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By applying the induction principle for the standard integers N and the transfer principle we get the principle of internal induction:
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By and applying
By applying this general principle, a great number of complex compounds of osmium, ruthenium, iridium, and rhenium, with triphenylphosphine, triphenylarsine, and triphenylstibine have been obtained in this laboratory during the past few years.
By 30 July the Greek army was outnumbered by the counter-attacking Bulgarian army, which attempted to encircle the Greeks in a Cannae-type battle, by applying pressure on their flanks.
By twice applying the transformation above from the stationary to the rotating frame, the absolute acceleration of the particle can be written as:
By 1912 and 1913, there are beginning to be many films from many American companies that rely on applying novel decoration to the story, rather than supplying any twists to the drama itself to sustain interest.
By applying his construction to the sequence of real algebraic numbers, Cantor produces a transcendental number.
By placing the molecules in wells in the gel and applying an electric field, the molecules will move through the matrix at different rates, determined largely by their mass when the charge to mass ratio ( Z ) of all species is uniform, toward the ( negatively charged ) cathode if positively charged or toward the ( positively charged ) anode if negatively charged.
By charging the right amount of water and applying heat, the system can be brought to any point in the gas region of the phase diagram.
By using this arrangement, many common operations can be implemented by uniformly applying the same operation to each pixel independently.
By applying Pontryagin duality, one can see that abelian profinite groups are in duality with locally finite discrete abelian groups.
By darkening areas of texture maps corresponding to corners, joints and recesses, and applying them via self-illumination or diffuse mapping, a radiosity-like effect of patch interaction could be created with a standard scanline renderer ( cf.
By an offshore drilling contractor effectively applying HSE Management in its organization, it can optimize risk to achieve levels of residual risk that are tolerable.
By applying such principles in an obvious way ( using repeated applications of modus ponens ), Holmes is able to infer from his observation that " the sides of Watson's shoes are scored by several parallel cuts " that:
" By this, James meant that truth is a quality, the value of which is confirmed by its effectiveness when applying concepts to practice ( thus, " pragmatic ").
By applying sprezzatura to his speech and everything else he does, the courtier appears to have grazia and impresses his audience, thereby achieving excellence and perfection.
By applying a bias voltage to a " gate " terminal, the channel is " pinched ", so that the electric current is impeded or switched off completely.
By applying his operational calculus to the analysis of this network he discovered ( 1887 ) what has become known as the Heaviside condition.
By applying a single spatial model on an entire domain, one makes the assumption that is a stationary process.
By applying Mauss's theory to data such as Mead's, Lévi-Strauss proposed what he called alliance theory.
By its standard practices of applying good scientific methods, mainstream is distinguished from pseudoscience as a demarcation problem and specific types of inquiry are debunked as junk science, cargo cult science and scientific misconduct etc.
By applying conventional cost-estimating techniques, he concluded that it would cost more than a billion US Dollars to develop this distribution by conventional proprietary means.
By and induction
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 induction, Hilbert's basis theorem establishes that, the ring of all polynomials in n variables with coefficients in, is a Noetherian ring.
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 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 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.
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.
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, we assume that for some integer the partially ordered set can be covered by disjoint chains and has at least one antichain of size.
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