If, for example, a string sounds the note C when plucked, a string twice as long will sound the same note an octave lower.

If P is a program which outputs a string x, then P is a description of x.

If M is a Turing Machine which, on input w, outputs string x, then the concatenated string < M > w is a description of x.

If the possibility of adding the empty string to a language is added to the strings recognized by the noncontracting grammars ( which can never include the empty string ) then the languages in these two definitions are identical.

( If one string runs out of letters to compare, then it is deemed to come first ; for example, " cart " comes before " carthorse ".

If the radix point is omitted then it is implicitly assumed to lie at the right ( least significant ) end of the string ( that is, the number is an integer ).

If the open string is in tune, but sharp or flat when frets are pressed, the bridge saddle position can be adjusted with a screwdriver or hex key to remedy the problem.

If the spheres only appear to rotate ( that is, we are watching stationary spheres from a rotating frame ), the zero tension in the string is accounted for by observing that the centripetal force is supplied by the centrifugal and Coriolis forces in combination, so no tension is needed.

# If V is a set of strings then V * is defined as the smallest superset of V that contains λ ( the empty string ) and is closed under the string concatenation operation.

# If V is a set of symbols or characters then V * is the set of all strings over symbols in V, including the empty string.

If you measure the three qubits, you will observe a three-bit string.

If a closed string splits and its two parts later reconnect, its worldsheet will look like a single pipe splitting to two and then reconnecting, which also looks like a torus connected to two pipes ( one representing the ingoing string, and the other — the outgoing one ).

If each mass point has the mass, the tension of the string is, the separation between the mass points is and are the offset of these points from their equilibrium points ( i. e. their position on a straight line between the two attachment points of the string ) the vertical component of the force towards point is

If the original string had several substrings that occurred often, then the transformed string will have several places where a single character is repeated multiple times in a row.

If a simple pendulum is suspended from the cusp of an inverted cycloid, such that the " string " is constrained between the adjacent arcs of the cycloid, and the pendulum's length is equal to that of half the arc length of the cycloid ( i. e. twice the diameter of the generating circle ), the bob of the pendulum also traces a cycloid path.

* If lead-acid batteries are used, all cells in the formerly good parallel strings will begin to sulfate due to the inability for them to be fully recharged, resulting in the storage capacity of these cells being permanently damaged, even if the damaged cell in the one degraded string is eventually discovered and replaced with a new one.

* Joel Spolsky ( for Apps Hungarian ): " If you read Simonyi's paper closely, what he was getting at was the same kind of naming convention as I used in my example above where we decided that meant " unsafe string " and meant " safe string.

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 surfaces are approximated by a finite number of planar patches, each of which is taken to have a constant radiosity B < sub > i </ sub > and reflectivity ρ < sub > i </ sub >, the above equation gives the discrete radiosity equation,

If f represents a very small but intense source of heat, then the preceding integral can be approximated by the delta distribution, multiplied by the strength of the source.

If is large compared to the other resistances ( like the input to an operational amplifier ), the output voltage can be approximated by the simpler equation:

If β < sub > 1 </ sub > and β < sub > 2 </ sub > are high enough ( hundreds ), this relation can be approximated with:

If the transfer function is a rational function with real poles and zeros, then the Bode plot can be approximated with straight lines.

If the target function is not easily differentiable, the differential with respect to each variable can be approximated as

If n is sufficiently large, the above binomial distribution may be approximated by a Gaussian ( normal ) distribution and thus the Pearson test statistic approximates a chi-squared distribution,

If the Seebeck coefficients are effectively constant for the measured temperature range, the above formula can be approximated as:

If the wavefunction is approximated by its value at distinct points, each iteration requires 3 pointwise multiplications, one FFT, and one inverse FFT.

If hyperfine structure is small compared with the fine structure ( sometimes called IJ-coupling by analogy with LS-coupling ), I and J are good quantum numbers and matrix elements of can be approximated as diagonal in I and J.

If the interval of the integral being approximated includes an inflection point, the error is harder to identify.

If we make a sufficiently small change in the parameters, then the resulting changes in the endogenous variables can be approximated arbitrarily well by.

If friction and bottoming-out effects are ignored, the spring rate of a stack of identical Belleville washers can be quickly approximated.

If a commodity is sold in whole units, and these are substantial for a consumer, then the individual demand curve can hardly be approximated by a continuous curve.

If the derivatives are unknown, they are typically approximated from the function values at points neighbouring the corners of the unit square, e. g. using finite differences.

If a self-contained formula for the solution is not available, the solution may be numerically approximated using computers.

If f is an arbitrary integrable function, it may be approximated in the L < sup > 1 </ sup > by a compactly supported smooth function g. Pick such a g so that || f-g ||< sub > L < sup > 1 </ sup ></ sub >< ε.

If the parameter β is critical at the value β < sub > c </ sub >, then the order parameter a will be well approximated by

If a real number x is approximated by any rational number a / b that is not in the sequence of mediants found by the algorithm above, then the sequence of mediants contains a closer approximation to x that has a denominator at most equal to b ; in that sense, these mediants form the best rational approximations to x.