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Page "Gauss's lemma (number theory)" ¶ 35
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Comparing and with
Comparing this data with the 2001 census shows that the number of permanent residents born on the island has increased by just 3, 000.
Comparing the available records with especially the Gest and also other ballads, Hunter developed a fairly detailed theory according to which Robin Hood was an adherent of the rebel Earl of Lancaster, defeated at the Battle of Boroughbridge in 1322.
Comparing the recovery from the 1981 – 82 recession ( 1983 – 1990 ) with the years between 1971 ( end of a recession ) and 1980 shows that the rate of growth of real GDP per capita averaged 2. 77 under Reagan and 2. 50 % under Nixon, Ford and Carter.
* Comparing two versions of " La Confidence " with the nursery rhyme version
Comparing engines on the dynamometer, a typical even-fire V6 shows instantaneous torque peaks of 150 % above mean torque and valleys of 125 % below mean torque, with a small amount of negative torque ( engine torque reversals ) between power strokes.
Comparing the angular expansion with the derived velocity of expansion will reveal the distance to the nebula.
Comparing this with the latter equation gives V < sub > 1 </ sub >• V < sub > 2 </ sub >
Comparing these basis functions with that for BPSK shows clearly how QPSK can be viewed as two independent BPSK signals.
Comparing the light curve, the amplitude and the radial velocity variations as compared to the light curve, Type II Cepheids constitute a different class of star with a luminosity relation offset from that of the δ Cepheids.
Comparing his measurements with data from his predecessors, Timocharis ( 320 – 260 BC ) and Aristillus (~ 280 BC ), he concluded that Spica had moved 2 ° relative to the autumnal equinox.
Comparing this with the length of the sidereal year, he calculated that the rate of precession was not less than 1 ° in a century.
Comparing the original scripts with the finished film, most of the characters ' initial scripted names were later changed.
Comparing Invasion of the Body Snatchers with Robert Aldrich's Kiss Me Deadly and Orson Welles ' Touch of Evil, Brian Neve found a sense of disillusionment rather than straightforward messages, with all three films being " less radical in any positive sense than reflective of the decline of screenwriters ' great liberal hopes ".
Comparing the recordings of Schnabel, from the beginning of modern recording, with those of Barenboim and then Pratt shows a distinct shift in how the structure of the sonata form is presented to the listener over time.
Comparing this material with Constantius of Lyon ' Life of St. Germanus of Auxerre, it suggests that the two are not the same person.
200px < center > Comparing with provinces of Sweden, one sees many similarities.
Comparing with the domestic networks of the 1960s and 1980s gives reason to assume that the situation during the 1970s should have been more or less the same, though.
# Comparing the narrations of the narrator with those of narrators of established reliability, comparing them seeking any distinctions that might be unique to that narrator, in particular, while contradicting the others.
Comparing with HSS saw blades, solid-carbide saw blades have higher hardness under high temperatures, and are more durable, but they also have a lower toughness .</ li >
Comparing pledgers with similar non-pledgers is the only way to be certain that the effect comes from the pledge rather than the pre-existing greater beliefs of pledgers that sexuality should be restrained to the matrimonial context.
Comparing the exonic structure shown in the first line ( green ) with the one in the second line ( yellow ) shows intron retention, whereas the comparison between the second and the third spliceform ( yellow vs. blue ) exhibits exon skipping.
* Comparing Thoreau ’ s journals with A Plea for Captain John Brown
* The impact of British counter terrorist strategies on political violence in Northern Ireland: Comparing deterrence and backlash models with Laura Dugan and Raven Korte ( 2009 )
Comparing with the administrative Kowloon City District, the Kowloon City area is vaguely bounded south by Prince Edward Road West and Prince Edward Road East, north with Lo Fu Ngam, east with Kai Tak Nullah and west with Kowloon Tsai.

Comparing and our
" Comparing the waterboarding of detainees to the North Vietnamese torture of American P. O. W. s, Ventura asserted, " We created our own Hanoi Hilton in Guantánamo.
" Comparing himself to a soldier drew national attention and Kellen quickly issued a statement " After speaking with the press, I immediately regretted my comments and felt embarrassed for my family, my team, the University of Miami, our fans, alumni and myself, " What I have learned from this experience is to take my triumphs and failures in stride.
" Glasser also posits a " Comparing Place " in which we compare and contrast our real world experiences against our Quality World perspective.

Comparing and first
Comparing the experience of outpatient commitment recipients over the first six months of commitment to the same period immediately prior to commitment, the OMH study found:
Comparing the process of unlearning to the “ breaking out ” process of birth, Rank was the first psychologist to suggest that a continual capacity to separate from “ internal mental objects ” – from internalized institutions, beliefs and neuroses ; from the restrictions of culture, social conformity and received wisdom – is the sine qua non for lifelong creativity.
His own works, which circulated in manuscript in his lifetime, include brief works on the Procession of the Holy Ghost, and letters to his brothers, to L. Bruni, Guauni, Traversari, and to Pallas Strozzi, as well as two which were eventually printed, his Erotemata Civas Questiones which was the first basic Greek grammar in use in Western Europe, first published in 1484 and widely reprinted, and which enjoyed considerable success not only among his pupils in Florence, but also among later leading humanists, being immediately studied by Thomas Linacre at Oxford and by Desiderius Erasmus at Cambridge ; and Epistolæ tres de comparatione veteris et novæ Romæ ( Three Letters Comparing Ancient and Modern Rome ).
Comparing characteristics of this basal angiosperm, other flowering plants and fossils may provide clues about how flowers first appeared — what Darwin called the " abominable mystery ".
Comparing these is rough, and only gives an idea of the relative difficulty ; the reason different systems exist in the first place is because it's difficult to compare grades between climbing media.
Comparing the game to the first Mega Man X, GamePros Chris Nicolella called Mega Man X2 " improved in almost every way ".
Comparing the first and the last home versions of DOA2, namely the Dreamcast American edition and the Japanese Hardcore edition, would show a lot of improvements including an enhanced gameplay and a doubled number of stages and costumes.
Talking about the camera work, director Terry Shakespeare said " We really concentrated on depth of field with the camera ," Comparing the two Bionicles, he felt " The first film had primary colors that were coded to the areas and a younger feel.
Comparing the experience of AOT recipients over the first six months of AOT to the same period immediately prior to AOT, the OMH study found:

Comparing and we
Comparing the x < sup > 2 </ sup > coefficients, we see that 4
Comparing the novel to King Solomon's Mines the review declared: " The book before us displays all the same qualities, and we anticipate for it a similar popularity.
Comparing with the general case, we see Z < sub > 1 </ sub > = R and Z < sub > 2 </ sub > is the impedance of the capacitor, given by
Comparing to the above, we have that, if we say that is the quotient of deaths for the selected locus and is again the quotient of deaths for the entire population.
Comparing this with the same situation of a Cl radical we see that this step is exothermic ( 397 kJ / mol-431 kJ / mol
Comparing this with other paradigms of word forms, we can note that in the English language the plural often consists of little more than adding an s to the end of the word.
Comparing both sides, we have
Comparing Ontology with Epistemology, Berkeley asked, " But, though it were possible that solid, figured, moveable substances may exist without the mind, corresponding to the ideas we have of bodies, yet how is it possible for us to know this?
"' Magic, or as we usually say ' Art ': A Framework for Comparing African and European Art ," in Enid Schildkrout and Curtis Keim, eds.
Comparing this to the definition of O ( 1 ), above, we see that the sections of O ( 1 ) are in fact linear homogeneous polynomials, generated by the themselves.

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