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.

By spring 1942, he was considering involvement in war work.

By considering NRM members innocent " victims " of psychological coercion these theories open the door for psychological treatments.

By contrast, socialism emphasises distributing output among trades as required by each trade, not necessarily considering how trades organise internally.

By selling vast quantities of shrimp and catfish to the U. S., Vietnam triggered antidumping complaints by the U. S., which imposed tariffs in the case of catfish and was considering doing the same for shrimp.

By 1942 Rockefeller had become increasingly impatient that his purchased property might never be added to the park, and wrote to the Secretary of the Interior Harold L. Ickes that he was considering selling the land to another party.

By the mid-1980s, therefore, it had become essential that the PNDC demonstrate that it was actively considering steps towards constitutionalism and civilian rule.

By 1702, Victor Amadeus was considering changing allegiance to the emperor again having entered secret correspondence with the emperor who promised him the Duchy of Montferrat.

By considering the impact of emotions, cognitive errors, irrational preferences, and the dynamics of group behavior, behavioral finance offers succinct explanations of excess market volatility as well as the excess returns earned by stale information strategies .... cognitive errors may also explain the existence of market inefficiencies that spawn the systematic price movements that allow objective TA analysis methods to work.

By 1925 she was considering how to prepare a laboratory guide in that field but " was persuaded by colleagues to write an advanced text " ( quoted in Hutchinson, p. 107 ).

By only considering geodesic distances or other isometric properties as done in spectral shape analysis, it is possible to retrieve all cats in a database of animals independent of the pose.

By trying the killer move before other moves, a game playing program can often produce an early cutoff, saving itself the effort of considering or even generating all legal moves from a position.

By considering bets on more than one event de Finetti could justify additivity.

By considering a coordinate transformation on a manifold as a map from the manifold to itself, the transformation of covariant indices of a tensor are given by a pullback, and the transformation properties of the contravariant indices is given by a pushforward.

By 08: 00 the Russians were occupying redoubts 1, 2 and 3, and, considering it too close to the enemy, had razed redoubt No. 4.

By 1925 he was considering appointing Stewart to the Senate, to remove him from active political involvement, but was handicapped by the absence of any other Alberta representation in his cabinet.

By considering the complex analytic structure induced on this compact surface we are led to the theory of compact Riemann surfaces.

By then considering perturbations by various mass terms they were able to calculate the superpotential in the presence of arbitrary numbers of colors and flavors, valid even when the theory is no longer weakly coupled.

By February, the opposition lords were considering accusing the Duke of York of high treason, which resulted in the king proroguing parliament on 24 February in order to protect his brother.

By 1985, their campaign had acquired sufficient traction for Congress to begin considering passing protectionist laws.

By considering the three possible outcomes ( Red Sox, Yankees, some other team ), you will see that regardless of which of the three outcomes eventuates, you lose.

By considering Riemann surface with boundary, we can couple it to the d = 1 conformal theory instead of coupling d = 2 theory to d = 0.

By not considering whether the person could afford the payments if they were to increase in the future, many of these loans may have put the borrowers at risk for default.

By considering the occurrences of values from, one has an alternate way to refer to, through.

By ordering the solids correctly — octahedron, icosahedron, dodecahedron, tetrahedron, cube — Kepler found that the spheres could be placed at intervals corresponding ( within the accuracy limits of available astronomical observations ) to the relative sizes of each planet ’ s path, assuming the planets circle the Sun.

By inclining the axes of the two spheres with respect to each other, and rotating them in opposite directions but with equal periods, Eudoxus could make a point on the inner sphere trace out a figure-eight shape, or hippopede.

By reference to the continual to-and-fro motion associated with that, the term was then applied in transportation and then in other spheres.

* By shape, gains advantage usually by using spheres or rollers, or by forming flexure bearings.

By taking Y to be some sphere that X embeds in, this reduces the index theorem to the case of spheres.

By convention, n corresponds to the number of nodes of the radial eigenfunction, l indicates the total number of nodal lines on spheres, and m tells how many of these nodal lines cross the equator.

By the 14th century Dante was describing his own imaginary journey through the astral spheres of Paradise.

By 1895 Germany was competing with France for Russia's favour, and British statesmen hoped to negotiate with the Russians to demarcate spheres of influence in Asia.

By relying on fundamental principles, Bernardin also sought to coordinate work on several different spheres of Catholic moral theology.

By the Treaty of Tordesillas, the two powers divided the world between them into exclusive spheres of influence, trade and colonization.

By the way, we've only just begun to search for things like Dyson spheres, so we can't really rule them out.

By knitting together " ordinary " sources to produce a meaningful, extraordinary socio-cultural narrative, Ulrich shows how a skilled practitioner functioned within the interstices of the private and public spheres.

By pressing the B button, the spheres switch position to shoot forward, sideways or backward, while the Silver Surfer continues to fire forward.

By the mid-20th century, it was increasingly clear to historians that the notion of " changeless China " was untenable.

By the 1930s, many revisions of the rules developed that were substantially different from Babcock's classical version ( including some that were considered fundamentals in other variants, such as the notion of a standard hand ).

By the twentieth century, the modern notion of science as a special brand of information about the world, practiced by a distinct group and pursued through a unique method, was essentially in place.

By the mid-5th century, land had become concentrated in the hands of a tiny elite, and the notion of all Spartan citizens being " equals " had become a farce.

By 1973, Harvey Milk, who would become the most famous resident of the neighborhood, opened a camera store, Castro Camera, and began political involvement as a gay activist, further contributing to the notion of the Castro as a gay destination.

By creation of a paradox, Plato's Euthydemus dialogue demonstrates the need for the notion of contradiction.

By the 1920s, the notion that the Hyades shared a common origin with the Praesepe Cluster was widespread, with Rudolf Klein-Wassink noting in 1927 that the two clusters are " probably cosmically related.

* By showing that the Anschluss was enormously popular in Austria, he helped to discredit the notion of Austria as a victim of Nazi aggression brought unwillingly into the Reich.

By the 7th century CE Indian mathematicians were familiar enough with the notion of infinity as to define it as the quantity whose denominator is zero.

:" By non-phoneticians any mode of pronunciation which is harsh or grating in effect is often supposed to be ' guttural '; with this notion the designation is popularly applied by Englishmen to the German ch, but not to k or g, though technically it belongs equally to them.

By contrast to the notion of civil tolerance, in early modern Europe the subjects were required to attend the state church ; This attitude can be described as territoriality or religious uniformity, and its underlying assumption is brought to a point by a statement of the Anglican theologian Richard Hooker: " There is not any man of the Church of England but the same man is also a member of the commonwealth ; nor any man a member of the commonwealth, which is not also of the Church of England.

By international law, the notion of a country's sovereign airspace corresponds with the maritime definition of territorial waters as being 12 nautical miles ( 22. 2 km ) out from a nation's coastline.

If F is any field, the separable closure F < sup > sep </ sup > of F is the field of all elements in an algebraic closure of F that are separable over F. This is the maximal Galois extension of F. By definition, F is perfect if and only if its separable and algebraic closures coincide ( in particular, the notion of a separable closure is only interesting for imperfect fields ).

By contrast, the more common usage of the term, as found in Catholic social teaching and in European Unioin law and social policy, encompasses the notion that " higher " or more remote levels of social organization have a duty to render assistance to the most immediate, competent level of organization, while respecting the primary jurisdiction of that more immediate level, and, ultimately, the dignity and freedoms of individuals participating in society.

By applying the preceding ideas to the local 1-parameter group of diffeomorphisms defined by a vector field on M, and differentiating with respect to the parameter, a notion of Lie derivative on any associated bundle is obtained.

By his own account, Hörbiger was observing the Moon when he was struck by the notion that the brightness and roughness of its surface was due to ice.

By abstracting the notion of formulae and focusing of their concrete uses, that is distinct occurrences, it allows to provide an abstract syntax for computer science, as loci can be seen as pointers on memory.

By contrast, Theta roles are a syntactic notion about the number, type and placement of obligatory arguments.

By virtue of these changes, the preamble was deleted, the chapters concerning political and economic forms of government were changed, the chapters concerning trade unions were rewritten and a uniform notion of possession was introduced.

By this time, however, other European powers had overwhelmingly rejected the notion that the Pope had the right to convey sovereignty of regions as vast as the New World.

By defining the notion this way, Aristotle indicates that a truly tragic hero must have a failing that is neither idiosyncratic nor arbitrary, but is somehow more deeply imbedded -- a kind of human failing and human weakness.

By depicting slavery as benevolent, the museum's exhibits reinforced the notion that Jim Crow was a proper solution to racial tensions that had escalated during Reconstruction.

By the middle of the century, an attempt to be objective was made in poetry by the group of writers known as the Parnassians -- which included Leconte de Lisle, Théodore de Banville, Catulle Mendès, Sully-Prudhomme, François Coppée, José María de Heredia and ( early in his career ) Paul Verlaine -- who ( using Théophile Gautier's notion of art for art's sake and the pursuit of the beautiful ) strove for exact and faultless workmanship, and selected exotic and classical subjects which they treated with a rigidity of form and an emotional detachment ( elements of which echo the philosophical work of Arthur Schopenhauer whose aesthetic theories would also have an influence on the symbolists ).

By 1900 the notion of " building-as-cure " was largely discredited, and in the following decades these large facilities became too expensive to maintain.