By comparing the form of several yupanas, researchers found that calculations were based using the Fibonacci sequence 1, 1, 2, 3, 5 and powers of 10, 20 and 40 as place values for the different fields in the instrument.

The largest species are red alder ( A. rubra ) on the west coast of North America, and black alder ( A. glutinosa ), native to most of Europe and widely introduced elsewhere, both reaching over 30 m. By contrast, the widespread Alnus viridis ( green alder ) is rarely more than a 5 m tall shrub.

By picturing Roman authority negatively proponents of this view believe that it is emphasizing the fact that Christian ’ s should obey and submit to Christ ’ s authority ( Acts 4: 19-20 ; 5: 29 ).

By working very hard, one may be able to make this part 5 times faster, but this only reduces the time for the whole computation by a little.

By expanding the conditions for which they were indicated, Astrazeneca's Seroquel and Eli Lilly's Zyprexa had become the biggest selling antipsychotics in 2008 with global sales of $ 5. 5 billion and $ 5. 4 billion respectively.

By convention, the top strand is written from the 5 ' end to the 3 ' end ; thus, the bottom strand is written 3 ' to 5 '.

By 1950 it had increased to between 3, 710, 107 and 4, 073, 967, and in 1962 it had reached 5. 7 million.

By the 1960s NATO had adopted the 5. 56 NATO cartridge.

By the 1990s, the US had adopted the M4 carbine, a derivative of the M16 family which fired the same 5. 56mm cartridge but was lighter and shorter ( in overall length and barrel length ), resulting in marginally reduced range and power.

By quickly setting up for the next play ( often within 5 – 10 seconds after the last play despite being afforded 45 seconds ) this hindered the other team's defense from substituting situational players, regrouping for tactics, and, some suggest, increased the defense's rate of fatigue ( This is attributed to the belief that the offense dictates when a play starts so they tend to be more mentally relaxed and prepared for the start of a play where the defense must remain on a higher level of alert before the play starts ).

By 1933, the party had approximately 3. 5 million members but as a result of the Great Purge party membership was cut down to 1. 9 million by 1939.

By the 1860s, there were around 5, 000 residents, and the population grew to around 10, 000 by the late 1880s.

By the end of the decade, similar calculators were priced less than $ 10 (£ 5 ).

By December 5, 1969, the entire four-node network was established.

By the year 2010 there were 5, 906 Dominican friars, including 4, 456 priests.

By 1968 Thomas had increased sales in the four fried chicken restaurants so much that he sold his share in them back to Sanders for more than $ 1. 5 million.

Therefore both and are inverses of By Theorem 1. 5,

By birthplace one can derive the following origins of the inhabitants: born on the Faroes 91. 7 %, in Denmark 5. 8 %, and in Greenland 0. 3 %.

By the mid-twenties the British film industry was losing out to heavy competition from Hollywood, the latter helped by having a much larger home market-in 1914 25 % of films shown in the UK were British, but by 1926 this had fallen to 5 %.

By the end of 2010, the party's support had dropped to as low as 5 %.

By use of a pulsed irrigation timer, existing overhead sprinklers may be used to deliver water at a low average precipitation rate ranging from 2. 5 to 5ml / Hour for frosts down to-5deg.

By 1970 the national census registered 8. 5 million people, about a 27 percent increase, while the most recent official census in 1984 recorded a figure of 12. 3 million — almost double the 1960 figure ( see table 2, Appendix ).

By 3: 00 p. m. the next day Bob Denard and his mercenaries had surrendered.

By Euclid's lemma p < sub > 1 </ sub > must divide one of the q < sub > j </ sub >; relabeling the q < sub > j </ sub > if necessary, say that p < sub > 1 </ sub > divides q < sub > 1 </ sub >.

By taking the intersection of p ( 1 ), p ( 2 ), p ( 3 ),... he formed p ( ω ), and then he noticed that p ( ω ) had a set of limit points p ( ω + 1 ), and so on.

By the Chinese Remainder Theorem, this ring factors into the direct product of rings of integers mod p. Now each of these factors is a field, so it is clear that the only idempotents will be 0 and 1.

By 1944 the last known Ivory-billed Woodpecker, a female, was gone from the cut-over tract ( Smithsonian p 98 ).

By neglecting to do this, the letter allowed good people to close their ears and their hearts .</ p >

By using the streamwise vector i parallel to the freestream in place of k in the integral, we obtain an expression for the pressure drag D < sub > p </ sub > ( which includes induced drag in a 3D wing ).

By sunset at 7: 34 p. m., the several hundred whites assembled outside the courthouse appeared to have the makings of a lynch mob.

By appropriate selection of the ratio of turns, a transformer thus enables an alternating current ( AC ) voltage to be " stepped up " by making N < sub > s </ sub > greater than N < sub > p </ sub >, or " stepped down " by making N < sub > s </ sub > less than N < sub > p </ sub >.

By this term I mean the phenomenon described by Melanie Klein in Envy and Gratitude " ( 1962, p. 96 ).

By 6: 30 p. m. the division of Brig.

By extension, the cross-covariance matrix between two random vectors X and Y ( X having n elements and Y having p elements ) is the n × p matrix

By the rank-nullity theorem, a system of n vectors in k dimensions ( where all dimensions are necessary ) satisfies a ( p = n − k )- dimensional space of relations.

By extrapolating the phenomenology of lattice points to the unit cells it is seen that the total number of degrees of freedom is 3pq when p is the number of primitive cells with q atoms / unit cell.

By 1989, the network ran game shows from noon to 5 p. m. five days a week.

" By the maternal side he was great grandson of Matthew Pilkington " from ' Worthyies of Bucks & men of note ' Robt Gibbs 1886 p 363.

By 12: 30 p. m. on 21 September, the pro-French Dacko proclaimed the fall of the Central African Empire and the restoration of the Central African Republic under his presidency.

By counting the number of stalls and urinals I attempted to form a loose estimate of how many men the hall would hold at one time.

By failing to do as he was told instantly -- to take out a permit or return the gun to his car -- he had played into Lord's hands.

By 1898, rustling losses had been driven down to the lowest level ever seen in Wyoming.

By now Curt was seeing clearly again.

By then Hez could see for himself, and so could the others.

By now Harmony could see that most of the adults in the train were winded and resting, or else siphoned off from the games by the challenging lure of the great cliff towering above them.

`` By God '', Waddell said, `` we don't want to upset the boy at this time of all times.

By prevailing over other claimants for the loyalties of men, the nation-state maintained an adequate measure of certainty and order within its territorial borders.

By subduing disparate lesser groups the nation has, to some degree at least, broadened the capacity for individual liberty.

`` By observing the conductor '', he says with a twinkle in his eyes, `` I learned how not to conduct ''.

By `` image '' is meant not only a visual presentation, but also remembered sensations of any of the five senses plus the feelings which are immediately conjoined therewith.

By the death of his father in 1888 he had come into possession of the family estate and had re-assumed its traditions.

By virtue of his self-reliance, his individualism and his freedom from external restraint, the private eye is a perfect embodiment of the middle class conception of liberty, which amounts to doing what you please and let the devil take the hindmost.

By upholding his own personal code of behavior, the private detective has placed himself in opposition to a society whose fabric is permeated with crime and corruption.

By monitoring, we mean some system of control over the types of information sent from the various centers.

By contrast, the energetic reaction of the leader to the full demands his decision imposes upon him strengthens the moral intuition and gives us the measure of the man.

By distinguishing superlunary ( celestial ) and sublunary ( terrestrial ) existence, and reinforcing this with the four-element physics of Empedocles, Aristotle came to speak of the stars as perfect bodies, which moved in only a perfect way, viz. in a perfect circle.

By her eighteenth birthday her bent for writing was so evident that Papa and Mamma gave her a Life Of Dickens as a spur to her aspiration.

By the time Lilian had been graduated from public school, her parents were doing quite well.

) By the time the streetcar pulled away, he had fallen in love with Paula.

By extending this help, we hope to make possible the enthusiastic enrollment of these nations under freedom's banner.

By now she was sure she was going to have a baby, deciding it would be born in India or Burma that November.

By this time she had learned that it was futile to argue with her young husband, yet the uncomfortable fact remained: the American Congregationalists were sending them as missionaries to the Far East and paying their salaries.

By early June they were a hundred miles off the coast of Ceylon, by which time all four missionaries were hardened seafarers.

By this time, as we shall see, the Tories were already planning to `` punish '' Steele for his political writing by expelling him from the House of Commons.