Sentence examples for formulae implies from inspiring English sources

If a degree of freedom xn appears only as a quadratic term anxn2 in the Hamiltonian H, then the first of these formulae implies that : k_{B} T = \Bigl\langle x_{n} \frac{\partial H}{\partial x_{n}}\Bigr\rangle = 2\langle a_n x_n^2 \rangle, which is twice the contribution that this degree of freedom makes to the average energy \langle H\rangle.

Equation (2.16) and the Sokhotzki-Plemelj formulae imply for Re (2.22).

As the formula implies, the effect of species 2 on species 1 (α1,2) in turn is determined by the population size and carrying capacity of species 2 (N2 and K2).

As Cicero's "Against Verres" triumph suggests, the "Against [X]" formula implies or mimics a scene of mano-a-mano combat with a fake-modest implicit personal subject: the brave author who is pitched against X, telling it like it is, let the chips fall where they may.

Hence, the difference of these formulas implies the desired result.

This formula implies a recursive equation to solve for h i s [8].

That is, if a set Γ of formulas implies a consequence C then a larger set Γ ∪ A will also imply C. A logic is nonmonotonic if its consequence relation lacks this property.

end{aligned} (7.3) Therefore if (xi >1+varepsilon ) then this formula implies the uniform with respect to m exponential decay of the Bessel function in t.   2.

Since (z_{n}^{1}(t)=z_{n}^{2}(t)) from the definition then the difference of these formulas implies the desired result.

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].