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.

Theorem: If K < sub > 1 </ sub > and K < sub > 2 </ sub > are the complexity functions relative to description languages L < sub > 1 </ sub > and L < sub > 2 </ sub >, then there is a constant c – which depends only on the languages L < sub > 1 </ sub > and L < sub > 2 </ sub > chosen – such that

If we take the simple molecular orbital description of the ground state and combine that function with the functions describing all possible excited states using unoccupied orbitals arising from the same set of atomic orbitals, we also reach the full configuration interaction wavefunction.

If they express much more than this, they are usually considered to be a hardware description language such as Verilog, VHDL, or any one of several specific languages designed for input to simulators.

The algorithm for deciding this is conceptually simple: it constructs ( the description of ) a new program t taking an argument n which ( 1 ) first executes program a on input i ( both a and i being hard-coded into the definition of t ), and ( 2 ) then returns the square of n. If a ( i ) runs forever, then t will never get to step ( 2 ), regardless of n. Then clearly, t is a function for computing squares if and only if step ( 1 ) terminates.

If no time range is given, use the start or end time provided in the presentation description.

If a new media stream is added to a presentation ( e. g., during a live presentation ), the whole presentation description should be sent again, rather than just the additional components, so that components can be deleted.

If the check in operation succeeds, then the version numbers of all files involved automatically increment, and the CVS-server writes a user-supplied description line, the date and the author's name to its log files.

If a job description is not available, then a systems analysis can be done to draw up a job description.

If the monks did hide the stone, they hid it well ; no other stone fitting its description has ever been found.

If one allows arbitrary temperature dependence of the prefactor, the Arrhenius description becomes overcomplete, and the inverse problem ( i. e., determining the prefactor and activation energy from experimental data ) becomes singular.

If you hear anything we've done in the last five or six years, that description is totally irrelevant ...

If dictionaries were logico-mathematical texts, then so-called circular definition would amount to infinite regress, where one of the steps involved in running the procedure is to run the procedure ; and, in the context of explanation ( as opposed to description in the form of dictionary definition ), this would be a vicious infinite regress.

If this machine U is supplied with a tape on the beginning of which is written the S. D description " of an action table of some computing machine M, then U will compute the same sequence as M ."

If a system has a probabilistic description, this description gives the probability of any configuration, and given any two different configurations, there is a state which is partly this and partly that, with positive real number coefficients, the probabilities, which say how much of each there is.

If, for example, the 43 letters long ( ignoring the spaces ) description " not divisible by any integer other than 1 and itself " were assigned to the number 43, then this would be true.

But let us have done with British-Americans and Irish-Americans and German-Americans, and so on, and all be Americans ... If a man is going to be an American at all let him be so without any qualifying adjectives ; and if he is going to be something else, let him drop the word American from his personal description.

If H < sub > f </ sub > is in this time complexity class, it means we can construct some machine K which, given some machine description and input x, decides whether the tuple (, x ) is in H < sub > f </ sub > within.

Almost all of her dialogue prior to line 32 (" If thou be he, then thou art prisoner ") is delivered direct to camera, including her incredulous description of the difference between the real Talbot, and the reports she has heard of him.

If the F-plasmid that is transferred has previously been integrated into the donor ’ s genome some of the donor ’ s chromosomal DNA may also be transferred with the plasmid DNA.

If there were no such assignment ( s ), the answer would be NO.

If the relative priorities of these substituents need to be established, R takes priority over S. When this happens, the descriptor of the stereocenter is a lowercase letter ( r or s ) instead of the uppercase letter normally used.

If the hoop is the hoop in order for the striker ’ s ball, the striker earns a bonus stroke.

If we assume the controller C, the plant P, and the sensor F are linear and time-invariant ( i. e., elements of their transfer function C ( s ), P ( s ), and F ( s ) do not depend on time ), the systems above can be analysed using the Laplace transform on the variables.

If, i. e., it has a large norm with each value of s, and if, then Y ( s ) is approximately equal to R ( s ) and the output closely tracks the reference input.

:” If we observe the totality of Pissarro ’ s work, we find there, despite fluctuations, not only an extreme artistic will, never belied, but also an essentially intuitive, purebred art.

If the orientation of the tangent relative to some starting position is θ ( s ), then ρ ( s ) is defined by the derivative dθ / ds:

If the depletion layer is large enough to catch the whole shower or to stop a heavy particle, a fairly accurate measurement of the particle ’ s energy can be made, simply by measuring the charge conducted and without the complexity of a magnetic spectrometer, etc.

If not, the null hypothesis is supported ( or, more correctly, not rejected ), meaning no effect of the independent variable ( s ) was observed on the dependent variable ( s ).

If called upon, the neighbouring amoeba midwife travels up to 200 μm towards the dividing amoeba, usually advancing in a straight trajectory with an average velocity of about 0. 5 μm / s.

If this does not simply reflect Gregory ’ s ignorance of Kentish affairs, which seems unlikely given the close ties between Kent and the Franks, then some assert that Æthelberht ’ s reign cannot have begun before 589.

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.