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Page "Quadratic form" ¶ 28
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Although and their
Although they were forced to maintain a sharper watch, this activity enabled them to ride in and rack their broncs without any particular attention being paid them.
Although the United States and the U.S.S.R. have been arguing whether there shall be four, five or six top assistants, the most important element in the situation is not the number of deputies but the manner in which these deputies are to do their work.
Although there is no question but that the process of washing fabrics involves a number of phenomena which are related together in an extremely complicated way and that these phenomena and their interrelations are not well understood at the present, this section attempts to present briefly an up-to-date picture of the physical chemistry of washing either fabrics or hard surfaces.
Although the present study was not a direct replication of their investigations, the results do not confirm their conclusion.
Although the elections were for local officials, it was not necessary to conduct the elections so as to prevent parties from publicly identifying their candidates.
Although they have also been concerned to stand squarely within the tradition of the apostolic church, they have exhibited no willingness whatever to sacrifice their modernity to their Christianity.
Although Tylor undertook a field trip to Mexico, both he and Frazer derived most of the material for their comparative studies through extensive reading, not fieldwork, mainly the Classics ( literature and history of Greece and Rome ), the work of the early European folklorists, and reports from missionaries, travelers, and contemporaneous ethnologists.
The Turkish language and the Islamic religion were gradually introduced as a result of the Seljuk conquest, and this period marks the start of Anatolia's slow transition from predominantly Christian and Indo-European and Semitic-speaking, to predominantly Muslim and Turkish-speaking ( Although some ethnic groups such as Armenians, Greeks, Assyrians and Georgians retained Christianity and their native languages ).
Although Romans who had been adopted into a new family usually retained their old nomen in cognomen form ( e. g. Octavianus for one who had been an Octavius, Aemilianus for one who had been an Aemilius, etc.
Although the sign still exists, the " of " has now been replaced by the URL of their website.
Although particles and their antiparticles have opposite charges, electrically neutral particles need not be identical to their antiparticles.
Although the Caiman has not been studied in-depth, scientists have learned that their mating cycles ( previously thought to be spontaneous or year-round ) are linked to the rainfall cycles and the river levels, which increases chances of survival for their offspring.
Although practical for the desert dust, the Almoravids insisted on wearing the veil everywhere, as a badge of " foreignness " in urban settings, partly as a way of emphasizing their puritan credentials.
Although in his later years, towards the end of the Trojan War, his old opponents took his side again against the Greeks under their queen Penthesilea " of Thracian birth ", who was slain by Achilles.
Although various Ambrosians were given the title of Blessed in recognition of their holiness: Antonio Gonzaga of Mantua, Filippo of Fermo, and Gerardo of Monza, the order was eventually dissolved by Pope Innocent X in 1650.
Although metics had no direct political influence many were wealthy business owners who could, and sometimes did, influence policy by not allowing their citizen employees time off to attend the assembly, as well as having the simple expedient of wealth.
Although most of the legions were lost, about 10, 000 Romans cut their way through to safety, maintaining unit cohesion.
Although there were low levels of preexisting antibiotic-resistant bacteria before the widespread use of antibiotics, evolutionary pressure from their use has played a role in the development of muiltidrug resistance varieties and the spread of resistance between bacterial species.
Although most dialects of English used in the former British Empire outside of North America and Australasia are, to various extents, based on British English, most of the countries concerned have developed their own unique dialects, particularly with respect to pronunciation, idioms and vocabulary.
Although page flipping was a hardware possibility, the limited memory forced most applications to do all their drawing directly to the visible screen, often resulting in graphical flicker or visible redraw.
Although there have been periodic initiatives to revive their use, airships have seen only niche application since that time.

Although and definition
Although not normally thought of as biotechnology, agriculture clearly fits the broad definition of " using a biotechnological system to make products " such that the cultivation of plants may be viewed as the earliest biotechnological enterprise.
Although the candela is now defined in terms of the second ( an SI base unit ) and the watt ( a derived SI unit ), the candela remains a base unit of the SI system, by definition.
Although sometimes referred to as a coalition government, according to the definition above, it was not.
Although the phrase " perfect game " appeared in record books as early as 1922, and was a common expression years before that, Major League Baseball did not formalize the definition of a " perfect game " until 1991, long after Young's death.
Although this sort of definition involves a form of circularity, it is not vicious, and the definition has been quite successful.
Although most often used for matrices whose entries are real or complex numbers, the definition of the determinant only involves addition, subtraction and multiplication, and so it can be defined for square matrices with entries taken from any commutative ring.
" Although the EPAC Ethics Task Force argued that both non-voluntary and involuntary euthanasia could not be included in the definition of euthanasia, there is discussion in the literature about excluding one but not the other.
Although this is an independent definition that does not refer to the older basis of ephemeris time, it uses the same quantity as the value of the ephemeris second measured by the cesium clock in 1958.
Although this is not the technical definition of the Hamiltonian in classical mechanics, it is the form it most commonly takes.
Although these cases illustrate the difficulty of assigning labels, the work of the original Impressionist painters may, by definition, be categorised as Impressionism.
Although it is difficult to produce a clear definition of Internet slang, the following types of slang may be observed.
Although there is no strict size definition, a small loch is often known as a lochan ( so spelled also in Scottish Gaelic ; in Irish it is spelled lochán ).
Although there is no universal agreement on the definition of life, scientists generally accept that the biological manifestation of life is characterized by organization, metabolism, growth, adaptation, response to stimuli and reproduction.
Although it still lacks a universally accepted definition, the crux of intelligence-led policing is an emphasis on the collection and analysis of information to guide police operations, rather than the reverse.
Although unpleasantness is an essential part of the IASP definition of pain, it is possible to induce a state described as intense pain devoid of unpleasantness in some patients, with morphine injection or psychosurgery.
Although sometimes said to derive from the Irish for a joist or beam, a more likely definition is as a variant of sparth.
Although widely adopted, this definition differs in important respects from the more classical definition of measurement adopted in the physical sciences, which is that measurement is the numerical estimation and expression of the magnitude of one quantity relative to another ( Michell, 1997 ).
Although he nowhere defines truth in terms of a thought's likeness to a thing or fact, it is clear that such a definition would fit well into his overall philosophy of mind.
Although it is possible to show that transformation laws indeed ensure independence from the basis, sometimes a more intrinsic definition is preferred.
Although not necessarily " voyeurism " in its original definition, as individuals in these given situations are aware of their audience, the concept behind " reality TV " is to allow unscripted social interaction with limited outside interference or influence.
Although the statutes did not explicitly limit the definition of marriage to male-female pairs, the court held that both the common dictionary definition of marriage, in addition to the legislative intent ( the relevant statutes were enacted in 1945 ) favored the interpretation of marriage as a union between a man and a woman.
Although not part of this definition, many authors require that the topology on G be Hausdorff ; this corresponds to the identity map being a closed inclusion ( hence also a cofibration ).

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