Here the number of trials is a random variable, not a fixed number.

Therefore, given any positive integer n, it produces a string with Kolmogorov complexity at least as great as n. The program itself has a fixed length U. The input to the program GenerateComplexString is an integer n. Here, the size of n is measured by the number of bits required to represent n, which is log < sub > 2 </ sub >( n ).

Here, the idea was to map mathematical notation to a natural number ( using a Gödel numbering ).

Here, i is the complex number whose square is the real number − 1 and is identified with the point with coordinates ( 0, 1 ), so it is not the unit vector in the direction of the x-axis ( this confusion is just an unfortunate historical accident ).

The result, 1977's Here You Come Again, became her first million-seller, topping the country albums chart and reaching No. 20 on the pop albums chart ; the Barry Mann-Cynthia Weil-penned title track topped the country singles chart, and became Parton's first top-ten single on the pop charts ( reaching number three ).

Here n is the number of electrons / mole product, F is the Faraday constant ( coulombs / mole ), and ΔE is cell potential.

Here we denote with the Bernoulli number of the second kind ( only because the historical reason of formation of this article ) which differ from the first kind only for the index 1.

The piece has enjoyed a number of major revivals, and several of its songs have become standards, including " Broadway Baby ", " I'm Still Here ", " Too Many Mornings ", " Could I Leave You?

Carlotta amuses everyone with a tale of how her dramatic solo was cut from the Follies because the audience found it humorous, but somehow the number works when she sings it today (" I'm Still Here ").

Here he composed a large number of motets and other sacred music, which, being brought to the notice of Pope Urban VIII, obtained for him an appointment in the choir of the Sistine Chapel at Rome with the contralto role.

Here, sgn ( p ) is the signature of each permutation ( i. e. + 1 if p is composed of an even number of transpositions, and − 1 if odd.

Here we have the composite number 90 made up of one atom of the prime number 2, two atoms of the prime number 3 and one atom of the prime number 5.

Here they are combined with a number of peripheral interfaces to reduce the overall complexity and power requirements of a design.

Here n is the number of digits of precision at which the natural logarithm is to be evaluated and M ( n ) is the computational complexity of multiplying two n-digit numbers.

Here Z is atomic number and n is a number which varies between 4 and 5.

Here represents the reflexive and transitive closure of the step relation meaning any number of consecutive steps ( zero, one or more ).

" Here Comes the Judge " peaked at number 19 on the Billboard charts.

During this period in London he also collaborated on a number of songs with Bruce Woodley of the Seekers, including " I Wish You Could Be Here ", " Cloudy ", and " Red Rubber Ball ", which would be a U. S. No. 1 hit for the Cyrkle in 1966.

The album opened to sales of 185, 000 and has since been certified platinum in the U. S. The first single " Right Here " has been the biggest success from the album thus far, garnering much mainstream radio play and peaking at number 1 on the mainstream rock chart.

Here the war would flame to its focus, and here Lewis Littlepage had come.

Here the two leaders, DePugh and Lauchli, hastened to put the group through its paces.

Here the New York Central Railroad, one of the Nation's most important carriers, has alone lost 47.6 percent of its passengers since 1949.

Here is truly a `` Great Recording of the Century '', and its greatness is by no means diminished by the fact that it is not quite perfect.

Here, this happy, roving son of good fortune proved that he could accept the disciplines of a new social-economic order fighting for its very existence and ideals in a truculent world.

Here it is necessary to point out that, whatever its effectiveness, thought coercion has in fact been used very extensively throughout history.

Here, again, a new term appears in the record, the Anglo-Saxon Chronicle for the first time using the word scottas, from which Scots derives, to describe the inhabitants of Constantine's kingdom in its report of these events.

' Let's Dance ', with its little narrative surrounding the young Aborigine couple, targeted ' youth ', and ' China Girl ', with its bare-bummed ( and later partially censored ) beach lovemaking scene ( a homage to the film From Here to Eternity ), was sufficiently sexually provocative to guarantee heavy rotation on MTV.

Here, the immune system adapts its response during an infection to improve its recognition of the pathogen.

Improv comedy techniques have also been used in television and stand-up comedy, in hit shows such as the recent HBO television show Curb Your Enthusiasm created by Larry David, the UK Channel 4 and ABC television series Whose Line Is It Anyway ( and its spinoffs Drew Carey's Green Screen Show and Drew Carey's Improv-A-Ganza ), Nick Cannon's improv comedy show Wild ' N Out, and Thank God You're Here.

Here, the joystick of the Kehl transmitter was used by an operator to steer the missile towards its target.

Murray Bookchin has put it this way " what of the syndicalist ideal of " collectivized " self-managed enterprises that are coordinated by like occupations on a national level and coordinated geographically by " collectives " on a local level ?... Here, the traditional socialist criticism of this syndicalist form of economic management is not without its point: the corporate or private capitalist, " worker-controlled " or not "” ironically, a technique in the repertoire of industrial management that is coming very much into vogue today as " workplace democracy " and " employee ownership " and constitutes no threat whatever to private property and capitalism ... In any case, " economic democracy " has not simply meant " workplace democracy " and " employee ownership.

Here, it is the time needed for the data encoded on a platter to rotate from its current position to a position adjacent to the read-write head as well as the seek time required for the actuator arm for the read-write head to be positioned above the appropriate track.

Here are just a few examples: In a lightweight racing dinghy like a Thistle, the hull should be kept level, on its designed water line for best performance in all conditions.

Here, the meaning of a word is constituted by its contextual relations.

Here he restricted it in this way: no language could contain its own truth predicate, that is, the expression is true could only apply to sentences in some other language.

Here Thomas would have seen poverty, crime and rampant disease at its worst.

Here, Wittgenstein ran into a problem he acknowledged widely: we cannot think about a picture outside of its representational form.

Here, Wordsworth gives his famous definition of poetry as " the spontaneous overflow of powerful emotions recollected in tranquility: it takes its origin from emotion recollected in tranquility.

Here the notion of causality is one of contributory causality as discussed above: If the true value, then a change in will result in a change in y unless some other causative variable ( s ), either included in the regression or implicit in the error term, change in such a way as to exactly offset its effect ; thus a change in is not sufficient to change y.

Here each ant is an autonomous unit that reacts depending only on its local environment and the genetically encoded rules for its variety of ant.

Here the commander of the Golden Horde, as the western section of the Mongol empire was called, fixed his golden headquarters and represented his sovereign the grand khan who lived with the Great Horde in the Orkhon Valley of the Amur.

Here the EU is defined as ' an association of sovereign national states ( Staatenverbund )'.

Here is then the sovereign function of Juno that is highlighted.