By considering the propagation of the negative energy modes of the electron field backward in time, Ernst Stueckelberg reached a pictorial understanding of the fact that the particle and antiparticle have equal mass m and spin J but opposite charges q.

: which is of the form suggested the previous year by M. J. Buckingham in Very High Frequency Absorption in Superconductors based on the fact that the superconducting phase transition is second order, that the superconducting phase has a mass gap and on Blevins, Gordy and Fairbank's experimental results the previous year on the absorption of millimeter waves by superconducting tin.

Others noted that almost all traits claimed to be uniquely cyberpunk could in fact be found in older writers ' works — often citing J. G. Ballard, Philip K. Dick, Harlan Ellison, Stanisław Lem, Samuel R. Delany, and even William S. Burroughs.

The fact that genes were split or interrupted by introns was discovered independently in 1977 by Phillip Allen Sharp and Richard J. Roberts, for which they shared the Nobel Prize in Physiology or Medicine in 1993.

In fact, the theoretical physicist, J. M. Ziman, proposed that science is public knowledge and thus includes mathematics.

In fact, L. E. J.

It is supported by the experimental fact that the lowest energy state of the nickel atom is a 4s < sup > 2 </ sup > 3d < sup > 8 </ sup > energy level, specifically the 3d < sup > 8 </ sup >(< sup > 3 </ sup > F ) 4s < sup > 2 </ sup > < sup > 3 </ sup > F, J = 4 level.

For positive J < sub > 0 </ sub > the thermodynamics of the Mattis spin glass corresponds in fact simply to a ferromagnet, just because these systems have no " frustration “ at all.

The Australian letter to number mapping was: A = 1, B = 2, F = 3, J = 4, L = 5, M = 6, U = 7, W = 8, X = 9, Y = 0, so the phone number BX 3701 was in fact 29 3701.

However, in the 1998 History Channel documentary entitled Ku Klux Klan: A Secret History, the speculation that Harding may have joined the group is highlighted by the fact that William J. Simmons, the founder of the modern Klan, once visited the President at the White House.

Since a one sided maximal ideal A is not necessarily two-sided, the quotient R / A is not necessarily a ring, but it is a simple module over R. If R has a unique maximal right ideal, then R is known as a local ring, and the maximal right ideal is also the unique maximal left and unique maximal two-sided ideal of the ring, and is in fact the Jacobson radical J ( R ).

This fact is corroborated, by J. Sturrock in his South Kanara and Madras Districts Manuals, and also by Haridas Bhattacharya in Cultural Heritage of India Vol.

In fact, Grohl has appeared in most countdowns run by Triple J, only excluding those in 1989, 1990, 2001, 2003, 2004, 2008 and 2010.

A tourist attraction of a completely different kind, the Lovelock Correctional Center was opened in 1995 and is best known for the fact that in 2008 O. J.

D. J. Taylor argues that these factors, and the fact that Gollancz was not a person to part with such a sum on speculation, suggest that Gorer was confusing Orwell's eventual earnings from the book with a small contribution for out of pocket expenses that Gollancz might have given him.

Notable was the fact that J McLandsborough, the original proposer of the line ( who dealt predominantly with water and sewerage engineering, but had experience of building the Otley and Ilkley Railway ) was appointed acting engineer ; whilst J. S. Crossley of the Midland Railway was appointed consultant engineer.

The elements of the story were reprinted in early historian Benson J. Lossing's The Pictorial Field Guide to the Revolution ( published in 1850 ) as historical fact, and the tale was widely repeated for generations after in school primers.

" He went on to note, " This version of the origin of the name is disputed by the editor of the Springfield Express, Mr. J. G. Newbill, who, in the issue of his paper, November 11, 1881, says: ' It has been stated that this city got its name from the fact of a spring and field being near by just west of town.

This not only explains why the Guidebook facilitated them to follow the trail of the Lost Library all over the world with its enormous knowledge base, but also the fact the Junior Woodchuck's logo, based on the letters J and two Ws, looks uncannily like the Ibis Emblem of the Guardians of the Lost Library.

In the Brian Herbert / Kevin J. Anderson Legends of Dune prequel series ( 2002 – 2004 ), however, it is confirmed that his lover Norma Cenva, a mathematical genius with great psychic power, had in fact invented the space-folding ships which would eventually be called heighliners.

That J and Ω usually have the same coordinate expression ( up to an overall sign ) is simply a consequence of the fact that the metric g is usually the identity matrix.

He attracted statewide attention in 1908 when he assisted Francis J. Heney in the graft prosecution of Abe Ruef and Mayor Eugene Schmitz, his success due in large measure to the fact that after Heney had been gunned down in the courtroom, he took the lead for the prosecution and won the case.

For example, noted philosopher Mortimer J. Adler wrote, " Those who oppose injurious discrimination on the moral ground that all human beings, being equal in their humanity, should be treated equally in all those respects that concern their common humanity, would have no solid basis in fact to support their normative principle.

that is, one must know something about D other than the fact that it is a linear operator.

Coefficients ( a < sub > 0 </ sub >, a < sub > 1 </ sub >, b < sub > 1 </ sub >, a < sub > 2 </ sub >, b < sub > 2 </ sub >, ...) are in fact an element of an infinite-dimensional vector space ℓ < sup > 2 </ sup >, and thus Fourier series is a linear operator.

In both texts a girl and a boy fall in love ( a " formula " with a symbolic operator between them would be " Boy + Girl ") despite the fact that they belong to two groups that hate each other (" Boy's Group-Girl's Group " or " Opposing forces ") and conflict is resolved by their death.

The fact that the two hypotheses incorporate different kinds of testing procedures is expressed in the formal language by prefixing the operator '*' to a different predicate.

During the production of the film, in fact, Hussein met and married Toni Gardner, who was working as a switchboard operator in Aqaba.

where is a Sturm – Liouville operator ( However it should be noted this operator may in fact be of the form where w ( x ) is the weighting function with respect to which the eigenfunctions of are orthogonal ) in the x coordinate.

The principal curvatures are the eigenvalues of the shape operator, and in fact the shape operator and second fundamental form have the same matrix representation with respect to a pair of orthonormal vectors of the tangent plane.

Just as the Schrödinger equation describes how pure states evolve in time, the von Neumann equation ( also known as Liouville-von Neumann equation ) describes how a density operator evolves in time ( in fact, the two equations are equivalent, in the sense that either can be derived from the other.

Codd's DIVIDE operator was in fact implemented that way.

But Perrow's conclusion that the accident was unavoidable is belied by the fact that a TMI control room operator wrote a memo warning of " a very serious accident " if the condensate system problems were not properly addressed.

Part of this sequence shows Caution riding an elevator up to his room, which was achieved thanks to the fact that the hotel used as the location had two glass-walled elevators side by side, allowing the camera operator to ride in one lift while filming Constantine riding the other car through the glass between the two.

Central to these distinctions is the fact that del is not simply a vector ; it is a vector operator.

The operator norm of a normal matrix N equals the spectral and numerical radii of N. ( This fact generalizes to normal operators.

In fact it turns out that the operator is self-adjoint, as follows from the theory outlined below.

In fact every bounded linear operator on a complex Banach space must have a non-empty spectrum.

In fact, the cost of cutting edge ( at the time ) UHF radio equipment meant that only the more serious CB operator would use the band, a nice though expensive haven for mature CB operators, and radio hams who didn't like the ' red tape ' of amateur radio.

This is in fact a well-defined operator.

The first choice of operator for this network had not in fact been KCRC, nor had the construction of a light rail network been decided when the plans for the new towns were first drawn up.

There was considerable security controversy over the ownership by a foreign corporation, particularly Arabic, of a U. S. port operation, this in spite of the fact the current operator was the British based P & O Ports,

( this is related to the fact that they are eigenvectors of the non-self-adjoint operator ).

An important fact is that the anomalous current non-conservation is proportional to the total derivative of a vector operator, ( this is non-vanishing due to instanton configurations of the gauge field, which are pure gauge at the infinity ), where the anomalous current is:

The extra factor of 2 in dimensions 4 mod 8 comes from the fact that in this case the kernel and cokernel of the Dirac operator have a quaternionic structure, so as complex vector spaces they have even dimensions, so the index is even.