Help


[permalink] [id link]
+
Page "Unique factorization domain" ¶ 1
from Wikipedia
Edit
Promote Demote Fragment Fix

Some Related Sentences

Note and unique
Note 2: The DTG may be used as a message identifier if it is unique for each message.
Note that the zero morphism in item 3 can be identified as the identity element of the hom-set Hom ( A, B ), which is an abelian group by item 1 ; or as the unique morphism A → O → B, where O is a zero object, guaranteed to exist by item 2.
Note When Viewing Census Income Rank: It is important to consider Indian Creek's unique situation being one the smallest incorporated municipalities in the United States with 38 home sites and 32 actual homes when viewing the US Census Data drawing on 33 people, 14 households, and 11 families.
... For a source to be considered acceptable to this project it must comply with the following standards: ( 1 ) site updated at least daily ; ( 2 ) all stories separately archived on the site, with a unique url ( see Note 1 below ); ( 3 ) source widely cited or referenced by other sources ; ( 4 ) English Language site ; ( 5 ) fully public ( preferably free ) web-access.
Note that by the unique lifting property, if f is not the identity and C is path connected, then f has no fixed points.
Note the drum-tight skin, a consequence of the unique tensioning system devised by Hargrave.
Note, that the third axiom is actually redundant, because the second and fourth axioms imply is also an identity, and identities are unique.
Note that an immediate corollary of ( 2 ) is that the coefficients in ( 1 ) are unique for each.
Note that the vectors x < sub > i </ sub > are not unique: With the Euclidean distance, they may be arbitrarily translated, rotated, and reflected, since these transformations do not change the pairwise distances.
Note that it does not explicitly contain the crystal system, although this is unique to each space group ( in the case of P3 < sub > 1 </ sub > 21, it is trigonal ).
Note: in this section, " up to " some equivalence relation E means that the canonical form is not unique in general, but that if one object has two different canonical forms, they are E-equivalent.
Note that this inverse system is not unique.
Note that there are important physiological differences between nodal cells and ventricular cells ; the specific differences in ion channels and mechanisms of polarization give rise to unique properties of SA node cells, most importantly the spontaneous depolarizations necessary for the SA node pacemaker activity.
Note that if g exists, it is unique ( due to the theorem about the uniqueness of analytic continuations ), at least if we ignore complications like branch cuts and so on.
Note that this design feature is not unique to BMW models.
Note that it may be not trivial to show that such derived estimator is the unique global maximizer for likelihood function.
Other band members still played together, sometimes with Jackson's cousin Steve Potts on percussion, providing their unique backdrops for Syl Johnson on the Delmark Records CD Back in the Game ( 1994 ), and the Mitchell-produced Al Green comeback I Can't Stop and its follow-up for the Blue Note label in 2003 and 2005.
Note that signed-digit representation is not necessarily unique.
Note that this implementation assumes the join attributes are unique, i. e., there is no need to output multiple tuples for a given value of the key.
Note that these do not always exist, nor if they exist are they unique.
( Here P < sub > i </ sub >( s ) denotes the unique element of P < sub > i </ sub > containing s. Note that this model excludes cases in which agents know things that are not true.
* HW 35 Has been in production for many years with a unique barrel lock, the HW35E A more expensive version with walnut stock and longer barrel ( Note: longer barrel did not increase power ) and the HW35 " K " ( Carbine ) type with a short barrel.
Note: A second version of Bacon's cipher uses a unique code for each letter.
( Note, however, that at the University of Cambridge, the MPhil degree is a one year degree qualification that combines taught sections with unique research.

Note and factorization
Note the terminological consistency: the determination of the amount by which an individual orthonormal basis function must be scaled in the spectral factorization of a function, F, is termed the " projection " of F onto that basis function.

Note and domains
Note that we require the domains of G < sub > 2 </ sub >, G < sub > 3 </ sub > to be broad enough to make the above properties meaningful.
Note that in OSPF the term Autonomous System Boundary Router ( ASBR ) is historic, in the sense that many OSPF domains can coexist in the same Internet-visible autonomous system, RFC1996.
Note that the domains of different plots can be subsets of R < sup > n </ sup > for different values of n.
Note that Principles A and B refer to " governing categories "-- domains which limit the scope of binding.
Note that for DNS use, the domain name string is assumed to have been normalized using Nameprep and ( for top-level domains ) filtered against an officially registered language table before being punycoded, and that the DNS protocol sets limits on the acceptable lengths of the output Punycode string.
Note that the polygons in the tiling are not fundamental domainsthe tiling by ( 2, 3, 7 ) triangles refines both of these and is not regular.
Note that some federal subjects have multiple second-level domains, and others ( not listed below ) have none.
Note that selection of DNA-binding domains is not necessarily performed using a one-hybrid system, but may also be performed using a two-hybrid system in which the binding domain is varied and the bait and prey proteins are kept constant.

Note and appear
Note that this approach falters, in part, with the verb " to appear ".
Note that this document type declaration can only appear after the optional XML declaration, and before the document body, if the document syntax conforms to XML.
Note that the orange circles appear of different sizes, even though equal.
) Note that we have omitted the Π < sub > j </ sub > n < sub > j </ sub > term, because each single-particle state can appear only once in a fermionic state.
Note that from the perspective of the smaller-mass object — from the moon, in the preceding example — a spacecraft might appear to orbit in an irregular path about the or point, but from the perspective above the orbital plane, it becomes clear that both the smaller mass and the spacecraft are orbiting the larger mass ( or more precisely, all of the objects are in orbit around the barycenter of the system ); they simply have overlapping orbital paths.
Note that many skeptics do not deny that things may appear in a certain way.
Note that white matter can sometimes appear darker than grey matter on a microscope slide because of the type of stain used.
** Note: Patient may die before any symptoms appear
Note that the phrase " It is better to burn than to disappear " does not appear in the French original.
Note that the above considerations are strictly speaking true for the geometric horizon only: the horizon as it would appear for an observer at sea level on a perfectly smooth Earth without an atmosphere.
Note that what affects the value of for different values of is only the factors and, which both appear in the numerator, and hence the posterior probability is proportional to both.
Note: Dream does not appear in every issue of The Sandman, nor did he appear in the first DC Comics The Sandman series, although several supporting characters in the Vertigo series did.
Note the minuscule broadening in the peak of the three-state protein's DSC curve, which may or may not appear statistically significant to the naked eye.
Note that return refers to the ex-ante expectation ; ex-post realisation of payoffs may make some stock-pickers appear successful.
Note how similar the color images appear.
Treating free charges separately from bound charges, Ampère's equation including Maxwell's correction in terms of the H-field is ( the H-field is used because it includes the magnetization currents, so J < sub > M </ sub > does not appear explicitly, see H-field and also Note ):
Note that T ' doesn't appear in the formulae even though it could be greater than T. This is because futures contracts are marked to market and so the payoff is realized when the option is exercised.
Note that the eigenvalues appear in the diagonal matrix.
The US edition also has a three paragraph ' Author's Note ' regarding Viriconium which did not appear in the UK editions.
Note that in contrast to classical theory, more than two linked components may appear.
Note that the word " antiquing " may also refer to the art of making an object appear antique through distressing or applying an antique looking paint application.
Note that the same rule may appear several times in the conflict set if it matches different subsets of data items.
( Note that any-dimensional manifold may appear as an object in.

0.781 seconds.