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 interstellar colonization is possible, then this assumption is invalid, and the equations of population dynamics would apply instead.

If the wavepacket has a relatively large frequency spread, or if the dispersion has sharp variations ( such as due to a resonance ), or if the packet travels over very long distances, this assumption is not valid.

If the assumption of a " Proto-Human " language is accepted, its date may be set anywhere between 200, 000 years ago ( the age of Homo sapiens ) and 50, 000 years ago ( the age of behavioral modernity ).

If the Zubrin / Andrews assumption were correct then d / dt ( mv < sub > 1 </ sub >) =

If we use NC reductions, that is, reductions which can operate in polylogarithmic time on a parallel computer with a polynomial number of processors, then all P-complete problems lie outside NC and so cannot be effectively parallelized, under the unproven assumption that NC ≠ P. If we use the weaker log-space reduction, this remains true, but additionally we learn that all P-complete problems lie outside L under the weaker unproven assumption that L ≠ P. In this latter case the set P-complete may be smaller.

If the computational Diffie – Hellman assumption holds in the underlying cyclic group, then the encryption function is one-way.

If the decisional Diffie – Hellman assumption ( DDH ) holds in, then

If instead of assuming a constant rate of usage, the assumption of a constant rate of growth of annually is made, the resource will instead last

If, however, there are some extreme events taken from thunder storms, others from snow pack melting, and others from hurricanes, then this assumption is most likely not valid.

If words and expressions that imply that women or men are inferior are constantly used, that assumption of inferiority tends to become part of our mindset ….

If one is dealing with continuous data, a typical assumption is that the continuous values associated with each class are distributed according to a Gaussian distribution.

If there were not, then the entire graph would be the union of finitely many finite sets, and thus finite, contradicting the assumption that the graph is infinite.

If that the justification of induction cannot be deductive, then it would beg the question for induction to be based on an inductive assumption about a connection.

" If they wish to assert their claim to Trans-Jordan and to avoid raising with other Powers the legal status of that area, they can only do so by proceeding upon the assumption that Trans-Jordan forms part of the area covered by the Palestine Mandate.

... it is incorrect to speak of an assumption as either true or false, since there is no way of proving it to be either ( If there were, it would no longer be an assumption ).

If such a dichotomy theorem is true, then CSPs provide one of the largest known subsets of NP which avoids NP-intermediate problems, whose existence was demonstrated by Ladner's theorem under the assumption that P ≠ NP.

If they share an assumption, belief or understanding of how the contract will be interpreted or what the legal effect will be, they are bound by that belief, assumption or understanding if:

If I ’ m persuaded that our life is predicated upon violence, that the entire structure of what we call civilization, the scaffolding that we ’ ve built up over the millennia, can collapse at any moment, then whatever I write is going to be affected by that assumption.

This most usually implicit assumption must be stated explicitly, otherwise the definition is incorrect: If water is added to a pot containing salty water, the concentration of salt decreases, although there is no chemical reaction.

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 any of the norms were violated, Merton determined the enterprise to be nonscience.

If a party has materially violated or breached its treaty obligations, the other parties may invoke this breach as grounds for temporarily suspending their obligations to that party under the treaty.

If a precondition is violated, the effect of the section of code becomes undefined and thus may or may not carry out its intended work.

' If this principle is violated, the very least that society can do is to see that the victims are compensated, as best they can be, by the perpetrators.

If Bell's inequalities are violated, either local realism or counterfactual definiteness must be incorrect ; but some physicists dispute that experiments have demonstrated Bell's violations, on the grounds that the sub-class of inhomogeneous Bell inequalities has not been tested or due to experimental limitations in the tests.

If exceeded, the player gets a penalty card for delay of game or late play and either loses his turn or gets another penalty every five seconds thereafter to either comply with any violated rules, or play a card.

If the database retained A's new value, atomicity and the constraint would both be violated.

If any of these rules is violated, an umpire will call the delivery a no ball.

If the rights of the South were violated, Toombs declared, " Let discord reign forever.

If any of these 3 prongs are violated, the government's action is deemed unconstitutional under the Establishment Clause of the First Amendment to the United States Constitution.

:" If you have violated the ten commandments,

If there is no such message or if the power constraint is violated, a decoding error is declared.

If, on the other hand, Quantum entanglement is correct the Bell inequality would be violated.

If the antipodal points were considered to be distinct, as in spherical geometry, then uniqueness would be violated, e. g., the lines of longitude on the Earth's surface all pass through both the north pole and the south pole.

If this is the case, exchange the element with its parent, and possibly also with its grandparent, and so on, until the minimum-heap property is no longer violated.

If any of these rules are violated, the offending minister is usually removed by the prime minister and, if the disagreement within the Cabinet is strong, a minister may resign, as did John Turner in 1975, over the subject of wage and price controls, and Michael Chong in 2006, over nationhood for " the Québécois ".

If their expectations are violated at either level of observation they will become distressed and enact an appropriate action to stop the chance of infidelity ( Cramer et al., 2008 ).

If equality of opportunity is violated, perhaps by discrimination which affects a subgroup or population over time, it is possible to make this determination using statistical analysis, but there are numerous difficulties involved.

If the police have violated the above rights, the charges may be dismissed by a judge or any statements made to the police may be ruled inadmissible by the judge in court.

If any condition is violated by the young offender, they will be required to appear in front of the court again at which point they may be incarcerated.

If a potential solution has been previously visited within a certain short-term period or if it has violated a rule, it is marked as " taboo " (" tabu " being a different spelling of the same word ) so that the algorithm does not consider that possibility repeatedly.

If this assumption is violated, the test will produce inaccurate results.

If the wavefunction is assumed to physically exist in real space-time, the principle of locality is violated during the measurement process via wavefunction collapse.

If a force is allowed to act on ( do work on ) only one part of such an unbound system, this is equivalent to allowing energy into or out of the system, and the condition of " closure " to mass-energy ( total isolation ) is violated.