Namely φ is universal for homomorphisms from G to an abelian group H: for any abelian group H and homomorphism of groups f: G → H there exists a unique homomorphism F: G < sup > ab </ sup > → H such that.

Namely, there exists a linear transformation φ such that, for any pair of points:

Namely, a Riesz group satisfies the Riesz interpolation property: if x < sub > 1 </ sub >, x < sub > 2 </ sub >, y < sub > 1 </ sub >, y < sub > 2 </ sub > are elements of G and x < sub > i </ sub > ≤ y < sub > j </ sub >, then there exists z ∈ G such that x < sub > i </ sub > ≤ z ≤ y < sub > j </ sub >.

Namely the category of quasicoherent sheaves of O-modules on a Proj of a commutative graded algebra is equivalent to the category of graded modules over the ring localized on Serre's subcategory of graded modules of finite length ; there is also analogous theorem for coherent sheaves when the algebra is Noetherian.

Namely, the one he received in the Valley of the Lost: Of all there were, but a single one born of the magic to bring forth truth will remain alive when the shadow's threat is lifted.

Namely, at the time of the formation of FK Gorki there were three other football clubs in Tuzla, Zrinjski, Obilić and Makabi, based around the Croatian, Serbian and Jewish population of Tuzla.

Namely, let V be any vector space with some scalar field K, and let T be a linear transformation mapping V into V. We say that a non-zero vector x of V is an eigenvector of T if ( and only if ) there is a scalar λ in K such that T ( x )

Let X be a topological vector space over K. Namely, X is a K vector space equipped with a topology so that vector addition and scalar multiplication are continuous.

Namely, if is a smooth function, with and smooth manifolds, its derivative is a smooth function.

Namely, these are rotations by angles which are rational multiples of π.

Namely, Dalu (), which means " continent ", and Neidi ( 内地 / 內地 ), literally " inner land ".

Namely, the computation may greatly amplify the rounding errors, which are inevitable in all but textbook examples on integers, and so give completely wrong results.

Namely, other recent authors have considered loons to share a rather close relationship with seabirds such as penguins ( Sphenisciformes ), tubenoses ( Procellariiformes ), waders ( Charadriiformes ) – and perhaps the newly-discovered clade Mirandornithes which unites grebes ( Podicipediformes ) and their closest living relatives, the flamingos ( Phoenicopteriformes ).

It was not their Intention in the least at that Time to molest their Neighbours and Fellow Christians with Collections, for it has the appearance last Fall, as if they should have a promising Crop this Harvest, but that Hope is all lost for the most part of the Grane is kill'd with the Frost, and the Rest is destroy'd by the Insects, and now they have such a heavy Debt to pay, which they are not able to discharge out of their own Pokets: So they are obliged to implore all good-minded Christians who has it in their Hearts to promote the kingdom of Christ to assist them and lay some mite for the said Building of the said Church in the Hands of their Fellow Brothers wiiich they have send for that purpose Namely Albertus Simon and Jacob Weager.

Namely the building, which was built by Szymon Piechowicz from Turobin, a chemist and a professor of medicine at the Zamość Academy, still houses a chemist's.

Namely, libertarians believe that no person should have the right to decide for others what goods are necessary for living and which aren't, or that luxuries are necessarily wasteful, and thus argue that anti-consumerism is a precursor to central planning or a totalitarian society.

Namely, for three years he was the president of the country whose very existence was something that the party of which he's a vice-president ( DPS ) strived to end.

Namely the class RP consists of all decision problems for which a randomized polynomial-time algorithm exists that always answers correctly when the correct answer is " no ", but is allowed to be wrong with a certain probability bounded away from one when the answer is " yes ".

Namely, in order to obtain that data, survey questions must be designed to collect measurable responses that are categorized in a logically sound and practical way, such that the form in which the questions are asked does not bias the results.

*: Now these are the nations which the L < SMALL > ORD </ SMALL > left, to prove Israel by them, even as many of Israel as had not known all the wars of Canaan ; 2: Only that the generations of the children of Israel might know, to teach them war, at the least such as before knew nothing thereof ; 3: Namely, five lords of the Philistines, and all the Canaanites, and the Sidonians, and the Hivites that dwelt in mount Lebanon, from mount Baal-hermon unto the entering in of Hamath.

Namely, these are rotations by angles which are rational multiples of π.

Namely, " its " near the end of the sentence is a possessive pronoun whose antecedent is the very predicate in which it occurs.

Namely, Pope John IV ordered transportation of parts of their relics, which he placed in a dedicated chapel close to the Lateran baptistry.

Namely, Kuzmin proved the case where the exponent b is a real quadratic irrational, which was later extended to an arbitrary algebraic irrational b by Gelfond.

Namely, the ' cheeks ' on either side of the forward-facing fighter recovery bay which were inspired by the Smoke deflectors ( or lifters ) that appeared on some later steam locomotives.

Namely, the lens covers which were spring loaded and landed where expected.

Namely, the two changes were commission-based links to online music retailers, and Google AdSense links ( which registered users can elect not to view ).

Namely the pluralism of ideals in the fifth-century polis, whereby the audience can still understand Ajax's motives and admire him for committing suicide to retain his honour and the fixed views he has of the world and human relationships which are part of the Homeric world.

Namely: Pueblo de Romblon, the Cabesera or Capital town established as pueblo in 1631 during the term of Las Islas Filipinas Spanish Governor-General Juan Niño de Tavora, Banton in 1622, Sibuyan ( Cajidiocan ) established in 1744 and Looc which was established in 1844.

Namely, its CEO, Ivo Pukanić, is known to advocate publishing unconfirmed news, which frequently led to unfounded accusations and even litigation.

Namely, if their purpose is based only or primarily on self-interest — disregarding higher principles, which is the hallmark of opportunism — then politics is the least likely vocation, since it requires that politicians serve a collective interest or cause bigger than themselves.

Namely that I, Affonso, King of the Portuguese, with the consent of all my people, so that it may be remembered by future generations, do provide by this protocol of confirmation that the Franks who shall remain with me in the siege of the city of Lisbon shall have and take into their power and possession the goods of whatever kind belonging to the enemy and that I and my men shall have no part whatever of them.

Namely, a propositional formula can be expressed in first-order logic by replacing each propositional variable with a predicate of zero arity ( i. e., a predicate with no arguments ).

Namely, for any infinitesimal surface element C with normal direction and area dA, the circulation along the perimeter of C is the dot product where is the vorticity at the center of C.

Namely, if C and D are triangulated categories with C compactly generated and F a triangulated functor commuting with arbitrary direct sums, then F is a left adjoint.

Namely, we will allow f < sub > n </ sub > to converge μ-almost everywhere on a subset E of S. We seek to show that

Namely, given a surface X lying in R < sup > 3 </ sup >, the Gauss map is a continuous map N: X → S < sup > 2 </ sup > such that N ( p ) is a unit vector orthogonal to X at p, namely the normal vector to X at p.

Namely, let X and Y be two compact figures in a metric space M ( usually a Euclidean space ); then D < sub > H </ sub >( X, Y ) is the infimum of d < sub > H </ sub >( I ( X ), Y ) along all isometries I of the metric space M to itself.

* There is a one-to-one correspondence between the two-sided ideals of M < sub > n </ sub >( R ) and the two-sided ideals of R. Namely, for each ideal I of R, the set of all n × n matrices with entries in I is an ideal of M < sub > n </ sub >( R ), and each ideal of M < sub > n </ sub >( R ) arises in this way.

Namely, if A is the symmetric matrix that defines the quadratic form, and S is any invertible matrix such that D = SAS < sup > T </ sup > is diagonal, then the number of negative elements in the diagonal of D is always the same, for all such S ; and the same goes for the number of positive elements.

Namely, the adjoint T < sup >∗</ sup >: H < sub > 2 </ sub > → H < sub > 1 </ sub > of T is defined as an operator with the property:

Namely, although eigenvalues attaining maximal absolute value may not be unique, the structure of maximal eigenvalues is under control: they have the form e < sup > i2πl / h </ sup > r, where h is some integer number — period of matrix, r is a real strictly positive eigenvalue, l = 0, 1, ..., h − 1.

Namely, we map a point x ∈ M to the function f < sub > x </ sub > ∈ L < sup >∞</ sup >( M ) defined by the formula f < sub > x </ sub >( y )