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 considering circumscribed spheres, the notion of Delaunay triangulation extends to three and higher dimensions.

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 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 direct substitution, the solution to this equation can be readily shown to be the scalar Green's function, which in the spherical coordinate system ( and using the physics time convention ) is:

By a proper choice of coordinate system, the ellipse can be described by the canonical implicit equation

By appending the additional coordinate " 1 " to every vector, one essentially considers the space to be mapped as a subset of a space with an additional dimension.

By calculating in the frame of reference of the moving lithosphere ( velocity v ), which have spatial coordinate x '

By then, Lee himself was too ill to coordinate his subordinates in springing a planned trap of the Union Army.

By determining the angles between the projection rays of the sensors and the basis, the intersection point, and thus the 3d coordinate, is calculated from the triangular relations.

By observing the flow into an elemental square in an x-y Cartesian coordinate system, we have:

By observing the flow into an elemental square in an r – θ polar coordinate system, we have:

In particular, if v = e < sub > j </ sub > is the jth coordinate vector then ∂< sub > v </ sub > f is the partial derivative of f with respect to the jth coordinate function, i. e., ∂ f / ∂ x < sup > j </ sup >, where x < sup > 1 </ sup >, x < sup > 2 </ sup >, ... x < sup > n </ sup > are the coordinate functions on U. By their very definition, partial derivatives depend upon the choice of coordinates: if new coordinates y < sup > 1 </ sup >, y < sup > 2 </ sup >, ... y < sup > n </ sup > are introduced, then

By the Hilbert Basis Theorem and some elementary properties of Noetherian rings, every affine or projective coordinate ring is Noetherian.

By analytic continuation of the correlation functions of a quantum field theory, the time coordinate may become imaginary, and then boosts become rotations.

By implementation of the council into the organisation structure of the Little Entente the member states declared their will to coordinate its economic interests too.

By analogy with the case when the θ < sub > U </ sub > came from coordinate systems, condition 3 means that φ < sub > U </ sub > is related to φ < sub > V </ sub > by h.

By setting the phase of the complex coordinate to zero, one obtains exactly one-fourth of the Fisher information metric, exactly as above.

By convention, proper time is usually represented by the Greek letter τ ( tau ) to distinguish it from coordinate time represented by t or T.

By contrast, coordinate time is the time between two events as measured by a distant observer using that observer's own method of assigning a time to an event.

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

By the year 2000 the two coordinate systems differed by about 25 cm.

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 shifting the coordinate system, this definition extends to an arbitrary point of k < sup > n </ sup > in place of the origin.

By 16: 10, further south near the east-west UTM coordinate line 00 Northing, 2nd ACR's E-(“ Eagle ”) Troop received fire from an Iraqi dismounted outpost, a dug-in Iraqi ZSU-23-4 and several occupied buildings in an Iraqi village.

By contrast, in cooperative platform games, both players typically occupy the same screen and must coordinate their actions, particularly with regard to the scrolling.