The tensor product X ⊗ Y from X and Y is a K-vector space Z with a bilinear function T: X × Y → Z which has the following universal property: If T ′: X × Y → Z ′ is any bilinear function into a K-vector space Z ′, then only one linear function f: Z → Z ′ with exists.

If both high priority substituents are on the same side of the double bond, i. e. in the cis configuration, then the stereoisomer is assigned a Z or Zusammen configuration.

If n ≥ 1 and is an integer, the numbers coprime to n, taken modulo n, form a group with multiplication as operation ; it is written as ( Z / nZ )< sup >×</ sup > or Z < sub > n </ sub >< sup >*</ sup >.

If rotations are also considered distinct, then the pentominoes from the first category count eightfold, the ones from the next three categories ( T, U, V, W, Z ) count fourfold, I counts twice, and X counts only once.

If G is a p-group, then so is G / Z, and so it too has a nontrivial center.

If a normal subgroup is not contained in Z < sub > i </ sub >, then its intersection with Z < sub > i + 1 </ sub > has size at least p < sup > i + 1 </ sup >.

An important example is the ring Z / nZ of integers modulo n. If n is written as a product of prime powers ( see fundamental theorem of arithmetic ):

If done correctly, the path of the ball will be Z shaped.

If done correctly, a " Z " shot will apply spin to the ball as well on the final bounce, causing it to rebound perpendicular to the second wall and fall parallel to the back wall, the closer the better.

If the transmission line is uniform along its length, then its behaviour is largely described by a single parameter called the characteristic impedance, symbol Z < sub > 0 </ sub >.

If the current and voltage come from a single wave ( with no reflection ), then V ( x ) / I ( x ) = Z < sub > 0 </ sub >, where Z < sub > 0 </ sub > is the characteristic impedance of the line.

* If every voter's preference between X and Y remains unchanged, then the group's preference between X and Y will also remain unchanged ( even if voters ' preferences between other pairs like X and Z, Y and Z, or Z and W change ).

* If ζ < sub > n </ sub > is a primitive n-th root of unity, then the ring of integers of the cyclotomic field Q ( ζ < sub > n </ sub >) is precisely Z.

# If h ( t ) is a non-zero scalar function of t, then Z ( t )

If they do, it is mostly straight cable, not gyro.

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 the Nymph is drifting too fast then you should perform an upstream mend.

If the nymph is drifting too slowly you should mend downstream.

If an art film has a story, it is usually a drifting sequence of vaguely defined or ambiguous episodes.

" If the game is completed at the Legendary difficulty level, the scene continues to show the piece of Forward Unto Dawn drifting towards a planet.

If the drift error is systematic, it can be canceled with a bias circuit which can be arranged and adjusted to supply the required compensating current.

If there is much current, or the vessel is moving while dropping the anchor, it may " kite " or " skate " over the bottom due to the large fluke area acting as a sail or wing.

# If the beat on the new record hits before the beat on the current record then the new record is too fast, reduce the pitch and manually slow the speed of the new record to bring the beats back in sync.

# If the beat on the new record hits after the beat on the current record then the new record is too slow, increase the pitch and manually increase the speed of the new record to bring the beats back in sync.

If the opponent drops the doubled stakes, he loses the game at the current value of the doubling cube.

If the current account is in surplus, the country's net international asset position increases correspondingly.

If, however, the court finds that the current dispute is fundamentally distinct from all previous cases ( called a " matter of first impression "), judges have the authority and duty to make law by creating precedent.

If so, the patient is asked for name, current location, and current day and time.

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 this process happens faster than it is naturally quenched by ions recombining, the new ions multiply in successive cycles until the gas breaks down into a plasma and current flows freely in a discharge.

If extension is executed properly the discus will be at the right angle to ride on the air current and thus be taken a farther distance.

If a player is the first to build an improvement to the final level ( out-building the current holder of the metropolis ), they take the metropolis from its current holder.

If the current trends continue, some population growth can be foreseen for the coming years.

If the current is driven in the opposite direction by imposing an external potential, then work is done on the cell to drive electrolysis.

If both are empty, then the current pixel can be painted and the painter can move following the right-hand rule.

If there are no more-significant bits, then take the value of the current bit position.

If used in a permanent installation, a split sensor allows the electric current to be tested without dismantling the existing circuit.

If the magnetic field is applied by a solenoid, the sensor output is proportional to the product of the current through the solenoid and the sensor voltage.

If all contracts awarded reach their stated target plateau production then this will increase Iraqi production from today's 2. 5 mb / d by 9. 4 mb / d to a total of 11. 9 mb / d, comparable to current Saudi declared capacity of 12. 5 mb / d.

* Nonlinearity: If the current through a ferromagnetic core coil is high enough that the magnetic core saturates, the inductance will not remain constant but will change with the current through the device.

If an inductor is connected to a direct current source with value I via a resistance R, and then the current source is short-circuited, the differential relationship above shows that the current through the inductor will discharge with an exponential decay: