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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 ).

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## Some Related Sentences

If and description

__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__

**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 and s

__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__

**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__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 and d

__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__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__

**.**

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

**.**

0.366 seconds.