Sentence examples for same expression for from inspiring English sources

With the inclusion of Λ, the expression for Misner-Sharp mass is And for the de Sitter case, with, one finds It is interesting to see that we obtain the same expression for the total energy associated with the non-static de Sitter metric from two different and most reliable directions: It is quite easy to physically verify the correctness of the above expression.

From this ratio, and after applying the standard expression to obtain modal damping from damped free vibration, the same expression for ζr1 is reached again, ζr1≈[1/(2π)] ln us0/us1)≈[1/(2π)] ln[(1+I)/(1−I ]2≈2/(πI).

It is easy to see that we could obtain the same expression for Green's function (6.19) in this case.

Clearly, this results in the same expression for I adm as in Case 1, namely I adm = λ x I ⊗ ( H H H ) - 1. (43).

In either case, the same expression for normalized diffusion is obtained, which is proportional to the inverse of normalized microviscosity rather than to the inverse of normalized bulk viscosity.

That is, one can use the same expression for Ψ to describe situations where Δ Q nk causes Δ R nk > δ R n, δ R k, namely, PT, and not ET. However, since PT occurs over short distances and the electronic coupling at short distances is usually large, the PT is electronically adiabatic.

It is stated that those plane stress components are expressed by the same expressions for those materials and the difference is only the magnitude of the permeability, though the magnetic fields Hx, Hy are different each other in the plates.

It is stated that the stress components are expressed by the same expressions for those materials and the difference is only the magnitude of the permeability, though the magnetic fields Hx, Hy are different each other in the plates.

for the plane H(θ d ) and the same expressions for the corresponding position of the plane H d ), given a certain range of φ and assuming θ<π and <π.

We can have the same expression also for ( u k ∗, u − k ) and ( û k, u − k ).

An explicit computation of the integral (36a) with (36b) yields immediately the same expression (35) for z(t).