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Page "Bernoulli's inequality" ¶ 34
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By and comparing
By comparing reaction cells sealed from the same manifold temperature dependency corresponding to activation energies ranging from 11 to 18 Af was observed while dependence on the first power of the light intensity seemed to be indicated in most cases.
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.
By comparing the length and intensity of various methods of therapies, it was proven that intensity is a better predictor of recovery than the method of therapy used.
By comparing different embryonic stages of different vertebrate species, he formulated the Recapitulation theory.
By comparing the parts of the genome that are not under natural selection and which therefore accumulate mutations at a fairly steady rate, it is possible to reconstruct a genetic tree incorporating the entire human species since the last shared ancestor.
By comparing mitochondrial DNA which is inherited only from the mother, geneticists have concluded that the last female common ancestor whose genetic marker is found in all modern humans, the so-called mitochondrial Eve, must have lived around 200, 000 years ago.
By comparing the genome compositions between genomes, scientists can better understand the evolutionary history of a given genome.
By comparing the relative positions of the moon and Mars with their anticipated positions, Vespucci was able to crudely deduce his longitude.
Soon however, Marl's records became more sample heavy, as can be seen by comparing the MC Shan LPs Down By Law ( 1987 ) and Born to be Wild ( 1988 ); the rhythms less electronic, with drum samples and patterns becoming more prominent.
By comparing the different natural languages, scholars hope to learn something about the nature of human intelligence and the innate biases and constraints that shape natural language, which are sometimes called universal grammar.
By comparing the times of the eclipses, the difference in longitude of Paris to Uranienborg was calculated.
By comparing the photographic plates of the Pleiades cluster taken in 1918 with images taken in 1943, van Maanen was able to identify those stars that had a proper motion similar to the mean motion of the cluster, and were therefore more likely to be members.
By comparing skulls of different ethnic groups it supposedly allowed for ranking of races from least to most evolved.
By measuring the frequency of the returned signal and comparing that with the original, the difference can be easily measured.
By comparing the spectra of stars such as Sirius to the Sun, they found differences in the strength and number of their absorption lines — the dark lines in a stellar spectra due to the absorption of specific frequencies by the atmosphere.
By comparing the spectrum to computed models of stellar evolution, the age, mass, radius and luminosity of Tau Ceti can be estimated.
By monitoring vegetation changes over time, droughts can be monitored by comparing the current vegetation state to its long term average.
By instead comparing the radiated power in a given direction to the actual power that the antenna receives from the transmitter, the power gain takes into account that poorer efficiency, making it a more useful figure of merit for the ability of a transmitter in sending a radio wave toward a receiver.
By expanding the left hand side and then comparing the real and imaginary parts under the assumption that x is real, it is possible to derive useful expressions for cos ( nx ) and sin ( nx ) in terms of cos x and sin x.
By comparing the arrival times of gamma showers with the separations of the spacecraft, a location can be determined, for follow-up with other telescopes.
By comparing this with the account of stupteria given by Dioscorides in the 123rd chapter of his 5th book, it is obvious that the two are identical.
* 1862 – By analysing the spectroscopic signature of the Sun and comparing it to those of other stars, Father Angelo Secchi determines that the Sun is itself a star.
By counting numbers of live and dead mites that developed every 15 days and comparing this with his initial count on the infant, he was able to estimate how long that infant was dead.
By writing as a Laurent series and explicitly comparing terms, one may verify that it satisfies the relation

By and mean
By monitoring, we mean some system of control over the types of information sent from the various centers.
By personal factors I mean those rooted in personality structure.
By extension, it can mean an underworld abode of lost souls, or hell.
By measuring the mean squared displacement over a time interval along with the universal gas constant, the temperature, the viscosity, and the particle radius, Avogadro's number can be determined.
By the Victorian era, ballad had come to mean any sentimental popular song, especially so-called " royalty ballads ", which publishers would pay popular singers to perform in Britain and the United States in " ballad concerts.
By cultism we mean the adherence to doctrines which are pointedly contradictory to orthodox Christianity and which yet claim the distinction of either tracing their origin to orthodox sources or of being in essential harmony with those sources.
By extension, the word for carrying or drawing a beer came to mean the serving of the beer and, in some senses, the act of drinking, or a drink of beer itself, regardless of serving method.
By the time Bramah's beer pumps became popular, the use of the word draught to mean the act of serving beer was well established and transferred easily to beer served via the hand pumps.
By " satisfactory " one would mean at least the equivalent of Plancherel theorem.
By contrast, the yarn in knitted fabrics follows a meandering path ( a course ), forming symmetric loops ( also called bights ) symmetrically above and below the mean path of the yarn.
By " open access " to this literature, we mean its free availability on the public internet, permitting any users to read, download, copy, distribute, print, search, or link to the full texts of these articles, crawl them for indexing, pass them as data to software, or use them for any other lawful purpose, without financial, legal, or technical barriers other than those inseparable from gaining access to the internet itself.
By the mid-15th century the term lollard had come to mean a heretic in general.
By metaphoric extension, the term " movable feast " was used by Ernest Hemingway to mean the memory of a splendid place that continues to go with the moving traveler for the rest of life, after he has had the experience of it and gone away.
By extension, the word manor is sometimes used in England to mean any home area or territory in which authority is held, often in a police or criminal context.
( By arithmetic he meant, in part, theorising on number, rather than what arithmetic or number theory have come to mean.
By contrast, the central and southern parts of Guangdong province experience an average January temperature of above, while the July mean is generally above.
By the time of Christ, the Greco-Roman world had started to use the term " myth " ( Greek muthos ) to mean " fable, fiction, lie "; as a result, the early Christian theologians used " myth " in this sense.
By inter-religious pluralism, we mean the views held within one major faith tradition ( e. g., Christianity ) about the validity or truth of other major faith traditions ( e. g., Judaism, Buddhism, Islam, etc .).
By synecdoche the term " Sabbath " in the New Testament may also mean simply a " se ' nnight " or seven-day week, namely, the interval between two Sabbaths.
By extension the term self-determination has come to mean the free choice of one's own acts without external compulsion.
By objects, Wittgenstein did not mean physical objects in the world, but the absolute base of logical analysis, that can be combined but not divided ( TLP 2. 02 – 2. 0201 ).
By extension, " onshore trust " has come to mean any trust resident in a high-tax jurisdiction.
By this I mean the principle that, in deciding what is good and what is bad for a given individual, the ultimate criterion can only be his own wants and his own preferences .”

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