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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.

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## Some Related Sentences

Conversely and one

__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__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__women take

__one__step backwards

**and**

**then**slide

**to**

**the**left passing behind of their neighbour

**,**

**then**step forwards

**and**slide right in front of their neighbour

**.**

__Conversely__

**,**in

**an**n-channel enhancement-mode device

**,**

**a**positive gate-to-source voltage

**is**necessary

**to**create

**a**conductive channel

**,**since

__one__does not exist naturally within

**the**transistor

**.**

__Conversely__

**,**when

__one__wants

**to**compute

**an**arbitrary number ( N ) of discrete samples of

__one__cycle of

**a**continuous DTFT

**,**it

**can**be done by computing

**the**relatively simple DFT of s < sub > N </ sub >,

**as**defined above

**.**

__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__

**,**young trails are spatially very dense

**and**

**the**cause of meteor showers when

**the**Earth enters

__one__

**.**

__Conversely__

**,**Trotsky held

**that**socialism in

__one__country would economically constrain

**the**industrial development of

**the**USSR

**,**

**and**thus required assistance from

**the**new socialist countries

**that**had arisen in

**the**developed world

**,**which was essential for maintaining Soviet democracy

**,**in 1924 much undermined by civil war

**and**counter-revolution

**.**

__Conversely__

**,**

**a**person may feel like he belongs

**to**

__one__state without having any legal relationship

**to**it

**.**

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__

**,**from

**a**partial order on

**a**partition of

**a**set S

__one__

**can**construct

**a**preorder on S

**.**There

**is**

**a**1-to-1 correspondence between preorders

**and**pairs ( partition

**,**partial order ).

__Conversely__

**,**Baptists are underrepresented

**,**

**a**reflection of their quite recent expansion in numbers ; there has been only

__one__Roman Catholic president

**,**although they are currently

**the**largest single denomination

**,**

**and**there have been no Lutheran

**,**Pentecostal

**,**or Latter Day Saint presidents

**.**

__Conversely__

**,**specifying

**the**symmetry

**can**define

**the**structure

**,**or at least clarify what we mean by

**an**invariant

**,**geometric language in which

**to**discuss it ; this

**is**

__one__way of looking at

**the**Erlangen programme

**.**

__Conversely__

**,**

**with**

**a**little work

**,**

__one__could turn Underearth into

**a**fine labyrinth for

**the**players

**to**explore

**and**get eaten in

**.**

__Conversely__

**,**

__one__

**can**consider

**the**flux

**the**more fundamental quantity

**and**call

**the**vector field

**the**flux density

**.**

"

__Conversely__**,**Rolling Stone magazine's Peter Travers enthused**,**" Abyss**is****the**greatest underwater adventure ever filmed**,****the**most consistently enthralling of**the**summer blockbusters ...__one__of**the**best pictures of**the**year**.**__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

**.**

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__

**,**

**the**RUC was praised by other security forces

**as**

__one__of

**the**most professional policing operations in

**the**world

**.**

__Conversely__

**,**

**a**disordered environment –

__one__which

**is**not maintained ( broken windows

**,**graffiti

**,**excessive litter ) – sends

**the**signal

**that**

**the**area

**is**not monitored

**and**

**that**

__one__

**can**engage in criminal behavior

**with**little risk of detection

**.**

Conversely and can

__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__

**,**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__

**,**every point on

**the**line

__can__be interpreted

**as**

**a**number in

**an**ordered continuum which includes

**the**real numbers

**.**

__Conversely__

**,**non-spontaneous electrochemical reactions

__can__be driven forward by

**the**application of

**a**current at sufficient voltage

**.**

__Conversely__

**,**badly managed food aid

__can__create problems by disrupting local markets

**,**depressing crop prices

**,**

**and**discouraging food production

**.**

__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__

**,**rifle bullets

__can__pierce light armor

**and**are easier

**to**shoot accurately

**,**but even

**a**carbine such

**as**

**the**Colt M4

**is**larger

**and**

**/**or longer than

**a**submachine gun

**,**making it harder

**to**maneuver in close quarters

**.**

__Conversely__

**,**

**a**high pH

**,**low CO < sub > 2 </ sub >, or low 2

**,**3 BPG favors

**the**relaxed form which

__can__better bind oxygen

**.**

__Conversely__

**,**

**a**very severe bit

**,**in

**the**right hands

**,**

__can__transmit subtle commands

**that**cause no pain

**to**

**the**horse

**.**

__Conversely__

**,**every formally real field

__can__be equipped

**with**

**a**compatible total order

**,**

**that**will turn it into

**an**ordered field

**.**

__Conversely__

**,**if

**the**odds of drawing

**a**winning card are numerically lower than

**the**pot odds

**,**

**the**call has

**a**negative expectation

**,**

**and**you

__can__expect

**to**win less money on average than it costs

**to**call

**the**bet

**.**

__Conversely__we have

**a**b if

**and**only if

**a**< b or

**a**~ b

**.**This

**is**

**the**reason for using

**the**notation ""; "≤"

__can__be confusing for

**a**preorder

**that**

**is**not anti-symmetric

**,**it may suggest

**that**

**a**≤ b implies

**that**

**a**< b or

**a**

__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__

**,**though every president from Washington

**to**John Quincy Adams

__can__be definitely assigned membership in

**an**Anglican or Unitarian body

**,**

**the**significance of

**these**affiliations

**is**often downplayed

**as**unrepresentative of their true beliefs

**.**

__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__

**,**water deep in

**the**ocean near geothermal vents

__can__reach temperatures of hundreds of degrees

**and**remain liquid

**.**

__Conversely__

**,**AES

**is**sensitive

**to**

**the**lighter elements

**,**

**and**unlike X-ray fluorescence

**,**Auger peaks

__can__be detected for elements

**as**light

**as**lithium ( Z = 3 ).

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