In fact, Italian and French share many more root words in common that do not even appear in Spanish.

The best-known FFT algorithms depend upon the factorization of N, but there are FFTs with O ( N log N ) complexity for all N, even for prime N. Many FFT algorithms only depend on the fact that is an th primitive root of unity, and thus can be applied to analogous transforms over any finite field, such as number-theoretic transforms.

Noting that the modifying component in Germanic compound words can take the form of a genitive or a bare root, he points to behavioural similarities between genitive determinants and the modifying element in regular Old Norse compound words, such as the fact that neither can be modified by a free-standing ( declined ) adjective.

( In fact, subtracting 1 and dividing the result by 9 always gives a triangular number, the sequence starting with 3, 55, 903, 3727815, ....) This can be reformulated as follows: adding the digits of any even perfect number ( except 6 ), then adding the digits of the resulting number, and repeating this process until a single digit ( called the digital root ) is obtained, always produces the number 1.

Recent findings in genetic research have suggested that a large number of genetic disorders, both genetic syndromes and genetic diseases, that were not previously identified in the medical literature as related, may be, in fact, highly related in the genetypical root cause of the widely-varying, phenotypically-observed disorders.

Good performance for a splay tree depends on the fact that it is self-optimizing, in that frequently accessed nodes will move nearer to the root where they can be accessed more quickly.

The natural history of aortic root dilatation is still unknown, but it is a fact that it is linked to aortic dissection and rupture, which has a high mortality rate.

Recent findings in genetic research have suggested that a large number of genetic disorders, both genetic syndromes and genetic diseases, that were not previously identified in the medical literature as related, may be, in fact, highly related in the genotypical root cause of the widely-varying, phenotypically-observed disorders.

The two types are differentiated by the fact that the hyphae of ectomycorrhizal fungi do not penetrate individual cells within the root, while the hyphae of endomycorrhizal fungi penetrate the cell wall and invaginate the cell membrane.

The name comes from the fact that it is the square root of the mean of the squares of the values.

The modicum of fact lying at the root of this false accusation was that they had seen Paul and Trophimus in each other's company in the city.

Between these two fear possibilities these poles of fear, the individual is thrown back and forth all his life, which accounts for the fact that we have not been able to trace fear back to a single root, or to overcome it therapeutically " ( ibid., p. 124 ).

Some scholars posit that the root rot-or rod-found in the name " Rhone " as well as in the name of many western European rivers, and whose original meaning seems to be " river ", is in fact Pre-Indo-European.

In fact, some phonetic complexes were originally simple pictographs that were later augmented by the addition of a semantic root.

( To see that the xy is a root of the x-resultant of z − xy and x < sup > 2 </ sup > − x − 1, one might use the fact that the resultant is contained in the ideal generated by its two input polynomials.

The language spoken in Gascony before Roman rule was part of the Basque dialectal continuum ( see Aquitanian language ); the fact that the word ' Gascon ' comes from the Latin root vasco / vasconem, which is the same root that gives us ' Basque ', implies that the speakers identified themselves at some moment as Basque.

" Mainline Protestant churches were slow to take root, in fact no churches at all were built in Demopolis until 1840.

At the root of the question is the fact that none of the chartering monarchs – Elizabeth I, Charles I, or George III – created a university distinct from Trinity College.

In fact we are not " taken down " to the tonic key, but to " non-diatonic chords and secondary dominants " combining with " chromatic melodic tension intensified through outrageous harmonisation and root movement ".

Solutions to such recurrence relations of higher order are found by systematic means, often using the fact that a < sub > n </ sub > = r < sup > n </ sup > is a solution for the recurrence exactly when t = r is a root of the characteristic polynomial.

The weakening of government if anything, Lynch suggests, came not before the 1384 coup but after it despite the fact that the coup had at its root Robert II's favouring of his third son, Alexander Stewart, Earl of Buchan ( known as the Wolf of Badenoch ).

This presents arguments based on the supposed real meaning of certain words, where that " real " meaning is in fact what the word meant centuries ago, or what its root word ( in Latin, Greek etc.

Contrary to the Milesian school, who would have one stable element at the root of all, Heraclitus taught that " everything flows " or " everything is in flux ," the closest element to this flux being fire ; he also extended the teaching that seeming opposites in fact are manifestations of a common substrate to good and evil itself.

The fact that the Deerstalker and the Jet were the only completely new designs this year doesn't mean that 1961 didn't see changes in models, actions and calibers.

He does not mean, in fact he addresses himself specifically to reject the proposition, that `` if we took the risk of surrendering, a new generation in Britain would soon begin to amass its strength in secret in order to reverse the consequences of that surrender ''.

In the 19th century a renewed interest in Renaissance polyphony coupled with an ignorance of the fact that vocal parts were often doubled by instrumentalists led to the term coming to mean unaccompanied vocal music.

However, the fact that the third chapter is written in a different style, as a liturgical piece, does not necessarily mean that Habakkuk was not also its author.

An " elementary " proof can be given using the fact that geometric mean of positive numbers is less than arithmetic mean

Though the fact of the irregularity of the lunar orbit was known in the 1st century BC, the starts of the months were calculated using the mean motions of both the sun and moon until 619, the second year of the Tang dynasty, when chronologists began to use true motions modeled using two offset opposing parabolas ( with small linear and cubic components ).

In fact, the distribution of the sample mean will be equal to the distribution of the samples themselves ; i. e., the sample mean of a large sample is no better ( or worse ) an estimator of x < sub > 0 </ sub > than any single observation from the sample.

: Having a CPI that is very high ( in some cases, very high is only 1. 2 ) may mean that the plan was too conservative, and thus a very high number may in fact not be good, as the CPI is being measured against a poor baseline.

Mailer described a factoid as " facts which have no existence before appearing in a magazine or newspaper ", and created the word by combining the word fact and the ending-oid to mean " similar but not the same ".

This can be seen easily from the fact that the sequences do converge to a common limit ( which can be shown by Bolzano – Weierstrass theorem ) and the fact that geometric mean is preserved:

While for p equal to 0 we assume that it's equal to the geometric mean ( which is, in fact, the limit of means with exponents approaching zero ):

where we used the fact that the arithmetic mean evaluates to the same number independent of the order of the terms.

For purposes of the Fifth Amendment, testimonial statements mean communications that explicitly or implicitly relate a factual assertion assertion of fact or belief or disclose information.

This term does not necessarily mean a low level of education, just that the midwife either chose not to become certified or licensed, or there was no certification available for her type of education ( as was the fact before the Certified Professional Midwife ( CPM ) credential was available ).

The fact is even though the first one is the most widely distributed today, when the Medieval authors refer to Midrash Tanchuma, they usually mean the second one.

In fact outside marsh and riparian zones, most of Nepal's native vegetation is adapted to withstand drought, although less so at higher elevations where cooler temperatures mean less water stress.

When Pluto was discovered 19 years later, its mean distance of 39. 48 AU and orbital period of 248 Earth years were close to Ketakar's prediction ( Pluto in fact has a 2: 3 resonance with Neptune ).

But the generic city, the general urban condition, is happening everywhere, and just the fact that it occurs in such enormous quantities must mean that it's habitable.

The existence of this graviton state and the fact that the equations describing string theory include Einstein's equations for general relativity mean that string theory is a quantum theory of gravity.

Truth is most often used to mean in accord with fact or reality or fidelity to an original or to a standard or ideal.

The fact that the toy car is significantly smaller than the real car is part of its representational form, or the differences between the picture and what it pictures, which Wittgenstein is interpreted to mean by Form der Darstellung.