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Some Related Sentences
Conversely and given
Conversely, a current
of one ampere is one coulomb
of charge going past
a given point per second:
Conversely, if
a Boolean ring A is
given, we can turn it into
a Boolean algebra by defining
x ∨
y :=
x +
y +
( x ·
y )
and x ∧
y :=
x ·
y.
Conversely, there are other stars
that never rise above
the horizon
, as seen from any
given point on
the Earth's surface
( except exactly on
the equator ).
Conversely, given central idempotents
a < sub > 1 </ sub >,...,
a < sub > n
</ sub > in R
that are pairwise orthogonal
and have sum
1, then R is
the direct sum
of the rings Ra
< sub > 1 </ sub >,…, Ra
< sub > n
</ sub >.

Given
a field ordering ≤
as in Def
1, the elements such that x ≥
0 forms
a positive cone
of F
. Conversely, given a positive cone P
of F
as in Def 2
, one can associate
a total ordering ≤<
sub > P
</ sub > by setting
x ≤
y to mean
y −
x ∈ P
. This total ordering ≤<
sub > P
</ sub > satisfies
the properties
of Def
1.
Conversely, only
the wiki users interested
in a given project need look at its associated wiki pages
, in contrast to high-traffic mailing lists which may burden subscribers
with many messages
, regardless
of their relevance
.
Conversely, given a harmonic function
, it is
the real part
of an analytic function
, ( at least locally ).

Each convex
set containing X must
( by
the assumption
that it is convex ) contain
all convex combinations
of points
in X
, so
the set of all convex combinations is contained
in the intersection
of all convex sets containing X
. Conversely, the set of all convex combinations is itself
a convex
set containing X
, so it also contains
the intersection
of all convex sets containing X
, and therefore
the sets
given by these two definitions must
be equal
.
Conversely, surveys conducted among living donors postoperatively
and in a period
of five years following
the procedure have shown extreme regret
in a majority
of the donors
, who said
that given the chance to repeat
the procedure
, they would not
.
Conversely, given an ordered tree
, and conventionally draw
the root at
the top
, then
the child nodes
in an ordered tree can
be drawn left-to-right
, yielding an essentially unique planar embedding
( up to embedded homotopy
, i
. e., moving
the edges
and nodes without crossing ).
Conversely, the influence
of the data at any
given point on
the initial line propagates
with the finite velocity c: there is no effect outside
a triangle
through that point whose sides are characteristic curves
.
Conversely, given any harmonic function
in two dimensions
, it is
the real part
of an analytic function
, at least locally
.
Conversely, if
( A
, m
, e
, inv ) is
a group object
in one
of those categories
, then m necessarily coincides
with the given operation on A
, e is
the inclusion
of the given identity element on A
, inv is
the inversion operation
and A
with the given operation is an abelian group
.
Conversely, if
the Turing Machine is expected polynomial-time
( for any
given x ), then
a considerable fraction
of the runs must
be polynomial-time bounded
, and the coin sequence used
in such a run will
be a witness
.
Conversely, suppose we are
given ( U
, V
, W ) satisfying
Conversely, given any ring
, we can
form a category by taking objects A
< sub > n
</ sub > indexed by
the set of natural numbers
( including zero )
and letting
the hom-set
of morphisms from to
be the set of-by-matrices over
, and where composition is
given by matrix multiplication
.
Conversely, it is hard to believe
, given the length
and intensity
of the struggle between Máel Sechnaill
and Brian
, that the High King would surrender his title without
a fight
.
Conversely, an algorithm to test for solvability
in arbitrary integers could
be used to test
a given equation for solvability
in natural numbers by applying
that supposed algorithm to
the equation obtained from
the given equation by replacing each unknown by
the sum
of the squares
of four new unknowns
.
Conversely, a disease
that is easily transmitted but has
a short duration might spread widely during 2002 but is likely to have
a low prevalence at any
given point
in 2003
( due to its short duration ) but
a high incidence during 2002
( as many people develop
the disease ).
Conversely, given a commutative diagram
, it defines
a poset category:
Conversely and G
Conversely, let G be any polynomial
such that Af
.
Conversely, if F is left adjoint to
G, and G is naturally isomorphic to
G ′ then F is also left adjoint to
G ′.

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, every Polish space is homeomorphic to
a G < sub > δ
</ sub >- subset
of the Hilbert cube
.

where e is
the identity
in G. Conversely, given a section s one defines
a trivialization Φ by
Conversely, G protein-coupled receptors are neither excitatory nor inhibitory
.
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
.

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
.

Given then
a normal extension L
of K
, with automorphism group Aut
( L / K ) =
G, and containing α
, any element g
( α ) for g
in G will
be a conjugate
of α
, since
the automorphism g sends roots
of p to roots
of p
. Conversely any conjugate β
of α is
of this
form:
in other words
, G acts transitively on
the conjugates
.

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, 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 ).
Conversely and algebraic

)
Conversely, it is often helpful to use
the geometry
of Cartesian coordinates
in two or three dimensions to visualize
algebraic relationships between two or three
of many non-spatial variables
.
Conversely, if is
a separable
algebraic extension
, and if L is any intermediate field
, then
and are separable extensions
.
Conversely and sense
Conversely, British English favours fitted
as the past tense
of fit generally
, whereas
the preference
of American English is more complex: AmEng prefers fitted for
the metaphorical
sense of having made an object " fit "
( i
. e., suited ) for
a purpose ;
in spatial transitive contexts
, AmEng uses fitted for
the sense of having made an object conform to an unchanged object
that it surrounds
( e
. g., " fitted X around Y ") but fit for
the sense of having made an object conform to an unchanged object
that surrounds it
( e
. g., " fit X into Y ");
and for
the spatial senses
( both intransitive
and transitive )
of having been matching
with respect to contour
, with no alteration
of either object implied
, AmEng prefers fit (" The clothes fit
.
Conversely, most realists
( specifically
, indirect realists ) hold
that perceptions or
sense data are caused by mind-independent objects
.
Conversely, the rejection
of syncretism
, usually
in the name
of " piety "
and " orthodoxy ", may help to generate
, bolster or authenticate
a sense of uncompromised cultural unity
in a well-defined minority or majority
.
Conversely, in the category
of rings
, there are no kernels
in the category-theoretic
sense ; indeed
, this category does not even have zero morphisms
.

"
Conversely, in the positive
sense, it would refer to " having it both ways " or " having
the best
of both worlds
.
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, those who had
a difficult time during middle adulthood may look back
and feel
a sense of despair
.
Conversely, an Ehresmann connection H ⊂ TP
( or v: TP → V ) on P defines
a principal G-connection ω if
and only if it is G-equivariant
in the sense that.
Conversely, the topological charge only makes
sense in the ordered phase
and not at
all in the disordered phase
, because
in some hand-waving way there is
a " topological condensate "
in the disordered phase which randomizes
the field from point to point
.
Conversely, synthetic languages often combine many lexical morphemes into single words
, making it difficult to boil them down to
the traditional
sense of words found more easily
in analytic languages ; this is especially difficult for polysynthetic languages
, such as Inuktitut
and Ubykh
, where entire sentences may consist
of a single word
.

for
all compactly supported functions ƒ
and h
. Conversely, () characterizes Δ completely
, in the sense that it is
the only operator
with this property
.
Conversely and to some surprisingly
, the word may
be used to mean " approve
of ," especially
in an official
sense.
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