By induction we conclude the statement is true for all r ≥ 0.

By the induction hypothesis,

By the end of the year, Alexander was also distinguished with his induction as a Knight of the Order of the Garter.

By Dr. Zaehner, the author of Mysticism, Sacred and Profane, their deliberate induction is regarded as immoral.

By the 1870s, efficient generators that produced alternating current ( alternators ) were available, and it was found that alternating current could power an induction coil directly, without an interrupter.

By means of mathematical induction, it is easily proven that the above procedure requires the minimal number of moves possible, and that the produced solution is the only one with this minimal number of moves.

By the principle of mathematical induction it follows that the result is true for all natural numbers.

By reasoning using " induction " Bacon meant the ability to gradually generalize a finding based on accumulating data-he advised proceeding by this method ( building a case from the ground up ).

By induction, SO ( n ) therefore has

By Faraday's law of induction we have

By his method of observation and induction as thus explained, his philosophy will be found to be marked off very clearly, on the one hand from the deductive construction of notions of an absolute system, as represented either by Schelling or Hegel, which Cousin regards as based simply on hypothesis and abstraction, illegitimately obtained ; and on the other, from that of Kant, and in a sense, of Sir W. Hamilton, both of which in the view of Cousin are limited to psychology, and merely relative or phenomenal knowledge, and issue in scepticism so far as the great realities of ontology are concerned.

By preventing the clonal expansion of lymphocytes in the induction phase of the immune response, it affects both the cell and the humoral immunity.

By contrast, in an induction motor the rotor rotates at a slower speed than the stator field.

By varying the line frequency with an inverter, induction motors can be kept on the stable part of the torque curve above the peak over a wide range of rotation speeds.

By induction on n it follows that the basis functions are non-negative for all values of and.

By induction, Axioms ( 3 ) and ( 4 ) are equivalent to the single statement

So, i. e. the commutant of the bicommutant of S is equal to the commutant of S. By induction, we have:

By the early 1990s, when his time of eligibility was beginning to run out, many Puerto Ricans, celebrities and ordinary citizens alike, began to campaign for his induction.

By applying the induction principle for the standard integers N and the transfer principle we get the principle of internal induction:

The same wire ( in practice a coil of wire ) is moved through the same magnetic field at a known speed v. By Faraday's law of induction, a potential difference U is generated across the ends of the wire, which is equal to BLv.

By induction, the hypothesis implies that M < sup > k </ sup > T

By induction, we assume that for some integer the partially ordered set can be covered by disjoint chains and has at least one antichain of size.

: Proof: By mathematical induction.

By early summer 1915, Hilbert's interest in physics had focused on general relativity, and he invited Einstein to Göttingen to deliver a week of lectures on the subject.

By Hilbert's basis theorem the ideal I is finitely generated ( as an ideal ).

By the 1990s, however, mentalité history had become interdisciplinary to the point of fragmentation, but still lacked a solid theoretical basis.

By 2007, national branches of the Anthroposophical Society had been established in fifty countries, and about 10, 000 institutions around the world were working on the basis of anthroposophy.

By the early 1960s, US research on the Nike Zeus missile system had developed to the point where small improvements would allow it to be used as the basis of a " real " ABM system.

By 1000 BC ancient civilizations were using technologies that formed the basis of the various branches of chemistry such as ; extracting metal from their ores, making pottery and glazes, fermenting beer and wine, making pigments for cosmetics and painting, extracting chemicals from plants for medicine and perfume, making cheese, dying cloth, tanning leather, rendering fat into soap, making glass, and making alloys like bronze.

By 1850, Parliament had enacted several statutes on a case-by-case basis to deal with issues regularly faced by certain types of organizations, like joint-stock companies, and with the impetus for most types of group litigation removed, it went into a steep decline in English jurisprudence from which it never recovered.

By April, complete motorcycles were in production on a very limited basis.

By 1894, Dewey had joined Tufts, with whom he would later write Ethics ( 1908 ), at the recently founded University of Chicago and invited Mead and Angell to follow him, the four men forming the basis of the so-called " Chicago group " of psychology.

By 1934, a board game called Monopoly had been created which formed the basis of the game sold by Parker Brothers and its parent companies through the rest of the 20th century, and into the 21st.

By about 1900 one finds managers trying to place their theories on what they regarded as a thoroughly scientific basis ( see scientism for perceived limitations of this belief ).

One son, Taro, had his heartbeat recorded in utero and used as the basis for the album Music to Be Born By.

By transferring upper triangularisation of operators of finite-dimensional complex vector space, there is an internal orthonormal Hilbert space basis for where runs from to, such that each of the corresponding-dimensional subspaces is-invariant.

By gradually changing from “ oooh ” to “ aaah ” and back again, a spectral glide is created, emulating the ‘ sweeping filter ’ effect that is the basis of the ‘ wah-wah ’ guitar effect.

Lansky's 1979 computer music piece " Her Song ", from the Six Fantasies On A Poem By Thomas Campion ( re-released on the album Fantasies and Tableaux, 1994 ), has also been sampled by Caural for his song " I Won't Race You ", from his 2006 album Mirrors For Eyes, with the main synthesized vocal line of Lansky's piece being used ( and being the basis for the title of the latter ).

By contrast existence is often restricted solely to that which has physical existence or has a direct basis in it in the way that thoughts do in the brain.

By connecting several p-n junctions together, researchers have been able to create the basis of all logic circuits: the AND, OR, and NOT gates have all been built from semiconductor nanowire crossings.

By 2010, 5 % of Americans consumed hummus on a regular basis, and it was present in 17 % of American households.

By 1869, Leonowens was in New York, where she opened a school for girls for a brief period on Staten Island, and began contributing travel articles to a Boston journal, Atlantic Monthly, including " The Favorite of the Harem ", reviewed by the New York Times as " an Eastern love story, having apparently a strong basis of truth ".

By the next decade, PostgreSQL had become a commercially viable database and is the basis for several products today which maintain its ORDBMS features.

By the end of the First Age, Taliska had developed into a language that served as the basis for Adûnaic, the vernacular tongue of the Númenóreans, as well as the languages of the Rohirrim and the Men of Dale.

By default, network routers handle traffic on a first-come, first-served basis.

By the time the more compact minuscule scripts arose circa AD 800, some of the evolved uncial styles formed the basis for these simplified, smaller scripts.

Elsewhere, Amazing Stories, Friends, The Tick, 3rd Rock from the Sun, Curb Your Enthusiasm, Histeria !, Wayside, Danny Phantom, CatDog, As Told By Ginger, Rugrats ( in " All Growed Up ", an episode which would form the basis of the spinoff All Grown Up !, for which she also provided voice work ), 7th Heaven, The Flintstones, Avatar: The Last Airbender and Metalocalypse.

By the turn of the century telephone service was available to the residents of Elbing on a party-line basis – four families for each telephone line.

By 1948, when RCA began using magnetic tape on a regular basis, high fidelity became the norm for Toscanini's, and all other commercial recordings.