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The electrostatic double layer contribution to their free energy is exactly expressed within the Debye Hückel approximation as a convergent multiple scattering expansion.
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The impulse responses can be exactly expressed as fixed point binary values.
For instance, boosting and genetic algorithms naturally fit into an iterative style and thus cannot be exactly expressed with MapReduce.
The amplitude for is converted into that at the equator by multiplying a provisional correction factor although its latitude dependence cannot be exactly expressed by cos γ as it contains the north-south asymmetric term (sin γ).
In this respect, if one can obtain the right λ k according to maneuver information, it implies that x ^ k can be exactly expressed as the modified value by adjusting λ k at each discrete time.
Specifically, we will show that, under the conditions on the C and B tensors, the Green's tensors can be exactly expressed as a simple line integral over a unit circle, and that the Eshelby's tensors for a general ellipsoidal inclusion can be derived as surface integrals over a unit sphere, entirely analogous to those of the classical elasticity.
Non-metric multidimensional scaling (NMDS) analyses applying the Bray-Curtis similarity index (regarding the presence and relative abundance of T-RFs) were used to plot the rank order of similarity of T-RFLP profiles in a way that allows distances to be exactly expressed on a two-dimensional sheet (greater distances represent greater dissimilarities).
The simplicity of the beautiful shapes is exactly what she expressed.
What Poincaré calls "objective reality common to many thinking beings" is exactly the "harmony expressed by mathematical laws" (Poincaré 1905b: 23; 1913b: 239).
28 30 This integration is exactly what was expressed by our participating GPs as an empirical solution to deal with the discrepancy between guideline adherence and providing optimal care in patients with multimorbidity.
The concentration equations are then exactly expressed in the general case of anisotropic elastic behavior and ellipsoidal inclusions with imperfect interface.
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CEO of Professional Science Editing for Scientists @ prosciediting.com