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Conversely, suppose that **ya is in the null space of Af.

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Brown Corpus

## Some Related Sentences

Conversely and suppose

:

__Conversely__**,**__suppose__**that**φ**is**a smooth real-valued function on M**in**a neighborhood**of**p**.**Since every smooth function has a local coordinate expression**,**we may express φ as a function**in****the**coordinates**.**

Conversely and is

__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__

**,**an adiabatic process

**that**

__is__irreversible and extracts no work

__is__

**in**an isenthalpic process

**,**such as viscous drag

**,**progressing towards a nonnegative change

**in**entropy

**.**

__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**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__

**,**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__

**,**because

**space**

__is__expanding

**,**and more distant objects are receding ever more quickly

**,**light emitted by us today may never " catch up " to very distant objects

**.**

__Conversely__

**,**modern biological sciences ( including even concepts such as molecular ecology ) are intimately entwined and dependent on

**the**methods developed through biotechnology and what

__is__commonly thought

**of**as

**the**life sciences industry

**.**

__Conversely__

**,**if

**the**second theory

__is__correct

**,**then

**the**Athenians were merely reacting to

**the**Persians attacking them

**.**

__Conversely__

**the**equilibrium position

__is__said to be " far to

**the**left " if hardly any product

__is__formed from

**the**reactants

**.**

__Conversely__

**,**

**the**islands do not receive

**the**upwellings ( cold streams )

**that**affect

**the**West African coast

**,**so

**the**air temperature

__is__cooler than

**in**Senegal

**,**but

**the**sea

__is__actually warmer

**,**because

**the**orographic relief

**of**some islands

**,**as Sao Miguel with steep mountains

**,**cover it with rich woods and luxuriant vegetation where

**the**dense moisture condense and soak

**the**plants

**,**rocks

**,**soil

**,**logs

**,**moss etc

**.**

__Conversely__

**in**francophone Canada

**,**one hundredth

**of**a Canadian dollar

__is__informally called a sou ( penny ), though cent

__is__official

**in**both English and French

**.**

__Conversely__

**,**an absence

**of**secure cycle-parking

__is__a recurring complaint by cyclists from cities with low modal share

**of**cycling

**.**

* 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 and space

__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__

**,**

**in**

**the**bleak Orwellian world

**of**" The High Ones "— where

**the**Soviets have won

**the**Third World War and gained control

**of**

**the**whole world —

**the**dissidents still have some hope

**,**precisely because

__space__flight has not been abandoned

**.**

__Conversely__

**,**a metrizable

__space__

**is**separable if and only if it

**is**second countable

**,**which

**is**

**the**case if and only if it

**is**Lindelöf

**.**

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__

**,**except

**in**dimension 2

**,**if

**the**curvature

**of**a Riemannian manifold has this form for some function K

**,**then

**the**Bianchi identities imply

**that**K

**is**constant and thus

**that**

**the**manifold

**is**( locally ) a

__space__form

**.**

Equipped with this notion

**of**length**,**a Riemannian manifold**is**a metric__space__**,**meaning**that**it has a distance function d ( p**,**q ) whose value at a pair**of**points p and q**is****the**distance from p to q**.**__Conversely__**,****the**metric tensor itself**is****the**derivative**of****the**distance function ( taken**in**a suitable manner ).__Conversely__

**,**every Polish

__space__

**is**homeomorphic to a G < sub > δ </ sub >- subset

**of**

**the**Hilbert cube

**.**

__Conversely__

**,**when a record

**is**deleted

**,**later records are moved down so

**that**

**the**free

__space__remains contiguous

**.**

__Conversely__

**,**if X

**is**projective

**,**then

**the**pullback

**of**under

**the**closed immersion

**of**X into a projective

__space__

**is**very ample

**.**

__Conversely__

**,**if X

**is**a Hausdorff

__space__and ker f

**is**a closed set

**,**then

**the**coimage

**of**f

**,**if given

**the**quotient

__space__topology

**,**must also be a Hausdorff

__space__

**.**

Any point x gives rise to a continuous function p < sub > x </ sub > from

**the**one element topological__space__1 ( all subsets**of**which are open ) to**the**__space__X by defining p < sub > x </ sub >( 1 ) = x**.**__Conversely__**,**any function from 1 to X clearly determines one point:**the**element**that**it " points " to**.**__Conversely__

**,**any such one form defines ( via pullback ) a G-equivariant horizontal 1-form on P

**,**and

**the**

__space__

**of**principal G-connections

**is**an affine

__space__for this

__space__

**of**1-forms

**.**

Conversely and Af

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