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If F is clear from context then Ω < sub > F </ sub > may be denoted simply Ω, although different prefix-free universal computable functions lead to different values of Ω.

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## Some Related Sentences

If and F

__If__( remember this

**is**an assumption ) the minimal polynomial for T decomposes Af where Af are distinct elements

**of**

__F__

**,**

**then**we shall show that the space V

**is**the direct sum

**of**the null spaces

**of**Af

**.**

__If__

__F__

**is**algebraically closed and p ( x )

**is**an irreducible polynomial

**of**

__F__

**,**

**then**it has some root a and therefore p ( x )

**is**a multiple

**of**x − a

**.**

__If__

__F__

**is**an antiderivative

**of**f

**,**and the function f

**is**defined on some interval

**,**

**then**every other antiderivative G

**of**f differs

**from**

__F__by a constant: there exists a number C such that G ( x ) =

__F__( x ) + C for all x

**.**

__If__the domain

**of**

__F__

**is**a disjoint union

**of**two or more intervals

**,**

**then**a

**different**constant

**of**integration

**may**

**be**chosen for each

**of**the intervals

**.**

__If__

__F__

**.**tularensis were used as a weapon

**,**the bacteria would likely

**be**made airborne for exposure by inhalation

**.**

__If__evolutionary processes are blind

**to**the difference between function

__F__being performed by conscious organism O and non-conscious organism O *, it

**is**unclear what adaptive advantage consciousness could provide

**.**

__If__

__F__and G are ( covariant ) functors between the categories C and D

**,**

**then**a natural transformation η

**from**

__F__

**to**G associates

**to**every object X in C a morphism in D such that for every morphism in C

**,**we have ; this means that the following diagram

**is**commutative:

__If__

**is**any unit vector

**,**the projection

**of**the curl

**of**

__F__onto

**is**defined

**to**

**be**the limiting value

**of**a closed line integral in a plane orthogonal

**to**as the path used in the integral becomes infinitesimally close

**to**the point

**,**divided by the area enclosed

**.**

__If__certain coordinate systems are used

**,**for instance

**,**polar-toroidal coordinates ( common in plasma physics ) using the notation ∇ ×

__F__will yield an incorrect result

**.**

__If__we assume the controller C

**,**the plant P

**,**and the sensor

__F__are linear and time-invariant ( i

**.**e., elements

**of**their transfer function C ( s ), P ( s ), and

__F__( s ) do not depend on time ), the systems above can

**be**analysed using the Laplace transform on the variables

**.**

__If__

__F__( r ) represents gravity

**,**it

**is**a negative term proportional

**to**1 / r

**<**sup

**>**2

**</**sup >, so the net acceleration in r in the rotating frame depends on a difference

**of**reciprocal square and reciprocal cube terms

**,**which are in balance in a circular orbit but otherwise typically not

**.**

__If__a vector field

__F__with zero divergence

**is**defined on a ball in R

**<**sup

**>**3

**</**sup >,

**then**there exists some vector field G on the ball with

__F__= curl ( G ).

__If__only layer C changes

**,**we should find a way

**to**avoid re-blending all

**of**the layers when computing

__F__

**.**Without any special considerations

**,**four full-image blends would need

**to**occur

**.**

If and is

__If__his dancers are sometimes made

**to**look as if they might

**be**creatures

**from**Mars

**,**this

__is__consistent with his intention

**of**placing them in the orbit

**of**another world

**,**a world in which they are freed

**of**their pedestrian identities

**.**

__If__a work

__is__divided into several large segments

**,**a last-minute drawing

**of**random numbers

**may**determine the order

**of**the segments for any particular performance

**.**

__If__Wilhelm Reich

__is__the Moses who has led them out

**of**the Egypt

**of**sexual slavery

**,**Dylan Thomas

__is__the poet who offers them the Dionysian dialectic

**of**justification for their indulgence in liquor

**,**marijuana

**,**sex

**,**and jazz

**.**

__If__he

__is__the child

**of**nothingness

**,**if he

__is__the predestined victim

**of**an age

**of**atomic wars

**,**

**then**he will consult only his own organic needs and go beyond good and evil

**.**

__If__he thus achieves a lyrical

**,**dreamlike

**,**drugged intensity

**,**he pays the price for his indulgence by producing work -- Allen Ginsberg's `` Howl ''

__is__a striking example

**of**this tendency -- that

__is__disoriented

**,**Dionysian but without depth and without Apollonian control

**.**

__If__love reflects the nature

**of**man

**,**as Ortega Y Gasset believes

**,**if the person in love betrays decisively what he

__is__by his behavior in love

**,**

**then**the writers

**of**the beat generation are creating a new literary genre

**.**

__If__the existent form

__is__

**to**

**be**retained new factors that reinforce it must

**be**introduced into the situation

**.**

__If__we remove ourselves for a moment

**from**our time and our infatuation with mental disease

**,**isn't there something absurd about a hero in a novel who

__is__defeated by his infantile neurosis??

__If__many

**of**the characters in contemporary novels appear

**to**

**be**the bloodless relations

**of**characters in a case history it

__is__because the novelist

__is__often forgetful today that those things that we call character manifest themselves in surface behavior

**,**that the ego

__is__still the executive agency

**of**personality

**,**and that all we know

**of**personality must

**be**discerned through the ego

**.**

__If__our sincerity

__is__granted

**,**and it

__is__granted

**,**the discrepancy can only

**be**explained by the fact that we have come

**to**believe hearsay and legend about ourselves in preference

**to**an understanding gained by earnest self-examination

**.**

If and clear

__If__I now risk some comparisons with Sons And Lovers let it

**be**

__clear__that I am not comparing the two works or judging their merits ; ;

__If__the lever

**is**pulled

**to**

__clear__a signal or move a switch

**,**the tappet moves a short distance lengthwise at the same time

**.**

__If__you can't see your way

__clear__

**to**have summer cooling included when building

**,**by all means make provision for its easy adding later

**.**

__If__so

**,**

**then**it

**is**

__clear__that in saying the suffering was bad we are not expressing our feelings only

**.**

On a trip

**to**Washington**,**with a final plea for help in East Tennessee in early 1863**,**he gave a speech in Indianapolis**,**saying: "__If__the institution**of**slavery denies the government the right**of**agitation**,**and seeks**to**overthrow it**,****then**the government has a__clear__right**to**destroy it**.**__If__the shuttlecock has dropped lower

**,**

**then**a smash

**is**impossible and a full-length

**,**high

__clear__

**is**difficult

**.**

__If__a pair

**is**forced

**to**lift or

__clear__the shuttlecock

**,**

**then**they must defend: they will adopt a side-by-side position in the rear midcourt

**,**

**to**cover the full width

**of**their court against the opponents ' smashes

**.**

__If__zeal for orthodoxy caused him

**to**overstep the limits

**of**discretion

**,**his real attitude towards Rome

**is**sufficiently

__clear__

**.**

__If__a player

**is**about

**to**drive and wants

**to**know if there are players in the target area

**,**they

**may**shout "

__clear__on hole 12?

__If__the indoor air

**is**very humid

**,**rather than moderately so

**,**water will first condense in small droplets and

**then**freeze into

__clear__ice

**.**

__If__he succeeded and built the Holy Temple in its proper place and gathered the dispersed ones

**of**Israel together

**,**this

**is**indeed the anointed one for certain

**,**and he will mend the entire world

**to**worship the Lord together

**,**as it

**is**stated: " For

**then**I shall turn for the nations a

__clear__tongue

**,**so that they will all procalim the Name

**of**the Lord

**,**and

**to**worship Him with a united resolve ( Zephaniah 3: 9 ).

__If__the key signature indicates G-sharp

**,**a local flat before a G makes it G-flat ( not G natural ), though often this type

**of**rare accidental

**is**expressed as a natural

**,**followed by a flat ()

**to**make this

__clear__

**.**

__If__both vaulters miss

**,**the bar goes down by a small increment

**,**and if both

__clear__

**,**the bar goes up by a small increment

**.**

__If__one equates Jesus as the human incarnation

**of**God the Father

**,**it will

**be**

__clear__Oneness proposes that the manifestation

**of**Father suffered when Jesus suffered

**.**

__If__it only defines rules and regulations for Internet Assigned Numbers Authority ( IANA ) registries it

**is**less

__clear__; most

**of**these documents are BCPs

**,**but some are on the standards track

**.**

While Spock makes it

__clear__that the events during the period**of**Surak are well documented (" The Savage Curtain "), he**is**completely uncertain in regard**to**the origin**of**the Romulans: "__If__the Romulans are an offshoot**of**my Vulcan blood -- and I think this likely --**then**attack becomes even more imperative**.**__If__the serve

**is**a

__clear__failure or

**is**doubted again by the umpire after the warning

**,**receiver scores a point

**.**

__If__a distinction

**is**made

**,**the line separating a ruby

**from**a pink sapphire

**is**not

__clear__and highly debated

**.**

__If__the distinction between confined and unconfined

**is**not

__clear__geologically ( i

**.**e., if it

**is**not known if a

__clear__confining layer exists

**,**or if the geology

**is**more complex

**,**e

**.**g., a fractured bedrock aquifer ), the value

**of**storativity returned

**from**an aquifer test can

**be**used

**to**determine it (

**although**aquifer tests in unconfined aquifers should

**be**interpreted differently than confined ones ).

__If__players complete the highest difficulty level

**,**they can continue playing

**to**accumulate a higher score

**,**but the number

**of**viruses

**to**

__clear__remains the same

**.**

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