Since the hazards of poor communication are so great, p can be justified as a habitable site only on the basis of unusual productivity such as is made available by a waterfall for milling purposes, a mine, or a sugar maple camp.

Since p ( x ) is irreducible, this means that p ( x ) = k ( x − a ), for some k ∈ F

Since 1990, AIX has served as the primary operating system for the RS / 6000 series ( later renamed IBM eServer pSeries, then IBM System p, and now IBM Power Systems ).

Since the takeover in 2011, NEEP Roma Holding S. p. A. owned all shares Sensi previously hold.

Since the early 20th century it has been commonly accepted that Old Irish Bel ( l ) taine is derived from a Common Celtic * belo-te ( p ) niâ, meaning " bright fire " ( where the element * belo-might be cognate with the English word bale in ' bale-fire ' meaning ' white ' or ' shining '; compare Anglo-Saxon bael, and Lithuanian / Latvian baltas / balts, found in the name of the Baltic ; in Slavic languages byelo or beloye also means ' white ', as in Беларусь ( White Russia or Belarus ) or Бе ́ лое мо ́ ре Sea ).

Since all probabilities p < sub > i </ sub > add up to one: p < sub > 1 </ sub > + p < sub > 2 </ sub > + ... + p < sub > k </ sub > = 1, the expected value can be viewed as the weighted average, with p < sub > i </ sub >’ s being the weights:

~ p ∨ p. Since p → p is true ( this is Theorem 2. 08, which is proved separately ), then ~ p ∨ p must be true.

Since 2 < sup >( q − 1 )</ sup > ≡ 1 ( mod q ), raising both sides of the congruence to the power x gives 2 < sup >( q − 1 ) x </ sup > ≡ 1, and since 2 < sup > p </ sup > ≡ 1 ( mod q ), raising both sides of the congruence to the power k gives 2 < sup > kp </ sup > ≡ 1.

Since every central subgroup is normal, it follows that every minimal normal subgroup of a finite p-group is central and has order p. Indeed, the socle of a finite p-group is the subgroup of the center consisting of the central elements of order p.

Since lunch is usually served between 2 and 4 p. m., another common time for tapas is weekend days around noon as a means of socializing before proper lunch at home.

* Jackson J. Spielvogel – Western Civilization – Volume II: Since 1500 ( 5th Edition ), p. 401

Since the Supreme Court's decision of that year this is more doubtful ; ;

( Since the time-span of the nation-state coincides roughly with the separate existence of the United States as an independent entity, it is perhaps natural for Americans to think of the nation as representative of the highest form of order, something permanent and unchanging.

Since it is not far from Viareggio, he will visit Puccini's house, as he never fails to do, to pay his respects to the memory of the composer of La Boheme, which he considers one of Puccini's masterpieces.

Since attack serves to stimulate interest in broadcasts, I added to my opening statement a sentence in which I claimed that German youth seemed to lack the enthusiasm which is a necessary ingredient of anger, and might be classified as uninterested and bored rather than angry.

Since the air is a continuum, the network of communication remains intact regardless of the positions or motions of the points ( the people ) in the net.

Since the difficulty of drawing the net is great, we will merely discuss it.

Since a civilizational crisis involves also a crisis in private interests and in the ruling class, reaction is normally found among those who feel themselves to be among the ruling class.

Since civilizational change is the most difficult to perceive and analyze, it seldom is given adequate attention.

Since the slogans have little application to reality and are sanctimonious to boot, the applause is faint even in areas of the world where we should expect to find the greatest affection for free government.

Since more is known about Quiney than about any other acquaintance of Shakespeare in Stratford, his career may be followed to its sudden end in 1602.

Since the great flood of these dystopias has appeared only in the last twelve years, it seems fairly reasonable to assume that the chief impetus was the 1949 publication of Nineteen Eighty-Four, an assumption which is supported by the frequent echoes of such details as Room 101, along with education by conditioning from Brave New World, a book to which science-fiction writers may well have returned with new interest after reading the more powerful Orwell dystopia.

Since Laos is of no more purely military value to Moscow itself than it is to Washington, this approach might be expected to head off Mr. Khrushchev for the moment.

Since little is known about autism, and almost nothing has been written for the layman, we'd like to share one experienced mother's comments.

Since the work is done by hand, the only limitation, it is said, `` is that of human conception ''.

Since the apparatus is new, it requires experimentation and changes in technique.

Since the obvious is not always true, the Republican National Committee wisely analyzed its defeat of last autumn and finds that it occurred, as suspected, in the larger cities.

Since he has just shown who is top dog, he may not be ready to receive this highest honor in the gift of the Soviet people.

Since appeals to morality, to humanity, and to sanity have had such small effect, perhaps our last recourse is the deterrent example.

Since the goal of our international planners is a World Government, this Atlantic Community would mark a giant step in that direction for, once American economic autonomy is absorbed, a larger grouping is a question of time.

Since he can neither accept nor reject them all, he must be governed by the time and energy available for his prime professional obligations.

Since Af are distinct prime polynomials, the polynomials Af are relatively prime ( Theorem 8, Chapter 4 ).

Since 2011 the Greens have their first prime minister, the one of Baden-Württemberg, in a Green-SPD-government.

Since the Liberal Democratic Party ( the LDP ) was in power, it has been convention that the President of the party serves as prime minister.

Since 2007 Kuwait has been ruled by Sheikh Sabah Al-Ahmad Al-Jabir Al-Sabah and his designated successor, Sheikh Jaber Al-Mubarak Al-Hamad Al-Sabah, the prime minister and crown prince.

Since 1974, the official residence of the prime minister is Beit Aghion, at the corner of Balfour and Smolenskin streets in Rehavia.

Since stepping down as prime minister, Lee has remained influential first as Senior Minister, and now as Minister Mentor.

Since the prime factorisation of every number is unique, so then is every binary encoding of the square-free integers.

Since then, all races have ended after dark, with the 2007 race ending in prime time, at 7: 07 pm ( EST ).

Since is not a power of a prime, it is the product of two coprime numbers greater than.

Since fully regaining independence Estonia has had 12 governments with 8 prime ministers: Mart Laar, Andres Tarand, Tiit Vähi, Mart Siimann, Siim Kallas, Juhan Parts, and Andrus Ansip.

Since 3 is prime, its only divisors are 1 and 3, so either H is G, or H is the trivial group.

If n is not a prime power, then every Sylow subgroup is proper, and, by Sylow's Third Theorem, we know that the number of Sylow p-subgroups of a group of order n is equal to 1 modulo p and divides n. Since 1 is the only such number, the Sylow p-subgroup is unique, and therefore it is normal.

Proof: Since p is a prime number the only possible values of gcd ( p < sup > k </ sup >, m ) are 1, p, p < sup > 2 </ sup >, ..., p < sup > k </ sup >, and the only way for gcd ( p < sup > k </ sup >, m ) to not equal 1 is for m to be a multiple of p. The multiples of p that are less than or equal to p < sup > k </ sup > are p, 2p, 3p, ..., p < sup > k − 1 </ sup > p = p < sup > k </ sup >, and there are p < sup > k − 1 </ sup > of them.

Every prime ideal P in a Boolean ring R is maximal: the quotient ring R / P is an integral domain and also a Boolean ring, so it is isomorphic to the field F < sub > 2 </ sub >, which shows the maximality of P. Since maximal ideals are always prime, prime ideals and maximal ideals coincide in Boolean rings.

Since the fundamental theorem of arithmetic applied to a non-zero integer n that is neither 1 nor − 1 also asserts uniqueness of the representation for p < sub > i </ sub > prime and e < sub > i </ sub > positive, a primary decomposition of ( n ) is essentially unique.

Since g > 1 and q is prime, g must have order q.

Since in the Ulam spiral adjacent diagonals are alternatively odd and even numbers, it is no surprise that all prime numbers lie in alternate diagonals of the Ulam spiral.

Since 2001, the United Nations has had a presence at the WSF through UNESCO, showing the institutional credibility achieved by the forum, seen by UNESCO as a " prime opportunity for dialogue and a laboratory of ideas for the renewal of public policies " through " critical reflection on the future of societies we want to create and for elaborating proposals in search of solidarity, justice, peace and human rights ".

Since Ultima Onlines prime in 2003, the overall subscriber base has seen a steady decline.

Since is a prime number, can be factorized.