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Page "Frobenius theorem (differential topology)" ¶ 5
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If and TN
If α is a differential k-form, i. e., a section of the exterior bundle Λ < sup > k </ sup > T * N of ( fiberwise ) alternating k-forms on TN, then the pullback of α is the differential k-form on M defined by the same formula as in the previous section:
If TN
If the decision is to grant TN status, the Canadian immediately enters the US and begins TN employment.
Canadian TN status workers appear to be responsible for US Medicare, State, Federal and Social Security taxes whether they are resident or non-resident ( working remotely ) in the U. S. If their legal residence is still in Canada, workers are also required to file Provincial and Federal income tax but can credit some part of the taxes paid in the United States.

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 exactly
If one follows the reports of the Congress, one finds that there still seems considerable uncertainty in the minds of the leaders themselves about what exactly to do in this matter.
If a litigant chooses to enforce a Federal right in a State court, he cannot be heard to object if he is treated exactly as are plaintiffs who press like claims arising under State law with regard to the form in which the claim must be stated -- the particularity, for instance, with which a cause of action must be described.
If most of them weren't exactly specific -- well, that's the way it is in life, I guess.
If the shooter " hits " the point value again ( any value of the dice that sum to the point will do ; the shooter doesn't have to exactly repeat the value combination of the come-out roll ) before rolling a seven, the Pass line wins and a new round starts, usually with the dice staying with the current shooter.
If punishable by exactly one year or less, it is classified as a misdemeanor.
* If f is an irreducible polynomial of prime degree p with rational coefficients and exactly two non-real roots, then the Galois group of f is the full symmetric group S < sub > p </ sub >.
If ω is directly proportional to k, then the group velocity is exactly equal to the phase velocity.
If the spheres really are rotating, the tension observed is exactly the centripetal force required by the circular motion.
If Judge Landis was suspicious of an attorney's line of questioning, he would begin to wrinkle his nose, and once told a witness, " Now let's stop fooling around and tell exactly what did happen, without reciting your life's history.
If each group contains less than half the population, then some of the population is exactly equal to the median.
If the desired output values are often incorrect ( because of human error or sensor errors ), then the learning algorithm should not attempt to find a function that exactly matches the training examples.
For example, a player bids 4: If he takes exactly 4 tricks, he scores 14.
If it is a deterministic computer, then it is in exactly one of these states with probability 1.
If an eavesdropper intercepts the two bits, she may know exactly what Bob needs to do in order to recover the desired state.
If they had any significant level of non-organic parts then something as simple as an x-ray scan would show them not to be human ( unless their creators designed the non-organic parts to have almost exactly the same structure and density as the organic components they were replacing, which would be both infeasible and highly improbable but not completely out of the question ).
If is off by a small amount, then the beat frequency is not exactly, which can lead to the speech distortion mentioned earlier.
If the payout is 4, 000 times the input amount, and it happens every 4, 000 times on average, the return to player is exactly 100 %, but the game would be dull to play.
If, as the writer believes Schiller, various private cases of action were available in satisfying commercial needs, the state was acting in exactly the same fashion as it does at the present day .”
If I tried too hard to tell them exactly how something happened, in the hope of correcting some fantasy, I was quite likely to be accused of trying to suppress Free Speech.
The second major variation is the song " Wenn alle untreu werden " ( German: " If everyone becomes unfaithful ") better known as " Das Treuelied ", which was written by the poet Max von Schenkendorf ( 1783 – 1817 ) and used exactly the same melody as the Wilhelmus.
Here the notion of causality is one of contributory causality as discussed above: If the true value, then a change in will result in a change in y unless some other causative variable ( s ), either included in the regression or implicit in the error term, change in such a way as to exactly offset its effect ; thus a change in is not sufficient to change y.
If the relative density is exactly 1 then the densities are equal ; that is, equal volumes of the two substances have the same mass.
If a signal contains a component at exactly B hertz, then samples spaced at exactly 1 /( 2B ) seconds do not completely determine the signal, Shannon's statement notwithstanding.
If the signals are close but not exactly on the same frequency the mix will not only include the audio from both carriers but depending on the carrier separation a whistle might be heard as well representing the difference in the carrier frequencies.

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