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Some Related Sentences
Conversely and any
Conversely, let G be
any polynomial such that Af
.
Conversely, any algebra whose associator
is alternating
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, 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, 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
.
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 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
.

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 algebra
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, many theorems that hold in universal
algebra do not generalise all the way to category theory
.
Conversely, once a basis
for A has been chosen
, the products of basis elements can be set arbitrarily
, and then extended in a unique way to a bilinear operator on A
, i
. e., so the resulting multiplication satisfies the
algebra laws
.
Conversely, for any topology the clopen ( i
. e
. closed and open ) subsets yield a Boolean
algebra.
Conversely, given a Hopf
algebra whose coalgebra structure
is given above
, we can recover a formal group law F from it
.
Conversely, given
any topological space X
, the collection of subsets of X that are clopen ( both closed and open )
is a Boolean
algebra.
Conversely, symmetric tensors are defined as invariants: given the natural action of the symmetric group on the tensor
algebra, the symmetric tensors are the subspace on
which the symmetric group acts trivially
.
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, given a generalized Cartan matrix
, one can recover its corresponding Lie
algebra.
Conversely, given
any Lie
algebra with a direct sum decomposition satisfying these three conditions
, the linear map σ
, equal to the identity on and minus the identity on
, is an involutive automorphism
.
Conversely and for
Conversely, if he gives a heavy rating to his own reading
, and finds more accurate facts in it than in the others
, a point
is chalked up
for the intrinsic
, objective meaningfulness of
this type of mediumistic material
.
Conversely, the Radical Republicans criticized him
for moving too slowly in abolishing slavery
.
Conversely, some elements do not maintain distinct allotropes in different phases –
for example phosphorus has numerous solid allotropes
, which all revert to the same P < sub > 4 </ sub > form when melted to the liquid state
.
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, the withdrawal syndrome may also be a trigger
for relapse
.
Conversely the use of
true brass seems to have declined in Western Europe during
this period in favour of gunmetals and other mixed alloys but by the end of the first Millennium AD brass artefacts are found in Scandinavian graves in Scotland
, brass was being used in the manufacture of coins in Northumbria and there
is archaeological and historical evidence
for the production of brass in Germany and The Low Countries areas rich in calamine ore
which would remain important centres of brass making throughout the medieval period
, especially Dinant – brass objects are still collectively known as dinanterie in French
.
Conversely, many fighter aircraft
, such as the F-16
, are often used as ' bomb trucks ,' despite being designed
for aerial combat
.
Conversely, certain general principles (
for example
, neighbourliness
, or charity ) are seen to be universal and consistent
.
Conversely, in more recent times
, Russian existentialist philosopher Lev Shestov viewed Job as the embodiment of the battle between reason (
which offers general and seemingly comforting explanations
for complex events ) and faith in a personal god
, and one man's desperate cry
for him
.
Conversely, the vast majority of early attempts at proper excavation techniques failed to accurately measure or record stratigraphy
, thereby failing to provide a secure context
for artefact finds making interpretations extremely limited in scope
.
Conversely, in the English language as a whole
, singular verb forms can often be used with nouns ending in "- s " that were once considered plural (
for example: " Physics
is my favorite academic subject ").
Conversely, the tiny meson mass mass differences responsible
for meson oscillations are often expressed in the more convenient inverse picoseconds
.
Conversely, in functional code
, the output value of a function depends only on the arguments that are input to the function
, so calling a function f twice with the same value
for an argument x will produce the same result f ( x ) both times
.
Conversely, the bodies of people who had certain medical conditions are useful
for research into those conditions
.
Conversely, if the data are sparse — that
is, if only K out of N Fourier coefficients are nonzero — then the complexity can be reduced to O ( K log N log ( N / K )), and
this has been demonstrated to lead to practical speedups compared to an ordinary FFT
for N / K > 32 in a large-N example ( N = 2 < sup > 22 </ sup >) using a probabilistic approximate algorithm (
which estimates the largest K coefficients to several decimal places ).
Conversely, one might expect that inertial motions
, once identified by observing the actual motions of bodies and making allowances
for the external forces ( such as electromagnetism or friction ), can be used to define the geometry of space
, as well as a time coordinate
.
Conversely, for many deductive systems
, it
is possible to prove the completeness theorem as an effective consequence of the compactness theorem
.
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