That is, the motivational internalist believes that there is an internal, necessary connection between one's conviction that X ought to be done and one's motivation to do X. Conversely, the motivational externalist ( or moral externalist ) claims that there is no necessary, internal connection between moral convictions and moral motives.

Conversely, using the last line as a definition one shows that the expression so defined is a connection compatible with the metric, i. e. is a Levi-Civita connection.

Conversely, if a suitable notion of parallel transport is available, then a corresponding connection can be obtained by differentiation.

Conversely, any operator satisfying the above properties defines a connection on E and a connection in this sense is also known as a covariant derivative on E.

Conversely, if ∇ is a connection on E and A is a one-form on M with values in End ( E ), then ∇+ A is a connection on E.

Conversely, a connection on E determines a connection on F ( E ), and these two constructions are mutually inverse.

The principal connection α on Q can be recovered from the form η by taking Q to be the associated bundle P ×< sub > H </ sub > G. Conversely, the form η can be recovered from α by pulling back along the inclusion P ⊂ Q.

A section Γ of dπ: TP / G → TM such that Γ: TM → TP / G is a linear morphism of vector bundles over M, can be identified with a principal connection in P. Conversely, a principal connection as defined above gives rise to such a section Γ of TP / G.

Conversely, the Roman connection introduced foreign influence beyond the control of local rulers, but also allowed rulers to display themselves on a wider, European stage, and to seek out more powerful sources of legitimacy.

where it is understood that d and ω refer to the exterior derivative and a matrix of 1-forms, respectively, acting on the components of ξ. Conversely, a matrix of 1-forms ω is a priori sufficient to completely determine the connection locally on the open set over which the basis of sections e is defined.

Conversely, it has also been said that the connection between virtual crimes and real crimes are " tenuous at best: It is the link between a brutal rape and a fictional story of a brutal rape.

A hypergraph H may be represented by a bipartite graph BG as follows: the sets X and E are the partitions of BG, and ( x < sub > 1 </ sub >, e < sub > 1 </ sub >) are connected with an edge if and only if vertex x < sub > 1 </ sub > is contained in edge e < sub > 1 </ sub > in H. Conversely, any bipartite graph with fixed parts and no unconnected nodes in the second part represents some hypergraph in the manner described above.

Conversely, David H. Rosenthal sees the development of hard bop as a response to both a perceived decline in bebop and the rise of rhythm and blues.

Conversely, one can show that given a manifold M and a principal H-bundle P over M, and a 1-form η with these properties, then P is locally isomorphic as an H-bundle to the principal homogeneous bundle G → G / H.

Conversely, in a conventional gas piston design such as the H & K 416, gas used to operate the firearm is isolated from the breech and contained within the gas cylinder then vented away from other working parts.

Conversely, let A be a self-adjoint operator on a Hilbert space H. Then

Conversely, a system of n quantities v < sup > i </ sup > that transform like the coordinates x < sup > i </ sup > on V defines a contravariant vector.

for all vectors w. Conversely, each covector α determines a unique vector v by this equation.

Conversely, if a highest weight module is integrable, then its highest weight vector v satisfies, where are complex numbers such that

Conversely, in The Mortgage Specialists, Inc. v. Implode-Explode Heavy Industries, Inc. the New Hampshire Supreme Court adopted a much broader definition of media that applies to blogs and website curators, reiterating that " freedom of the press is a fundamental personal right which is not confined to newspapers and periodicals.

# Conversely if u is a solution of Laplace's equation, then there exist functions v which solve the Cauchy – Riemann equations together with u.

For example, Chern v. Bank of America held that a loan officer ’ s statement over the phone about interest rates was “ advertising .” Conversely, Bank of the West v. Superior Court implied that advertising might require “ widespread promotional activities directed to the public-at-large ” and that mere “ personal solicitations are not advertising .”

Conversely, in National Collegiate Athletic Association v. Smith, the Supreme Court has found that the National Collegiate Athletic Association is not a state actor for the purposes of 28 U. S. C.

Conversely, if ƒ: C → C is a function which is differentiable when regarded as a function on R < sup > 2 </ sup >, then ƒ is complex differentiable if and only if the Cauchy – Riemann equations hold.

** Conversely, if ƒ: I → R is absolutely continuous and thus differentiable almost everywhere, and satisfies | ƒ ′( x )| ≤ K for almost all x in I, then ƒ is Lipschitz continuous with Lipschitz constant at most K.

As stated earlier, an adjunction between categories C and D gives rise to a family of universal morphisms, one for each object in C and one for each object in D. Conversely, if there exists a universal morphism to a functor G: C → D from every object of D, then G has a left adjoint.

Conversely, starting from this equivalence we can recover U as the composite Rel → Sup → Set of the forgetful functor for Sup with this embedding of Rel in Sup.

Conversely, a complete variety is close to being a projective variety: Chow's lemma states that if X is a complete variety, there is a projective variety Z and a birational morphism Z → X.

Conversely, a function u: E < sub > 1 </ sub > → E < sub > 2 </ sub > defined on a basis of E < sub > 1 </ sub > can be uniquely extended to a linear function.

Conversely, the following characterization of derived functors holds: given a family of functors R < sup > i </ sup >: A → B, satisfying the above, i. e. mapping short exact sequences to long exact sequences, such that for every injective object I of A, R < sup > i </ sup >( I )= 0 for every positive i, then these functors are the right derived functors of R < sup > 0 </ sup >.

Conversely, given a left kG module M, then M is a k vector space, and multiplication with an element g of G yields a k-linear automorphism of M ( since g is invertible in kG ), which describes a group homomorphism G → GL ( M ).

Suppose S is an immersed submanifold of M. If the inclusion map i: S → M is closed then S is actually an embedded submanifold of M. Conversely, if S is an embedded submanifold which is also a closed subset then the inclusion map is closed.

Conversely, given any element u ∈ F ( A ) we may define a natural transformation Φ: Hom ( A ,–) → F via

Conversely, if G contains a proper non-trivial normal subgroup N, then the composition of the natural surjective group homomorphism G → G / N with the regular representation of G / N produces a representation π of G which has kernel N. Taking χ to be the character of some non-trivial subrepresentation of π, we have a character satisfying the hypothesis in the direct statement above.

Conversely, if the measured potential is negative, the electrode is more oxidizing than the SHE ( such as Zn in ZnSO < sub > 4 </ sub > where the standard electrode potential is − 0. 76 V ).

Conversely, to switch off a p-channel device requires V < sub > GS </ sub > positive.

Given a vector space V over a field K, the span of a set S ( not necessarily finite ) is defined to be the intersection W of all subspaces of V which contain S. W is referred to as the subspace spanned by S, or by the vectors in S. Conversely, S is called a spanning set of W.

Conversely, if W is subspace of V, then W is itself a vector space under the operations induced by

Conversely, suppose we are given ( U, V, W ) satisfying

Conversely, V. s.

Conversely, if F has characteristic zero, then given an homogeneous polynomial ƒ of degree n on V, the polarization of ƒ is a multilinear function on the n-th Cartesian product of V. The polarization is defined by

Conversely, the normed division algebras immediately give rise to trialities by taking each V < sub > i </ sub > equal to the division algebra, and using the inner product on the algebra to dualize the multiplication into a trilinear form.

Conversely, if V is such a complex representation, then U can be recovered as the fixed point set of j ( the eigenspace with eigenvalue 1 ).

Conversely, given two one-parameter unitary groups U ( t ) and V ( s ) satisfying the braiding relation

Conversely, such a rational parameterization induces a field homomorphism of the field of functions of V into.

Conversely, Sequenza IX had grown out of a piece for clarinet and electronics which Berio later withdrew ( this original piece was known as Chemins V ; it is a different piece to the one now known by that name ).

Conversely, the V. C. s, all colonists from different worlds, often used the term ' earthworm ' to describe Smith and his compatriots.