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Specifically, if K / Q is a finite Galois extension then to each ( positive ) prime p which does not ramify in K and to each prime ideal P lying over p in K there is a unique element g of Gal ( K / Q ) satisfying the condition g ( x ) = x < sup > p </ sup > ( mod P ) for all integers x of K. Varying P over p changes g into a conjugate ( and every conjugate of g occurs in this way ), so the conjugacy class of g in the Galois group is canonically associated to p. This is called the Frobenius conjugacy class of p and any element of
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Specifically and if
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Specifically, a topological space is compact if, whenever a collection of open sets covers the space, some subcollection consisting only of finitely many open sets also covers the space.
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Specifically, if hair texture were simply the result of adaptively arbitrary human aesthetic preferences, one would expect that the global distribution of the various hair textures would be fairly random.
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Specifically, if the cylinders are oriented parallel to one another, there is very little volume that is excluded from the center-of-mass of the approaching cylinder ( it can come quite close to the other cylinder ).
Specifically, umpires were now given the power — and the responsibility — to intervene if they considered a bowler was deliberately aiming at a batsman with intent to injure.
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Specifically, if F is a vector space of linear functionals on X which separates points of X, then the continuous dual of X with respect to the topology σ ( X, F ) is precisely equal to F.
Specifically, if the vacuum energy is negative and its absolute value is substantially larger than it appears to be in the observed universe ( say, a factor of 10 larger ), holding all other variables ( e. g. matter density ) constant, that would mean that the universe is closed ; furthermore, its lifetime would be shorter than the age of our universe, possibly too short for the intelligent life to form.
Specifically, the above argument would become a fallacious ad baculum if the conclusion stated:
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A category C is said to have limits of type J if every diagram of type J has a limit in C. Specifically, a category C is said to
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Specifically and K
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The absolute value is defined so as to measure the change in size of a set after multiplying it by an element of K. Specifically, define |·|: K → R by
Specifically, since the Ramsey number R ( 3, 3 )= 6, any two-coloring of the complete graph on 6 vertices ( K < sub > 6 </ sub >) must contain a monochromatic triangle, and therefore is not a tied position.
Specifically, it is defined as the largest cardinality of an algebraically independent subset of L over K.
Specifically, Michael Luby and Charles Rackoff analyzed the Feistel cipher construction, and proved that if the round function is a cryptographically secure pseudorandom function, with K < sub > i </ sub > used as the seed, then 3 rounds is sufficient to make the block cipher a pseudorandom permutation, while 4 rounds is sufficient to make it a " strong " pseudorandom permutation ( which means that it remains pseudorandom even to an adversary who gets oracle access to its inverse permutation ).
Specifically, it implies that as a Galois extension of K, L is uniquely determined by the set of primes of K that split completely in it.
Specifically, the oxalate moiety adopts the planar, D < sub > 2h </ sub > conformation in the solid-state structures of M < sub > 2 </ sub > C < sub > 2 </ sub > O < sub > 4 </ sub > ( M = Li, Na, K ).
Specifically, given an algebra A over a ring or a field K, a K-derivation is a K-linear map D: A → A that satisfies Leibniz's law:
The Dedekind zeta function satisfies a functional equation relating its values at s and 1 − s. Specifically, let Δ < sub > K </ sub > denote discriminant of K, let r < sub > 1 </ sub > ( resp.
Specifically, L is the gas-liquid partition constant on hexadecane at 298 K ; E the excess molar refraction ; S the ability of a solute to stabilize a neighboring dipole by virtue of its capacity for orientation and induction interactions ; A the solute ’ s effective hydrogen bond acidity ; and B the solute ’ s effective hydrogen-bond basicity.
Specifically and /
Specifically, the H factor is described as sincere, honest, faithful / loyal, modest / unassuming, fair-minded, VERSUS sly, deceitful, greedy, pretentious, hypocritical, boastful and pompous.
Specifically, Brunvand argued that the Petruchio / Katherina story represents a subtype of Type 901 (' Shrew-taming Complex ') in the Aarne – Thompson classification system.
Specifically, A and E will no longer be the meter / pixel measurement on their respective axes.
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Specifically, a signed semiring consists of a pair ( Γ, ε ) where Γ is a semiring and ε: Γ → Z / 2Z is a homomorphism of additive monoids.
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Specifically there were practitioners of the technique that said of a mesmerized person " the person is back animal " meaning " the person is back in a natural mental state where she / he recovers his / her most primitive part of the mind ".
Specifically, diagenesis “ is the cumulative physical, chemical and biological environment ; these processes will modify an organic object ’ s original chemical and / or structural properties and will govern its ultimate fate, in terms of preservation or destruction ”.
Specifically, it explored the feasibility of symmetric and asymmetric data rates exceeding 10 Mbit / s on short phone lines.
Specifically in low income neighborhoods, the presence of a local grocery store is correlated with lower BMI / overweight risk.
Specifically, Visual PinMAME is for emulating CPUs and the connected ROMs used in modern pinball tables, as opposed to tables with solid-state electronics / electro-mechanical mechanisms that contain no ROMs or advanced ICs in their hardware design.
Specifically, it denoted the perspective that human behavior is largely determined by a person's immediate social environment, that modes of social organization were not supernatural or metaphysical constructs but products of the social system and social environment, which were in turn products of the level of technology / mode of production ( the material world ), and were therefore constantly changing.
Specifically, the manuals and other content at MediaWiki. org are Creative Commons-licensed, while the set of help pages intended to be freely copied into fresh wiki installations and / or distributed with MediaWiki software is public domain.
" Specifically on the subject of creation / evolution, some Anglicans view " Big Bang cosmology " as being " in tune with both the concepts of creation out of nothing and continuous creation.
Specifically, people with mildly elevated levels of bilirubin ( 1. 1 mg / dl to 2. 7 mg / dl ) were at lower risk for CAD and at lower risk for future heart disease.
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