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More precisely, the characteristic property of B ( m, n ) is that, given any group G with m generators g < sub > 1 </ sub >,…, g < sub > m </ sub > and of exponent n, there is a unique homomorphism from B ( m, n ) to G that maps the ith generator x < sub > i </ sub > of B ( m, n ) into the ith generator g < sub > i </ sub > of G. In the language of group presentations, free Burnside group B ( m, n ) has m generators x < sub > 1 </ sub >,…, x < sub > m </ sub > and the relations x < sup > n </ sup > = 1 for each word x in x < sub > 1 </ sub >,…, x < sub > m </ sub >, and any group G with m generators of exponent n is obtained from it by imposing additional relations.
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More and precisely
More precisely, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function.
More precisely, Ural – Altaic came to subgroup Finno-Ugric and Samoyedic as " Uralic " and Turkic, Mongolic, and Tungusic as " Altaic ", with Korean sometimes added to Altaic, and less often Japanese.
More precisely, if S
More precisely, a binary operation on a non-empty set S is a map which sends elements of the Cartesian product S × S to S:
More precisely, given any small positive distance, all but a finite number of elements of the sequence are less than that given distance from each other.
More precisely, objects can be reachable in only two ways:
More precisely, it tries to classify problems that can or cannot be solved with appropriately restricted resources.
More precisely:
More generally, to insist that all evidence converge precisely with no deviations would be naïve falsificationism, equivalent to considering a single contrary result to falsify a theory when another explanation, such as equipment malfunction or misinterpretation of results, is much more likely.
More precisely, the positions of the pixels and subpixels on the screen must be exactly known to the computer to which it is connected.
( More precisely, this is true of the sines of the angles.
More importantly, however, he went on to maintain the same high level of performance throughout the season, kicking precisely 100 goals for the year to become the first player to top the ton since Richmond's Jack Titus in 1940.
" More precisely, it is " the quantitative analysis of actual economic phenomena based on the concurrent development of theory and observation, related by appropriate methods of inference.
More precisely, a full moon occurs when the geocentric apparent ( ecliptic ) longitudes of the Sun and Moon differ by 180 degrees ; the Moon is then in opposition with the Sun .< ref >
More precisely, all known FFT algorithms require Θ ( N log N ) operations ( technically, O only denotes an upper bound ), although there is no known proof that better complexity is impossible.
More precisely, because of the relation between spin and statistics, a particle containing an odd number of fermions is itself a fermion: it will have half-integer spin.
More precisely, and technically, a Feynman diagram is a graphical representation of a perturbative contribution to the transition amplitude or correlation function of a quantum mechanical or statistical field theory.
More precisely, he showed that a random graph on vertices, formed by choosing independently whether to include each edge with probability has, with probability tending to 1 as goes to infinity, at most cycles of length or less, but has no independent set of size Therefore, removing one vertex from each short cycle leaves a smaller graph with girth greater than in which each color class of a coloring must be small and which therefore requires at least colors in any coloring.
More precisely, a groupoid G is:
( More precisely, the nodes are spherical harmonics that appear as a result of solving Schrödinger's equation in polar coordinates.
More precisely, the square of x is not invertible because it is impossible to deduce from its output the sign of its input.
More precisely, the law states that alleles of different genes assort independently of one another during gamete formation.
More precisely, it returns a new list whose elements are in reverse order compared to the given list.
More precisely, these proofs have to be verifiable in polynomial time by a deterministic Turing machine.
More precisely, it is the instant when the Moon and the Sun have the same ecliptical longitude.
More and characteristic
More specifically, " habitats can be defined as regions in environmental space that are composed of multiple dimensions, each representing a biotic or abiotic environmental variable ; that is, any component or characteristic of the environment related directly ( e. g. forage biomass and quality ) or indirectly ( e. g. elevation ) to the use of a location by the animal.
More abstractly, the convex-hull operator Conv () has the characteristic properties of a closure operator:
More generally, if is the characteristic polynomial of a matrix A, then
More generally, if the polyhedron has Euler characteristic ( where g is the genus, meaning " number of holes "), then the sum of the defect is
" More than any other characteristic, it is the ruffed grouse's ability to thrive on a wide range of foods that has allowed it to adapt to such a wide and varied range of habitat on this continent.
More generally, if an irreducible ( non-zero ) polynomial f in F does not have distinct roots, not only must the characteristic of F be a ( non-zero ) prime number p, but also f ( X )= g ( X < sup > p </ sup >) for some irreducible polynomial g in F. By repeated application of this property, it follows that in fact, for a non-negative integer n and some separable irreducible polynomial g in F ( where F is assumed to have prime characteristic p ).
) More generally, if F is any field of ( non-zero ) prime characteristic for which the Frobenius endomorphism is not an automorphism, F possesses an inseparable algebraic extension.
More generally, a ring of characteristic p ( p a prime ) is called perfect if the Frobenius endomorphism is an automorphism.
More important than range in voice classification is tessitura, or where the voice is most comfortable singing, and vocal timbre, or the characteristic sound of the singing voice.
More generally, it is true that when K contains n distinct nth roots of unity, which implies that the characteristic of K doesn't divide n, then adjoining to K the nth root of any element a of K creates a Kummer extension ( of degree m, for some m dividing n ).
More recently, magnetic resonance imaging ( MRI ) has been used to localize lesions in the brain characteristic of peduncular hallucinosis.
More controversial open stud books are those where there are few, if any qualifications for animals other than a single trait, such as a " color breed ," particularly when the color is not a true-breeding characteristic.
More of a tendency than a defining characteristic, zappers can fluctuate from the habit, depending on what is on at any given time, personal feelings toward a show, amongst other variables.
More recently, receiver operating characteristic ( ROC ) curves have been used to evaluate the tradeoff between true-and false-positive rates of classification algorithms.
More specifically, the microtubules are arranged in a characteristic pattern known as the “ 9x2 + 2 ," as shown in the image at right.
More characteristic were the German " language islands "-towns inhabited by important German minorities and surrounded by Czechs.
More accustomed to turbulent political movements between the change of Cabinets — one characteristic more particular of Japanese contemporary history — two Genro members dictated the election of Admiral Kato Tomosaburo as the new Prime Minister.
More individual and characteristic are the romance about Charlemagne, entitled Fierabras le Giant ( 1478 ), by Jean Bagnyon, and the poem named Congé pris du siècle siculier ( 1480 ), by Jacques de Bugnin.
More recently, documentation of gravels characteristic of the Gunnison River and located at the western mouth of Unaweep Canyon provide evidence for occupation of the canyon by an ancestral Gunnison River Hence, the ancestral Gunnison River may have carved the canyon.
More generally, any verbal subgroup is always fully characteristic.
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