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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 a groupoid G in
the algebraic sense
, let G
< sub > 0
</ sub > be the set of all elements
of the form x * x
< sup >− 1
</ sup
> with x varying through G
and define G
( x * x
< sup >-1
</ sup >, y * y
< sup >-1
</ sup >) as
the set of all elements f such that y * y
< sup >-1
</ sup
> * f * x * x
< sup >-1
</ sup
> exists
.
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, 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 any
Conversely, let G
be any polynomial such that Af
.
Conversely, any algebra whose associator
is alternating
is clearly alternative
.
Conversely, any algebra for which this
is true
is clearly alternative
.
Conversely, a subset R defines
a binary function if
and only if
, for
any x in X
and y in Y
, there exists
a unique z in Z such that
( x
, y
, z
) belongs
to R
.
Conversely the equilibrium position
is said
to be " far
to the left " if hardly
any product
is formed
from the reactants
.

* The spectrum
of any bounded linear operator on
a Banach space
is a nonempty compact subset
of the complex
numbers C
. Conversely, any compact subset
of C arises in this manner
, as
the spectrum
of some bounded linear operator
.

*
Conversely, corresponding
to any partition
of X
, there exists an equivalence relation ~ on X
.
Conversely, any surjection between sets determines
a partition on its domain
, the set of preimages
of singletons in
the codomain
.
Conversely, Derek Bickerton
and others argue that
the advent
of abstract words provided
a mental basis for analyzing higher-order relations
, and that
any communication system that remotely resembles human language utterly relies on cognitive architecture that co-evolved alongside language
.
Conversely any planar graph
can be formed
from a map in this way
.
Conversely, a person may feel like he belongs
to one state without having
any legal relationship
to it
.
Conversely, the interior
of the box has
a constant
, zero potential energy .< ref
> Actually
, any constant
, finite potential
can be specified within
the box
.
Conversely, extremely thin jewelry
can cause
the same tearing in what
is commonly referred
to as
the " cheese cutter effect ", either during sudden torsion or
over a long period
of wearing
, especially if
the thin jewelry bears
any weight
.
Conversely, any Hermitian positive semidefinite
matrix M
can be written as M =
A < sup >*</ sup
> A ; this
is the Cholesky decomposition
.
Conversely, if
a double sharp were added
to any other note not containing
a sharp or flat as indicated
by the key signature then
the note will
be raised two semitones or
a whole step with respect
to the chromatic scale
.
Conversely in rings with unity
, any simple left R module arises this way
.
Conversely, supplementation with L-phenylalanine
, L-tyrosine
, L-DOPA
, or
any of the cofactors will increase their respective concentrations
.
Conversely, any choice
of μ
, full rank
matrix U
, and positive diagonal entries Λ
< sub > i
</ sub > yields
a non-singular multivariate normal distribution
.
Conversely, in
the absence
of spatial continuity
can take
any value
.

It
is a fact that
the ring is a principal ideal
ring ; that
is, for
any ideal I in
, there exists an integer
n in I such that every element
of I
is a multiple
of n. Conversely, the set of all multiples
of an arbitrary integer
n is necessarily an ideal
, and is usually denoted
by ( n ).
Conversely and ring

This
ring is the endomorphism
ring of A. Conversely, every
ring ( with identity
) is the endomorphism
ring of some object in some preadditive
category.
Conversely, given a Boolean
ring R
, we define
the join operation
by a ' b =
a + b + ab
, and the meet operation as
multiplication.
Conversely, the valuation on
a discrete valuation
ring can be extended
to a valuation on
the quotient field giving
a discrete valued field
, whose associated discrete valuation
ring is just
.
Conversely, if this identity holds in
a ring R for all pairs
of elements
a and b
of the ring, then R
is commutative
.
Conversely, Haystacks was an accomplished wrestler
, and he consequently took
the majority
of the decisions
, many
by countout
( as Humphrey often could not get himself back into
the ring by the count
of 20 ).

Statement 4 then implies that
a basis
of M / mM lifts
to a minimal
set of generators
of M
. Conversely, every minimal
set of generators
of M
is obtained in this way
, and any two such sets
of generators are related
by an invertible
matrix with entries in
the ring.

If f
is unramified at
a point x
, then f
is quasi-finite at x
. Conversely, if f
is quasi-finite at x
, and if also
, the local
ring of x in
the fiber f
< sup >− 1
</ sup >( f
( x )),
is a field
and a finite separable extension
of κ
( f
( x )), then f
is unramified at x .< ref
> EGA IV
< sub > 4
</ sub >, Théorème 17
. 4
. 1 .</ ref
>
Conversely, every distributive lattice
is isomorphic
to a ring of sets ; in
the case
of finite distributive lattices
, this
is Birkhoff's representation theorem
and the sets may
be taken as
the lower sets
of a partially ordered
set.
0.160 seconds.