By reversing the steps in the Euclidean algorithm, the GCD can be expressed as a sum of the two original numbers each multiplied by a positive or negative integer, e. g., 21 = × 105 + × 252.

By the end of the 16th century, Italy had absorbed the northern influences, with Venice, Rome, and other cities being centers of musical activity, reversing the situation from a hundred years earlier.

By reversing the flow of refrigerant, the heat pump refrigeration cycle is changed from cooling to heating or vice versa.

By then reversing the field they would be attracted to the far end, moving down the surface.

By passing an ultrasonic beam through the tissues, bouncing it off a reflective plate, then reversing the direction of the beam and repeating the measurement, the volume of blood flow can be estimated.

By reversing known mutations in a Y-chromosome lineage, a hypothetical ancestral sequence for the MRCA, Y-chromosomal Adam, can be inferred.

* By reversing the process of producing a spectrogram, it is possible to create a signal whose spectrogram is an arbitrary image.

By the late 20th century, new fields like genomics and proteomics were reversing this trend, with organismal biologists using molecular techniques, and molecular and cell biologists investigating the interplay between genes and the environment, as well as the genetics of natural populations of organisms.

By reversing these techniques, currencies could be reinforced.

By reversing the ester of the meperidine skeleton, a then-legally uncontrolled drug approaching the potency of morphine was produced.

By contrast, anti-inflammatory treatment trials for existing Alzheimer's disease have typically shown little to no effect on halting or reversing the disease.

Let V and W be handlebodies of genus g, and let ƒ be an orientation reversing homeomorphism from the boundary of V to the boundary of W. By gluing V to W along ƒ we obtain the compact oriented 3-manifold

By reversing the applied potential or providing a discharge path, the device bleaches.

By January 2001 Real Sociedad were bottom of the league and the new manager, John Toshack, turned to the prodigious Alonso in the hope of reversing the team's fortunes.

By constantly reversing the direction, the box pattern can be formed.

By reversing this construction, John Milnor and Sergei Novikov ( among many others ) were able to answer questions about the existence and uniqueness of high-dimensional manifolds: this is now known as surgery theory.

By reversing this law, we can infer that different countries do not share an efficient common market from the fact that prices for the same good are different.

By reversing the current, this concept can also heat the contents instead of cooling them, useful for keeping meals hot from a drive-through, or even to keep items from freezing in severely cold climates.

By threatening to make the Alpha Lanterns kill themselves if Ganthet does not cooperate, Henshaw forces Ganthet to work on reversing the augments that turned the Green Lanterns into Alpha Lanterns, hoping that he can use the resulting information to restore his original mortal body.

By channeling a large electric current through the compressed carbon granules in the microphone, a small sound signal could produce a much larger electric signal.

By contrast, if we look at a point on the left and placed a small paddle wheel there, the larger " current " on its left side would cause the paddlewheel to rotate counterclockwise, which corresponds to a curl in the positive z direction.

By historical convention, a positive current is defined as having the same direction of flow as any positive charge it contains, or to flow from the most positive part of a circuit to the most negative part.

By the end of 1997 the consolidated public sector deficit decreased to 4. 6 % of GDP — with public sector spending falling from 62 % of GDP to below 50 %— the current account deficit was reduced to 2 % of GDP, and government debt was paid down to 94 % of annual export earnings.

By sensing the current provided to a load and using the device's applied voltage as a sensor voltage it is possible to determine the power dissipated by a device.

By the early 20th century Dutch dominance extended to what was to become Indonesia's current boundaries.

By the turn of the 20th century, the heyday of individualist anarchism had passed, although aspects of the individualist anarchist tradition were later revived with modifications by Murray Rothbard and his anarcho-capitalism in the mid-20th century, as a current of the broader libertarian movement.

By challenging students ' current ideas, students can adjust their ideas to more closely resemble actual theories or concepts.

By 1956, the city had grown to, and doubled in size over the next decade to its current size of roughly.

By presenting the card, the purchaser is typically entitled to either a discount on the current purchase, or an allotment of points that can be used for future purchases.

By means of a series of electrodes ( dynodes ) at ever-higher potentials, these electrons are accelerated and substantially increased in number through secondary emission to provide a readily detectable output current.

By May 1969 Britain ’ s current account position was in surplus, thanks to a growth in exports, a drop in overall consumption and, in part, the Inland Revenue correcting a previous underestimation in export figures.

By January 1837, an alliance of 107 Boers, sixty Rolong, and forty Coloured men, organised as a commando under the leadership of Potgieter and Gert Maritz, attacked Mzilikazi's settlement at Mosega, which suffered heavy losses, and early in 1838 Mzilikazi fled north beyond the Limpopo ( to current day Zimbabwe ), never to return to the Transvaal.

By encouraging the inclusion of semantic content in web pages, the Semantic Web aims at converting the current web dominated by unstructured and semi-structured documents into a " web of data ".

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 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 the 16th century the word theosophy was being used in at least one of its current meanings.

By becoming President under current terms, Grant would at best leave the office at age 56 with no income, assuming he served two terms.

By 1859, the University had moved to its current site in the Sydney suburb of Camperdown.

By hitting A, T and B simultaneously, Keen is granted all of the current level's crystal keys / keycards, 1 extra life and 99 shots for the ray gun.

" By signing a 10-year ( contract ) with the Teamsters ( and with over 30 other unions representing city employees ), the current administration and City Council unduly hamstrung not only the current management of city government, but the next six years of management as well, a period that extends well beyond the elected terms of the incoming administration and City Council ," according to a March 2011 report from the Office of the Inspector General of the City of Chicago.

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 adding a series or shunt resistor, more than one range of voltage or current could be measured with one movement.