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This shows in particular that is a natural number for any natural numbers n and k. There are many other combinatorial interpretations of binomial coefficients ( counting problems for which the answer is given by a binomial coefficient expression ), for instance the number of words formed of n bits ( digits 0 or 1 ) whose sum is k is given by, while the number of ways to write where every a < sub > i </ sub > is a nonnegative integer is given by.
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A fundamental theorem due to Georg Cantor shows that it is possible for infinite sets to have different cardinalities, and in particular the set of real numbers and the set of natural numbers do not have the same cardinal number.
* In situ hybridization shows which cells are expressing a particular RNA transcript.
Besides the advantages offered by such a plan, in setting immediately before the eyes of the student the final results of the investigation in a more concrete form, and thereby rendering easier his insight into the nature of particular Indo-European languages, there is, I think, another of no less importance gained by it, namely that it shows the baselessness of the assumption that the non-Indian Indo-European languages were derived from Old-Indian ( Sanskrit ).
Relationship-An establishing shot might be a long shot of a room that shows all the characters from a particular scene.
However, even though it cannot be determined whether a particular file is incompressible, a simple theorem about incompressible strings shows that over 99 % of files of any given length cannot be compressed by more than one byte ( including the size of the decompressor ).
The work shows that the transcription start site for genes expressed in a particular tissue, are nucleosome depleted while, the same set of genes in other tissue where they are not expressed, are nucleosome bound.
If S contains two elements that are not pairwise orthogonal ( in particular, the set of all quantum states includes such pairs ) then an argument like that given above shows that the answer is no.
In particular, Braess paradox shows that adding a new road can lengthen travel times for all drivers.
There is speculation that Regiomontanus had arrived at a theory of heliocentrism before he died ; a manuscript shows particular attention to the heliocentric theory of the Pythagorean Aristarchus, mention was also given to the motion of the earth in a letter to a friend.
* Though normal television programming resumed after nearly a full week of news coverage following the attack, some daily talk shows such as The Tonight Show with Jay Leno, Late Night with Conan O ' Brien, The Daily Show and Late Show with David Letterman took additional time before beginning to broadcast new installments, with Letterman in particular stating that he was not sure he wanted to continue to do the show.
The hypothesis that the Ancient Roman custom of crucifixion may have developed out of a primitive custom of arbori suspendere — hanging on an arbor infelix ( unfortunate tree ) dedicated to the gods of the nether world — is rejected by William A. Oldfather, who shows that this form of execution ( the supplicium more maiorum, punishment in accordance with the custom of our ancestors ) consisted of suspending someone from a tree, not dedicated to any particular gods, and flogging him to death.
In particular, Viola's obsession with capturing the essence of emotion through recording of its extreme display began at least as early as his 1976 work, The Space Between the Teeth, a video of himself screaming, and continues to this day with such works as the 45-second Silent Mountain ( 2001 ), which shows two actors in states of anguish.
In addition, critics of Ethnic American reality shows frequently state that the portrayals of a particular ethnic group are inaccurate or fictionalized as opposed to " real ".
The matrix M may be regarded as a diagonal matrix D that has been re-expressed in coordinates of the basis P. In particular, the one-to-one change of variable y = Pz shows that z < sup >*</ sup > Mz is real and positive for any complex vector z if and only if y < sup >*</ sup > Dy is real and positive for any y '; in other words, if D is positive definite.
Analysis of a particular antenna ( such as a Hertzian dipole ), shows that this constant is, where is the free-space wavelength.
* Iron Maidens famous fictional mascot, Eddie, was lobotomised on-stage during one of Maiden's live shows ; this concert was filmed for German TV but that particular segment was cut out due to being deemed " Too violent ".
British shows are also sometimes shown on the three commercial television networks in Australia ; in particular Network Seven screened many popular UK sitcoms during the 1970s.
But the typicality theorem shows that, absent some particular reason to believe one of those special initial conditions was in fact realized, Born rule behavior is what one should expect.
The latter shows that the coefficient of X < sup >− 1 </ sup > in ƒ is of particular interest ; it is called formal residue of ƒ and denoted Res ( ƒ ).
A more detailed study by the Brazilian Center for Physics Research ( CBPF ) on the element's isotopes shows similar results ( in particular that < sup > 296 </ sup > Uus is the most stable isotope in its region ), but goes further up to < sup > 337 </ sup > Uus.
Moreover, Gödel's second incompleteness theorem shows that the consistency of sufficiently strong effective theories of arithmetic can be tested in a particular way.
Apollo comes in for particular ridicule as Ovid shows how irrational love can confound the god out of reason.
Another artifact from the 1st dynasty shows a cow lying down on an ivory engraving with the inscription " Hathor in the Marshes " indicating her association with vegetation and the papyrus marsh in particular.
In this overture he shows how folk songs could be given symphonic dimensions while paying particular attention to the element of protyazhnaya or melismatically elaborated lyric song.
shows and is
DeKalb budget shows county is on beam
The board's action shows what free enterprise is up against in our complex maze of regulatory laws.
The present attempts of the politicians to contaminate ordinary Britons shows that this British common sense is unwilling to pull somebody else's chestnuts out of the fire by new military adventures ''.
And the Chinese, as the Albanian incident shows, have strong suspicions that Khrushchev is anxious to secure a `` shameful '' peace with the West.
If your computation on Form 1040 or Form 1040A shows you owe additional tax, it should be remitted with your return unless you owe less than $1, in which case it is forgiven.
Superintendents at dog shows state it is becoming more difficult to obtain a licensed Handler to Judge Junior Showmanship Competition.
Mrs. Freight ( Knight Dream-Miss Reed ) shows promise and does it in good form, and her best time is about 2:35.
`` It is as though '', I said on the historic three-hour, coast-to-coast radio broadcast which I bought ( following Father Coughlin and pre-empting the Eddie Cantor, Manhattan Merry-go-round and Major Bowes shows ) `` That Man in the White House, like some despot of yore, insisted on reading my diary, raiding my larder and ransacking my lingerie!!
The last column shows the rate of exchange that would have been observed at a relative intensity of 4 ( 14.7 cm. distance ) calculated on the assumptions that the incident light intensity is inversely proportional to the square of the distance of the lamp from the cell and that the rate is directly proportional to the incident light intensity.
The following information on snakes varying greatly in size ( but all with less than a 10-foot maximum ) shows, when considered with the foregoing, that there is probably no correlation between the length of a snake and the time required for it to mature.
It is no coincidence that the hebephrenic patient, the most severely dedifferentiated of all schizophrenic patients, shows, as one of his characteristic symptoms, laughter -- laughter which now makes one feel scorned or hated, which now makes one feel like weeping, or which now gives one a glimpse of the bleak and empty expanse of man's despair ; ;
The differentiation, however, is not very much greater, as shown by the fact that Athabascan shows 3.46 stems per meaning slot as against 2.75 for Yokuts, with a slightly greater number of languages represented in our sample: 24 as against 21.
The 2% increase in retail sales in October to a 4-month high is encouraging in this connection as well as the most recent consumer survey by the National Industrial Conference Board, which shows a decided pickup in consumer spending plans.
If we consider a process in which the outcome of one stage is known before passage to the next, then the principle of optimality shows that the policy in subsequent stages should be optimal with respect to the outcome of the first.
The accumulated information on this point shows that first intercourse, even when it is achieved with minimum pain or difficulty, is seldom an overwhelming sexual experience to a woman.
In the field of entertainment there is no spur to financial daring so effective as audience boredom, and the first decade of the new device was not over before audiences began staying away in large numbers from the simple-minded, one-minute shows.
I said `` Darn it, that's the automatic signal that shows when the ignition key is on.
A new report on the earnings records of toll roads in the most recent 12-month period -- ending in February or March -- shows what is happening.
Research shows that if can be beneficial to help others if there is a chance that they can and will reciprocate the help.
But Minsky shows ( as do Melzak and Lambek ) that his machine is Turing complete with only four general types of instructions: conditional GOTO, unconditional GOTO, assignment / replacement / substitution, and HALT.
One of the most interesting aspects of the axiom of choice is the large number of places in mathematics that it shows up.
1st century BCE ), shows how the distance to the Sun can be computed geometrically, using the different lengths of the noontime shadows observed at three places 1000 li apart and the assumption that the Earth is flat.
The end result of antimatter meeting matter is a release of energy proportional to the mass as the mass-energy equivalence equation, E = mc < sup > 2 </ sup > shows.
1.288 seconds.