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 can demand the existence of a tensor product that is left adjoint to the internal Hom functor.

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, 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 )

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, 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, 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.

*: 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, there exist topological manifolds which admit no C < sup > 1 </ sup >− structure, a result proved by, and later explained in the context of Donaldson's theorem ( compare Hilbert's fifth problem ).

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 )

Namely, the legal rules and principles that: ( 1 ) define the authority and structure of administrative agencies ; ( 2 ) specify the procedural formalities employed by agencies ; ( 3 ) determine the validity of agency decisions ; and ( 4 ) define the role of reviewing courts and other governmental entities in relation to administrative agencies.

Accordingly, Dapao had five 5 sub territory “ Lima ka Agama, Inged ” with a ruler Datu, traditionally, under the umbrella of Picong Sultanate but geographically and politically belong to Pualas, Namely ; 1 ) Apo 2 ) Imbang 3 ) Tanaon 4 ) Iyaran 5 ) Kormatan.

Namely, the Russians confiscated two silver crowns, a silver spoon, a silver beaker, a silver spiral bracelet, " precious drapery " and numerous pelts and precious furs ( Bahrushin 1955, 2: 146 ).

Namely, the measures should be taken with positive and negative signs in such a way that the sum of the signs of for all parts that enclose a given point is 1 if belongs to, and 0 otherwise.

Namely, Γ ( I ) is a subgroup of the group of norm 1 elements in the quaternion algebra generated as an associative algebra by the generators i, j and relations.

Namely to 1 / 4 of what the maritime postal rates were, with the sea element reduced to 1d.

Namely, section 9. 1 states that when one invokes rights, it should be in a manner with respecting " democratic values, public order and the general well-being of the citizens of Québec " and that law may limit rights.

Namely, the section 9. 1 statements about how one should use rights does not mention legislatures, and thus the Quebec Charter has relevance to private law.

Namely, a transsexual who has completed gender reassignment surgery is certainly not considered cross-dressing, unless they were to wear clothes of the gender opposite of what they have transitioned to.

Namely, the y-axis is necessarily the perpendicular to the x-axis through the point marked 0 on the x-axis.

Namely, it is a " hostel " for hitchhikers, sized and specially designated to hold multiple hitchhikers at one time.

Namely, the unitary transformation that is the change of basis ( from the standard product basis into the Bell basis ) can also be implemented by quantum gates.

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, it is necessary that these functions decrease sufficiently rapidly to zero ( in the neighborhood of infinity ) in order to insure the existence of the Fourier integral.

Namely, the matrix is reduced to an upper triangular matrix by using elementary row operations, as in the first part of the Gaussian elimination method, taking care to preserve the sign of its determinant.

Namely, one considers the phase space of the corresponding classical system ( e. g. for an ensemble of quantum harmonic oscillators, the phase space of a classical harmonic oscillator is considered ).

Namely, matrix is obtained by multiplying each element of u by the complex conjugate of each element of v.

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, Z is " If this sentence is true then Y ".

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, 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, the question of how the interaction takes place, where in dualism ' the mind ' is assumed to be non physical and by definition outside of the realm of science.

Namely, if a polynomial over with leading coefficient is reducible over then it is reducible over for any prime.

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

Namely, introducing the projectivization of the rank n complex vector bundle as the fiber bundle on B whose fiber at any point is the projective space of the fiber.

Namely, it is defined as

Namely, the government protects what it calls " normal religious activity ," defined in practice as activities that take place within government-sanctioned religious organizations and registered places of worship.