Sentence examples for formula implies that from inspiring English sources

For minimal submanifolds in a Euclidean ball, the classical monotonicity formula implies that if such a submanifold passes through the centre of the ball, then its area is at least that of the equatorial disk.

Even more startling to our world-view is the notion this formula implies, that the universe has a bandwidth limit of 1 bit per Planck area.

Green's formula implies that for two functions y, χ ∈ D ( I ), the limit [ y, χ ] = lim x → ∞ [ y, χ ] ( x ) exists and is finite.

The absolute value in the detection formula implies that the detection region is indeed a two-sheet cone as advised by Merhav and Sabbag [1].

end{aligned}Then the Gauss Jacobi quadrature formula implies that begin{aligned} sum _{k=1}^n lambda _{k,n}|P(x_{k,n})|^2 =int _{-1}^1 |P y)|^2w_{alpha,beta } y),dy,quad Pin Pi _{n-1}.

comm).. Thus the formula implies that lower temperatures result in greater growth, which is not necessarily the case for northern climates where temperatures in winter can be low enough to retard growth [45].

This work was undertaken because the pore energy formulas existing in the literature predict qualitatively different behavior of large pores: the original formula proposed by Abidor et al. in 1979 implies that the electrical force expanding the pore increases linearly with pore radius, while later extensions of this formula imply that this force decreases to zero for large pores.

Because Bode's law (which gave the sequence of planetary distances in terms of a numerological formula) implied that there should be a planet between Mars and Jupiter, Olbers proposed that asteroids are the broken-up remnants of a medium-sized planet that once orbited in the asteroid belt region.

The decision by the prosecutor, Antonio Marini, was in part a declaration of despair, for the formula "for lack of proof" implies that evidence exists supporting both the guilt and the innocence of the defendants, and that the court is powerless to reach a conclusive decision.

Moreover, these formulas imply that the network topology is known and can only give a formal ratio of main fluxes without its verification.

Recurrence formulas imply that the backtracking procedure does not create twice the same node: each formula computes the cost for v v between pairs of nodes where at least one is a descendant of v or v.