Sentence examples for expressions holds from inspiring English sources

Obtained expressions holds for arbitrary orientation of the dipole moment and the principal axes of the quadrupole moment of the emitter with respect to the radius-vector r connecting the center of the emitter with the center of the nanoparticle.

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The following expressions hold: (i).

Then, the following expressions hold.

Similar expressions hold for the reciprocal signals.

As the similar expressions hold for x b,2k, we exclude the expressions for x b,2k−1 without loss of generality.

Assume that b(x) and m(x) are continuous functions of the spatial coordinate x, and the following expressions hold.

Classic analytical expressions hold that as the axial load increases, the cylinder achieves an overall helically buckled state in which the buckled cylinder forms a helix spiraling around the inner surface of the constraining cylinder.

Similarly, the following expressions hold for (32): begin{array}{*{20}l} nabla_{boldsymbol{x}}g(boldsymbol{x}, boldsymbol{rho}) &= 2 left left(boldsymbol{w}^{circ 2}_{in}right)^{intercal}boldsymbol{x} - d^{2} right) cdot boldsymbol{w}^{circ 2}_in, end{array} (35).

At this moment, the following expressions hold: left{begin{array}{l}Eleft {t}_1right)=Lleft {t}_1right) {tau}_{mathrm{S}}left {t}_1right)+{tau}_{mathrm{R}}left {t}_1right)={tau}_1rightrray}_1right

Without loss of generality, we may assume that, as n → ∞, the following expressions hold: ∥ u n ∥ p, ρ → ∞, I ( u n ) → c, I ′ ( u n ) → 0. Define u ¯ n = u n ∥ u n ∥ p, ρ.