If a description of s, d ( s ), is of minimal length ( i. e. it uses the fewest number of characters ), it is called a minimal description of s. Thus, the length of d ( s ) ( i. e. the number of characters in the description ) is the Kolmogorov complexity of s, written K ( s ).

If a ) testimonies conflict one another, b ) there are a small number of witnesses, c ) the speaker has no integrity, d ) the speaker is overly hesitant or bold, or e ) the speaker is known to have motives for lying, then the epistemologist has reason to be skeptical of the speaker's claims.

* In the Tales of Old Dartmoor episode ( recorded in 1956 ) of The Goons radio comedy series, Grytpype-Thynne arranges for the prison to put to sea to visit the Château d ' If in France as part of a plan to find the treasure of the Count of Monte Cristo hid there.

* If < math > a < b </ math > and < math > c < d </ math > then < math > a + c < b + d </ math >;

If R is a commutative ring, and a and b are in R, then an element d of R is called a common divisor of a and b if it divides both a and b ( that is, if there are elements x and y in R such that d · x = a and d · y = b ).

If d is a common divisor of a and b, and every common divisor of a and b divides d, then d is called a greatest common divisor of a and b.

If the target is a hard and heavy object, or if it is resting on some sort of anvil, the head can travel only a very short distance d before stopping.

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.

* We are allowed to " add inequalities ": If a ≤ b and c ≤ d, then a + c ≤ b + d

French-Canadian band Harmonium had a short career in the mid ' 70s during which their most notable release was Si on avait besoin d ' une cinquième saison ( If We Needed A Fifth Season ) ( 1975 ).

If X and Y are subsets of the real numbers, d < sub > 1 </ sub > and d < sub > 2 </ sub > can be the standard Euclidean norm, || · ||, yielding the definition: for all ε > 0 there exists a δ > 0 such that for all x, y ∈ X, | x − y | < δ implies | f ( x ) − f ( y )| < ε.

If we suppose the screen is far enough from the slits ( that is, s is large compared to the slit separation d ) then the paths are nearly parallel, and the path difference is simply d sin θ.

If scatterers are arranged symmetrically with a separation d, these spherical waves will be in sync ( add constructively ) only in directions where their path-length difference 2d sin θ equals an integer multiple of the wavelength λ.

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 polarities are correct, the platform rotates in such a direction as to reduce the accelerometer output to zero.

If the polarity is correct, the platform will turn until the heading error angle is zero.

If the minimum legal value for every index is 0, then B is the address of the element whose indices are all zero.

If the path of the particle or centre of mass of the rigid body passes through the given origin, its angular momentum is zero.

If all four players pass in the first round, the deal is not played ; in rubber bridge the deal is not scored and the hand is redealt by the original dealer, while in duplicate the score is recorded as zero for each pair and returned to the board.

If the remaining array to be searched is reduced to zero, then the key cannot be found in the array and a special " Not found " indication is returned.

If we attempt to use the above formula to compute the derivative of f at zero, then we must evaluate 1 / g ′( f ( 0 )).

If they are successful, they receive two points, if they are not, then they receive zero points.

If a simply stable system response neither decays nor grows over time, and has no oscillations, it is marginally stable: in this case the system transfer function has non-repeated poles at complex plane origin ( i. e. their real and complex component is zero in the continuous time case ).

If the desired user's code has nothing in common with the signal the correlation should be as close to zero as possible ( thus eliminating the signal ); this is referred to as cross correlation.

If the code is correlated with the signal at any time offset other than zero, the correlation should be as close to zero as possible.

If the dot product is zero, the two vectors are said to be orthogonal to each other.

If these conditions do not hold, the formula describes a more general affine transformation of the plane provided that the determinant of A is not zero.

If h is negative, then a + h is on the low part of the step, so the secant line from a to a + h is very steep, and as h tends to zero the slope tends to infinity.

If h is positive, then a + h is on the high part of the step, so the secant line from a to a + h has slope zero.

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 the remainder is zero the answer produced is ' yes ', otherwise it is ' no '.

If they fail to perform the dive announced, even if they physically cannot execute the dive announced or if they perform a more difficult dive, they will receive a score of zero.

If a dive is performed which is as submitted but not as ( incorrectly ) announced, it is declared failed and scores zero according to a strict reading of the FINA law.

If an explosive molecule contains just enough oxygen to convert all of its carbon to carbon dioxide, all of its hydrogen to water, and all of its metal to metal oxide with no excess, the molecule is said to have a zero oxygen balance.

If the moments of the aligned and anti-aligned ions balance completely so as to have zero net magnetization, despite the magnetic ordering, then it is an antiferromagnet.

If the arguments are both greater than zero then the algorithm can be written in more elementary terms as follows:

If a and b are not both zero, the greatest common divisor of a and b can be computed by using least common multiple ( lcm ) of a and b:

If this rule is interpreted as saying that straight-line motion is an indication of zero net force, the rule does not identify inertial reference frames, because straight-line motion can be observed in a variety of frames.