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Page "Mathematical formulation of quantum mechanics" ¶ 95
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Although and spin
Although there are no known magnetic monopoles in nature, there are magnetic dipoles in the form of the quantum-mechanical spin associated with particles such as electrons ( although the accurate description of such effects falls outside of classical electromagnetism ).
Although muonium is short-lived, physical chemists use it in a modified form of electron spin resonance spectroscopy for the analysis of chemical transformations and the structure of compounds with novel or potentially valuable electronic properties.
Although rare now, in the past there were bowlers who used the off-break action who deliberately did not impart any considerable spin on the ball but relied on line and length to frustrate batsmen.
Although Dirac did not at first fully appreciate what his own equation was telling him, his resolute faith in the logic of mathematics as a means to physical reasoning, his explanation of spin as a consequence of the union of quantum mechanics and relativity, and the eventual discovery of the positron, represents one of the great triumphs of theoretical physics, fully on a par with the work of Newton, Maxwell, and Einstein before him.
Although this orientation does not remain fixed, it changes in response to an external torque much less and in a different direction than it would without the large angular momentum associated with the disk's high rate of spin and moment of inertia.
Although Lynn comments that the word " spin " has " probably entered the political vocabulary since the series ," Iannucci suggests that the show " taught us how to unpick the verbal tricks that politicians think they can get away with in front of the cameras.
Although Luttinger liquids are physically the same as Fermi liquids, the restriction to one dimension gives rise to several qualitative differences such as the absence of a quasiparticle peak in the momentum dependent spectral function and the presence of spin density waves.
** Although, this model, which is restricted only on the frozen spin networks, exhibits a non-stationary expansion of the universe.
Although neutrons are uncharged, they carry a spin, and therefore interact with magnetic moments, including those arising from the electron cloud around an atom.
Although he wore one of the remainder of his career, he never missed an opportunity to slip into a cap when facing medium pace or spin.
Although several plot threads spin out of the book, and Barker has promised at least one sequel, none have been written, and it is left to the imagination of the reader to work out what happens next.
Although it was not understood at the time, this was also the first of what are now called recycled pulsars: neutron stars that have been spun-up to fast spin rates by the transfer of mass onto their surfaces from a companion star.
Although the decision to spin off the company's technical equipment division predated her arrival, one of her first major responsibilities as chief executive was overseeing the separation of the unit into the standalone Agilent Technologies.
Although general relativity can accommodate particles with spin, including spin-1 / 2, by using the tetrad formalism, it cannot couple the spin to orbital angular momentum.
Although struggling to bat against off spin in one game, he scored 94 while sharing a partnership of 200 runs with W. G. Grace in another.
Although primarily a batsman, Hossain is a part-time left arm spin bowler.
Although Verity had figures of eight for 107, he was expected to be more successful as the pitch conditions were perfect for spin bowling.
Although most previous and current research on frustration focuses on spin systems, the phenomenon was first studied in ordinary ice.
Although the pitch was helpful for spin, a total of 74 overs in the match yielded 3 / 146, as Johnston was unable rekindle the form of 1948 following his knee injury.
Although unable to spin or flight the ball as well as previously, Rhodes bowled a very accurate length and used his great experience effectively.
Although Trott was a versatile batsman, spin bowler and outstanding fielder, "... it is as a captain that he is best remembered, an understanding judge of human nature ".
Although Arianna Huffington has stated that her paper is " not positioned ideologically in terms of how we cover the news ," representatives of the Republican Party have indicated that they believe The Huffington Posts headline writers, bloggers, and commentators are hostile to their views and tend to negatively spin articles, and especially headlines, about Republican Party candidates.
Although usually observed in liquids, the photo-CIDNP effect has also been detected in solid state, for example on < sup > 13 </ sup > C and < sup > 15 </ sup > N nuclei in photosynthetic reaction centres, where significant nuclear polarization can accumulate as a result of spin selection processes in the electron transfer reactions.

Although and Pauli
Although Bohr, Fowler, Pauli, and other physicists agreed with Chandrasekhar's analysis, at the time, owing to Eddington's status, they were unwilling to publicly support Chandrasekhar .< sup >, pp. 110 – 111 </ sup > Through the rest of his life, Eddington held to his position in his writings, including his work on his fundamental theory.
Although he came to Hamburg to work with Pauli, Rabi found Otto Stern working there with two English-speaking postdoctoral fellows, Ronald Fraser and John Bradshaw Taylor.
Although Beck's and St. Pauli Girl beers are very similar in nature, the latter only recently has been sold in Germany.
Although Pauli did not publish his six-dimensional theory, he gave two talks about it in Zürich.

Although and principle
Although this concept remains a guiding principle of the profession, it is a concept that has been widely critiqued within the conservation profession and is now considered by many to be " a fuzzy concept ".
Although Disraeli forged a personal friendship with John Bright, a Lancashire manufacturer and leading Radical, Disraeli was unable to convince Bright to sacrifice principle for political gain.
Although classical liberals aspired to a minimum of state activity, they accepted the principle of government intervention in the economy from the early 19th century with passage of the Factory Acts.
Although computing a power spectrum from a map is in principle a simple Fourier transform, decomposing the map of the sky into spherical harmonics, in practice it is hard to take the effects of noise and foreground sources into account.
Although the Church of the Holy Sepulchre has its tomb just a few yards away from its Golgotha, there is no particular reason to regard this close juxtaposition as a necessity ; however, Gordon followed this principle, concluding that his site for Golgotha must also be the approximate location for Jesus ' burial, identifying a nearby tomb, now called the Garden Tomb, as the location for the event.
Although not described as a democracy by the founding fathers, the United States founders also shared a determination to root the American experiment in the principle of natural freedom and equality.
Although ancient Greek philosophers believed in individual virtue ethics, philosophers like " Plato, Aristotle, and the Stoics not accept the formal principle that whatever the good is, we should seek only our own good, or prefer it to the good of others.
Although some Protestants reject the concept of an ecumenical council establishing doctrine for the entire Christian faith, Roman Catholics, Anglicans, Eastern Orthodox and Oriental Orthodox all accept the authority of ecumenical councils in principle.
Although ephemeris time was defined in principle by the orbital motion of the Earth around the Sun, it was usually measured in practice by the orbital motion of the Moon around the Earth.
Although this principle was held by all emperors after Constantine, it met with increasing resistance and ultimately rejection by bishops in the west after the effective end of Imperial power in there.
Although Muslim teaching at this time strongly opposed the printing of Islamic or Arabic texts, non-Muslim printing was not, in principle, forbidden ; indeed attempts were made in the 1570s by anti-Trinitarian Christians to establish a printing press in the Turkish capital to publish radical Protestant works.
Although a new electoral law was passed that respected the principle of universal ( male ) suffrage, the stricter residential requirement of the new law actually had the effect of disenfranchising 3, 000, 000 of 10, 000, 000 voters.
Although IPv6 packet headers are at least twice the size of IPv4 packet headers, packet processing by routers is generally more efficient, thereby extending the end-to-end principle of Internet design.
Although Haddad notes that the authenticity of both hadeeth is questionable, he nevertheless concludes that the underlying principle of superiority internal jihad does have a reliable basis in the Quran and other writings.
Although a Dutch spectacle maker created the compound lens and inserted it in a microscope around the turn of the seventeenth century, and Galileo had applied the principle of the compound lens to the making of his microscope patented in 1609, its possibilities as a microscope had remained unexploited for half a century, until Robert Hooke improved the instrument.
Although observance of, or disregard for, the Law was primarily a matter of political expediency rather than legal principle, it was broadly understood to prevail in domains that were originally Frankish or at some time accepted Salian Frankish juridical principles.
Although the principle is useful in many contexts, spaced repetition is commonly applied in contexts in which a learner must acquire a large number of items and retain them indefinitely in memory.
Although initially given unofficial Test status ( and included as Test matches in some record books, notably Wisden ), this was later withdrawn and a principle was established that official Test matches can only be between nations.
Although the principle is more visually intuitive in the wave mechanics formalism, it was first derived and is more easily generalized in the matrix mechanics formalism.
Although he is commonly known for Occam's razor, the methodological principle that bears his name, William of Ockham also produced significant works on logic, physics, and theology.
Although Gropius and Meyer only designed the facade, the glass curtain walls of this building demonstrated both the modernist principle that form reflects function and Gropius's concern with providing healthful conditions for the working class.
Although it relied on the weaker legal principle of Informed Consent and not the much stronger Precautionary Principle language sought by advocates, the protocol was considered by most to be a victory that could enhance both biosafety and biosecurity.
Although absorption spectroscopy and emission spectroscopy are different in principle, they are closely related in practice ; any technique for emission spectroscopy can also be used for absorption spectroscopy.
Although Steward and Barnett seemed to be suggesting that anthropology as such should restrict itself to purely academic affairs, people within and without the academy have continued to debate the ways non-anthropologists have used this principle in public policy concerning ethnic minorities or in international relations ( see this interview or this article on cultural relativism and human rights for examples of this debate ).

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