by Heinrich Olbers in Bremen.
After subjugating all Austrasia, he marched against Radbod and pushed him back into his territory, even forcing the concession of West Frisia ( later Holland ).
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