Proof: By symmetry, it suffices to prove that there is some constant c such that for all bitstrings s

By extending the symmetry group O ( 4 ) to the dynamical group O ( 4, 2 ),

By a general property of the Fourier transform, that symmetry means it is the complex conjugate of:

By introducing an additional tunneling interaction between each layer, this model successfully explained the anisotropic symmetry of the order parameter in the HTS as well as the emergence of the HTS.

By identifying each square with reference to the player on move, descriptive notation better reflects the symmetry of the game's starting position (" both players opened with P-K4 and planned to play B-KN2 as soon as possible "), and because the pieces captured are named, it is easy to skim over a game record and see which ones have been taken at any particular point.

By another symmetry, we could also have elected to determine the number of black / black hands rather than the number of red / red hands, and discovered the same distributions by that method.

By symmetry each of the marbles has the same chance to be drawn in the draw.

By twisting the ring, the symmetry of the system changes and becomes allowed ( see also Möbius – Hückel concept for details ).

By contrast, a natural theory of electroweak symmetry breaking is an asymptotically-free gauge theory with fermions as the only matter fields.

By symmetry of second derivatives, for any " nice " function we have

By September 19, an upper-level anticyclone was well established over Georges and satellite pictures suggested that the hurricane was beginning to strengthen rapidly, as indicated by the cooling cloud tops, increased symmetry of the deep convection, and the warming and contracting of the well-defined 40 mi ( 63 km ) wide eye as rapid intensification continued, and Georges peaked at a very dangerous Category 4 storm with 155 mph ( 250 km / h ) wind and a 937 minimal pressure late on September 19 and early September 20.

By contrast, in some fossil corals, adjacent septa lie in order of increasing age, a pattern that is termed serial and that produces a bilateral symmetry.

By symmetry the odd order terms in the expansion are zero.

By the very interaction the spherical symmetry of the subsystems is broken, but the angular momentum of the total system remains a constant of motion.

By symmetry, the orbit must be planar, and we are free to arrange the coordinate frame so that the equatorial plane is the plane of the orbit.

By symmetry:

By symmetry, rotations of this plane around the z axis give all the bitangent planes through the center.

By CPT symmetry, there is a set of right-handed fermions with the opposite quantum numbers.

By symmetry it can be seen that the voltages induced along the various sides of the loop will cancel each other when a signal arrives along the loop axis.

By the symmetry of the defining formula, this shows that the resultant is a polynomial expression of the coefficients of both < var > P </ var > and < var > Q </ var >.

By breaking the rotational symmetry a bit and varying the electrostatic potential along the mean path of the spherical aberration is minimized.

By considering the coordinate space we can consider the symmetry in geometric terms.

By `` image '' is meant not only a visual presentation, but also remembered sensations of any of the five senses plus the feelings which are immediately conjoined therewith.

By limiting American strength too much to nuclear strength, this country limited its ability to fight any kind of war besides a nuclear war.

By this standard, it is determined that where two stations operating on the same frequency are involved, objectionable interference from station A exists at any point within the service area of station B where station A's signal is of an intensity one-twentieth or more of the strength of station B's signal at that point.

By using the appropriate version any one of these factors can be determined for any combination of the other three.

By varying the formula, this curve may be moved forward or backward along the coordinates to produce any desired compression strength / density ratio.

By means of charts showing wave-travel times and depths in the ocean at various locations, it is possible to estimate the rate of approach and probable time of arrival at Hawaii of a tsunami getting under way at any spot in the Pacific.

By the time Felix turned up it was early afternoon, which, one would think, would be late enough so that by then, except for small children and a few hardy souls who had not yet sobered up, it could have been expected that people would no longer be having any sort of active interest in the previous night's noisemakers and paper hats.

By March 1861, no leaders of the insurrection had proposed rejoining the Union on any terms.

By the Brønsted-Lowry definition, any compound which can easily be deprotonated can be considered an acid.

By contrast, the Rijndael specification per se is specified with block and key sizes that may be any multiple of 32 bits, both with a minimum of 128 and a maximum of 256 bits.

Whenever any result is sought by its aid, the question will then arise — By what course of calculation can these results be arrived at by the machine in the shortest time?

By the late 19th century, improved instruments were designed which could be mounted in any position and allowed accurate measurements in electric power systems.

By virtue of being a Java application, it is available on any platform supported by Java.

By a further act of 1541 — which was not repealed until 1845 — artificers, labourers, apprentices, servants and the like were forbidden to play bowls at any time except Christmas, and then only in their master's house and presence.

By 2011, 165 countries had signed the treaty and none are known-though some are still suspected-to possess any biological weapons.

By managing all four populations as one-through strategic transfers, gene-loss is reduced from 8 % per decade to 2 % per decade, without any increase in bongo numbers in Kenya.

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 extension, the term is also used to refer to any system administrator who displays ( or wishes he could get away with ) the qualities of the original.

By the end of World War 2, Canadians communicated by telephone, more than any other country.

By the early 2000s, the CD largely replaced the audio cassette player as standard equipment in new automobiles, with 2010 being the final model year for any car in the US to have a factory-equipped cassette player.

By contrast, the Fascist and Nazi regimes of Italy and Germany tended to confine their coercive activities to purely political aims, without any serious attempt to force the ideological conversion of their opponents.

By extension, it has come to include an extreme and unreasoning partisanship on behalf of any group to which one belongs, especially when the partisanship includes malice and hatred towards rival groups.