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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 FF < sub > Critical </ sub > ( Numerator DF, Denominator DF, α )
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 is also surjective, then the Banach space X is called reflexive.
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 φ is a scalar valued function and F is a vector field, then
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 the circumstances are faced frankly it is not reasonable to expect this to be true.
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 they avoid the use of the pungent, outlawed four-letter word it is because it is taboo ; ;
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 it is an honest feeling, then why should she not yield to it??
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 he is good, he may not be legal ; ;
If the man on the sidewalk is surprised at this question, it has served as an exclamation.
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 he is a traditionalist, he is an eclectic traditionalist.
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 to be innocent is to be helpless, then I had been -- as are we all -- helpless at the start.

If and clear
If there were only darkness, all would be clear.
If there were only the mess, all would be 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 the world were clear, art would not exist.
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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